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					                                                             UNIFYING CONCEPTS AND PROCESSES
                                  Standard 1: Students will understand and use Mathematics in Problem Solving.
Benchmarks, Grades 9-12
    STANDARD                                                   CORRELATION
1.1    Analyze problem-solving approaches to                    In the first year, IMP builds on students’ intuitive notions of and methods for
       investigate and understand mathematical                  problem solving o develop over the course of the curriculum an in-depth
       content.                                                 understanding of mathematical concepts and techniques and of the ways to apply
                                                                them. Students routinely experiment with examples, look for and articulate
                                                                patterns, make, test and prove conjectures, and make connections among
                                                                mathematical ideas. Students are encouraged to write about these methods on a
                                                                regular basis, including in their write-ups of Problems of the Week (POW’s). Here
                                                                they reflect on the techniques that they applied to solve problems so their methods
                                                                can be clearly understood by others.
                                                                Additionally, the curriculum requires student to present their thinking in both a
                                                                large class and small group environment. In these settings, students are exposed to
                                                                different approaches to solving problems and learn to critically evaluate their
                                                                efficiency, effectiveness, and accuracy.
                                                                Various techniques for solving problems are suggested or presented by the teacher
                                                                throughout the four years of the curriculum.
                                                                Patterns
                                                                  
                                                                 HW2-Who‟s Who?
                                                                As the Cube Turns
                                                                  
                                                                 HW17-How Did We Get Here?




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                      Key Curriculum Press /1
      STANDARD                                               CORRELATION
1.2    Formulate problems from global                         The majority of the units in the IMP curriculum center on a unit problem. Students
       mathematical situations.                               read about a scenario, identify the problem to be solved, generate appropriate
                                                              assumptions, and develop mathematics and methods to solve the problem. These
                                                              problems are generated from a variety of settings, including made-up games,
                                                              literature, science, world population, and a circus. The unit problems of The Game
                                                              of Pig, Do Bees Build It Best?, Meadows or Malls?, and High Dive are good examples
                                                              from each of the four years.
                                                              Additional, smaller examples:
                                                              The Game of Pig
                                                                
                                                               POW7-Making a Game
                                                              Is There Really a Difference?
                                                                
                                                               POW6-Is There Really a Difference?
                                                              Cookies
                                                              • CW-Producing Programming Problems
1.3    Select the best strategies to solve a wide             A basic strength of the IMP curriculum is the exposure students have to the many
       variety of problems in diverse contexts.               possible ways to solve a wide variety of problems. The IMP units with their central
                                                              problems and the smaller problems within each of the units also provide students
                                                              with a diversity of contexts and challenges. Students are encouraged to write-up
                                                              their methods for solving Problems of the Week (POW’s). Additionally, students
                                                              make oral presentations to the whole class and in small group settings. In these
                                                              settings, students can learn how others thought about solving problems, and
                                                              recognize efficient or effective techniques.
                                                              Various techniques for solving problems are suggested or presented by the teacher
                                                              throughout the four years of the curriculum. These opportunities in the classroom
                                                              allow students to develop a broad range of strategies and techniques for solving
                                                              problems. Students must select a strategy to solve problems in the various contexts
                                                              of the entire curriculum. Through this ongoing process of selection, reselection, and
                                                              reflection, students find strategies that work best for them as well as best for
                                                              various types of problems.



New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                     Key Curriculum Press /2
1.4    Verify and interpret results with respect to Again, this expectation is ongoing throughout the curriculum. Because the
       the original problem situation.              curriculum is problem driven, students must determine the reasonableness of their
                                                    solutions in the context of the original situation. No answer key at the back of the
                                                    book exists.
      STANDARD                                     CORRELATION
1.5    Analyze solutions and strategies for use in The IMP curriculum centers on modeling real phenomena with mathematics.
       mathematical modeling.                       Students analyze solutions and strategies throughout IMP. Three examples are
                                                    given below.
                                                    The Pit and the Pendulum
                                                    This unit problem asks students to predict how long twelve swings of a thirty-foot
                                                    pendulum will take. Students experiment with and explore measurement variation
                                                    for the sake of developing an appropriate scale model. From tests of various scale
                                                    models, students predict the period of the thirty-foot pendulum from trends in the
                                                    periods of the smaller pendulums.
                                                    Meadows or Malls?
                                                    In this unit, students model a problem about land development with a system of
                                                    linear equations, extending concepts of linear programming to problems with
                                                    several variables. They develop and apply matrix algebra to solve the central unit
                                                    problem, and graphing linear equations in three variables and recognizing that
                                                    these graphs are planes in 3-space.
                                                    High Dive
                                                    In this unit, students determine when a circus diver must be released from a
                                                    rotating Ferris Wheel in order to land in a cart of water wheeling past along a track.
                                                    Students carefully reconsider the potential implications of the assumptions they
                                                    made in modeling the original problem toward the end of the unit.
                                                    • HW30-The Danger of Simplification




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                            Key Curriculum Press /3
      STANDARD                                   CORRELATION
1.6    Use manipulatives, calculators,            A tenet of the IMP classroom is that just as these tools are part of the resources
       computers, and other tools as appropriate mathematicians bring to the work they do, they are to be available to students. .
       in order to strengthen mathematical        They are an integral part of the curriculum. Here is an example from one unit from
       thinking, understanding, and power to      each of the four years.
       build upon foundational concepts.          The Pit and the Pendulum
                                                  In this unit, students must predict from a set of data. Since it is unlikely they have
                                                  studied a wide variety of functions at this stage in their mathematics education,
                                                  students do an activity called Graphing Free-for-All in which they explore a wide
                                                  variety of graphs. This adds to their repertoire of functions from which to select for
                                                  their model.
                                                  Do Bees Build It Best?
                                                  Students develop the Pythagorean Theorem in this unit. In the activity cited here,
                                                  students compare areas as a step toward developing the Pythagorean theorem:
                                                    
                                                   CW-Tri-Square Rug Games
                                                  Meadows or Malls?
                                                  Students are able to access complex linear programming problems (such as the six
                                                  variable unit problem) because they learn to use the calculator to make possible the
                                                  complex algebraic processes that would otherwise be necessary.
                                                  As the Cube Turns
                                                  Students use the calculator in a game of figuring out one trig ratio if given another.
                                                  In this investigation, students derive trigonometric identities.
                                                    
                                                   HW12-Double Trouble
                                                    
                                                   HW13-A Broken Button
                                                  Additionally, in this unit, students pull together unit topics in an end of the unit,
                                                  self-created animation project.
                                                    
                                                   POW5-An Animated POW




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                           Key Curriculum Press /4
                                                             UNIFYING CONCEPTS AND PROCESSES
                                  Standard 2: Students will understand and use Mathematics in Communications.
Benchmarks, Grades 9-12
    STANDARD                                                   CORRELATION
2.1    Analyze personal mathematical thinking                   Each unit concludes with students assembling a portfolio. These portfolios always
       for validity and applicability to specific               include a reflective piece on the mathematics studied during the unit. Many of
       problems.                                                these reflections ask students to discuss what mathematics they learned and how it
                                                                can be applied.
                                                                A few examples highlight the role the portfolios play:
                                                                Patterns
                                                                  
                                                                 HW2-Who‟s Who
                                                                The Pit and the Pendulum
                                                                  
                                                                 HW27-Beginning Portfolios
                                                                Cookies
                                                                  
                                                                 HW26-Continued Portfolio Selection
                                                                Pennant Fever
                                                                  
                                                                 HW16-Which Is Which?
                                                                High Dive
                                                                  
                                                                 HW8-Acceleration Variations and Sine Summary
                                                                  
                                                                 HW31-A Trigonometric Reflection
                                                                As the Cube Turns
                                                                  
                                                                 HW17-How Did We Get Here?
                                                                The Pollster’s Dilemma
                                                                  
                                                                 HW18-Confidence and Clarabell




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                      Key Curriculum Press /5
      STANDARD                                      CORRELATION
2.2    Use drawings, discussions, reading,           Students do this throughout all four years of the curriculum. Each student will
       writing, and listening to access, learn, and present to their groups and to the entire class regularly, whether it be a response to
       communicate mathematical ideas.               a class activity or a prepared presentation of a larger, Problem of the Week. These
                                                     presentations prompt questioning and discussion within the groups or the
                                                     classroom.
                                                     Additionally, students complete formal write-ups of these Problems of the Week
                                                     eight to ten times per semester. Within these write-ups, students must
                                                     communicate effectively using the language of mathematicians. A few examples
                                                     are:
                                                     Overland Trail
                                                     • Days 15-18: Making Predictions With Graphs
                                                     Cookies
                                                     • Days 4-7: Picturing Cookies
2.3    Select the most economical and illustrative Students do this throughout the four years of the curriculum. Each student will
       method to communicate mathematical            present to their groups and to the entire class regularly, whether it be a response to
       concepts, thoughts, and problem solutions a class activity or a prepared presentation of a larger Problem of the Week.
       including mathematical notation, charts,      Additionally, students complete formal write-ups of these Problems of the Week
       slides, graphs, maps, drawings, pictures,     eight to ten times per semester. Within these write-ups, students must
       sound recordings, video, e-mail, and          communicate effectively using the language of mathematicians—notation, charts,
       others.                                       graphs, etc. For example, in Orchard Hideout, students use circles and dots on graph
                                                     paper to model different size orchards, creating diagrams to clarify their ideas. In
                                                     Meadows or Malls?, they build physical models or use the corner of a room to
                                                     physically represent the x, y, z planes. In As the Cube Turns, students approach the
                                                     challenge of representing a three-dimensional object on a two-dimensional screen
                                                     through the use of both physical materials and a story about two spiders and a
                                                     thread of web that connects them.




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                              Key Curriculum Press /6
      STANDARD                                   CORRELATION
2.4    Analyze mathematical ideas through the     Students explore and make sense of mathematics and mathematical ideas with
       use of learning tools such as              these tools daily, throughout the whole curriculum. Numerous and varied activities
       manipulatives, calculators, and            in the curriculum require using manipulatives and graphing calculators. Graphing
       computers.                                 calculators help students address a complex linear programming problem in
                                                  Meadors or Malls? Students use the graphing calculator throughout As the Cube
                                                  Turns. Some other examples are:
                                                  Patterns
                                                  • Days 13-14 The Chef‟s Hot and Cold Cubes
                                                  Shadows
                                                  • Classwork: Shadow Data Gathering
                                                  Solve ItI
                                                  • HW 7: You‟re the Jester
2.5    Describe the economy, power, and           Again, this benchmark is supported daily throughout the curriculum. Only one
       elegance of mathematical notation and its example from each year is used to illustrate:
       role in the development of mathematical    The Overland Trail
       ideas.                                       
                                                   CW-“The Overland Trail” Portfolio
                                                  Solve It!
                                                    
                                                   HW24-A Distributive Summary
                                                  Meadow or Malls
                                                    
                                                   HW37-Beginning Portfolios – Part II
                                                  Know How
                                                    
                                                   CW-Knowing What You Know
                                                  • HW4-What to Know When




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                       Key Curriculum Press /7
      STANDARD                                               CORRELATION
2.6    Reading presentations of mathematics                   Students will critically analyze one another’s presentations and problem write-ups.
       with understanding.                                    Below are a few specific examples:
                                                              Patterns
                                                               
                                                               Day5: Students read each other’s problem statements of the POW1 write-up for
                                                                  clarity.
                                                               
                                                               Day7: Students read an example of a POW-style write-up. They note the style of
                                                                  the write-up and discuss reactions.
                                                              Cookies
                                                               
                                                               Day18: Students are to read each others’ papers for the purpose of noting
                                                                  weakness in clarity.
                                                              Fireworks
                                                               
                                                               Day2: Students read Quadratics and other Polynomials for understanding.
                                                              Orchard Hideout
                                                               
                                                               Day1: Students read A Geometric Summary for understanding.
                                                               
                                                               Day19: Students read The Standard Equation of the Circle for understanding.
                                                              Meadows or Malls?
                                                               
                                                               Day 10: Students read The Three Variable Coordinate System for understanding.
                                                               
                                                               Day27: Students read Matrix Basics for understanding.
                                                               
                                                               Day31: Students read Matrices and Linear Systems for understanding.
                                                              High Dive
                                                               
                                                               Day6-Extending the Sine
                                                              As the Cube Turns
                                                               
                                                               HW24-Flipping Points




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                    Key Curriculum Press /8
      STANDARD                                               CORRELATION
2.6    continued                                              Know How
                                                              Students complete a project in which they learn about a new mathematical concept
                                                              by relying on reading mathematical text.
                                                               
                                                               CW-Radian Measure
                                                               
                                                               HW2-The Law of Sines
                                                               
                                                               HW3-The Ellipse
                                                               
                                                               HW5-A Fractional Situation
                                                               
                                                               HW6-Complex Numbers
                                                               
                                                               CW-Know How Project
                                                              The World of Functions
                                                               
                                                               Day12-Students read Approaching Infinity
                                                              The Pollster’s Dilemma
                                                               
                                                               Day6-Students read The Central Limit Theorem




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                  Key Curriculum Press /9
                                                             UNIFYING CONCEPTS AND PROCESSES
                                      Standard 3: Students will understand and use Mathematics in Reasoning.
Benchmarks, Grades 9-12
    STANDARD                                                   CORRELATION
3.1    Develop and test conjectures and            This benchmark is one of the pedagogical foundations of the curriculum. Students
       mathematical arguments.                     develop and test conjectures and mathematical arguments daily throughout the
                                                   four years of the curriculum.
3.2    Evaluate reasoning strategies to select the Students evaluate reasoning strategies in the context of solving problems daily.
       most appropriate reasoning method to        Most classroom presentations of methods to solve problems include several
       solve a given problem.                      presentations of different techniques to solve the same problem. Class discussions
                                                   clarify the variety of techniques and students are provided the opportunities to
                                                   determine what works best for them.
3.3    Judge the validity of mathematical          Students must develop and present mathematical arguments daily. They listen to,
       arguments.                                  evaluate, and judge the validity of these mathematical arguments. The classroom
                                                   structure relies on arguments being presented, discussed, refined, reworked,
                                                   and/or discarded.
3.4    Construct and evaluate logical arguments. This benchmark is another one of the pedagogical foundations of the curriculum.
                                                   Students must develop and present logical arguments daily. Students listen to,
                                                   evaluate, and judge the validity of these logical arguments. The classroom
                                                   structure relies on arguments being presented, discussed, refined, reworked,
                                                   and/or discarded. Students learn to always make their assumptions explicit. Here
                                                   are a few examples in which logic is explicitly considered in the curriculum:
                                                   Patterns
                                                     
                                                    CW-A Proof Gone Bad
                                                   All About Alice
                                                     
                                                    POW14-More from Lewis Carroll
                                                     
                                                    POW15-A Logical Connection
                                                   Orchard Hideout
                                                     
                                                    Day3-The previous activities and homeworks generate a classroom discussion
                                                       of “If…then…” statements and the notion of converse.
                                                   Know How
                                                     
                                                    HW3-Now Let‟s Prove It!
New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                        Key Curriculum Press /10
      STANDARD                                               CORRELATION
3.5    Formulate counter examples to                          Again, this benchmark is supported in the pedagogical foundations of the
       understand mathematical reasoning.                     curriculum. Students must develop and present arguments daily. Students listen
                                                              to, evaluate, and judge the validity of these arguments. The classroom structure
                                                              relies on arguments being presented, discussed, refined, reworked, and/or
                                                              discarded. The use of counterexamples plays an ongoing role in developing
                                                              generalizations.
                                                              Shadows
                                                                
                                                               CW-Is There a Counterexample?
                                                                
                                                               HW9-Triangular Counterexamples




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                  Key Curriculum Press /11
                                                             UNIFYING CONCEPTS AND PROCESSES
                                      Standard 4: Students will understand and use Mathematical Connections.
Benchmarks, Grades 9-12
    STANDARD                                     CORRELATION
4.1    Relate mathematical procedures in one      Patterns
       representation to procedures in equivalent  HW10-Pulling Out Rules
                                                    
       representations.                           Solve It!
                                                    
                                                   HW16-Views of the Distributive Property
                                                    
                                                   HW30-A Solving Sampler
                                                  Meadows or Malls?
                                                  Students generate both graphical and symbolic methods/algorithms for solving
                                                  linear programming problems in two variables. These methods are extended to
                                                  three variable systems as well. The graphical model is relied on to generalize a
                                                  symbolic method for any size linear programming problem.
                                                    
                                                   CW-What Wood Would Woody Want?
                                                    
                                                   HW15-The “More Cookies” Region and Strategy
                                                    
                                                   HW24-Constraints Without a Context
                                                    
                                                   CW-Eastside Westside Story
                                                    
                                                   HW35-Getting Ready for “Meadows or Malls?”
                                                    
                                                   CW-“Meadows or Malls” Revisited
                                                  As the Cube Turns
                                                    
                                                   HW15-Comin‟ Round Again (and Again…)
                                                  The World of Functions
                                                  Students formally define arithmetic operations on symbolic forms of functions.
                                                  Students relate these operations to the tabular and graphical forms of the functions.
                                                    
                                                   CW-The Arithmetic of Functions
                                                  • HW18-The Arithmetic of Graphs




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                         Key Curriculum Press /12
      STANDARD                                               CORRELATION
4.2    Compare and contrast equivalent                        This notion of equivalent representations of the same concept is the foundation for
       representations of the same concept.                   the development of most mathematical concepts throughout the four years of the
                                                              curriculum.
                                                              The Overland Trail
                                                               
                                                               CW-Out Numbered
                                                               
                                                               HW13-Situations, Graphs, Tables, and Rules
                                                               
                                                               HW14-Rules, Tables, and Graphs
                                                               
                                                               CW-Previous Travelers
                                                              Solve It!
                                                               
                                                               CW-A Lot of Changing Sides
                                                               
                                                               HW13-Why Are They Equivalent?
                                                               
                                                               HW14-One Each Way
                                                               
                                                               CW-Distributing the Area
                                                               
                                                               HW15-The Distributive Property and Mystery Lots
                                                               
                                                               HW16-Views of the Distributive Property
                                                               
                                                               CW-Taking Some Out, Part I
                                                               
                                                               HW18-Subtracting Some Sums
                                                               
                                                               CW-Taking Some Out, Part II
                                                               
                                                               HW19-Randy, Sandy, and Dandy Return
                                                               
                                                               HW24-A Distributive Summary
                                                              Pennant Fever
                                                               
                                                               HW6-Diagrams, Baseball, and Losing „Em All
                                                              The World of Functions
                                                               
                                                               CW-Functions in Verse
                                                               
                                                               HW29-Beginning Portfolio Selection
                                                              The Pollster’s Dilemma
                                                              • HW11-A Distribution Example




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                    Key Curriculum Press /13
      STANDARD                                    CORRELATION
4.3    Assess the relationship among               Mathematical topics are inherently interrelated. This notion is evident to IMP
       mathematical topics.                        students as they develop mathematical understanding in the context of real
                                                   problems. Because of this structure in which students learn and experience
                                                   mathematics, students are always working in and around several of the various
                                                   standards. Examples from each of the four years:
                                                   The Pit and the Pendulum
                                                     
                                                    HW27-Beginning Portfolios
                                                   Cookies
                                                   • HW27-Cookies Portfolio. Students consider how key mathematical ideas were
                                                       developed and how they worked together to solve the unit problem.
                                                   Orchard Hideout
                                                     
                                                    HW24-“Orchard Hideout” Portfolio
                                                   As the Cube Turns
                                                     
                                                    HW17-How Did We Get Here?
                                                   The World of Functions
                                                     
                                                    HW24-Fish, Ladders, and Bacteria
                                                   The Pollster’s Dilemma
                                                     
                                                    HW2-Pennant Fever Reflection
                                                   • CW-Roberto and the Coin Revisited
4.4    Incorporate the use of technology into the Again, this benchmark is supported in the pedagogical foundations of the
       application of mathematical reasoning       curriculum. These modern tools are always to be available to students just as they
       and problem solving to other disciplines.   are available to mathematicians in their work.




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                        Key Curriculum Press /14
      STANDARD                                               CORRELATION
4.5    Evaluate mathematical solutions for                    Each unit problem presents an opportunity for students to connect analysis and
       problems in daily life and in the greater              results to daily life and the greater society. Students are encouraged to reflect on
       society.                                               these connections in their portfolio and in end of the unit discussions. They are
                                                              challenged to make decisions about real-life problem situations; for example. when
                                                              they assume the role of consultant or elected representative. It requires students to
                                                              go beyond simply finding numerical answers. The unit problems of the following
                                                              units are particularly worth noting: The Pit and the Pendulum, Is There Really a
                                                              Difference?, Cookies, Meadows or Malls?, Small World, Isn‟t It?, Pennant Fever, and
                                                              Pollster‟s Dilemma.
                                                              Additionally, certain activities stand out:
                                                              Is There Really a Difference?
                                                               
                                                               HW12-Drug Dragnet: Fair or Foul?
                                                              As the Cube Turns
                                                               
                                                               POW4-A Wider Windshield Wiper, Please
                                                              The Pollster’s Dilemma
                                                               
                                                               CW-Let‟s Vote on It!
                                                              • HW17-A Teaching Dilemma




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                     Key Curriculum Press /15
                                                             NUMBER AND OPERATIONS CONCEPTS
                                Standard 5: Students will understand and use numbers and number relationships.
Benchmarks, Grades 9-12
    STANDARD                                     CORRELATION
5.1    Extend number-sense skills to include      Do Bees Build it Best?
       irrational numbers.                          
                                                   CW-Any Two Sides Work
                                                    
                                                   HW13-Make the Lines Count
                                                    
                                                   HW18-Simply Square Roots
                                                  All About Alice
                                                    
                                                   HW9-It‟s in the Graph
                                                    
                                                   HW10-Stranger Pieces of Cake
                                                  Fireworks
                                                    
                                                   HW5-Factoring Begun. In class discussion, students consider the significance of
                                                      irrational roots and what “not factorable” means.
                                                  Orchard Hideout
                                                    
                                                   HW1-Geometry and a Mini-Orchard
                                                    
                                                   CW-Polygoning the Circle. Ensuing class discussion makes sense of the
                                                      transcendental number .
                                                  Small World, Isn’t It?
                                                    
                                                   CW-Find That Base!
                                                    
                                                   HW28-The Limit of Their Generosity
                                                    
                                                   HW29-California‟s Population with e‟s
5.2    Apply number-sense skills within the real It is difficult to pinpoint specific examples of this benchmark because students
       number system.                             develop and are asked to draw upon their number-sense skills throughout the
                                                  entire IMP curriculum. Because students are asked to make sense of problem
                                                  situations for themselves, this number sense is the framework within which
                                                  students create meaning. The IMP curriculum builds in the expectation that
                                                  students must apply number-sense skills daily.
                                                  Any item that is mentioned in Standard 5-7 would provide a good example for this
                                                  benchmark.



New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                       Key Curriculum Press /16
      STANDARD                                    CORRELATION
5.2    continued                                   POW6-SubDivvy and POW7-Crack the Code! in the Year 3 unit Meadows or Malls?
                                                   are specific samples of how students experience and work with the properties of
                                                   the real number system.
                                                   The Pollster’s Dilemma
                                                   • HW9-Gaps in the Table
5.3    Apply ratios, proportions, and percents in The Overland Trail
       more complex mathematical situations.       • Day 17-28: Students consider ideas of direct variation, slope (informally), and
                                                       rate-time-distance problems.
                                                   The Pit and the Pendulum
                                                   • POW13-Corey the Camel
                                                   Shadows
                                                    
                                                    HW7-The Statue of Liberty‟s Nose
                                                    
                                                    HW8-Make it Similar
                                                    
                                                    HW10-Similar Problems
                                                    
                                                    HW11-From Top to Bottom
                                                    
                                                    HW16-Ins and Outs of Proportion
                                                    
                                                    HW22-Right Triangle Ratios
                                                    
                                                    Day23-25: Students generate the right triangle trigonometry definitions.
                                                   Solve It!
                                                   • HW26-More Variable Solutions
                                                   Is There Really a Difference?
                                                    
                                                    CW-Measuring Weirdness
                                                    
                                                    HW12-Drug Dragnet: Fair or Foul?
                                                    
                                                    CW-Does Age Matter?
                                                    
                                                    HW16-Assigning Probabilities
                                                   Do Bees Build It Best?
                                                    
                                                    HW17-More Fencing, Bigger Corrals
                                                    
                                                    HW27-Cereal Box Sizes
                                                   All About Alice
                                                    
                                                    HW7-Continuing the Pattern


New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                        Key Curriculum Press /17
      STANDARD                                               CORRELATION
5.3    continued                                              Small World, Isn’t It?
                                                              Students are asked to analyze the derivative of exponential functions and note the
                                                              proportionality properties that distinguish exponential functions from other
                                                              families of functions.
                                                                
                                                               CW-Slippery Slopes
                                                                
                                                               HW20-How Does It Grow?
                                                                
                                                               CW-The Power of Powers
                                                                
                                                               HW23-The Power of Powers, Continued
                                                              
                                                                  CW-Find That Base!
                                                              As the Cube Turns
                                                                
                                                               CW-Fractional Snacks
                                                                
                                                               HW21-More Walking for Clyde
                                                                
                                                               CW-Monorail Delivery
                                                                
                                                               CW-And Fred Brings the Lunch
                                                                
                                                               HW25-Where‟s Bonita?
                                                              • CW-Lunch in the Window




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                    Key Curriculum Press /18
5.4    Analyze and interpret numerical                       Patterns
       relationships in one- and two-dimensional              
                                                              CW-The Chef‟s Hot & Cold Cubes
       graphs, both manually and using tools                 The Overland Trail
       such as graphing calculators and                       
                                                              CW-Wagon Train Sketches and Situations
       computers.
                                                              
                                                              HW11-Graph Sketches
                                                              
                                                              CW-In Need of Numbers
                                                              
                                                              HW12-The Issues Involved (Students consider issues related to scaling axes and
                                                                inferring form graphs.)
                                                              
                                                              CW-Out Numbered (Students generalize relationships from graphs.)
                                                              
                                                              CW-“Out of Action” and “Sublette‟s Cutoff” Revisited
                                                             Solve It!
                                                             • CW- The Graph Solves the Problem
                                                                Is There Really a Difference?
                                                                                                             2
                                                              
                                                              Day17-18: Students develop and interpret a  probability graph.
                                                             Cookies
                                                              
                                                              HW2-Investigating Inequalities
                                                              
                                                              CW-Picturing Cookies-Part I
                                                             • CW-Picturing Cookies-Part II




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                 Key Curriculum Press /19
      STANDARD                                               CORRELATION
5.4    continued                                              All About Alice
                                                                
                                                               HW9-It‟s in the Graph
                                                              • CW-All Roads Lead to Rome
                                                              Fireworks
                                                                
                                                               CW-The Ups and Downs of Quadratics
                                                              Small World, Isn’t It?
                                                                
                                                               CW-ZOOOOOOOOM!
                                                                
                                                               HW15-On a Tangent
                                                                
                                                               HW21-The Significance of a Sign
                                                                
                                                               HW27-Comparing Derivatives
                                                              High Dive
                                                              Students define polar coordinates and develop expressions for rectangular
                                                              coordinates in terms of polar coordinates. Example activities include:
                                                                
                                                               CW-Some Polar Practice
                                                              • HW17-Polar Coordinates on the Ferris Wheel
                                                              As the Cube Turns
                                                              Students apply algebraic and trigonometric reasoning to translate and rotate points
                                                              in two dimensions. Additionally, students will project points in 3-space to a two
                                                              dimensional plane. For example:
                                                                
                                                               HW15-Comin‟ Round Again (and Again…)
                                                                
                                                               HW29-Mirrors in Space




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                   Key Curriculum Press /20
                                                             NUMBER AND OPERATION CONCEPTS
                                Standard 6: Students will understand and use number systems and number theory.
Benchmarks, Grades 9-12
    STANDARD                                                   CORRELATION
6.1    Use order relations within the real number Throughout the Patterns unit, students observe and generalize numerical patterns.
       system.                                    For example:
                                                   
                                                   HW7-Extended Bagels
                                                   
                                                   CW-Consecutive Sums
                                                  Note: this unit sets the stage for student thinking throughout the remaining four
                                                  years of the IMP curriculum.
                                                  The Overland Trail
                                                   
                                                   POW8-The Haybaler Problem
                                                   
                                                   POW11-High-Low Differences
                                                  Solve It!
                                                   
                                                   HW6-The Mystery Bags Game
                                                  Cookies
                                                   
                                                   POW12-Kick It!
                                                  Throughout the All About Alice unit students compare relative sizes of very large
                                                  and very small numbers using exponents, scientific notation, and logarithms. Some
                                                  examples:
                                                   
                                                   HW14-Alice on a Log
                                                   
                                                   CW-Taking Logs to the Axes
                                                   
                                                   HW15-Base 10 Alice
                                                   
                                                   HW16-Warming Up to Scientific Notation
                                                   
                                                   CW-Big Numbers
                                                  Fireworks
                                                   
                                                   CW-Factored Intercepts. Students recognize the role the zero property of
                                                      multiplication plays in solving equations.
6.2    Apply number theory concepts to a          The Pit and the Pendulum
       variety of problem situations.              
                                                   POW14-Eight Bags of Gold
                                                   
                                                   POW15-Twelve Bags of Gold
New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                       Key Curriculum Press /21
      STANDARD                                               CORRELATION
6.2    continued                                              Shadows
                                                               
                                                               POW17-Cutting the Pie
                                                              Solve It!
                                                               
                                                               POW1-A Digital Proof
                                                               
                                                               POW2-Tying the Knots
                                                               
                                                               POW3-Divisor Counting
                                                              Is There Really a Difference?
                                                               
                                                               POW4-A Timely Phone Tree
                                                               
                                                               POW5-Punch the Clock
                                                              Cookies
                                                               
                                                               POW12-Kick It!
                                                               
                                                               POW13-Shuttling Around
                                                              Orchard Hideout
                                                               
                                                               POW9-A Marching Strip
                                                              Meadows or Malls?
                                                               
                                                               POW6-SubDivvy
                                                               
                                                               POW7-Crack the Code!
                                                              Small World, Isn’t It?
                                                               
                                                               POW9-Planning the Platforms
                                                               
                                                               POW10-Around King Arthur‟s Table
                                                              High Dive
                                                               
                                                               POW1-The Tower of Hanoi
                                                              Know How
                                                               
                                                               POW6-Which Weights Weigh What?
                                                              World of Functions
                                                               
                                                               POW7-One Mile at a Time
                                                              During this unit, students will analyze functions using ideas of finite differences,
                                                              both formally and informally.
                                                               
                                                               CW-Linear Tables
                                                               
                                                               CW-Quadratic Tables
                                                               
                                                               CW-Quadratic Tables by Algebra

New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                      Key Curriculum Press /22
      STANDARD                                      CORRELATION
6.2    continued                                      
                                                      HW6-A General Quadratic
                                                      
                                                      CW-Exponential Tables
                                                     • HW7-A Cubic Pattern
6.3    Identify how seemingly different              Patterns
       mathematical situations may be                 
                                                      HW22-Border Varieties
       essentially the same (for example, the        The Overland Trail
       intersection of two lines is the same as the  CW-More Fair Share on Chores
                                                      
       solution to a system of linear equations).
                                                      
                                                      HW23-More Fair Share for Hired Hands
                                                      
                                                      CW-Water Conservation
                                                      
                                                      HW25-The Big Buy
                                                     Shadows
                                                      
                                                      POW17-Cutting the Pie
                                                     Solve It!
                                                      
                                                      HW12-Who‟s Right?
                                                      
                                                      HW16-Views of the Distributive Property
                                                     Cookies
                                                      
                                                      CW-Profitable Pictures
                                                     Fireworks
                                                      
                                                      HW4-Make Your Own Intercepts
                                                     Orchard Hideout
                                                     In this unit, students study coordinate geometry. They rely on the Pythagorean
                                                     theorem to generate a wide variety of relationships, including the distance formula
                                                     and general formula defining circles. Example activities include:
                                                      
                                                      HW4-In, On, or Out?
                                                      
                                                      HW6-The Distance Formula
                                                      
                                                      HW18-Defining Circles
                                                     Meadows or Malls?
                                                      
                                                      HW36-Beginning Portfolios – Part I




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                          Key Curriculum Press /23
      STANDARD                                               CORRELATION
6.3    continued                                              Small World, Isn’t It?
                                                              Students generate the number e in two seemingly unrelated contexts. First,
                                                                                                                                            x
                                                              students look for the base (b) of an exponential function of the form f(x) = b so that
                                                              f(x) = f(x). Next, students rediscover e in the context of compounding interest.
                                                              Pennant Fever
                                                                
                                                               CW-Pascal‟s Triangle
                                                                
                                                               HW24-Hi There!
                                                                
                                                               HW25-Pascal‟s Triangle and the Combinatorial Coefficients
                                                                
                                                               CW-Combinations, Pascal‟s Way
                                                                
                                                               HW26-Binomials and Pascal – Part I
                                                                
                                                               HW27-Binomials and Pascal – Part II
                                                              • HW28-A Pascal Portfolio
                                                              As the Cube Turns
                                                              • HW27-Spiders and Cubes
6.4    Compare and contrast the real number                   All About Alice
       system and its various subsystems with                 Students consider the nature of roots, logarithms and their irrationality.
       regard to structural characteristics.                  Meadows or Malls?
                                                              Students examine whether matrix operations have certain properties such as
                                                              associativity and commutativity. Students also identify the matrix identity for
                                                              multiplication. The following activities highlight these student experiences:
                                                                
                                                               HW31-Solving the Simplest
                                                                
                                                               HW32-Things We Take for Granted
                                                              Small World, Isn’t It?
                                                              Students consider the nature of irrational and transcendental numbers.
                                                              The World of Functions
                                                                
                                                               POW8-A Spin on Transitivity
                                                                
                                                               HW22-Order Among the Functions
                                                              • HW26-An Inventory of Inverses




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                      Key Curriculum Press /24
      STANDARD                                               CORRELATION
6.5    Develop and analyze algorithms.                        The IMP curriculum provides a structure for students to constantly develop
                                                              algorithms for solving a variety of problems. Students analyze the accuracy and/or
                                                              effectiveness of peer’s algorithms. Some specific examples of these:
                                                              Shadows
                                                                
                                                               CW-Mirror Magic
                                                                
                                                               HW19-To Measure a Tree
                                                              • CW-A Shadow of a Doubt
                                                              Solve It!
                                                                
                                                               HW6-The Mystery Bags Game
                                                              • Day13-21: Students generate the necessary algorithms for applying the
                                                                  Distributive Property within symbolic algebraic representations. Key examples
                                                                  include:
                                                                
                                                               CW-A Lot of Changing Sides
                                                                
                                                               HW13-Why Are They Equivalent?
                                                                
                                                               CW-Distributing the Area
                                                                
                                                               HW15-The Distributive Property and Mystery Lots
                                                                
                                                               CW-Taking Some Out, Part I
                                                                
                                                               HW18-Subtracting Some Sums
                                                                
                                                               CW-Taking Some Out, Part II
                                                              • HW24-A Distributive Summary
                                                              Cookies
                                                                
                                                               CW-Get the Point. Students develop an algorithm to algebraically solve for the
                                                                  point of intersection of two linear functions.
                                                                
                                                               POW13-Shuttling Around
                                                              Fireworks
                                                                
                                                               CW-Who‟s Perfect
                                                                
                                                               HW6-More About Perfection. In these two activities, students generate a method
                                                              to “complete the square.”


New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                  Key Curriculum Press /25
      STANDARD                                               CORRELATION
6.5    continued                                              Meadows or Malls?
                                                              Students generate algorithms to solve two variable linear programming problems.
                                                              One algorithm is graphic in nature, the other relies purely on symbolic algebraic
                                                              arguments. Students compare and contrast the benefits of each algorithm. Next,
                                                              each is extended to three variable problems. Students see that the graphing
                                                              becomes more complex. As students consider linear programming problems
                                                              beyond three variables, they realize that only the algebraic algorithm is practical.
                                                              Students conclude the unit by formulating a algorithm to solve any size linear
                                                              programming problems relying on matrix algebra and calculator technology.
                                                              Small World, Isn’t It?
                                                                
                                                               HW9-Points, Slopes, and Equations
                                                                
                                                               CW-A Basis for Disguise
                                                                
                                                               HW29-California Population with e‟s
                                                              As the Cube Turns
                                                              One primary focus of this unit is for students to develop a structural understanding
                                                              of programming language. This begins with students reading and writing their
                                                              own plain-language programs. They will translate these plain-language programs
                                                              into the language of a graphing calculator. Some example activities include:
                                                                
                                                               HW2-Programming Without a Calculator
                                                                
                                                               HW3-Learning the Loops
                                                                
                                                               HW5-Moving‟ On
                                                                
                                                               HW6-Some Back and Forth
                                                                
                                                               CW-Swing That Line!
                                                                
                                                               HW19-What‟s Going on Here?




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                    Key Curriculum Press /26
                                                             NUMBER AND OPERATION CONCEPTS
                                      Standard 7: Students will understand and use computation and estimation.
Benchmarks, Grades 9-12
    STANDARD                                                   CORRELATION
7.1    Develop, analyze, and explain methods        The IMP curriculum provides a structure for students to constantly develop and
       for solving a variety of problem situations. explain their methods for solving a variety of problems. The development of these
                                                    methods may be done individually or collaboratively. Explanations may be written
                                                    or stated verbally in small groups, formal presentations, or as part of a classroom
                                                    discussion. Students analyze the accuracy and/or effectiveness of peers’ methods,
                                                    as well as examples presented in the curriculum itself. Some specific examples of
                                                    these:
                                                    Patterns
                                                     
                                                     CW-A Proof Gone Bad
                                                    Shadows
                                                     
                                                     HW13-Inventing Rules
                                                     
                                                     HW16-Ins and Outs of Proportions
                                                    Solve It!
                                                     
                                                     HW6-The Mystery Bags Game
                                                    Do Bees Build It Best?
                                                     
                                                     CW-Going into the Gallery
                                                    Cookies
                                                    Students develop a set of steps to solve two variable linear programming problems.
                                                    This is summarized by students in :
                                                     
                                                     HW23-Beginning Portfolio Selection
                                                    Students must thoroughly write-up all POW’s. Students are expected to present
                                                    and explain their thinking and methods for solving these problems. The example
                                                    below is only one of many that illustrates this feature of IMP that pervades through
                                                    all four years:
                                                    Meadows or Malls?
                                                     
                                                     POW5-That‟s Entertainment. Again, this POW is an excellent example of this
                                                        ongoing expectation throughout the four years of IMP.



New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                          Key Curriculum Press /27
      STANDARD                                   CORRELATION
7.1    continued                                  High Dive
                                                  This unit is marked by an overwhelming set of generalizations and equations that
                                                  students develop (and justify) for solving problems. A sample:
                                                    
                                                   CW-Free Fall
                                                    
                                                   HW10-A Practice Jump
                                                    
                                                   HW11-Where Does He Land?
                                                  • CW-Generalizing the Platform
7.2    Extend solutions of problems to formulate The Overland Trail
       predictions.                                 
                                                   CW-Previous Travelers
                                                    
                                                   HW17-The Basic Student Budget
                                                  The Pit and the Pendulum
                                                  This unit’s problem (predict the period of a thirty foot pendulum) asks students to
                                                  not only develop proper small scale models of a pendulum, but also to collect data
                                                  from them to formulate a prediction for the period of a thirty foot pendulum. The
                                                  capstone activity is:
                                                    
                                                   CW-The Thirty-Foot Prediction
                                                  Cookies
                                                    
                                                   POW13-Shuttling Around
                                                  High Dive
                                                    
                                                   POW1-The Tower of Hanoi
                                                  The Pollster’s Dilemma
                                                    
                                                   POW10-The King‟s Switches




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                        Key Curriculum Press /28
      STANDARD                                               CORRELATION




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                 Key Curriculum Press /29
7.3    Justify the reasonableness of solutions and IMP requires students to justify the reasonableness of their conclusions or
       predictions.                                predictions throughout its curriculum. IMP challenges students with big problems
                                                   that take time to solve. Here are examples of smaller problems in the context of
                                                   units:
                                                   The Overland Trail
                                                    
                                                    CW-Who Will Make It?
                                                    
                                                    HW18-Out of Action
                                                   The Pit and the Pendulum
                                                    
                                                    HW20-Mehrdad the Market Analyst
                                                    
                                                    CW-Bird Houses
                                                    
                                                    CW-The Thirty-Foot Pendulum
                                                   Solve It!
                                                    
                                                    HW13-Why Are They Equivalent?
                                                   Do Bees Build it Best?
                                                    
                                                    HW4-An Area Shortcut?
                                                    
                                                    HW19-Falling Bridges
                                                   Orchard Hideout
                                                    
                                                    HW22-Big Earth, Little Earth
                                                   Meadows or Malls?
                                                    
                                                    POW5-That‟s Entertainment. Students must complete a write-up of all the
                                                      POW’s they do. Students are expected to justify and defend solutions they find.
                                                      Again, this POW is an excellent example of this ongoing expectation throughout
                                                      the four years of the IMP.
                                                   Small World, Isn’t It?
                                                    
                                                    CW-Return to “Small World, Isn‟t It?”
                                                   The World of Functions
                                                    
                                                    CW-Better Braking
                                                   The Pollster’s Dilemma
                                                    
                                                    CW-The Pollster‟s Dilemma” Revisited



New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                       Key Curriculum Press /30
                                                      GEOMETRY AND MEASUREMENT CONCEPTS
                                          Standard 8: Students will have a foundation in geometric concepts.
Benchmarks, Grades 9-12
    STANDARD                                                 CORRELATION
8.1    Interpret and draw three-dimensional                   Do Bees Build it Best?
       objects.                                               Students strengthen their three-dimensional spatial visualization skills.
                                                               
                                                               CW-Building the Biggest
                                                               
                                                               HW1-What to Put It In?
                                                               
                                                               HW21-Flat Cubes
                                                               
                                                               CW-Flat Boxes
                                                               
                                                               HW22-Not a Sound
                                                               
                                                               CW-A Voluminous Task
                                                               
                                                               HW23-Put Your Fist into It
                                                               
                                                               HW24-A Sculpture Garden
                                                               
                                                               CW-The World of Prisms‟
                                                               
                                                               CW-Shedding Light on Prisms
                                                               
                                                               HW25-Pythagoras and the Box
                                                               
                                                               HW26-Back on the Farm
                                                               
                                                               CW-Which Holds More?
                                                               
                                                               HW27-Cereal Box Sizes
                                                               
                                                               CW-A Tessellating We Go
                                                              Orchard Hideout
                                                               
                                                               HW20-Cylindrical Soda
                                                              Meadows or Malls?
                                                               
                                                               HW10-What Do They Have in Common?
                                                               
                                                               CW-Just the Plane Facts
                                                               
                                                               HW15-The “More Cookies” Region and Strategy
                                                              As the Cube Turns
                                                               
                                                               CW-A Return to the Third Dimension

New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                     Key Curriculum Press /31
      STANDARD                                               CORRELATION
8.2    Deduce properties of figures using                     Shadows
       transformations and using coordinates.                   
                                                               POW16-Spiralaterals
                                                                
                                                               HW1-Shadows and Spiralaterals
                                                              Students develop intuitive ideas about “same shape” and learn formal definitions
                                                              of similarity and congruence.
                                                              • CW-How to Shrink It?
                                                              Students discover criteria for polygons to be similar and, in particular, for triangles
                                                              to be similar.
                                                                
                                                               CW-Why are Triangles Special?
                                                                
                                                               CW-Are Angles Enough?
                                                                
                                                               HW11-From Top to Bottom
                                                                
                                                               HW15-Inside Similarity
                                                              Do Bees Build it Best?
                                                                
                                                               POW8-Just Count the Pegs
                                                                
                                                               POW9-Tessellation Pictures
                                                                
                                                               POW10-Possible Patches
                                                              Cookies
                                                              Students see that setting a linear expression equal to different constants gives a
                                                              family of parallel lines.
                                                                
                                                               HW8-Curtis and Hassan Make Choices
                                                              Fireworks
                                                                
                                                               CW-The Ups and Downs of Quadratics
                                                              Orchard Hideout
                                                                
                                                               Day6- Students identify symmetry within a unit coordinate circle. The also
                                                                  notice similar triangles.
                                                                
                                                               HW18-Defining Circles
                                                              Meadows or Malls?
                                                                
                                                               HW24-Constraints Without a Context. In this activity, students must argue which
                                                                  combinations of constraints could not possibly create potential corners of a
                                                                  three-dimensional feasible region.
                                                              High Dive
                                                                
                                                               CW-At Certain Points in Time
New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                      Key Curriculum Press /32
      STANDARD                                  CORRELATION
8.2    continued                                 As the Cube Turns
                                                  
                                                  CW-Move That Line!
                                                  
                                                  HW10-Cornering the Cabbage
                                                 • HW11-Goin‟ Round the Origin
8.3    Classify figures in terms of congruence   Shadow:
       and similarity and apply these            Students apply properties of similar triangles to physical situations.
       relationships.                             
                                                  HW6-Draw the Same Shape
                                                  
                                                  CW-How to Shrink It?
                                                  
                                                  HW8-Make it Similar
                                                  
                                                  HW10-Similar Problems
                                                  
                                                  HW12-Very Special Triangles
                                                  
                                                  HW15-Inside Similarity
                                                  
                                                  HW18-Mirror Madness
                                                  
                                                  CW-More Triangles for Shadows
                                                  
                                                  CW-The Return of the Tree
8.4    Represent problem situations with         The Game of Pig
       geometric models and apply properties of Students create area models to represent probability situations.
       figures.                                   
                                                  HW7-Portraits of Probabilities
                                                  
                                                  HW12-Pointed Rugs
                                                  
                                                  HW14-A Fair Rug Game?
                                                  
                                                  HW16-Streak Shooting Shelly
                                                  
                                                  CW-Martian Basketball
                                                  
                                                  CW-Little Pig Strategies
                                                  
                                                  HW23-Continued Little Pig Investigation
                                                 • HW24-Even More Little Pig Investigation




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                         Key Curriculum Press /33
      STANDARD                                               CORRELATION
8.4    continued                                              Shadows
                                                              Students develop geometric models of mirror reflections and lamp and sun
                                                              shadows.
                                                                
                                                               CW-How Long is a Shadow?
                                                                
                                                               CW-Mirror Magic
                                                                
                                                               HW19-To Measure a Tree
                                                                
                                                               HW21-The Sun Shadow Problem
                                                              An analysis of the properties of this model allows students to define a generalized
                                                              relationship among the shadow model variables.
                                                              • CW-A Shadow of a Doubt
                                                              Students apply properties of similarity to solve problems.
                                                                
                                                               CW-A Shadow of a Doubt
                                                                
                                                               CW-More Triangles for Shadows
                                                                
                                                               CW-The Return of the Tree
                                                              Do Bees Build it Best?
                                                              Students model throughout the unit as a means for developing mathematics to
                                                              solve unit problem.
                                                              Orchard Hideout
                                                              Again, students model throughout the unit as a means for developing mathematics
                                                              to solve unit problem. A few examples:
                                                                
                                                               Day2- Students “coordinatize” the unit problem.
                                                                
                                                               POW2-Equally Wet
                                                                
                                                               POW3-On Patrol
                                                                
                                                               CW-Cable Ready
                                                              Meadows or Malls?
                                                                
                                                               HW15-The “More Cookies” Region and Strategy
                                                                
                                                               HW16-Finishing Off the Cookies
                                                                
                                                               HW24-Constraints Without a Context
New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                    Key Curriculum Press /34
      STANDARD                                               CORRELATION
8.4    continued                                              Pennant Fever
                                                               
                                                               CW-Choosing for Chores
                                                               
                                                               HW3-Baseball Probabilities
                                                               
                                                               HW4-Possible Outcomes
                                                               
                                                               CW-How Likely is All Wins?
                                                               
                                                               HW6-Diagrams, Baseball, and Losing „Em All
                                                               
                                                               CW-“Race for the Pennant!” Revisited
                                                              High Dive
                                                               
                                                               CW-High Dive
                                                              • HW1-The Ferris Wheel
                                                              As the Cube Turns
                                                               
                                                               POW4-A Wider Windshield Wiper, Please
                                                               
                                                               HW10-Cornering the Cabbage
                                                              The World of Functions
                                                               
                                                               CW-Return of the Shadow




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                   Key Curriculum Press /35
8.5    Deduce properties of and relationships                Patterns
       between figures from given assumptions.               Students investigate the interior angle sum of polygons.
                                                               
                                                              CW-Pattern Block Angles
                                                               
                                                              CW-Degree Discovery
                                                               
                                                              HW17-Diagonally Speaking
                                                               
                                                              HW18-Polygon Angles
                                                               
                                                              HW19-An Angular Summary
                                                             Shadows
                                                             Students develop properties of triangles from given assumptions.
                                                               
                                                              HW9-Triangular Counterexamples
                                                               
                                                              POW18-Trying Triangles
                                                             Do Bees Build it Best?
                                                             Students create formulas for the areas of rectangles, triangles, parallelograms, and
                                                             trapezoids.
                                                               
                                                              HW6-The Ins and Outs of Area
                                                               
                                                              HW7-Forming Formulas




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                    Key Curriculum Press /36
      STANDARD                                               CORRELATION
8.5    continued                                              Students discover that the ratio of the areas of similar figures is equal to the square
                                                              of the ratio of their corresponding linear dimensions.
                                                                
                                                               HW17-More Fencing, Bigger Corrals
                                                                
                                                               CW-More Opinions About Corrals
                                                                
                                                               CW-Building the Best Fence
                                                              Students develop principles relating the volume and surface area of a prism to the
                                                              area and perimeter of its base.
                                                                
                                                               CW-The Ins and Outs of Boxes
                                                                
                                                               CW-Shedding Light on Prisms
                                                              Students discover that the ratio of the surface areas of similar solids is equal to the
                                                              square of the ratio of their corresponding linear dimensions, and that the ratio of
                                                              the volumes of similar solids is equal to the cube of the ratio of their corresponding
                                                              linear dimensions.
                                                                
                                                               HW27-Cereal Box Sizes
                                                              Orchard Hideout
                                                                
                                                               Day 4-Students deduce the notion of tangent line to a circle in the context of line
                                                                  of sight through an orchard.
                                                                
                                                               CW-Lines of Sight for Radius Six
                                                              Meadows or Malls?
                                                                
                                                               CW-Just the Plane Fact
8.6    Identify congruent and similar figures                 Shadow:
       using transformations.                                 Students intuitively explore various transformations.
                                                                
                                                               HW15-Inside Similarity
                                                              Orchard Hideout
                                                                
                                                               Day 6-Students identify symmetry within a unit coordinate circle and notice
                                                                  similar rotated or translated triangles.
                                                              High Dive
                                                              Throughout this unit, students use congruent triangles within a unit circle to
                                                              develop trigonometric identities.




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                      Key Curriculum Press /37
      STANDARD                                               CORRELATION
8.7    Analyze properties of Euclidean                        Orchard Hideout
       transformations and relate                              
                                                               CW-The Other Gap
       transformations to vectors.                             
                                                               CW-Lines of Sight for Radius Six
                                                              High Dive
                                                               
                                                               CW-Testing the Definition
                                                               
                                                               HW15-What‟s Your Cosine?
                                                               
                                                               CW-The Ideal Skateboard
                                                               
                                                               HW27-Racing the River
                                                               
                                                               CW-One O‟Clock Without Gravity
                                                               
                                                               CW-Release at Any Angle
                                                              As the Cube Turns
                                                              Students derive formulas for the sine and the cosine of the sum of two angles.
                                                               
                                                               HW12-Double Trouble
                                                               
                                                               CW-The Sine of a Sum




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                    Key Curriculum Press /38
                                                      GEOMETRY AND MEASUREMENT CONCEPTS
                                               Standard 9: Students will understand and use measurement.
Benchmarks, Grades 9-12
    STANDARD                                                 CORRELATION
9.1    Apply measurement as a tool in other                  This is an integral part of the IMP curriculum, and here are some examples:
       disciplines and in everyday problem                   Patterns
       situations.                                           Students measure angles to solve problems and to generalize relationships.
                                                               
                                                              CW-A Protracted Engagement
                                                               
                                                              HW17-Diagonally Speaking
                                                               
                                                              CW-Degree Discovery
                                                             Pit and the Pendulum
                                                             Measurement is used throughout the unit to collect and analyze data as a means for
                                                             developing mathematics to solve the unit problem.
                                                             Do Bees Build it Best?
                                                             Students use measurement concepts to find area, surface area, and volume.
                                                               
                                                              CW-Nailing Down Area
                                                               
                                                              HW2-Approximating Areas
                                                               
                                                              HW4-An Area Shortcut?
                                                               
                                                              CW-A Voluminous Task
                                                               
                                                              HW23-Put Your Fist Into It
                                                               
                                                              CW-Shedding Light on Prisms
                                                             Orchard Hideout
                                                             In this unit, students model an orchard with trees at lattice points. Upon
                                                             introduction to the problem, students draw a model and use a straightedge and
                                                             ruler to begin estimating coordinate distances.




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                 Key Curriculum Press /39
      STANDARD                                               CORRELATION
9.2    Identify and use the appropriate units and             This is an integral part of the IMP curriculum, and here are some examples:
       tools of measurement to the degree of                  Patterns
       accuracy required in particular problems.              Students measure angles to solve problems and to generalize relationships.
                                                                
                                                               CW-A Protracted Engagement
                                                                
                                                               HW17-Diagonally Speaking
                                                                
                                                               CW-Degree Discovery
                                                              Pit and the Pendulum
                                                              Measurement is used throughout the unit to collect and analyze data as a means for
                                                              developing mathematics to solve unit problem.
                                                              Do Bees Build it Best?
                                                              Students use measurement concepts to find area, surface area, and volume.
                                                                
                                                               CW-Nailing Down Area
                                                                
                                                               HW2-Approximating Areas
                                                                
                                                               HW4-An Area Shortcut?
                                                                
                                                               CW-A Voluminous Task
                                                                
                                                               HW23-Put Your Fist Into It
                                                                
                                                               CW-Shedding Light on Prisms
                                                              Orchard Hideout
                                                              In this unit, students model an orchard with trees at lattice points. Upon
                                                              introduction to the problem, students draw a model and use a straightedge and
                                                              ruler to begin estimating coordinate distances.




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                  Key Curriculum Press /40
                                                       STATISTICS AND PROBABILITY CONCEPTS
                                                 Standard 10: Students will understand and use statistics.
Benchmarks, Grades 9-12
    STANDARD                                                 CORRELATION
10.1 Construct and draw inferences from                      This is done throughout the four year curriculum. Students construct charts, tables,
     charts, tables, and graphs that summarize               and graphs of empirical data generated in the classroom from experiments and
     data from inside and outside the school                 from purely mathematical patterns. Students analyze these charts, tables, and
     environment.                                            graphs to generalize trends, often for predictions. A few examples:
                                                             The Overland Trail
                                                             Students graph tables of information and create lines of best fit to make predictions
                                                             and estimates.
                                                               
                                                              CW-Previous Travelers
                                                             The Pit and the Pendulum
                                                               
                                                              HW17-A Picture is Worth a Thousand Words
                                                               
                                                              HW20-Mehrdad the Market Analyst
                                                             Is There Really a Difference?
                                                               
                                                              Days 1-3: double bar graphs
                                                               
                                                              CW-Graphing the Difference
                                                               
                                                              HW16-Assigning Probabilities
                                                               
                                                              POW6-Is There Really a Difference?
                                                             Small World, Isn’t It?
                                                               
                                                              CW-Small World, Isn‟t It?
                                                             The World of Functions
                                                               
                                                              CW-Brake!
                                                               
                                                              CW-Brake! Revisited
                                                               
                                                              HW20-“Small World, Isn‟t It?” Revisited
                                                             The Pollster’s Dilemma
                                                               
                                                              CW-The Pollster‟s Dilemma
                                                               
                                                              CW-Let‟s Vote on It!
                                                             • CW-What Does It Mean?



New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                    Key Curriculum Press /41
     STANDARD                                                CORRELATION
10.2 Use curve fitting to predict from data.                  The Overland Trail
                                                              Students intuitively sketch lines of best fit, then develop these graphical estimates
                                                              into algebraic representations.
                                                                
                                                               CW-Previous Travelers
                                                                
                                                               HW15-Broken Promises
                                                                
                                                               HW16-Sublette‟s Cutoff
                                                                
                                                               CW-Who Will Make It?
                                                                
                                                               HW17-The Basic Student Budget
                                                                
                                                               HW18-Out of Action
                                                                
                                                               CW-“Out of Action” and Sublette‟s Cutoff” Revisited
                                                              The Pit and the Pendulum
                                                                
                                                               HW20-Mehrdad the Market Analyst
                                                                
                                                               CW-Bird Houses
                                                                
                                                               CW-The Thirty-Foot Prediction
                                                              All About Alice
                                                                
                                                               HW9-It‟s in the Graph
                                                              Small World, Isn’t It?
                                                                
                                                               CW-Small World, Isn‟t It?
                                                                
                                                               HW8-California, Here I Come!
                                                                
                                                               CW-Return to “Small World, Isn‟t It?”
                                                              The World of Functions
                                                                
                                                               HW15-And Now…Back to Marcus Dunkalot
                                                                
                                                               CW-Let‟s Regress
                                                              • CW-Better Braking




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                      Key Curriculum Press /42
     STANDARD                                                CORRELATION
10.3 Apply measures of central tendency,                      The Pit and the Pendulum
      variability, and correlation.                           This unit’s main focus is normal distribution and standard deviation. Students
                                                              develop and apply these concepts throughout the unit.
                                                               
                                                               HW7-What‟s Normal?
                                                               
                                                               CW-What‟s Rare?
                                                               
                                                               HW9-Penny Weight
                                                               
                                                               CW-Mean School Data
                                                               
                                                               CW-Data Spread
                                                               
                                                               HW11-Dinky and Minky Spread Data
                                                               
                                                               HW12-The Best Spread
                                                               
                                                               HW14-Penny Weight Revisited
                                                               
                                                               HW15-Can Your Calculator Pass This Soft Drink Test?
                                                               
                                                               HW16-Standard Pendulum Data and Decisions
                                                               
                                                               CW-Pendulum Variations
                                                               
                                                               HW18-Pendulum Conclusions
                                                              Is There Really a Difference?
                                                               
                                                               CW-Bacterial Culture
                                                               
                                                               HW10-Decisions with Deviation
                                                              The Pollster’s Dilemma
                                                               
                                                               CW-A Normal Poll
                                                               
                                                               CW-From Numbers to Proportions
                                                               CW-Different p, Different 
                                                               
                                                               
                                                               HW16-Mean, Median, and Mode




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                   Key Curriculum Press /43
     STANDARD                                                CORRELATION
10.4 Define sampling and recognize its role in                Is There Really a Difference?
      statistical claims.                                     • POW6-Is There Really a Difference
                                                              Students consider the characteristics of a good sample.
                                                                
                                                               HW2-Who Gets A‟s and Measles?
                                                                
                                                               HW3-Quality of Investigation
                                                                
                                                               CW-Two Different Differences
                                                                
                                                               HW17-A Collection of Coins
                                                              In the above activities, as well as those which follow, students develop tools for
                                                              determining when differences in samples mean that the larger populations are
                                                              likely to be different.
                                                                
                                                               CW-Loaded or Not?
                                                                
                                                               CW-Measuring Weirdness
                                                              The Pollster’s Dilemma
                                                                
                                                               CW-The Pollster‟s Dilemma
                                                                
                                                               HW1-No Bias Allowed!
                                                                
                                                               CW-Sampling Seniors
                                                                
                                                               HW3-Throw Back the Little Ones
                                                                
                                                               HW4-Graphs of the Theory
                                                                
                                                               CW-The Theory of Polls
                                                                
                                                               HW5-Civics in Action
                                                                
                                                               HW13-Putting Your Formulas to Work
                                                                
                                                               HW14-Is Twice As Many Twice As Good
                                                                
                                                               CW-Let‟s Vote on It!
                                                                
                                                               CW-The Worst Case Scenario
                                                                
                                                               CW-“The Pollster‟s Dilemma” Revisited




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                      Key Curriculum Press /44
10.5 Design an experiment to study a problem                  Is There Really a Difference?
     and use the correct statistical procedures                
                                                               POW6-Is There Really a Difference?
     to summarize and analyze the data.                       The Pollster’s Dilemma
                                                               
                                                               CW-Back to the Circus
                                                               
                                                               CW-Let‟s Vote on It!
                                                               
                                                               HW19-How Big?
     STANDARD                                                CORRELATION
10.6 Analyze the effects of data                              The Pit and the Pendulum
      transformations on measures of central                   
                                                               CW-Making Friends with Standard Deviation
      tendency and variability.                                
                                                               HW13-Deviations
                                                              Pollster’s Dilemma
                                                               
                                                               HW13-Putting Your Formulas to Work
                                                               
                                                               HW14-Is Twice As Many Twice As Good?
                                                               
                                                               CW-The Worst Case Scenario
                                                               
                                                               CW-Polling Puzzles
                                                              • HW20-How Much Better is Bigger?




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                  Key Curriculum Press /45
                                                       STATISTICS AND PROBABILITY CONCEPTS
                                               Standard 11: Students will understand and use probability.
Benchmarks, Grades 9-12
    STANDARD                                                 CORRELATION
11.1 Use simulations to estimate probability.                 The Game of Pig
                                                              Use of simulations, including electronic simulations, to estimate probability is a
                                                              major focus throughout this unit, especially evident in:
                                                               
                                                               HW15-A Sixty-Percent Solution
                                                               
                                                               HW17-Aunt Zena at the Fair (students use a calculator’s random number
                                                                 generator)
                                                               
                                                               HW19-The Carrier‟s Payment Plan Quandary
                                                               
                                                               CW-Using the Programmed Simulation
                                                               
                                                               CW-The Game of Little Pig
                                                              Pennant Fever
                                                               
                                                               CW-Simulate a Deal
                                                              The Pollster’s Dilemma
                                                               
                                                               CW-Sampling Seniors




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                      Key Curriculum Press /46
     STANDARD                                                CORRELATION
11.2 Use experimental or theoretical                          The Game of Pig
      probability to represent and solve                      Use of experimental and theoretical probability to solve problems is a major focus
      problems involving uncertainty.                         throughout this unit, especially evident in:
                                                               
                                                               CW-The Gambler‟s Fallacy
                                                               
                                                               POW5-What‟s On Back?
                                                               
                                                               HW9-Rollin‟, Rollin‟ Rollin‟
                                                               
                                                               CW-The Theory of Two-Dice Sums
                                                               
                                                               HW15-A Sixty-Percent Solution
                                                               
                                                               CW-The Theory of One-and-One
                                                               
                                                               HW19-The Carrier‟s Payment Plan Quandary
                                                               
                                                               HW21-Another Carrier Dilemma
                                                               
                                                               CW-Little Pig Strategies, and its series of activities concluding in CW-The Best
                                                                 Little Pig
                                                              Pennant Fever
                                                              Students solve probability problems throughout this unit, relying primarily on
                                                              theoretical models.
                                                              The Pollster’s Dilemma
                                                               
                                                               CW-The Theory of Three Person Polls
                                                               
                                                               CW-The Theory of Polls
                                                               
                                                               HW5-Civics in Action
                                                              • HW13-Putting Your Formulas to Work




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                    Key Curriculum Press /47
11.3 Apply the definition of a random variable               The Game of Pig
     to experimental design.                                 Students write a calculator program to create a simulation for CW-Using the
                                                             Programmed Simulation. A random number (integer) is selected and stored into the
                                                             calculator’s memory.
                                                             The Pit and the Pendulum
                                                             Students plan and perform controlled scientific experiments.
                                                              
                                                              HW3-If I Could Do It Over Again
                                                              
                                                              CW-Time is Relative
                                                              
                                                              HW4-What‟s Your Stride?
                                                              
                                                              CW-Pendulum Variations




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                 Key Curriculum Press /48
     STANDARD                                                CORRELATION
11.4 Create and interpret discrete probability                The Game of Pig
      distributions.                                          Students make and interpret frequency bar graphs (histograms):
                                                               
                                                               HW3-Expecting the Unexpected
                                                               
                                                               HW9-Rollin‟, Rollin‟, Rollin‟
                                                              The Pit and the Pendulum
                                                              Students collect, express, and analyze data using frequency bar graphs
                                                              (histograms).
                                                               
                                                               CW-Time is Relative
                                                               
                                                               HW4-What‟s Your Stride?
                                                               
                                                               HW5-Pulse Analysis
                                                               
                                                               CW-The Standard Pendulum
                                                               
                                                               HW16-Standard Pendulum Data & Decisions
                                                              Is There Really a Difference?
                                                              Throughout this unit, students collect, express, and analyze data using double bar
                                                                                                              2
                                                              graphs. Students also construct an empirical  distribution chart, generalize the
                                                                                                                          2
                                                              curve, and interpret this curve as a probability chart for  statistics.
                                                               
                                                               CW-Graphing the Difference
                                                               
                                                               CW-Random But Fair
                                                              Pennant Fever
                                                               
                                                               HW29-Graphing the Games
                                                              he Pollster’s Dilemma
                                                               
                                                               HW4-Graphs of the Theory
                                                               
                                                               HW5-Civics in Action
                                                               
                                                               HW12-Why Is That Batter Sneezing?




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                    Key Curriculum Press /49
     STANDARD                                   CORRELATION
11.5 Describe the normal curve and apply its     The Pit and the Pendulum
      properties to answer questions about data Students estimate the likelihood of events based on the properties of the normal
      that are assumed to be normally            curve.
      distributed.                                
                                                  HW10-An (AB)Normal Rug
                                                 Students use standard deviation to decide whether a variation in experiment
                                                 results is significant.
                                                  
                                                  HW16-Standard Pendulum Data & Decisions
                                                  
                                                  CW-Pendulum Variations
                                                  
                                                  HW18-Pendulum Conclusions
                                                 Is There Really a Difference?
                                                  
                                                  CW-Bacterial Culture
                                                  
                                                  HW10-Decisions with Deviation
                                                 The Pollster’s Dilemma
                                                  
                                                  CW-Deviations of Swinging
                                                  
                                                  HW6-Means and More in Middletown
                                                  
                                                  HW7-Gifts Aren‟t Always Free
                                                  
                                                  CW-Normal Areas
                                                  
                                                  HW8-More Middletown Musings
                                                  
                                                  HW17-A Teaching Dilemma




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                      Key Curriculum Press /50
     STANDARD                                                CORRELATION
11.6 Solve enumeration and finite probability                 The Game of Pig
      problems.                                               Students solve finite probability problems throughout this unit.
                                                              Pennant Fever
                                                              Students develop generalizable counting principles by first constructing organized
                                                              lists, then correctly apply the multiplication principle and the concepts of
                                                              permutation and combination.
                                                                
                                                               HW12-Top That Pizza!
                                                                
                                                               CW-Double Scoops
                                                                
                                                               HW13-Triple Scoops
                                                                
                                                               CW-More Cones for Johanna
                                                                
                                                               HW14-Cones from Bowls, Bowls from Cones
                                                                
                                                               CW-Bowls for Jonathan
                                                                
                                                               HW15-At the Olympics
                                                                
                                                               HW16-Which is Which?
                                                                
                                                               CW- Formulas for nPr and nCr
                                                              Finite probability examples:
                                                                
                                                               POW12-Let‟s Make a Deal
                                                                
                                                               POW13-Fair Spoons
                                                              High Dive
                                                                
                                                               POW2-Paving Patterns
                                                              The Pollster’s Dilemma
                                                                
                                                               HW2-Pennant Fever Reflection
                                                                
                                                               HW3-Throw Back the Little Ones
                                                                
                                                               HW10-A Plus for the Community
                                                                
                                                               HW12-Why Is That Batter Sneezing?




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                   Key Curriculum Press /51
                                                             FUNCTION AND ALGEBRA CONCEPTS
                                        Standard 12: Students will understand and use patterns and functions.
Benchmarks, Grades 9-12
    STANDARD                                                   CORRELATION




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                      Key Curriculum Press /52
12.1 Model everyday experiences with a                       Patterns
     variety of functions.                                    
                                                              HW22-Border Varieties
                                                             The Overland Trail
                                                              
                                                              CW-Wagon Train Sketches and Situations
                                                              
                                                              HW11-Graph Sketches
                                                              
                                                              CW-Previous Travelers
                                                              
                                                              CW-Who Will Make It?
                                                              
                                                              HW17-The Basic Student Budget
                                                              
                                                              HW18-Out of Action
                                                              
                                                              CW-Graphing Calculator In Outs
                                                              
                                                              CW-Getting the Gold
                                                             The Pit and the Pendulum
                                                             This unit problem is solved with a function generated by students.
                                                             Shadows
                                                             Again, students solve this unit problem by developing a symbolic relationship
                                                             among four variables affecting shadow length.
                                                              
                                                              CW-Shadow Data Gathering
                                                              
                                                              CW-A Shadow of a Doubt
                                                             Solve It!
                                                              
                                                              CW-Memories of Yesteryear
                                                              
                                                              HW2-Building a Foundation
                                                             Cookies
                                                             Students solve this unit problem, a profit dilemma at a bakery, by developing the
                                                             appropriate system of linear inequalities to summarize constraints and then
                                                             determine the maximum of a feasible region. Additionally:
                                                              
                                                              HW4-Inequality Stories
                                                              
                                                              HW21-Inventing Problems
                                                              
                                                              CW-Producing Programming Problems




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                   Key Curriculum Press /53
     STANDARD                                                CORRELATION
12.1 continued                                                • Fireworks
                                                               
                                                               HW1-A Corral Variation
                                                               
                                                               HW8-How Much Can They Drink?
                                                              Small World, Isn’t It?
                                                              In this unit, students create meaning to exponential growth and decay functions.
                                                              Students generate several exponential functions for situations, most notably:
                                                               
                                                               HW21-Blue Book
                                                               
                                                               HW25-California and Exponents
                                                               
                                                               HW29-California Population with e‟s
                                                               
                                                               CW-Return to “Small World, Isn‟t It?”
                                                              High Dive
                                                               
                                                               CW-At Certain Points in Time
                                                               
                                                               HW10-A Practice Jump
                                                               
                                                               CW-Cart Travel Time
                                                               
                                                               CW-First-Quadrant Platform
                                                              The World of Functions
                                                               
                                                               HW3-More Families
                                                               
                                                               HW4-Story Sketches III
                                                               
                                                               CW-Return of the Shadow
                                                               
                                                               CW-Families Have Many Different Members
                                                               
                                                               HW16-Midnight Express
                                                               
                                                               HW17-In the Lead
                                                               
                                                               HW19-Name That Family!
                                                               
                                                               HW23-Cozying Up to Composition




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                   Key Curriculum Press /54
     STANDARD                                 CORRELATION
12.2 Represent and analyze relationships using Throughout all four years of the curriculum, students effectively use the Rule of 3
      tables, graphs, rules, and equations.    to represent and analyze relationships
                                               Patterns
                                                 
                                                HW5-Inside Out
                                                 
                                                HW7-Extended Bagels
                                                 
                                                HW10-Pulling Out Rules
                                                 
                                                HW16-Another In-Outer
                                                 
                                                HW20-Squares and Scoops
                                                 
                                                HW23-Cutting Through the Layers
                                               The Overland Trail
                                                 
                                                CW-Wagon Trains and Story Sketches
                                                 
                                                HW11-Graph Sketches
                                                 
                                                CW-In Need of Numbers
                                                 
                                                HW12-The Issues Involved
                                                 
                                                CW-Out Numbered
                                                 
                                                HW13-Situations, Graphs, Tables, and Rules
                                                 
                                                CW-Previous Travelers
                                                 
                                                CW-Graphing Calculator In Outs
                                                 
                                                CW-Fair Share on Chores
                                                 
                                                CW-More Fair Share on Chores
                                                 
                                                HW23-More Fair Share for Hired Hands
                                                 
                                                CW-Water Conservation
                                                 
                                                HW25-The Big Buy
                                                 
                                                HW27-Catching Up at Auburn
                                                 
                                                CW-Getting the Gold




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                      Key Curriculum Press /55
New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4   Key Curriculum Press /56
      STANDARD                                               CORRELATION




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                 Key Curriculum Press /57
12.2 continued                                               The Pit and the Pendulum
                                                              
                                                              HW21-So Little Data, So Many Rules
                                                              
                                                              CW-Graphing Free-for-All
                                                              
                                                              HW22-Graphs in Search of Equations I
                                                              
                                                              HW23-Graphs in Search of Equations II
                                                              
                                                              HW24-Graphing Summary
                                                              
                                                              HW25-Graphs in Search of Equations III
                                                             Shadows
                                                              
                                                              CW-Looking for Equations
                                                              
                                                              POW17-Cutting the Pie
                                                             Solve It!
                                                              
                                                              HW29-Functioning in the Math World
                                                             Is There Really a Difference?
                                                              
                                                              CW-Graphing the Difference
                                                              
                                                              HW16-Assigning Probabilities
                                                             Do Bees Build It Best?
                                                              
                                                              HW6-The Ins and Outs of Area
                                                              
                                                              POW8-Count the Pegs
                                                              
                                                              CW-The Ins and Outs of Boxes
                                                             Cookies
                                                             Students develop an understanding of graphs of inequalities and extend this to the
                                                             notion that a feasible region is a picture of the common set of solutions to a system
                                                             of equations.
                                                              
                                                              CW-Picturing Cookies-Part I
                                                              
                                                              CW-Picturing Cookies-Part II
                                                             All About Alice
                                                              
                                                              HW1-Graphing Alice
                                                              
                                                              HW7-Continuing the Pattern
                                                              
                                                              HW9-It‟s in the Graph
                                                              
                                                              CW-Taking Logs to the Axes
                                                             Fireworks
                                                              
                                                              HW8-How Much Can They Drink?
New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                    Key Curriculum Press /58
     STANDARD                                                CORRELATION
12.2 continued                                                Meadows or Malls?
                                                              Students consider three-dimensional graphical models depicting the relationships
                                                              among three variables.
                                                               
                                                               HW10-What Do They Have in Common?
                                                               
                                                               HW11-Trying Out Triples
                                                               
                                                               HW12-More Cookies
                                                               
                                                               HW15-The “More Cookies” Region and Strategy
                                                              Small World, Isn’t It?
                                                               
                                                               HW16-What‟s It All About?
                                                              High Dive
                                                               
                                                               CW-Free Fall
                                                              As the Cube Turns
                                                               
                                                               HW14-Oh, Say What You Can See
                                                              The World of Functions
                                                               
                                                               CW-Rumble, Grumble
                                                               
                                                               HW21-The Composition of Functions
                                                              • CW-The Cost of Pollution
12.3 Translate among tabular, symbolic, and                   The Overland Trail
     graphical representations of functions.                   
                                                               CW-Out Numbered
                                                               
                                                               HW13-Situations, Graphs, Tables, and Rules
                                                               
                                                               HW14-Rules, Tables, and Graphs
                                                               
                                                               HW19-What We Needed
                                                               
                                                               CW-“Out of Action” and “Sublette‟s Cutoff” Revisited
                                                               
                                                               HW21-Biddy Mason
                                                              • HW22-Fair Share for Hired Hands
                                                              Solve It!
                                                               
                                                               HW11-Line It Up
                                                               
                                                               CW-Where‟s Speedy?
                                                               
                                                               HW28-Swinging Pendulum
                                                              • HW29-Functioning in the Math World
                                                              Cookies
                                                              • HW17-A Reflection on Money
New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                  Key Curriculum Press /59
12.3 continued                                               All About Alice
                                                               
                                                              HW7-Continuing the Pattern
                                                             • CW-Taking Logs to the Axes
                                                             The World of Functions
                                                               
                                                              CW-Linear Tables
                                                               
                                                              CW-Quadratic Tables
                                                               
                                                              HW8-Mystery Tables
                                                               
                                                              CW-Brake! Revisited
                                                               
                                                              HW13-Fitting Mia‟s Bird Houses Again
                                                               
                                                              HW14-Mystery Tables II
                                                               
                                                              HW28-Transforming Graphs, Tables, and Situations
12.4 Model a variety of problem situations                   Several units in IMP focus on a type of function and give students many
     using the same type of function.                        opportunities to write and use the same type of function in a variety of problem
                                                             situations. There is an emphasis in The Overland Trail and Cookies on linear
                                                             functions, in Shadows on direct and inverse variation, in Fireworks on quadratic
                                                             function, in Small World, Isn‟t It? on exponential functions, and in High Dive on
                                                             cyclic functions. Highlights are listed below.
                                                             The Overland Trail
                                                             Students develop the notion that linear functions all have a constant rate of change.
                                                             Shadows
                                                               
                                                              HW10-Similar Problems
                                                               
                                                              CW-Mirror Magic
                                                             Cookies
                                                             Students repeatedly graph linear functions in the context of solving linear
                                                             programming problems.
                                                             All About Alice
                                                               
                                                              CW-Taking Logs to the Axes
                                                             Fireworks
                                                             • HW9-Corrals and Pens Again. Students consider quadratics in a variety of forms
                                                                 in two new situations.



New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                    Key Curriculum Press /60
     STANDARD                                                CORRELATION
12.4 continued                                                Small World, Isn’t It?
                                                              Students create symbolic, tabular, and graphical models of a variety of exponential
                                                              situations, including:
                                                                
                                                               CW-How Much for Broken Eggs?
                                                                
                                                               HW17-Small, But Plentiful
                                                                
                                                               HW19-The Forgotten Account
                                                                
                                                               HW22-Blue Book
                                                                
                                                               HW26-Calfifornia and Exponents
                                                                
                                                               HW29-California Population with e‟s
                                                                
                                                               CW-Return to “Small World, Isn‟t It?”
                                                              High Dive
                                                              Students consider various sinusoidal situations and develop symbolic and
                                                                  graphical models to represent the situation.
                                                              The World of Functions
                                                                
                                                               HW1-Story Sketches
                                                                
                                                               HW2-Story Sketches II
                                                                
                                                               HW5-Back to the Basics
                                                                
                                                               HW9-Bigger Means Smaller
                                                                
                                                               HW11-An Average Drive
                                                               
                                                               CW-What Will It Be Worth?
                                                              The Pollster’s Dilemma
                                                               
                                                               CW-Graphing Distributions
12.5 Analyze the effects of parameter changes                 As stated above, several units focus on a variety of types of functions. The fourth
     on the graph of functions.                               year unit, The World of Functions, summarizes and formalizes the effects of
                                                              parameter changes. Highlights are listed below.
                                                              The Overland Trail
                                                              Students note how the magnitude and sign of the coefficient in a linear function
                                                              affects the graph, days 15-21.

New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                     Key Curriculum Press /61
      STANDARD                                               CORRELATION




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                 Key Curriculum Press /62
12.5 continued                                               The Pit and the Pendulum
                                                             Students do an introductory investigation into families of functions.
                                                              
                                                              CW-Graphing Free-for-All
                                                              
                                                              HW24-Graphing Summary
                                                              
                                                              CW-The Thirty-Foot Prediction
                                                             Solve It!
                                                              
                                                              HW11-Line It Up
                                                              
                                                              CW-Get It Straight
                                                             Cookies
                                                             These two activities and following classroom discussions analyze families of
                                                             parallel lines.
                                                              
                                                              CW-Profitable Pictures
                                                              
                                                              CW-Hassan‟s a Hit!
                                                             All About Alice
                                                              
                                                              Day2, HW1,9
                                                             • CW-Taking Logs to the Axes
                                                             Fireworks
                                                              
                                                              CW-The Ups and Downs of Quadratics
                                                             Small World, Isn’t It?
                                                              
                                                              CW-Tweaking the Function
                                                             High Dive
                                                              
                                                              HW4-Graphing the Ferris Wheel
                                                              
                                                              HW5-Ferris Wheel Graph Variations
                                                              
                                                              CW-The “Plain” Sine Graph
                                                              
                                                              HW7-More Beach Adventures
                                                             The World of Functions
                                                              
                                                              CW-Double Dose of Functions
                                                              
                                                              HW27-Slide That Function
                                                             • HW28-Transforming Graphs, Tables, and Situations


New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                  Key Curriculum Press /63
     STANDARD                                  CORRELATION
12.6 Explore and represent everyday situations The Overland Trail
      using the sine and cosine functions.       
                                                 HW20-More Graph Sketches
                                                High Dive
                                                 
                                                 HW4-Graphing the Ferris Wheel
                                                 
                                                 HW5-Ferris Wheel Graph Variations
                                                 
                                                 HW6-Sand Castles
                                                 
                                                 HW12-Carts and Periodic Functions
                                                As the Cube Turns
                                                 
                                                 HW11-Goin‟ Round the Origin
                                                 
                                                 HW12-Double Trouble
                                                 
                                                 HW14-Oh, Say What You Can See
                                                 
                                                 HW15-Comin‟ Round Again (and Again…)
                                                The World of Functions
                                                 
                                                 HW2-Story Sketches II
                                                 
                                                 HW4-Story Sketches III




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                               Key Curriculum Press /64
                                                             FUNCTIONS AND ALGEBRA CONCEPTS
                                         Standard 13: Students will understand and apply algebraic concepts.
Benchmarks, Grades 9-12
    STANDARD                                                   CORRELATION
13.1 Represent situations that involve variable                 This notion is fundamental to the development of symbolic mathematics in the IMP
     quantities with expressions, equations,                    curriculum. The key units of this development are noted below, along with a few
     inequalities, and matrices.                                example activities.
                                                                Patterns
                                                                 
                                                                 HW11-Add It Up (summation notation)
                                                                Overland Trail
                                                                 
                                                                 CW-The Family
                                                                 
                                                                 HW4-Family Constraints
                                                                 
                                                                 HW6-Shoe Laces
                                                                 
                                                                 CW-Ox Expressions
                                                                 
                                                                 HW9-Ox Expressions at Home
                                                                 
                                                                 HW26-Water for One More
                                                                The Pit and the Pendulum
                                                                 
                                                                 CW-Bird Houses
                                                                 
                                                                 CW-The Thirty Foot Prediction
                                                                Shadows
                                                                The student’s goal in this unit is to model the shadow situation symbolically.
                                                                Additionally:
                                                                 
                                                                 HW10-Similar Problems
                                                                 
                                                                 HW18-Mirror Madness
                                                                 
                                                                 CW-A Shadow of a Doubt
                                                                Solve It!
                                                                 
                                                                 CW-Memories of Yesteryear
                                                                 
                                                                 HW2-Building a Foundation
                                                                 
                                                                 HW10-What Will it Answer?



New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                   Key Curriculum Press /65
      STANDARD                                               CORRELATION




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                 Key Curriculum Press /66
13.1 continued                                               Do Bees Build it Best?
                                                              
                                                              HW7-Forming Formulas
                                                              
                                                              CW-Tri-Square Rug Games
                                                              
                                                              CW-Building the Best Fence
                                                              
                                                              CW-Shedding Light on Prisms
                                                             • HW25-Pythagoras and the Box
                                                             Cookies
                                                              
                                                              CW-Feasible Diets
                                                              
                                                              HW7-Picturing Pictures
                                                              
                                                              CW-Big State U
                                                             All About Alice
                                                              
                                                              CW-Alice in Wonderland
                                                              
                                                              HW15-Base 10 Alice
                                                             Fireworks
                                                              
                                                              HW1-A Corral Variation
                                                             Orchard Hideout
                                                              
                                                              HW4-In, On, or Out? Following classroom discussion students create a symbolic
                                                                 relationship for points in, on, or outside a circle of radius r centered at the
                                                                 origin.
                                                              
                                                              HW6-The Distance Formula
                                                              
                                                              HW7-A Snack in the Middle
                                                              
                                                              HW18-Defining Circles
                                                             Meadows or Malls?
                                                              
                                                              HW2-Heavy Flying
                                                             Throughout the unit students meet this benchmark. However, this unit is marked
                                                             by the shift into matrices to represent and solve linear programming problems. Key
                                                             activities include:
                                                              
                                                              CW-Inventing an Algebra
                                                              
                                                              CW-Flying Matrices
                                                              
                                                              HW28-Matrices in the Oven
                                                              
                                                              HW29-Fresh Ingredients
New Mexico Mathematics Unifying Concepts and Processes        
                                                              CW-“Meadows or Malls?” Revisited
Correlation with Interactive Mathematics Program, Year 1-4                                                                  Key Curriculum Press /67
     STANDARD                                                CORRELATION
13.1 continued                                                Small World, Isn’t it?
                                                               
                                                               CW-What a Mess!
                                                               
                                                               HW13-The Growth of the Oil Slick
                                                               
                                                               HW22-The Sound of a Logarithm
                                                              Pennant Fever
                                                               
                                                               CW-Formulas for nPr and nCr
                                                               
                                                              HW30-Binomial Probabilities
                                                             As the Cube Turns
                                                               
                                                              HW15-Comin‟ Round Again (and Again…)
                                                               
                                                              CW-Rotation Matrix in Three Dimensions
                                                             The World of Functions
                                                               
                                                              CW-Quadratic Tables by Algebra
                                                               
                                                              HW6-A General Quadratic
                                                             The Pollster’s Dilemma
                                                             • CW-The Search is On
13.2 Use tables and graphs as tools to interpret             Students use tables and graphs to interpret expressions, equations, and inequalities
     expressions, equations, and inequalities.               throughout the four years of the IMP. Students are often directed to use tables and
                                                             graphs by the curriculum itself. They become part of the student strategy for
                                                             solving problems. Furthermore, many algebraic generalizations are developed
                                                             through tabular or graphical analyses. A few key examples are noted below.
                                                             The Overland Trail
                                                             Students build the connections among tables, graphs, rules, and the original
                                                             situation.
                                                               
                                                              HW13-Situations, Graphs, Tables, and Rules
                                                             • HW14-Rules, Tables, and Graphs
                                                             Solve It!
                                                               
                                                              CW-The Graph Solves the Problem
                                                               
                                                              CW-The Graphing Calculator Solver
                                                             Cookies
                                                             Students interpret and solve two-variable linear programming problems by
                                                             generating a graph of the feasible region defined by the constraints presented.
New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                   Key Curriculum Press /68
      STANDARD                                               CORRELATION
13.2 continued                                                All About Alice
                                                               
                                                               HW9-It‟s in the Graph
                                                               
                                                               CW-All Roads Lead to Rome
                                                               
                                                               CW-Taking Logs to the Axes
                                                              Small World, Isn’t It?
                                                               
                                                               HW27-Comparing Derivatives
                                                              High Dive
                                                              The unit problem cannot be solved using symbolic manipulation. Many students
                                                              will solve the equation they’ve developed by determining the point of intersection
                                                              on a graph.
                                                               
                                                               CW-Moving Cart, Turning Ferris Wheel
                                                               
                                                               CW-“High Dive” Concluded
                                                              The World of Functions
                                                               
                                                               CW-Functions in Verse
                                                               
                                                               HW25-Linear Functions in Verse
                                                              • CW-Double Dose of Functions




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                   Key Curriculum Press /69
      STANDARD                                               CORRELATION




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                 Key Curriculum Press /70
13.3 Operate on expressions and matrices and                 Overland Trail
     solve equations and inequalities.                         
                                                              HW8-To Kearney by Equation
                                                             Shadows
                                                               
                                                              HW13-Inventing Rules
                                                               
                                                              CW-The Sun Shadow
                                                             Solve It!
                                                               
                                                              HW7-You‟re the Jester
                                                               
                                                              HW9-More Letters, Numbers, and Mystery Bags
                                                               
                                                              HW25-All by Itself
                                                               
                                                              HW26-More Variable Solutions
                                                               
                                                              HW27-A Mixed Bag
                                                             Do Bees Build It Best?
                                                               
                                                              HW18-Simply Square Roots
                                                             Cookies
                                                               
                                                              HW13-Getting on Good Terms
                                                               
                                                              HW18-More Linear Systems
                                                               
                                                              CW-“How Many of Each Kind?” Revisited
                                                               
                                                              HW19-A Charity Rock
                                                               
                                                              HW20-Back on the Trail
                                                             Fireworks
                                                             • CW-Fireworks Height Revisited
                                                             Meadows or Malls?
                                                             Students develop the necessary techniques and understanding of matrix operations
                                                             to solve matrix equations of any size.
                                                               
                                                              HW31-Solving the Simplest
                                                               
                                                              CW-Finding an Inverse
                                                               
                                                              HW33-Inverses and Equations
                                                             High Dive
                                                               
                                                              HW2-As the Ferris Wheel Turns
                                                               
                                                              HW9-Not So Spectacular
                                                               
                                                              CW-Moving Cart, Turning Ferris Wheel
                                                               
                                                              HW25-Falling Time for Vertical Motion
New Mexico Mathematics Unifying Concepts and Processes         
                                                              CW-High Dive Concluded
Correlation with Interactive Mathematics Program, Year 1-4                                                                Key Curriculum Press /71
     STANDARD                                                CORRELATION
13.3 continued                                                The World of Functions
                                                              • CW-Back to the Corral
13.4 Identify the implications and usefulness of Shadows
     mathematical abstractions and symbolism.  HW21-The Sun Shadow Problem
                                                  
                                                 Solve It!
                                                  
                                                  HW30-A Solving Sampler
                                                 Is There Really a Difference?
                                                  
                                                  HW25-Beginning Portfolio Selection
                                                 Do Bees Build it Best?
                                                  
                                                  HW28-A Portfolio of Formulas
                                                 All About Alice
                                                  
                                                  HW17-An Exponential Portfolio
                                                 Meadows or Malls?
                                                  
                                                  HW37-Beginning Portfolios – Part II
                                                 Small World, Isn’t It?
                                                  
                                                  HW30-Beginning Portfolios – Part I
13.5 Use matrices to solve linear systems.       In the unit Meadows or Malls? students learn to express linear systems in terms of
                                                 matrices and develop the matrix operations required to understand the role of
                                                 matrices in the solution process. Some examples are:
                                                  
                                                  CW-Finding an Inverse
                                                  
                                                  CW-Calculators Again
                                                  
                                                  CW-“Meadows or Malls?” Revisited
13.6 Apply trigonometry to problem situations Shadows
     involving triangles.                         
                                                  CW-The Tree and the Pendulum
                                                  
                                                  HW23-Smokey and the Dude
                                                  
                                                  CW-The Sun Shadow
                                                 Do Bees Build It Best?
                                                  
                                                  HW9-More Gallery Measurements
                                                  
                                                  HW10-Shadows and Sailboats
                                                  
                                                  HW20-Leslie‟s Floral Angles
New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                        Key Curriculum Press /72
13.6 continued                                               Orchard Hideout
                                                               
                                                              CW-Hexagoning the Circle
                                                               
                                                              HW12-Octagoning the Circle
                                                               
                                                              CW-Polygoning the Circle
                                                               
                                                              CW-Cable Ready
                                                               
                                                              CW-The Other Gap
                                                               
                                                              CW-Lines of Sight for Radius Six
                                                               
                                                              CW-Hiding in the Orchard
                                                             High Dive
                                                             Students will use right triangle trigonometry throughout this unit. Some examples
                                                             include:
                                                               
                                                              HW2-As the Ferris Wheel Turns
                                                               
                                                              HW3-A Clear View
                                                               
                                                              CW-The Ideal Skateboard
                                                               
                                                              HW27-Racing the River
                                                             As the Cube Turns
                                                               
                                                              HW11-Goin‟ Round the Origin
                                                               
                                                              HW12-Double Trouble
                                                               
                                                              CW-The Sine of a Sum
                                                               
                                                              HW13-A Broken Button
                                                               
                                                              HW14-Oh, Say What You Can See
                                                              
                                                              HW15-Comin‟ Round Again (and Again…)
                                                              
                                                              HW19-What‟s Going on Here?
                                                              
                                                              CW-Follow That Point!
                                                              
                                                              HW31-One Turn of a Cube
                                                              
                                                              CW-Rotation Matrix in Three Dimensions
                                                             Know How
                                                              
                                                              CW-Radian Measure
                                                              
                                                              HW2-The Law of Sines
                                                             The World of Functions
                                                             • HW24-Fish, Ladders, and Bacteria
New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                 Key Curriculum Press /73
     STANDARD                                     CORRELATION
13.7 Determine maximum and minimum                 The Overland Trail
      points of a graph and interpret the results  HW2-Hats for Families
                                                     
      in problem situations.                       Do Bees Build it Best?
                                                     
                                                    HW16-Don‟t Fence Me In (determine maximum value)
                                                   Cookies
                                                   In the context of solving linear programming problems, students determine the
                                                   maximum or minimum of a linear function over a region. For example:
                                                     
                                                    CW-Profitable Pictures
                                                     
                                                    HW8-Curtis and Hassan
                                                     
                                                    CW-Big State U
                                                     
                                                    CW-“How Many of Each Kind” Revisited
                                                     
                                                    CW-Producing Programming Problems
                                                   Fireworks
                                                     
                                                    HW9-Corrals and Pens Again
                                                   Small World, Isn’t It?
                                                     
                                                    HW21-The Significance of a Sign
                                                   High Dive
                                                     
                                                    HW5-Ferris Wheel Graph Variations
13.8 Describe limiting processes by examining The Pit and the Pendulum
      infinite sequences, series, and areas under  HW10-An (AB)Normal Rug (estimate area under curve)
                                                     
      curves.                                      Do Bees Build It Best?
                                                     
                                                    CW-Building the Best Fence
                                                   All About Alice
                                                     
                                                    HW7-Continuing the Pattern in Alice
                                                   Orchard Hideout
                                                   Day11-14: Students analyze the proportionality constant between the area of a
                                                   polygon and the radius of an inscribed circle, following the trend in this constant of
                                                   proportionality as the number of sides increases towards infinity. This work
                                                   deepens or makes clearer the meaning of for students. This analysis is also done
                                                   for the ratio between radius and perimeter.


New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                           Key Curriculum Press /74
     STANDARD                                                CORRELATION
13.8 continued                                                Small World, Isn’t It?
                                                               
                                                               CW-Find That Base!
                                                               
                                                               CW-The Generous Banker
                                                               
                                                               HW28-The Limit of Their Generosity
                                                              The World of Functions
                                                               
                                                               CW-Don‟t Divide That!
                                                               
                                                               CW-The End of the Function
                                                               
                                                               HW12-Creating the Ending You Want
                                                              The Pollster’s Dilemma
                                                               
                                                               CW-Normal Areas




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                           Key Curriculum Press /75
13.9 Evaluate the logic of algebraic procedures. The Overland Trail
                                                  
                                                  CW-Ox Expressions
                                                  
                                                  HW9-Ox Expressions at Home
                                                 Shadows
                                                  
                                                  HW13-Inventing Rules
                                                  
                                                  HW16-Ins and Outs of Proportion
                                                 Solve It!
                                                 Students develop generalizable techniques to solve equations and see that algebraic
                                                 methods will solve any linear equation.
                                                  
                                                  HW6-The Mystery Bag Gam
                                                  
                                                  CW-Scrambling Equations
                                                  
                                                  HW21-More Scrambled Equations and Mystery Bags
                                                  
                                                  CW-Old Friends and New Friends
                                                  
                                                  HW22-New Friends Visit Your Home
                                                 
                                                    HW23-From One Variable to Two
                                                 Students develop the Distributive Property.
                                                  
                                                  HW12-Who‟s Right?
                                                  
                                                  CW-A Lot of Changing Sides
                                                  
                                                  HW13-Why Are They Equivalent?
                                                  
                                                  HW14-One Each Way
                                                  
                                                  CW-Distributing the Area
                                                  
                                                  HW15-The Distributive Property and Mystery Lots
                                                  
                                                  HW16-Views of the Distributive Property
                                                 • CW-A Distributive Summary
     STANDARD                                   CORRELATION




New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                      Key Curriculum Press /76
13.9 continued                                               Students understand subtraction of sums in parentheses.
                                                              
                                                              CW-Taking Some Out, Part I
                                                              
                                                              HW18-Subtracting Some Sums
                                                              
                                                              HW19-Randy, Sandy, and Dandy Return
                                                             Cookies
                                                              
                                                              HW2-Investigating Inequalities
                                                              
                                                              CW-My Simplest Inequality
                                                              
                                                              HW3-Simplifying Cookies
                                                              
                                                              CW-Get the Point
                                                             All About Alice
                                                             Students develop meaning of exponential and logarithmic properties and laws via
                                                             contextual situations, algebraic laws, graphing, and number patterns.
                                                              
                                                              CW-Here Goes Nothing
                                                              
                                                              CW-Many Meals for Alice
                                                              
                                                              HW5-In Search of the Law
                                                              
                                                              CW-A Half Ounce of Cake
                                                              
                                                              HW11-Confusion Reigns
                                                              
                                                              CW-All Roads Lead to Rome
                                                             Fireworks
                                                             Students develop and discuss meaningful methods to “complete the square”.
                                                              
                                                              CW-Who‟s Perfect?
                                                             • HW6-More About Perfection
                                                             Meadows or Malls?
                                                              
                                                              Day18-19: Students develop the notion of solving systems by Gaussian
                                                                 elimination.
                                                              
                                                              Day 32-33: After students develop elimination methods to solve systems more
                                                                 easily, they develop the necessary ideas regarding multiplicative inverse and
                                                                 the identity matrix in order to solve matrix equations.
                                                             High Dive
                                                              
                                                              HW13-Planning for Formulas
                                                             Know How
                                                              
                                                              HW5-A Fractional Situation
                                                             The Pollster’s Dilemma
                                                              
                                                              CW-The Search is On
New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                  Key Curriculum Press /77
New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4   Key Curriculum Press /78

				
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