# NM_IMP

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```					                                                             UNIFYING CONCEPTS AND PROCESSES
Standard 1: Students will understand and use Mathematics in Problem Solving.
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.
The Game of Pig

 POW7-Making a Game
Is There Really a Difference?

 POW6-Is There Really a Difference?
• 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.
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
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.
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

 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
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
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

 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.

 Day18: Students are to read each others’ papers for the purpose of noting
weakness in clarity.
Fireworks

Orchard Hideout

 Day1: Students read A Geometric Summary for understanding.

 Day19: Students read The Standard Equation of the Circle for understanding.

 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.


 HW2-The Law of Sines

 HW3-The Ellipse

 HW5-A Fractional Situation

 HW6-Complex Numbers

 CW-Know How Project
The World of Functions

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.
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,
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


 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.

 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.
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
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


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
• 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

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.
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.
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

 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

 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

 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

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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.

 HW2-Investigating Inequalities


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Correlation with Interactive Mathematics Program, Year 1-4                                                                 Key Curriculum Press /19
STANDARD                                               CORRELATION

 HW9-It‟s in the Graph
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.
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

 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

 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

 POW12-Kick It!

 POW13-Shuttling Around
Orchard Hideout

 POW9-A Marching Strip

 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



New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                      Key Curriculum Press /22
STANDARD                                      CORRELATION
6.2    continued                                      

 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


 POW17-Cutting the Pie
Solve It!

 HW12-Who‟s Right?

 HW16-Views of the Distributive Property

 CW-Profitable Pictures
Fireworks

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

 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:

 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

 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
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.
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


 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
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:

 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

 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


 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

 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?

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.
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


 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

 HW10-What Do They Have in Common?

 CW-Just the Plane Facts

 HW15-The “More Cookies” Region and Strategy
As the Cube Turns


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

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
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

 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



 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-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
Students develop geometric models of mirror reflections and lamp and sun

 CW-How Long is a Shadow?

 CW-Mirror Magic

 HW19-To Measure a Tree

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-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


 HW15-The “More Cookies” Region and Strategy


 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


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
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-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

 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


 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.
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?


 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?


 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.
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

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


 CW-Bird Houses

 CW-The Thirty-Foot Prediction

 HW9-It‟s in the Graph
Small World, Isn’t It?

 CW-Small World, Isn‟t It?

 HW8-California, Here I Come!

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


 HW11-Dinky and Minky Spread Data


 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-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.
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


 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


 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


 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.
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.
Again, students solve this unit problem by developing a symbolic relationship
among four variables affecting shadow length.


 CW-A Shadow of a Doubt
Solve It!

 CW-Memories of Yesteryear

 HW2-Building a Foundation
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

High Dive

 CW-At Certain Points in Time

 HW10-A Practice Jump

 CW-Cart Travel Time

The World of Functions

 HW3-More Families

 HW4-Story Sketches III


 CW-Families Have Many Different Members

 HW16-Midnight Express


 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


 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

 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
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.



 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
Students consider three-dimensional graphical models depicting the relationships
among three variables.

 HW10-What Do They Have in Common?

 HW11-Trying Out Triples


 HW15-The “More Cookies” Region and Strategy
Small World, Isn’t It?

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
• HW17-A Reflection on Money
New Mexico Mathematics Unifying Concepts and Processes
Correlation with Interactive Mathematics Program, Year 1-4                                                                  Key Curriculum Press /59

 HW7-Continuing the Pattern
• CW-Taking Logs to the Axes
The World of Functions

 CW-Linear 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.

 HW10-Similar Problems

 CW-Mirror Magic
Students repeatedly graph linear functions in the context of solving linear
programming problems.

 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

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
These two activities and following classroom discussions analyze families of
parallel lines.

 CW-Profitable Pictures

 CW-Hassan‟s a Hit!

 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

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.
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
The student’s goal in this unit is to model the shadow situation symbolically.

 HW10-Similar Problems


 CW-A Shadow of a Doubt
Solve It!

 CW-Memories of Yesteryear

 HW2-Building a Foundation


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

 CW-Feasible Diets

 HW7-Picturing Pictures

 CW-Big State U

 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

 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        
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


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
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

 HW9-It‟s in the Graph


 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

 HW13-Inventing Rules

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

 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
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

 HW17-An Exponential Portfolio

 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

13.6 Apply trigonometry to problem situations Shadows
involving triangles.                         
 CW-The Tree and the Pendulum

 HW23-Smokey and the Dude

Do Bees Build It Best?

 HW9-More Gallery Measurements


 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-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?


 HW31-One Turn of a Cube

 CW-Rotation Matrix in Three Dimensions
Know How


 HW2-The Law of Sines
The World of Functions
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)
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

 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

 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

 HW2-Investigating Inequalities

 CW-My Simplest Inequality


 CW-Get the Point
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

Fireworks
Students develop and discuss meaningful methods to “complete the square”.

 CW-Who‟s Perfect?

 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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