Lesson 7
Creating Double Number Line Diagrams
Problem 1
A recipe for cinnamon rolls uses 2 tablespoons of sugar per teaspoon of cinnamon for the filling. Complete the double number line diagram to show the amount of cinnamon and sugar in 3, 4, and 5 batches.
![Double number line. Cinnamon, teaspoons. Sugar, tablespoons.](https://staging-cms-im.s3.amazonaws.com/dfyE7G6414BY9XmKiqe96GjJ?response-content-disposition=inline%3B%20filename%3D%226-6.2.C.PP_Image_4.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.C.PP_Image_4.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T155124Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c2bb6b641ad8a4b872030f7bf0b07dea65a5875b6305aa9cc4ed85b404c192c3)
Solution
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Problem 2
One batch of meatloaf contains 2 pounds of beef and \(\frac{1}{2}\) cup of bread crumbs. Complete the double number line diagram to show the amounts of beef and bread crumbs needed for 1, 2, 3, and 4 batches of meatloaf.
![Double number line. Beef, pounds. Bread crumbs, cups.](https://staging-cms-im.s3.amazonaws.com/CErgcgkn5zzY3xvZWvNJ3Nnh?response-content-disposition=inline%3B%20filename%3D%226-6.2.C.PP_Image_9.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.C.PP_Image_9.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T155124Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=2b2c3338c88a3d802a9248cb25e8fdbe0cedbf6d49fa1aab034d0796ab26874a)
Solution
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Problem 3
A recipe for tropical fruit punch says, “Combine 4 cups of pineapple juice with 5 cups of orange juice.”
- Create a double number showing the amount of each type of juice in 1, 2, 3, 4, and 5 batches of the recipe.
- If 12 cups of pineapple juice are used with 20 cups of orange juice, will the recipe taste the same? Explain your reasoning.
- The recipe also calls for \(\frac13\) cup of lime juice for every 5 cups of orange juice. Add a line to your diagram to represent the amount of lime juice in different batches of tropical fruit punch.
Solution
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Problem 4
One batch of pink paint uses 2 cups of red paint and 7 cups of white paint. Mai made a large amount of pink paint using 14 cups of red paint.
- How many batches of pink paint did she make?
- How many cups of white paint did she use?
Solution
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(From Unit 2, Lesson 4.)Problem 5
- Find three different ratios that are equivalent to the ratio \(3:11\).
- Explain why your ratios are equivalent.
Solution
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(From Unit 2, Lesson 5.)Problem 6
Here is a diagram that represents the pints of red and yellow paint in a mixture.
![A discrete diagram. Top row, pints of red paint, six red squares. Bottom row, pints of yellow paint, 2 yellow squares.](https://staging-cms-im.s3.amazonaws.com/eAoeHmjG4ktxqPBZ8jcpK2Ro?response-content-disposition=inline%3B%20filename%3D%226-6.2.A1.PP.Image.Rev.0707.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.A1.PP.Image.Rev.0707.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T155124Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=20e0d8115e1c6ab3d172d3b7cc0d98b6b8d399519acab97a1d6f6fda1265922c)
Select all statements that accurately describe the diagram.
The ratio of yellow paint to red paint is 2 to 6.
For every 3 pints of red paint, there is 1 pint of yellow paint.
For every pint of yellow paint, there are 3 pints of red paint.
For every pint of yellow paint there are 6 pints of red paint.
The ratio of red paint to yellow paint is \(6:2\).
Solution
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(From Unit 2, Lesson 2.)