Mathematics Curriculum Framework
November 2000

## Learning Standards by Strand

### Patterns, Relations, and Algebra for Grades 5-6

 Understand patterns, relations, and functions Represent and analyze mathematical situations and structures using algebraic symbols Use mathematical models to represent and understand quantitative relationships Analyze change in various contexts

#### Learning Standards

Students engage in problem solving, communicating, reasoning, connecting, and representing as they:
 6.P.1 Analyze and determine the rules for extending symbolic, arithmetic, and geometric patterns and progressions, e.g., ABBCCC; 1, 5, 9, 13 ...; 3, 9, 27, .... 6.P.2 Replace variables with given values and evaluate/simplify, e.g., 2() + 3 when = 4. 6.P.3 Use the properties of equality to solve problems, e.g., if + 7 = 13, then = 13 - 7, therefore = 6; if 3 x = 15, then 1/3 x 3 x = 1/3 x 15, therefore = 5. 6.P.4 Represent real situations and mathematical relationships with concrete models, tables, graphs, and rules in words and with symbols, e.g., input-output tables. 6.P.5 Solve linear equations using concrete models, tables, graphs, and paper-pencil methods. 6.P.6 Produce and interpret graphs that represent the relationship between two variables in everyday situations. 6.P.7 Identify and describe relationships between two variables with a constant rate of change. Contrast these with relationships where the rate of change is not constant.

#### Exploratory Concepts and Skills

• Use physical models to investigate and describe how a change in one variable affects a second variable.
• Use models to develop understanding of slope as constant rate of change.
• Model situations with proportional relationships and solve problems.

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