Colorado Model Content Standards: Mathematics Grade 6		DOK	% of score points
1	Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.	2	20%
1.1	Demonstrate meanings of integers*, rational numbers*, percents, exponents, square roots* and pi (p) using physical materials and technology in problem solving situations.	2
1.1a	Locate commonly used positive rational numbers* including terminating decimals through hundredths, fractions (halves, thirds, fourths, eighths, and tenths), mixed numbers, and percents on a number line.	1
1.1b	Using physical materials or pictures to demonstrate the meaning and equivalence of commonly-used fractions and/or percents (for example, write the fractions, decimal, and percent value for the shaded portion of a partially shaded circle).	2
1.2	Read and write and order integers, rational numbers and common irrational numbers* such as v2, v5, and p.	2
1.2a	Read, write, order and compare common fractions, decimals, and percents in a variety of forms.	2
1.3	Apply number theory concepts (for example, primes, factors, multiples) to represent numbers in various ways.	1
1.3a	Identify and use the concepts of factor, multiple, prime, composite, and square numbers.	1
1.3b	Describe numbers by characteristics (divisibility, even, odd, prime, composite, square.	1
1.4	Use the relationships among fractions, decimals, and percents, including the concepts of ratio and proportion, in problem-solving situations*.	2
1.4a	Demonstrate equivalence relationships among fractions, decimals and percents in problem solving situations (for example, two students out of eight is the same as 25%)	2
1.5	Develop, test, and explain conjectures* about properties of integers and rational numbers.	3
1.5a	Develop, test, and explain conjectures about properties of numbers (associative, commutative, identity, distributive multiplicative property of zero on whole and rational numbers.)	3
1.6	Use number sense* to estimate and justify the reasonableness of solutions to problems involving integers, rational numbers, and common irrational numbers* such as v2, v5, and p.	2
1.6a	Use number sense to estimate, determine, and justify the reasonableness of solutions involving whole numbers, decimals, and common fractions (only sums and differences for fractions and decimals). For example: Is 1/2 + 1/3 closer to 0, 1/2 or 1?	2
2	Students use algebraic methods to explore, model, and describe patterns and functions involving numbers, shapes, data, and graphs in problem-solving situations and communicate the reasoning used in solving these problems.	2	20%
2.1	Represent, describe, and analyze patterns* and relationships using tables, graphs, verbal rules, and standard algebraic notation.	2
2.1a	Represent, describe, and analyze geometric and numeric patterns using tables, words, symbols, concrete objects, or pictures.	2
2.1b	Use a variable to represent an unknown (letter, box, symbol).	1
2.2	Describe patterns using variables, expressions, equations, and inequalities in problem-solving situations.	2
2.2a	Solve problems by representing and analyzing patterns using tables, words, concrete objects, or pictures.	2
2.3	Analyze functional relationships to explain how a change in one quantity results in a change in another (for example, how the area of a circle changes as the radius increases, or how a person’s height changes over time).	2
2.3a	Predict and describe how a change in one quantity results in a change in another quantity in a linear relationship (for example, A creature gains 3 oz. a day, how much will it have gained over 10 days?)	2
2.4	Distinguish between linear and nonlinear functions* through informal investigations.	3
2.4a	Explain whether data presented in a chart or graph is changing at a constant rate.	3
2.5	Solve simple linear equations in problem-solving situations using a variety of methods (informal, formal, and graphical) and a variety of tools (physical materials, calculators, and computers).	2
2.5a	Solve problems using tables, concrete objects, or pictures involving linear relationships with whole numbers.	2
3	Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning used in solving these problems.	2	20%
3.1	Read and construct displays of data using appropriate techniques (for example, line graphs, circle graphs, scatter plots*, box plots*, stem-and-leaf plots*) and appropriate technology.	2
3.1a	Organize and construct a line graph, bar graph, and frequency table from a given set of data.	2
3.1b	Read, interpret and draw conclusions from a line graph, bar graph, circle graph and frequency table.	2
3.2	Display and use measures of central tendency*, such as mean, median and mode and measures of variability*, such as range and quartiles.	1
3.2a	Find and use measures of central tendency including mean, median, and mode.	1
3.2b	Find and use the range from a given set of data (for example, find the range from 2 to 12. Note: the range is 10).	1
3.4	Formulate hypotheses, drawing conclusions, and making convincing arguments based on data analysis.	3
3.4a	Analyze data and draw conclusions to predict outcomes based on data displays such as line graphs, bar graphs, or frequency tables.	3
3.6	Make predictions and compare results using both experimental and theoretical probability drawn from real-world problems*.	2
3.6a	Using a chance device, such as a number cube or spinner, design a fair game and an unfair game, and explain why they are fair and unfair respectively.	3
3.6b	Make predictions based on data obtained from simple probability experiments.	2
3.6c	Describe an event as likely or unlikely and explain the degree of likelihood using words such as certain, very likely, not likely, or impossible.	1
3.7	Use counting strategies to determine all the possible outcomes from an experiment (for example, the number of ways students can line up to have their picture taken).	2
3.7a	Determine the number of possible outcomes for simple events using a variety of methods such as: organized lists or tree diagrams.	2
4&5	4. Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems. 5. Students use a variety of tools and techniques to measure, apply the results in problem-solving situations, and communicate the reasoning used in solving these problems.	2	25%
4.2	Describe, analyze and reason informally about the properties (for example, parallelism, perpendicularity, congruence) of two- and three-dimensional figures.	3
4.2a	Identify, compare, and analyze the attributes of two-and three-dimensional shapes and develop vocabulary to describe the attributes (for example, acute, obtuse, right angle, parallel lines, perpendicular lines, intersecting lines, and line segments).	2
4.2b	Make and test conjectures about geometric relationships and develop logical arguments to justify conclusions.	3
4.4	Solve problems using coordinate geometry*.	2
4.4a	Plot points on a coordinate graph in quadrant 1	1
4.4b	Draw a graph (in quadrant 1) from a given scenario or table.	2
4.5	Solving problems involving perimeter and area in two dimensions, and involving surface area and volume* in three dimensions.	2
4.5a	Solve problems involving the perimeter of polygons.	1
4.5b	Solve problems involving area of polygons (square, rectangle, parallelogram, rhombus, triangle)	2
4.6	Transforming geometric figures using reflections*, translations*, and rotations* to explore congruence.	2
4.6a	Identify congruent shapes using reflections, rotations, and translations.	2
4.6b	Show lines of symmetry* on a two-dimensional figure.	2
5.1	Estimate, use and describe measures of distance, perimeter, area, volume, capacity*, weight, mass, and angle comparison.	2
5.1a	Determine the appropriate unit of measure, metric and US customary, when estimating distance, capacity, and weight.	2
5.1b	Estimate and use standard and/or metric units for length, weight and temperature.	2
5.1c	Estimate the area of a polygon.	2
5.2	Estimate, make, and use direct and indirect measurements to describe and make comparisons.	2
5.2a	Estimate, make and use direct and indirect measurements to describe and make comparisons.	2
5.3	Read and interpret various scales including those based on number lines, graphs, and maps.	2
5.3a	Read and interpret scales on number lines, graphs, and maps.	2
5.3b	Select the appropriate scale for a given problem (for example, using the appropriate scale when setting up a graph or determining the order of numbers on a number line).	2
5.4	Develop and use formulas and procedures to solve problems involving measurement.	1
5.4a	Use formulas and/or procedures to solve problems involving the perimeter of a polygon.	1
5.4b	Use formulas and/or procedures to solve problems involving the area of squares, rectangles, parallelograms, rhombus, and triangles.	1
5.5	Describe how a change in an object’s linear dimensions affects its perimeter, area, and volume.	3
5.5a	Demonstrate how changing one of the dimensions of a rectangle or triangle affects its perimeter and area using concrete materials or graph paper.	3
6	Students link concepts and procedures as they develop and use computational techniques, including estimation, mental arithmetic, paper-and-pencil, calculators, and computers, in problem-solving situations and communicate the reasoning used in solving thes	2	15%
6.1	Use models to explain how ratios, proportions, and percents can be used to solve real-world problems.	1
6.1a	Use concrete materials or pictures to determine commonly used percentages (for example, 25%, 50%) in problem-solving situations.	1
6.2	Construct, use and explain procedures to compute and estimate with whole numbers, fractions, decimals, and integers.	2
6.2a	Demonstrate conceptual meaning or addition and subtraction of fractions and decimals, in problem solving situations.	2
6.2b	Use and explain strategies to add/subtract decimals and fractions in problem solving situations (common fractions with like and unlike denominators, mixed numbers, and decimals to thousandth.)	2
6.2c	Find equivalent representations by decomposing and composing whole numbers [for example, 48 x 12 = (48 x 10) + (48 x 2)]	2
6.2d	Demonstrate proficiency with the four basic operations using whole numbers.	1
6.3	Develop, apply and 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.	3
6.3a	Develop, apply and 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.	3
6.4	Select and use appropriate methods for computing with commonly used fractions and decimals, percents, and integers in problem-solving situations from among mental arithmetic*, estimation, paper-and-pencil, calculator, and computer methods, and determining	2
6.4a	Apply appropriate computation methods to solve problems involving whole numbers, common fractions, and decimals (use only addition and subtraction of fractions and decimals).	1
6.4b	In a problem solving situation, determine whether the results are reasonable and justify those results with accurate computation.	2