Unit 2: Introducing Ratios

Students learn about ratios and equivalent ratios, representing them with discrete diagrams, double number lines, tables, and tape diagrams, and reason about contexts such as recipes, color mixtures, unit pricing, constant speed, and part-part-whole situations.

Worksheets

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Unit

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Concept

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Practice

Set 1

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Set 2

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Advanced

Set 1

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Set 2

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What this unit covers

A What Are Ratios? · 2 lessons

Goals

• Create and interpret discrete diagrams that represent situations involving ratios.
• Create and interpret sentences that describe ratios.

Lessons

1. Introducing Ratios and Ratio Language
2. Representing Ratios with Diagrams

B Equivalent Ratios · 3 lessons

Goals

• Explain equivalent ratios in terms of the quantities in a recipe being multiplied by the same number to create a different size batch of something with the same taste or same shade.
• Generate equivalent ratios and justify that they are equivalent.

Lessons

1. Recipes
2. Color Mixtures
3. Defining Equivalent Ratios

C Representing Equivalent Ratios · 5 lessons

Goals

• Given prices and quantities or distances and times, calculate the price for 1 object or the distance traveled in 1 unit of time. Express each using the word “per.”
• Justify whether two situations do or do not happen at the same rate, by determining if the ratios in the situations are equivalent.
• Use a double number line diagram to represent and find equivalent ratios.

Lessons

1. Introducing Double Number Line Diagrams
2. Creating Double Number Line Diagrams
3. How Much for One?
4. Constant Speed
5. Comparing Situations by Examining Ratios

D Solving Ratio and Rate Problems · 4 lessons

Goals

• Choose multipliers strategically when solving multi-step problems involving equivalent ratios.
• Use a table of equivalent ratios to solve problems.

Lessons

1. Representing Ratios with Tables
2. Navigating a Table of Equivalent Ratios
3. Tables and Double Number Line Diagrams
4. Solving Equivalent Ratio Problems

E Part-Part-Whole Ratios · 2 lessons

Goals

• Choose representations and solution methods to reason about ratios and sums of quantities.
• Use diagrams or other strategies to solve problems involving ratios and the total amount.

Lessons

1. Part-Part-Whole Ratios
2. Solving More Ratio Problems

F Let’s Put It to Work · 1 lesson

Lessons

1. A Fermi Problem

Helpful to know first

The curriculum says this unit builds on these.

Grade 3 Math · Unit 6 Measuring Length, Time, Liquid Volume, and Weight

Open unit →

Grade 4 Math · Unit 5 Multiplicative Comparison and Measurement

Open unit →

Grade 5 Math · Unit 6 More Decimal and Fraction Operations

Open unit →