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Colorado Math Standards - 5th Grade
MathScore aligns to the Colorado Math Standards for 5th Grade. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.
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Number Sense
1.1 Demonstrate meanings for whole numbers, and commonly-used fractions and decimals (for example, 1/3, 3/4, 0.5, 0.75), and representing equivalent forms of the same number through the use of physical models, drawings, calculators, and computers.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. (Positive Number Line )
1.1b Using concrete materials, demonstrate the equivalence of commonly-used fractions, terminating decimals, and percents (for example, 7/10 = 0.7 = 70%). (Percentage Pictures )
1.1c Demonstrate the meaning of square numbers using pictorial or concrete materials.
1.2 Read and write whole numbers and know place-value concepts and numeration through their relationships to counting, ordering, and grouping. (Decimal Place Value )
1.2a Read, write, and order positive rational numbers, including commonly-used fractions and terminating decimals through hundredths. (Order Large Numbers , Order Decimals , Fraction Pictures )
1.2b Compare commonly-used proper fractions and terminating decimals. (Compare Mixed Values , Fraction Comparison , Compare Decimals , Basic Fraction Comparison )
1.3 Use numbers to count, to measure, to label, and to indicate location.
1.3a Identify factors, multiples, and prime/composite numbers. (Prime Numbers , Factoring )
1.3b Recognize equivalent representations for the same number and generate them by decomposing and composing numbers (for example,36 can be represented as 30+6, 20+16, 9x4, 40-4, three dozen and/or the square of 6).
1.3c Describe numbers by their characteristics (for example, even, odd, prime, square). (Odd or Even , Prime Numbers )
1.4 Use the relationships among fractions, decimals, and percents, including the concepts of ration and proportion, in problem-solving situations.
1.4a Demonstrate the equivalent relationships among commonly used fractions, decimals, and percents using pictorial or concrete materials. (Percentage Pictures )
1.5 Develop, test, and explain conjectures about properties of integers and rational numbers.
1.5a Develop, test, and explain conjectures about properties of whole numbers and commonly-used fractions and decimals.
1.5b Use number properties (commutative, associative, identity) to evaluate numeric expressions and solve equations. (Addition Grouping , Associative Property 1 , Associative Property 2 , Commutative Property 1 , Commutative Property 2 )
1.6 Using number sense to estimate and justify the reasonableness of solutions to problems involving integers, rational numbers, and common irrational numbers such as √2 √5 and π.
1.6a Use number sense to estimate sums and differences of fractions and decimals using benchmarks (for example, 5/6 + 7/8 must be equal to an amount less than 2, since each fraction is less than 1). (Money Addition , Money Subtraction )
1.6b Use appropriate techniques to estimate, determine, and then justify the reasonableness of solutions to problems involving whole numbers. (Rounding Large Numbers , Decimal Rounding to .01 , Estimated Addition , Estimated Subtraction )
Algebraic Methods
2.1 Represent, describe, and analyze patterns and relationships using tables, graphs, verbal rules, and standard algebraic notation.2.1a Represent, describe, and analyze geometric and numeric patterns (whole numbers). (Patterns: Numbers , Function Tables , Function Tables 2 )
2.1b Recognize that a variable is used to represent an unknown quantity. (Algebraic Sentences )
2.1c Identify such properties as commutativity, associativity, and distributivity and use them to compute with whole numbers. (Addition Grouping , Associative Property 1 , Associative Property 2 , Commutative Property 1 , Commutative Property 2 , Basic Distributive Property )
2.2 Describe patterns using variables, expressions, equations, and inequalities in problem-solving situations.
2.2a Solve problems by representing and analyzing patterns using words, tables, and graphs. (Function Tables , Function Tables 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).
2.3a Describe how a change in one quantity results in a change in another quantity.
2.4 Distinguish between linear and nonlinear functions through informal investigations.
2.4a Match a description of a situation with its continuous graph.
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).
2.5a Use tables, charts, concrete objects, or pictures to solve problems involving linear relationships and whole numbers.
Data Analysis, Statistics, and Probability
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.3.1a Differentiate between categorical and numerical data.
3.1b Organize, construct, and interpret displays of data including tables, charts, pictographs, line plots, bar graphs, and line graphs. (Tally and Pictographs , Bar Graphs , Line Graphs )
3.1c Read, interpret, and draw conclusions from various displays of data. (Tally and Pictographs , Bar Graphs , Line Graphs )
3.1d From a given scenario, choose the correct graph from possible graph representations.
3.2 Display and use measures of central tendency, such as mean, median and mode and measures of variability, such as range and quartiles.
3.2a Distinguish between the median and mode of a data sheet.
3.2b Determine the range of a set of data.
3.3 Evaluate arguments that are based on statistical claims.
3.3a Analyze data and draw conclusions based on data displays such as tables, charts, line graphs, bar graphs, pictographs, and line plots. (Line Graphs )
3.4 Formulate hypotheses, drawing conclusions, and making convincing arguments based on data analysis.
3.4a Describe how data collection methods affect the nature of the data set.
3.4b Make convincing arguments based on data analysis.
3.5 Determine probabilities through experiments or simulations.
3.5a Describe events such as likely or unlikely and explain the degree of likelihood using words, such as certain, equally likely, and impossible.
3.5b Use zero to represent the probability of an impossible even and one to represent the probability of a certain event. (Probability )
3.5c Use common fractions to represent the probability of events that are neither certain nor impossible. (Probability )
3.6 Make predictions and compare results using both experimental and theoretical probability drawn from real-world problems.
3.6a Using one chance device, such as a number cube or a spinner, design a fair game and an unfair game, and explain why they are fair and unfair.
3.6b Make predications based on data obtained from simple probability experiments.
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).
3.7a Solve problems using strategies for finding all possible combinations and/or arrangements.
Geometry
4.1 Construct two-and three-dimensional models using a variety of materials and tools.4.1a Represent a three-dimensional shape in two dimensions (for example, recognize a three dimensional figure from its net).
4.2 Describe, analyze and reason informally about the properties (for example, parallelism, perpendicularity, congruence) of two- and three-dimensional figures.
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). (Triangle Types , Parallel and Perpendicular Lines )
4.2b Make and test conjectures about geometric relationships and develop logical arguments to justify conclusions.
4.4 Solve problems using coordinate geometry.
4.4a Given a coordinate graph, read coordinate pairs in quadrant one.
4.4b Choose the coordinate graph, which represents a given data set.
4.4c Use maps and grids to locate points, create paths and measure distances within a coordinate system. (Line Segments )
4.5 Solving problems involving perimeter and area in two dimensions, and involving surface area and volume in three dimensions.
4.5a Solve problems involving the perimeter of polygons. (Perimeter )
4.5b Solve problems involving the area of rectangles and squares. (Compare Rectangle Area and Perimeter )
4.6 Transforming geometric figures using reflections, translations, and rotations to explore congruence.
4.6a Predict and describe the results of flipping, sliding, or turning a two-dimensional shape.
4.6b Show lines of symmetry for geometrical shapes.
Measurement
5.1 Estimate, use and describe measures of distance, perimeter, area, volume, capacity, weight, mass, and angle comparison.5.1a Determine the appropriate unit of measure (metric and US customary) when estimating distance, capacity, and weight.
5.1b Estimate the length of common objects.
5.1c Estimate the perimeter of polygons.
5.1d Estimate the measures of angles (for example, 90°, less than 90°, more than 90°).
5.1e Describe angles as acute, obtuse and right.
5.3 Read and interpret various scales including those based on number lines, graphs, and maps.
5.3a Read and interpret scales on number lines, graphs, and maps. (Bar Graphs , Line Graphs )
5.3b Select the appropriate scale for a given problem (for example, using the appropriate scale when setting up a graph).
5.4 Develop and use formulas and procedures to solve problems involving measurement.
5.4a Find the perimeter and area of rectangles and squares, using appropriate units. (Compare Rectangle Area and Perimeter )
5.5 Describe how a change in an object's linear dimensions affects its perimeter, area, and volume.
5.5a Demonstrate how changing one of the dimensions of a rectangle affects its perimeter (using concrete materials or graph paper). (Requires outside materials )
5.5b Demonstrate how change in one of the dimensions of a rectangle affects its area (using concrete materials or graph paper). (Requires outside materials )
5.6 Select and use appropriate units and tools to measure to the degree of accuracy required in a particular problem-solving situation.
5.6a Select and use the appropriate unit and tool to measure to the degree of accuracy required in a particular problem.
5.6b Measure the sides of rectangles, squares, and triangles to the nearest 1/4 inch and nearest centimeter.
Mathematical Reasoning
6.1 Use models to explain how ratios, proportions, and percents can be used to solve real-world problems.6.1a Use concrete materials or pictures, determine commonly used percentages (for example, 25%, 50%) in problem-solving situations. (Percentage Pictures )
6.2 Construct, use and explain procedures to compute and estimate with whole numbers, fractions, decimals, and integers.
6.2a Demonstrate the conceptual meaning of the four basic arithmetic operations (addition, subtraction, multiplication, and division). (Understanding Multiplication , Understanding Division )
6.2b Use and explain strategies to add, subtract, multiply and divide whole numbers in problem-solving situations. (Missing Factor , Missing Term , Long Addition , Long Subtraction , Multiplication By One Digit , Long Division By One Digit , Division with Remainders )
6.2c Demonstrate proficiency of addition, subtraction, multiplication and division of whole numbers in problem-solving situations. (Basic Word Problems , Arithmetic Word Problems , Basic Word Problems 2 , Word Problems With Remainders )
6.2d Use and explain strategies to add and subtract commonly-used fractions with like denominators in problem-solving situations. (Basic Fraction Addition , Basic Fraction Subtraction )
6.2e Use and explain strategies to add and subtract commonly-used decimals in problem-solving situations. (Making Change )
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.
6.3a Determine from real-world problems whether an estimated or exact answer is acceptable. (Estimated Multiply Divide Word Problems )
6.3b Use and explain a variety of estimation techniques to solve problems. (Rounding Large Numbers , Decimal Rounding to .01 , Decimal Rounding , Estimated Addition , Estimated Subtraction , Money Addition , Money Subtraction )
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 whether the results are reasonable.
6.4a Determine whether information given is a problem-solving situation is sufficient, insufficient, or extraneous.
6.4b Given a real-world problem, use and appropriate method (mental arithmetic, estimation, paper-and-pencil, calculator) to correctly solve the problem.
6.4c Given a math sentence, use any one of the four operations with whole numbers, create and illustrate a real-world problem.
6.4d In a problem-solving situation, determine whether the results are reasonable and justify those results with correct computations.
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