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Montrose RE-1J Curriculum Maps This curriculum map was aligned using the 2005 CSAP Item Maps to determine the frequency and weight of particular standards. This document is a prototype and should be modified during the 2006-2007 school year by teachers. Please keep accurate records and notes about revisions that need to be made. We will meet throughout the 2006-2007 school year. Your input is very important in the development of a useful aligned curriculum across the district. Please feel free to add in materials, references, supplemental materials, and anything else that may help make this document user friendly. For more information on these curriculum maps, please contact the office of the Assistant Superintendent for Curriculum and Instruction, (970) 249-7726. CR = Item was tested on the 2005 CSAP as a Constructed Response question MC = Item was tested on the 2005 CSAP as a Multiple Choice question Explanation of Color Codes Used in Curriculum Map Red Zone: Highest priority, most frequently tested on CSAP. Green Zone: Individual grade level or content are teachers believe these are important to know and do for CSAP. Yellow Zone: High priority, next most frequently tested on CSAP. Blue Zone: Mid-priority, not heavily tested on CSAP. Revised August 8, 2006 6th Grade Math RE-1J Quarter_1_ Numbers are state assessment frameworks numbers Benchmark Description Essential Skills Notes/Resources and Assessment Objective 1.3a Identify and use factor, multiple, CM: Prime Time number theory prime, composite, concepts square number 3.1a Organize and line graphs, bar CM: Data About Us construct displays of graphs, Math Practice data using a given set frequency table CPM: Chapter 2 of data organize and construct displays of data using a given set of data 3.1b Read from various interpret, draw CM: Data About Us displays of data conclusions from: CPM: Chapter 1,10 line graph, bar graph, circle graph, frequency table Standard 1 Number sense students develop All number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems 6.3a Estimation techniques develop, apply and All explain a variety of different estimation strategies in problem- solving situations and explain why an estimate may be acceptable in place of an exact answer. use estimation techniques before performing operations. 6.4b Estimate, exact, and in a problem-solving All reasonable results situation, determine Revised August 8, 2006 whether the results are reasonable and justify those results with accurate computation Standard 6 Computation: four basic operations All students link concepts using whole numbers and procedures as they develop and use computational techniques, including estimation, including mental arithmetic, paper-and-pencil, calculators, and computers, in problem-solving situations and communicate the reasoning involved in solving these problems Benchmark Description Essential Skills Notes/Resources and Assessment Objective 1.6a Use number sense to whole numbers, All estimate, determine, decimals, common and justify the fractions, only sums reasonableness of and differences for solutions fractions and decimals (ex: is ½ + 1/3 closer to 0, ½, or 1?) 3.2a Data distributions and find and use measures CM: Data About Us interpretations of central tendency CPM: Chapter 1,10 including mean, median, and mode 3.4a Convincing arguments interpret, predict CM: Data About Us based on data: outcomes based on CPM: Chapter 1,10 analyze data and draw line graphs, bar conclusions based on graphs, and frequency data displays tables 3.4a Data collection demonstrate the CM: Data About Us methods meaning of random CPM: Chapter 10 sampling and biased versus unbiased Revised August 8, 2006 samples 5.3a Read, interpret, and on number lines, CM: Data About Us apply scales graphs, maps CPM: Chapter CPM: Chapter 1,2 Benchmark Description Essential Skills Notes/Resources and Assessment Objective 1.3b Describe numbers by divisibility, even/odd, CM: Prime Time their characteristics prime/composite, square 1.5a Develop, test, and associative, Math Practice explain conjectures commutative, identity, CPM: Chapter 1,3 about properties of distributive, integers and rational multiplicative property numbers of zero, on whole numbers, common fractions, decimals 3.2b Data distributions and find and use the range CM: Data About Us interpretations from a given set of data CPM: Chapter 1,3 (for example, find the range from 2-12. Note: range is 10) 4.4a Locating points on a plot points on a CM: Data About Us grid coordinate graph in CPM: Chapter 3 quadrant one 4.4b Representations on choose the coordinate CM: Data About Us coordinate grids graph which represents CPM: Chapter 3 a given data set 5.3b Select the appropriate use the appropriate CM: Data About Us scale for a given scale when setting up a CPM: Chapter 3 problem graph, determine the order of numbers on a number line 6.2c Procedures for the find equivalent Math Practice four operations representations by CPM: Chapter 3 decomposing and composing whole numbers (for ex: 48 x 12 = (48 x 10) + (48 x 2) Revised August 8, 2006 6th Grade Math RE-1J Quarter _2_ Numbers are state assessment frameworks numbers Benchmark Description Essential Skills Notes/Resources and Assessment Objective 1.4a Equivalent forms of demonstrate CM: Bits and Pieces I rational numbers equivalence CPM: Chapter 3,5,7 relationships among fractions, decimals, and percents in problem-solving situations (for ex: two students out of eight is the same as 25%) 6.1a Using proportional to determine CM: Bits and Pieces II reasoning commonly-used CPM: Chapter 7 percentages (for example, 10%, 33%, 75%) and to demonstrate the equivalence of fractions, decimals, and percents 6.2b Procedures for simplify fractions; CM: Bits and Pieces II computing with demonstrate with CPM: Chapter 7 fractions and proficiency addition decimals: use and and subtraction of explain strategies to fractions including add/subtract fractions mixed numbers. with like and unlike denominators, mixed numbers, and decimals to thousandth. 1.2a Read, write and order common fractions, CM: Bits and Pieces I integers, rational terminating and CPM: Chapter 3,5,7 numbers and common repeating decimals, irrational numbers percents in a variety of forms 6.3a Estimation techniques develop, apply and All explain a variety of different estimation strategies in problem- solving situations and Revised August 8, 2006 explain why an estimate may be acceptable in place of an exact answer. use estimation techniques before performing operations. 6.4b Estimate, exact, and in a problem-solving All reasonable results situation, determine whether the results are reasonable and justify those results with accurate computation Benchmark Description Essential Skills Notes/Resources and Assessment Objective 1.1a Locate numbers on a common positive CM: Bits and Pieces I number line rational numbers, CPM: Chapter 1 terminating decimals through hundredths, fractions (halves, thirds, fourths, eighths, and sixteenths) mixed numbers, percents 1.1b Recognize and use use physical materials CM: Bits and Pieces I equivalent or pictures to CPM: Chapter 2,5 representations of demonstrate the numbers in a variety meaning and of forms equivalence of fractions, decimals, and percents (for example, write the fractions, decimal, and percent value for the shaded portion of a partially shaded circle. 1.6a Use number sense to whole numbers, All estimate, determine, decimals, common and justify the fractions, only sums Revised August 8, 2006 reasonableness of and differences for solutions fractions and decimals (ex: is ½ + 1/3 closer to 0, ½, or 1?) 3.7a Finding combinations determine the number CM: How Likely Is It? and permutations of possible outcomes CPM: Chapter 10 for simple events using a variety of methods such as organized lists or tree diagrams 6.4a Applying computation apply appropriate CM: Bits and Pieces II computation methods CPM: Chapter All to solve problems involving whole numbers, common fractions, decimals (use only addition and subtraction of fractions of decimals) Benchmark Description Essential Skills Notes/Resources and Assessment Objective 3.6a Probability models using a chance device, such CM: How Likely Is as a number cube or a It? spinner, design a fair game CPM: Chapter 10 and an unfair game, and explain why they are fair and unfair 3.6b Probability predictions make predictions based on CM: How Likely Is data obtained from simple It? probability experiments CPM: Chapter 10 3.6c Probability determination describe the likelihood of an CM: How Likely Is event as a number from zero It? to one or using words such CPM: Chapter 10 as certain, very likely, not likely, or impossible 6.2a Operations with fractions demonstrate conceptual CM: Bits and Pieces meaning of addition and II subtraction of fractions and CPM: Chapter 7 decimals in problem solving situations Revised August 8, 2006 6th Grade Math RE-1J Quarter _3 Numbers are state assessment frameworks numbers Benchmark Description Essential Skills Notes/Resources and Assessment Objective 2.1a Represent, describe, using tables, words, CM: Bits and Pieces II and analyze symbols, concrete CPM: Chapter 4 geometric and objects or pictures, numeric patterns involving whole numbers 2.3a Pattern properties: use whole numbers, CM: Bits and Pieces I relation between predict and describe CPM: Chapter 10 quantities how a change in one quantity results in a change in another quantity in a linear relationship (for example, a creature gains three ounces a day, How much will it have gained over 10 days?) 2.5a Solve simple linear with whole numbers, CM: Bits and Pieces II equations in using tables, concrete CPM: All problem-solving objects situations using a variety of methods (informal, formal, and graphical) and a variety of tools (physical materials, calculators, and computers) 4.2a Attributes and acute, obtuse, right CM: Shapes and Designs vocabulary: identify, angle, isosceles, CPM: Chapter 4 compare, and equilateral, parallel analyze the attributes lines, perpendicular of two-dimensional lines, intersecting lines shapes and use rays, line segments standard vocabulary to describe the parallelograms, attributes rhombuses, triangular prisms, use correct geometric symbols for parallelism, Revised August 8, 2006 perpendicularity, and triangles 4.5a Polygon and circle solve problems CM: Covering and measures involving the perimeter Surrounding of polygons and CPM: Chapter 4,9 circumference of circles 4.5b Area measures solve problems CM: Covering and involving areas of Surrounding polygons (square, CPM: Chapter 4,9 rectangle parallelogram, rhombus, triangle and circles) 5.4b Measuring area use formulas and CM: Covering and procedures to solve Surrounding problems involving the CPM: Chapter 4 area of squares, rectangles, parallelograms, rhombuses, and triangles 6.3a Estimation develop, apply and All techniques explain a variety of different estimation strategies in problem- solving situations and explain why an estimate may be acceptable in place of an exact answer. use estimation techniques before performing operations. 6.4b Estimate, exact, and in a problem-solving All reasonable results situation, determine whether the results are reasonable and justify those results with accurate computation Revised August 8, 2006 Benchmark Description Essential Skills Notes/Resources and Assessment Objective 1.6a Use number sense to whole numbers, All estimate, determine, decimals, common and justify the fractions, only sums reasonableness of and differences for solutions fractions and decimals (ex: is ½ + 1/3 closer to 0, ½, or 1?) 4.6b Symmetry use lines of symmetry CM: Shapes and Designs identification to solve problems (for example, use a symmetry line in a rhombus to create two isosceles triangles) 5.1 Angle properties describe angles as CM: Covering and acute, obtuse or right Surrounding CPM: Chapter 8 estimate measures of angles, measure angles and draw complements and supplements 5.4a Measuring procedures develop and use CM: Covering and formulas or Surrounding procedures to solve CPM: Chapter 4 problems involving the perimeter of a polygon Revised August 8, 2006 Benchmark Description Essential Skills Notes/Resources and Assessment Objective 4.2b Geometric conjectures make and test CM: Shapes and Designs conjectures about CPM: Chapter 4 geometric relationships and develop logical arguments to justify conclusions 4.6a Congruence and to identify congruent CM: Covering and transformations: Use shapes Surrounding reflections (flips), CPM: Chapter 4 translations (slides), and rotations (turns) 5.1a Choosing tools and determine the Math Practice appropriate units to appropriate unit of measure measure (metric and US customary) when estimating distance, capacity, and weight 5.1b Using estimation estimate and use Math Practice standard and metric units for length, weight, and temperature 5.1c Estimating perimeter estimate the area of a CM: Covering and and area polygon Surrounding CPM: Chapter 4 5.2a Estimate, make and For example, to CM: Covering and use direct and indirect estimate the length of Surrounding measurements of a room using strides length 5.5a Effect of dimension demonstrate how CM: Covering and changes changing one of the Surrounding dimensions of a rectangle or triangle affect its perimeter and area using concrete materials or graph paper Revised August 8, 2006 6th Grade Math RE-1J Quarter _4_ Numbers are state assessment frameworks numbers Benchmark Description Essential Skills Notes/Resources and Assessment Objective 1.1 Integers Define, compare, and CPM: Chapter 1,3 order integers 1.1b Decimal meanings count change up to Math Practice (money) the amount given CPM: Chapter 7 5.3c Time tell time on a standard Math Practice clock, determine elapsed time given start and finish times 6.2 Order of operations demonstrate order of Math Practice CPM: Chapter 3 operations including exponents with whole numbers 6.3a Estimation techniques develop, apply and All explain a variety of different estimation strategies in problem- solving situations and explain why an estimate may be acceptable in place of an exact answer. use estimation techniques before performing operations. 6.4b Estimate, exact, and in a problem-solving All reasonable results situation, determine whether the results are reasonable and justify those results with accurate computation Revised August 8, 2006 Benchmark Description Essential Skills Notes/Resources and Assessment Objective 1.1 Integers add, subtract, multiply CMP: Chapter and divide 1.6a Use number sense to whole numbers, All estimate, determine, decimals, common and justify the fractions, only sums reasonableness of and differences for solutions fractions and decimals (ex: is ½ + 1/3 closer to 0, ½, or 1?) 6.4a Applying apply appropriate All computation computation methods to solve problems involving whole numbers, common fractions, decimals (addition, subtraction, multiplication, division) Revised August 8, 2006 Benchmark Description Essential Skills Notes/Resources and Assessment Objective 1.1c Exponent meanings perfect squares Math Practice through 100 CM: Prime Time 1.1d Real number identify subset of CPM: Chapter 1,3 meanings and integers, including comparisons counting (natural) and whole numbers 1.4b Number demonstrate investigations multiplication inverse of positive rational numbers, demonstrate that division by zero is undefined 2.1b Use of variables in use a variable to Math Practice patterns and represent an unknown CPM: All representations (letter, box, or symbol) 2.2a Describe patterns tables, graphs, words, Math Practice using a variety of concrete objects, methods symbols, pictures References for Resources: (CM) Connected Mathematics = information for these materials can be found at http://www.mth.msu.edu/cmp/ (CPM) College Preparatory Math – District text book Linderman, Bill. Math Practice: Reinforce and Mater Basic Math Skills. Quack & Company, Inc. 2003, Carson- Dellosa Publishing, Inc. Revised August 8, 2006