Unit 2: Ratios, Rates, and Percentages

Students develop an understanding of ratios, equivalent ratios, rates, unit rates, and percentages, and use representations such as discrete diagrams, double number lines, tables, and tape diagrams to solve problems.

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Concept

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What this unit covers

A What Are Ratios? · 3 lessons

Goals

• Create and interpret discrete diagrams that represent situations involving ratios.
• 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. Representing Ratios with Diagrams
2. Mixtures
3. Defining Equivalent Ratios

B Representing Equivalent Ratios · 8 lessons

Goals

• Choose multipliers strategically when solving multi-step problems involving equivalent ratios.
• Use a double number line diagram to represent and find equivalent ratios.
• Use a table of equivalent ratios to solve problems.

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
6. Representing Ratios with Tables
7. Navigating a Table of Equivalent Ratios
8. Solving Equivalent Ratio Problems

C 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

D Units of Measurement and Unit Conversion · 3 lessons

Goals

• Recognize that when we measure things in two different units, the pairs of measurements are equivalent ratios. Apply this understanding to convert a measurement from one unit to another unit.
• Use a “rate per 1” to solve problems involving unit conversion.

Lessons

1. Anchoring Units of Measurement
2. Measuring with Different-Size Units (Optional)
3. Converting Units

E Rates · 4 lessons

Goals

• Apply reasoning about ratios and unit rates to solve problems and explain the solution methods.
• Calculate the two unit rates associated with a ratio and interpret them in the context of a situation.

Lessons

1. Comparing Speeds and Prices
2. Interpreting Rates
3. Equivalent Ratios Have the Same Unit Rates
4. Solving Rate Problems

F Percentages · 6 lessons

Goals

• Choose a strategy to solve problems involving percentages and explain the solution method.
• Create tape diagrams, double number line diagrams, or tables to represent situations involving percentages.

Lessons

1. What Are Percentages?
2. Representing Percentages in Different Ways
3. Benchmark Percentages
4. Solving Percentage Problems
5. Finding This Percent of That
6. Finding the Percentage (Optional)

G Let's Put It to Work · 2 lessons

Lessons

1. A Fermi Problem
2. Painting a Room

Helpful to know first

The curriculum says this unit builds on these.

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

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Grade 3 Math · Unit 5 Fractions as Numbers

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Grade 4 Math · Unit 5 Multiplicative Comparison and Measurement

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Grade 5 Math · Unit 6 More Decimal and Fraction Operations

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