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6-8 Accelerated 6 Unit 2 Lesson 2

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K-5 Math •6-8 Math 9-12 Math

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•Accelerated 6 Accelerated 7

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Unit 1 •Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

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Lesson 1 •Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19 Lesson 20 Lesson 21 Lesson 22 Lesson 23 Lesson 24 Lesson 25 Lesson 26 Lesson 27 Lesson 28

K-5
6-8
9-12

Accelerated 6
Accelerated 7

Grade 6
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Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
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Lesson 13
Lesson 14
Lesson 15
Lesson 16
Lesson 17
Lesson 18
Lesson 19
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Lesson 21
Lesson 22
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Lesson 24
Lesson 25
Lesson 26
Lesson 27
Lesson 28

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Curriculum

IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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IM® 6-8 Math v.360, an IM v.360 curriculum, is ©2024 by Illustrative Mathematics®, and licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).

IM 6-8 Math v.360, an IM v.360 curriculum, is a derivative of IM 6-8 Math.

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Adaptations and additions to create IM 6–8 Math v.360 Accelerated are ©2025 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY-NC 4.0).

Adaptations to add additional English language learner supports are ©2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Lesson 2

2.1 Warm-up 2.2 Activity 2.3 Activity 2.4 Activity Student Lesson Summary

Unit 2, Lesson 2

Mixtures

Accelerated 6

2.1

Warm-up

Flower Pattern

This flower is made up of yellow hexagons, red trapezoids, and green triangles.

<p>A figure that contains 6 yellow hexagons, 2 red trapezoids, and 9 green triangles.</p>

Write sentences to describe the ratios of the shapes that make up this pattern.
How many of each shape would be in two copies of this flower pattern?

Are You Ready for More?

2.2

Activity

Powdered Drink Mix

Here are diagrams representing three mixtures of powdered drink mix and water:

<p>A discrete diagram for three quantities.</p>

How would the taste of Mixture A compare to the taste of Mixture B?
Use the diagrams to complete each statement:
1. Mixture B uses cups of water and teaspoons of drink mix.
  
  The ratio of cups of water to teaspoons of drink mix in Mixture B is .
2. Mixture C uses cups of water and teaspoons of drink mix.
  
  The ratio of cups of water to teaspoons of drink mix in Mixture C is .
How would the taste of Mixture B compare to the taste of Mixture C?

Are You Ready for More?

2.3

Activity

Batches of Cookies

A recipe for one batch of cookies calls for 5 cups of flour and 2 teaspoons of vanilla.

Draw a diagram that shows the amount of flour and vanilla needed for two batches of cookies.
How many batches can you make with 15 cups of flour and 6 teaspoons of vanilla? Show the additional batches by adding more ingredients to your diagram.
How much flour and vanilla would you need for 5 batches of cookies?
Whether the ratio of cups of flour to teaspoons of vanilla is , , or , the recipes would make cookies that taste the same. We say that these ratios are equivalent.
1. Find another ratio of cups of flour to teaspoons of vanilla that is equivalent to these ratios.
2. How many batches can you make using this new ratio of ingredients?

Are You Ready for More?

2.4

Activity

Perfect Purple Water

The recipe for Perfect Purple Water says, “Mix 8 ml of blue water with 3 ml of red water.”

Jada mixes 24 ml of blue water with 9 ml of red water. Andre mixes 16 ml of blue water with 9 ml of red water.

Which person will get a color mixture that is the same shade as Perfect Purple Water? Explain or show your reasoning.
Find another combination of blue water and red water that will also result in the same shade as Perfect Purple Water. Explain or show your reasoning.

Are You Ready for More?

Student Lesson Summary

A recipe for fizzy juice says, “Mix 5 cups of cranberry juice with 2 cups of soda water.”

To double this recipe, we would use 10 cups of cranberry juice with 4 cups of soda water. To triple this recipe, we would use 15 cups of cranberry juice with 6 cups of soda water.

This diagram shows a single batch of the recipe, a double batch, and a triple batch:

<p>Equivalent ratios of a recipe for fizzy juice.</p>

We say that the ratios , , and are equivalent. Even though the amounts of each ingredient within a single, double, or triple batch are not the same, they would make fizzy juice that tastes the same.

When mixing colors, doubling or tripling the amount of each color will create the same shade of the mixed color. In fact, you can always multiply the amount of each color by the same number to create a different amount of the same mixed color.

For example, a batch of dark orange paint uses 4 ml of red paint and 2 ml of yellow paint.

To make two batches of dark orange paint, we can mix 8 ml of red paint with 4 ml of yellow paint.
To make three batches of dark orange paint, we can mix 12 ml of red paint with 6 ml of yellow paint.

Here is a diagram that represents 1, 2, and 3 batches of this recipe.

<p>A discrete diagram for two quantities labeled “red paint (ml)” and “yellow paint (ml)”.</p>

<p>The data are as follows: 1 batch orange, 4 red squares and 2 yellow squares. 2 batches orange, 8 red squares and 4 yellow squares. Three batches orange, 12 red squares and 6 yellow squares.</p>

We say that the ratios , , and are equivalent because they describe the same color mixture in different numbers of batches, and they make the same shade of orange.

Glossary

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