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Concepts that use Proportional Reasoning. Grade 8. Number Concepts/Number and Relationship Operations (GCO A). A7 – when comparing and ordering fractions, one strategy is to use common denominators. Proportional reasoning can be used to create equivalent fractions. Chapter 6, pages 262–267.

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## Concepts that use Proportional Reasoning

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**A7 – when comparing and ordering fractions, one strategy**is to use common denominators. Proportional reasoning can be used to create equivalent fractions. • Chapter 6, pages 262–267**A9 – this outcome introduces the conceptual understanding**needed for proportional reasoning. • Students use the typical problems (If a 3-pack of juice costs $1.10, what would 12 juice cost?) to help explore the relationships found “within” and “between” ratios. • This outcome should be addressed in connection with B2 and D1. • Chapter 4, pages 158–167**B2 – this outcome, a continuation of A9, is where students**learn various strategies to solve proportions. • Cross multiplication should be used only when the numbers involved do not lend themselves to more intuitive methods. • Understanding and being able to use the multiplicative relationship is essential in proportional reasoning. • Chapter 4, pages 158–177**B3 – some percent problems can be solved using**proportions. • Example: If 20% of a number is 0.46, what would 110% of the number be? • Chapter 4, pages 148–157, 168–177**B5/B6 – When adding and subtracting fractions, it might be**necessary to use equivalent fractions to get a common denominator. • Chapter 2, pages 56–69, 101–103**C1 – this outcome is about representing a relationship**between 2 quantities in a variety of formats. There are many opportunities when working with the table of values, graph and when making generalizations (predicting the nth term) to use proportional reasoning. • Chapter 8, pages 330–340, 368–375**C2 – when working with linear relationships, there are**opportunities within the table of values and the graph to use proportional reasoning. • Chapter 8, pages 341–347, 368–375**C4 – this outcome introduces the conceptual understanding**of slope. Students should recognize that for linear relationships, the ratio of the vertical change to the horizontal change is consistent anywhere along the line. • Chapter 8, pages 348–360**C6 – students should be able to solve equations of the**type as long as the unknown is in the numerator. • Chapter 7, pages 310–321, 325, 38–381**D1 – this outcome addresses contexts that encourage the**use of Proportional Reasoning—scale drawings and other measurement problems as well as enlargements and reductions. If problems include the conversion of SI units, then D2 is being addressed. • Chapter 4, pages 158–177**E2 – this outcome addresses the development of the**properties of dilatations. Developmental work for and problems that apply these properties use proportional reasoning. • Chapter 9, pages 388–394, 410–417**E3 – the development of the properties of similar 2-D**shapes and applications of these properties provide many opportunities to use proportional reasoning. • Chapter 9, pages 395–402**F3 – in this outcome students are learning to construct**circle graphs. Students would use proportional reasoning if they determine the size of the sectors using • Chapter 5, pages 220–225**In the G outcomes, there are applications of a concept that**require students to gather information and extend that information to solve a problem. • Conducting surveys and using experimental probability to predict theoretical probably are examples of these applications. Students would likely set up proportions to solve these problems. • Chapter 5

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