Unit 2

Introducing Ratios

Unit Narrative

This unit introduces students to ratios and equivalent ratios. It builds on previous experiences students had with relating two quantities, such as converting measurements starting in grade 3, multiplicative comparison in grade 4, and interpreting multiplication as scaling in grade 5. The work prepares students to reason about unit rates and percentages in the next unit, proportional relationships in grade 7, and linear relationships in grade 8.

First, students learn that a ratio is an association between two quantities, for instance, “There are 3 pencils for every 2 erasers.” Students...

to access Pre-Unit Assessments.

Section A

Section Goals

Section Narrative

This short section introduces students to the concept of ratio and ways to represent it.

Students begin by using ratios and ratio language to describe collections of physical objects. They see that quantities in a collection can be described and represented in different ways, using both numbers and words. Next, students draw diagrams to represent situations involving one or more...

Let’s describe two quantities at the same time.

Let’s use diagrams to represent ratios.

to access Section Checkpoints.

Section A

Let’s describe two quantities at the same time.

Let’s use diagrams to represent ratios.

Section B

Section Goals

Section Narrative

In this section, students learn about equivalent ratios.

Students first make sense of equivalent ratios through concrete experiences involving recipes. They learn that scaling a recipe up or down—to create multiple batches or a fraction of a batch—produces a result that is the same as the original recipe in some important way. For example, tripling the amount of each ingredient...

Let’s explore how ratios affect the way a recipe tastes.

Let’s see what color-mixing has to do with ratios.

Let’s investigate equivalent ratios some more.

to access Section Checkpoints.

Section B

Let’s explore how ratios affect the way a recipe tastes.

Let’s see what color-mixing has to do with ratios.

Let’s investigate equivalent ratios some more.

Section C

Section Goals

Section Narrative

This section introduces new ways to represent and describe equivalent ratios, deepening students’ understanding of them.

Students see that double number line diagrams are useful for reasoning about equivalent ratios. For example, this diagram shows that the ratios , , , , and are equivalent. Mixing cranberry juice and soda water in these amounts will create drinks that taste the...

Let’s use number lines to represent equivalent ratios.

Let's draw double number line diagrams like a pro.

Let’s use ratios to describe how much things cost.

Let’s use ratios to work with how fast things move.

Let’s use ratios to compare situations.

to access Section Checkpoints.

Section C

Let’s use number lines to represent equivalent ratios.

Let's draw double number line diagrams like a pro.

Let’s use ratios to describe how much things cost.

Let’s use ratios to work with how fast things move.

Let’s use ratios to compare situations.

Section D

Section Goals

Section Narrative

In this section, students use tables to reason about situations involving equivalent ratios.

Students first observe how a table is used to represent and find equivalent ratios. They see that the values in a table don’t need to be listed in order, so they can choose the multipliers strategically.

For instance, to find the pay for 8 hours given a...

Let’s use tables to represent equivalent ratios.

Let’s use a table of equivalent ratios like a pro.

Let’s contrast double number lines and tables.

Let's practice getting information from our partner.

to access Section Checkpoints.

Section D

Let’s use tables to represent equivalent ratios.

Let’s use a table of equivalent ratios like a pro.

Let’s contrast double number lines and tables.

Let's practice getting information from our partner.

Section E

Section Goals

Section Narrative

In this section, students reason about situations in which the quantities in the ratio have the same units and questions can be asked about the individual quantities (the parts) and their sum (the total). Students learn to use tape diagrams as a way to represent such situations. They also interpret ratios expressed in “parts” rather than standard units, such as...

Let’s look at situations where you can add the quantities in a ratio together.

Let’s compare all our strategies for solving ratio problems.

to access Section Checkpoints.

Section E

Let’s look at situations where you can add the quantities in a ratio together.

Let’s compare all our strategies for solving ratio problems.

Section F

Section Narrative

In the final section, students have the opportunity to apply their thinking from throughout the unit. As this is a short section followed by an End-of-Unit Assessment, there are no section goals or checkpoint questions.

Let’s solve a Fermi problem.

to access Section Checkpoints.

Section F

Let’s solve a Fermi problem.

to access End-of-Unit Assessments.

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Introducing Ratios

Unit Narrative

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