IXL - Colorado fifth-grade math standards

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Skills available for Colorado fifth-grade math standards

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Standards document:

2010 Common Core State Standards 2010 Common Core State Standards
2010 Colorado Academic Standards 2010 Colorado Academic Standards
2009 Colorado Academic Standards 2009 Colorado Academic Standards
2005 Colorado Model Content Standards 2005 Colorado Model Content Standards

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5-8.1 Students develop number sense and use numbers and number relationships in problem-solving situations and communicate the reasoning used in solving these problems.

5-8. 1.1 demonstrate meanings for integers, rational numbers, percents, exponents, square roots, and pi use physical materials and technology in problem-solving situations;
5-8. 1.2 read, write, and order integers, rational numbers, and common irrational numbers such as square root of 2, square root of 5, and pi;
5-8. 1.3 apply number theory concepts (for example, primes, factors, multiples) to represent numbers in various ways;
5-8. 1.4 use the relationships among fractions, decimals, and percents, include the concepts of ratio and proportion, in problem-solving situations;
5-8. 1.5 develop, test, and explain conjectures about properties of integers and rational numbers; and
5-8. 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 square root of 2, square root of 5, and pi.

5-8.2 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.

5-8. 2.1 represent, describe, and analyze patterns and relationships using tables, graphs, verbal rules, and standard algebraic notation;
5-8. 2.2 describe patterns using variables, expressions, equations, and inequalities in problem-solving situations;
5-8. 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);
- Algebra: Function tables (Fifth grade - Q.7)
- Coordinate graphing: Write the linear function shown in a graph (Sixth grade - Q.6)
5-8. 2.4 distinguish between linear and nonlinear functions through informal investigations; and
- Coordinate graphing: Identify linear and nonlinear functions (Sixth grade - Q.9)
5-8. 2.5 solve simple linear equations in problem-solving situations using a variety of methods (informal, formal, graphical) and a variety of tools (physical materials, calculators, computers).

5-8.3 Students use data collection and analysis, statistics, and probability in problem-solving situations and communicate the reasoning used in solving these problems.

5-8. 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;
5-8. 3.2 display and use measures of central tendency, such as mean, median, and mode, and measures of variability, such as range and quartiles;
5-8. 3.3 evaluate arguments that are based on statistical claims;
5-8. 3.4 formulate hypotheses, draw conclusions, and make convincing arguments based on data analysis;
5-8. 3.5 determine probabilities through experiments or simulations;
- Probability and statistics: Calculate probability (Fifth grade - Y.4)
- Probability: Probability of one event (Sixth grade - BB.2)
5-8. 3.6 make predictions and compare results using both experimental and theoretical probability drawn from real-world problems; and
- Probability and statistics: Make predictions (Fifth grade - Y.5)
- Probability: Make predictions (Sixth grade - BB.3)
5-8. 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).

5-8.4 Students use geometric concepts, properties, and relationships in problem-solving situations and communicate the reasoning used in solving these problems.

5-8. 4.1 construct two- and three-dimensional models using a variety of materials and tools;
5-8. 4.2 describe, analyze, and reason informally about the properties (for example, parallelism, perpendicularity, congruence) of two- and three-dimensional figures ;
5-8. 4.3 apply the concepts of ratio, proportion, and similarity in problem-solving situations;
5-8. 4.4 solve problems using coordinate geometry;
5-8. 4.5 solve problems involving perimeter and area in two dimensions, and involving surface area and volume in three dimensions; and
5-8. 4.6 transform geometric figures using reflections, translations, and rotations to explore congruence.
- Geometry: Reflection, rotation, and translation (Fifth grade - B.8)
- Geometry: Reflection, rotation, and translation (Sixth grade - Z.16)

5-8.5 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.

5-8. 5.1 estimate, use, and describe measures of distance, perimeter, area, volume, capacity, weight, mass, and angle comparison;
5-8. 5.2 estimate, make, and use direct and indirect measurements to describe and make comparisons;
- Measurement: Estimate customary measurements (Sixth grade - Y.1)
5-8. 5.3 read and interpret various scales including those based on number lines, graphs, and maps;
- Ratios, proportions, and percents: Scale drawings (Fifth grade - V.7)
- Coordinate graphing: Find points on a function graph (Sixth grade - Q.5)
5-8. 5.4 develop and use formulas and procedures to solve problems involving measurement;
5-8. 5.5 describe how a change in an object's linear dimensions affects its perimeter, area, and volume; and
- Geometry: Rectangles: relationship between perimeter and area (Sixth grade - Z.25)
5-8. 5.6 select and use appropriate units and tools to measure to the degree of accuracy required in a particular problem-solving situation.
- Decimal numbers: Round decimals (Sixth grade - B.7)

5-8.6 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 these problems.