Unit :4a (SAUSD)Ratios & Proportional Reasoning

  • Math Talks: Proportional Reasoning - this is a Google Presentation containing Math Talks and other activities to promote student discourse in the classroom. This presentation is under construction and new content will be added. If you have content to add, please leave a message on the discussion page.

Unit Overview
Topic & subtopics
Common Core State Core Standards:
Concept, Definition, Application

  • Ratios
  • Rates
  • Unit Rate
  • Proportions
  • Constant of Proportionality
  • Solve problems involving tables and graphs
  • Scale drawings of geometric figures
7.RP Analyze proportional relationships and use them to solve real-world and mathematical problems.

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.
a. 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.
b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
c. Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.
d. 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.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale. (Note: Refrain from using term similar here)

Supporting Standards
7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
7.EE Use properties of operations to generate equivalent expressions.
7.EE.2Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.

Support Material & Resources

  • Independent vs. Dependent Variables Song- I used this after NY Engage Lesson 8. So cute, I had student watch & take notes. This was the intro to the topic. Then I had them apply these 2 terms to the problems we had already done. We also looked t these terms in relationship to tables, graphs & the equation.

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