Lesson 4
Color Mixtures
Problem 1
Here is a diagram showing a mixture of red paint and green paint needed for 1 batch of a particular shade of brown.
![A discrete diagram for two quantities labeled "red paint, in cups" and "green paint, in cups". The data are as follows: red paint, 2 squares. green paint, 3 squares.](https://staging-cms-im.s3.amazonaws.com/QxE7exhmVVCj6NpsT3DWha5c?response-content-disposition=inline%3B%20filename%3D%226.2.B.PP_Image_6.png%22%3B%20filename%2A%3DUTF-8%27%276.2.B.PP_Image_6.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T072354Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=747810cef759002e2e675469bdda2898557317caa528b746b322590b8e5c5b51)
Add to the diagram so that it shows 3 batches of the same shade of brown paint.
Solution
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Problem 2
Diego makes green paint by mixing 10 tablespoons of yellow paint and 2 tablespoons of blue paint. Which of these mixtures produce the same shade of green paint as Diego’s mixture? Select all that apply.
For every 5 tablespoons of blue paint, mix in 1 tablespoon of yellow paint.
Mix tablespoons of blue paint and yellow paint in the ratio \(1:5\).
Mix tablespoons of yellow paint and blue paint in the ratio 15 to 3.
Mix 11 tablespoons of yellow paint and 3 tablespoons of blue paint.
For every tablespoon of blue paint, mix in 5 tablespoons of yellow paint.
Solution
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Problem 3
To make 1 batch of sky blue paint, Clare mixes 2 cups of blue paint with 1 gallon of white paint.
- Explain how Clare can make 2 batches of sky blue paint.
- Explain how to make a mixture that is a darker shade of blue than the sky blue.
- Explain how to make a mixture that is a lighter shade of blue than the sky blue.
Solution
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Problem 4
A smoothie recipe calls for 3 cups of milk, 2 frozen bananas and 1 tablespoon of chocolate syrup.
- Create a diagram to represent the quantities of each ingredient in the recipe.
- Write 3 different sentences that use a ratio to describe the recipe.
Solution
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(From Unit 2, Lesson 2.)Problem 5
Write the missing number under each tick mark on the number line.
![Number line. 7 tick marks. Labels starting at first tick: 0, blank, 6, blank, blank, 15, blank.](https://staging-cms-im.s3.amazonaws.com/A5ntgV7C5WvBtTYopFpsSD1T?response-content-disposition=inline%3B%20filename%3D%226-6.2.A1.PP.Image.Rev.0303.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.A1.PP.Image.Rev.0303.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T072354Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f168b08c8113ac6752057c4d83eb97a5a04b17e2d253d59b967da8166c64872a)
Solution
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(From Unit 2, Lesson 1.)Problem 6
Find the area of the parallelogram. Show your reasoning.
![A parallelogram in a grid. The parallelogram has two vertical sides that are 3 units tall and two sides that rise 4 units over 7 units across.](https://staging-cms-im.s3.amazonaws.com/AdqgGFmNCKwJzYZmsaf2MVed?response-content-disposition=inline%3B%20filename%3D%226-6.1.B.PP.New.Image.06.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.B.PP.New.Image.06.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T072354Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6ce73f920b738edb20bf9c0b9830203508ede22201775a019ae0ea243427111d)
Solution
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(From Unit 1, Lesson 4.)Problem 7
Complete each equation with a number that makes it true.
- \(11 \boldcdot \frac14= \text{_______}\)
- \(7 \boldcdot \frac14= \text{_______}\)
- \(13 \boldcdot \frac{1}{27}= \text{_______}\)
- \(13 \boldcdot \frac{1}{99}= \text{_______}\)
-
\(x \boldcdot \frac{1}{y}= \text{_______}\)
(As long as \(y\) does not equal 0.)
Solution
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(From Unit 2, Lesson 1.)