Lesson 5
Creating Double Number Line Diagrams
Let's draw double number line diagrams like a pro.
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=20240722T141617Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=27dd868b3c3a051a1cef35e2f5b82acc618abb57080b349634cd93c4d4d6fb7d)
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=20240722T141617Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b8d725b9b18ef75d4be3ab0a588701d8fc54a64b0406dbebd9629af11d5934e0)
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.
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?
Problem 5
- Find three different ratios that are equivalent to the ratio \(3:11\).
- Explain why your ratios are equivalent.
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=20240722T141617Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ad78f77a76500aca1a7e86584d190c00d65ea863a8aeb2462fb5403431171f71)
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 \(6:2\).