Lesson 4Color Mixtures

Learning Goal

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

Learning Targets

I can explain the meaning of equivalent ratios using a color mixture as an example.
I can use a diagram to represent a single batch, a double batch, and a triple batch of a color mixture.
I know what it means to double or triple a color mixture.

Warm Up: Number Talk: Adjusting a Factor

Find the value of each product mentally.

$6 \cdot 15$
$12 \cdot 15$
$6 \cdot 45$
$13 \cdot 45$

Activity 1: Turning Green

Your teacher mixed milliliters of blue water and milliliters of yellow water in the ratio $5 : 15$ .

Problem 1

In the left cylinder, mix 5 ml of blue and 15 ml of yellow. This is a single batch of green.
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Suppose you have one batch of green but want to make more. Which of the following would produce the same shade of green?
If you’re unsure, try creating the mixture in the right cylinder. Start with the amounts in a single batch (5 ml of blue and 15 ml of yellow) and …
1. add 20 ml of blue and 20 ml of yellow
2. double the amount of blue and the amount of yellow
3. triple the amount of blue and the amount of yellow
4. mix a single batch with a double batch
5. double the amount of blue and triple the amount of yellow
- For one of the mixtures that produces the same shade, write down the number of ml of blue and yellow used in the mixture.
- For the same mixture that produces the same shade, draw a diagram of the mixture. Make sure your diagram shows the number of milliliters of blue, yellow, and the number of batches.
Someone was trying to make the same shade as the original single batch, but started by adding 20 ml of blue and 20 ml of yellow. How can they add more but still create the same shade of green?
Invent a recipe for a bluer shade of green. Write down the amounts of yellow and blue that you used, and draw a diagram. Explain how you know it will be bluer than the original single batch of green before testing it out.

Print Version

Draw a diagram to represent the amount of each color that you will combine to double your teacher’s recipe.
Use a marker to label an empty cup with the ratio of blue water to yellow water in this double batch.
Predict whether these amounts of blue and yellow will make the same shade of green as your teacher’s mixture. Next, check your prediction by measuring those amounts and mixing them in the cup.
Is the ratio in your mixture equivalent to the ratio in your teacher’s mixture? Explain your reasoning.

Problem 2

Tripling the original recipe:

Draw a diagram to represent triple your teacher’s recipe.
Label an empty cup with the ratio of blue water to yellow water.
Predict whether these amounts will make the same shade of green. Next, check your prediction by mixing those amounts.
Is the ratio in your new mixture equivalent to the ratio in your teacher’s mixture? Explain your reasoning.

Problem 3

Next, invent your own recipe for a bluer shade of green water.

Draw a diagram to represent the amount of each color you will combine.
Label the final empty cup with the ratio of blue water to yellow water in this recipe.
Test your recipe by mixing a batch in the cup. Does the mixture yield a bluer shade of green?
Is the ratio you used in this recipe equivalent to the ratio in your teacher’s mixture? Explain your reasoning.

Are you ready for more?

Someone has made a shade of green by using 17 ml of blue and 13 ml of yellow. They are sure it cannot be turned into the original shade of green by adding more blue or yellow. Either explain how more can be added to create the original green shade, or explain why this is impossible.

Activity 2: 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.

Lesson Summary

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.

"A discrete diagram that contain red and yellow squares. The top row is labeled "red paint, in ml" and contain 12 red squares that are grouped by 4's. The bottom row is labeled "yellow paint, in ml" and contain 6 yellow squares grouped by 2's. There is a brace that contains 4 red squares and 2 yellow squares labeled "1 batch orange." A second brace contains 8 red squares and 4 yellow squares labeled "2 batches orange." A third brace contains 12 red squares and 6 yellow squares labeled "3 batches orange."

We say that the ratios $4 : 2$ , $8 : 4$ , and $12 : 6$ are equivalent because they describe the same color mixture in different numbers of batches, and they make the same shade of orange.