Comparing & Scaling
Standards & Objectives | |
File Size: | 122 kb |
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Goals for Comparing & Scaling
Students should...
- Understand ratios, rates, and percents
- Understand proportionality in tables, graphs, and equations
- Develop and use strategies for solving problems that require proportional reasoning
Investigation 1
Vocabulary | |
File Size: | 225 kb |
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Investigation 1 focuses on different strategies for comparing quantities—using ratios, fractions, percents. Students learn what different types of comparative statements say about data given. They are asked to write comparative statements using ratios and differences that describe data. Questions are asked that engage students in making comparisons and checking the accuracy of given statements. The important question of how you decide whether to use a difference, ratio, fraction, or percent to make a particular comparison is raised. Students use a variety of strategies for making comparisons, and identify how information in each of these forms provides the information needed to derive any of the other forms. Students investigate how ratios can be formed and scaled up or down to find equivalent ratios. This Investigation contrasts proportional reasoning with additive reasoning. It clarifies when additive reasoning is not appropriate.
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Investigation 2
Vocabulary | |
File Size: | 291 kb |
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There are many different ways to make comparisons. In this Investigation, students isolate ratios and rates as being useful comparisons to use in a variety of situations. The situations in this Investigation motivate students to find and use unit rates. They then compare unit rates within a problem to decide which option is best. Students can use other strategies to solve problems as well, such as rate tables, equations, and graphs. Students also begin to see patterns in graphs and tables of proportional relationships.
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Investigation 3
Vocabulary | |
File Size: | 162 kb |
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In this Investigation, students use various proportional reasoning strategies they developed in Investigations 1 and 2 and apply those strategies in different contexts. Specifically, Problem 3.1 provides a consumer math context, an important real‑world application of proportional reasoning. Students use ratios, proportions, unit rates, rate tables, and equations to practice converting quantities to different measurement units. They look for connections among the representations of proportional relationships and among their solution strategies.
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