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

• 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

Number Concepts/Number and Relationship Operations

(GCO B)

• 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

Patterns and Relations(GCO C)

• 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

a cb d

Measurement(GCO D)

• 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

Geometry(GCO E)

• 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

Data Management(GCO F)

• 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

360a cb

Probability(GCO G)

• 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