### Grade 7: Ratio and Proportional Relationships

#### Common Core Standards

**Content Standards**

7. RP.1 - Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

7. RP.2 - Recognize and represent proportional relationships between quantities.

7.RP.2a - Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

7.RP.2b - Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

7.RP.2c - Represent proportional relationships by equations.

7.RP.2d - Explain what a point (*x*, *y*) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, *r*) where r is the unit rate.

7. RP.3 - Use proportional relationships to solve multistep ratio and percent problems.

**Standards for Mathematical Practice**

MP.1 Make sense of problems and persevere in solving them.

MP.2 Reason abstractly and quantitatively.

MP.4 Model with mathematics.

MP.6 Attend to precision.

#### Description of Unit

This 3-4 week unit “Ratio and Proportional Relationships ”** **from the NYC Department of Education** **focuses on analyzing proportional relationships and using them to solve real-world problems. The unit deepens students’ understanding and use of unit rates; develops their understandings of proportional relationships as represented in words tables, equations, graphs and diagrams; and engages them in multi-step ratio and percent problem-solving. Instruction is being done through problem-based learning. The teacher would benefit from reading the Supports for English Language Learners and Students with Disabilities (located at the end) before starting any lessons or tasks as many of the suggestions can be used with all students throughout the unit.

#### Cautions

Connecticut teachers should be aware of the following:

- Teachers might connect to the geometry standard with scale drawings.
- Teachers may also need to include supports for procedural skills such as finding a unit rate and graphing a proportional relationship.
- There is minimal use of technology.
- Teachers will need to design enrichment or extensions for students.
- Pre-assessment and self-assessment instruments were not included.

#### Rationale for Selection

- Standards for content and practice are explicitly addressed throughout the unit, both in instruction and assessment, with some connections across domains.
- Questions on the formative assessments, in the question banks and on the performance task, are relevant application problems, always within a context.
- A balance of procedural and conceptual understanding is expected, as evidenced in the performance assessment.
- The unit uses and encourages precise and accurate mathematics and academic language (vocabulary), as well as concrete and abstract representations.