Lesson 6
Introducing Double Number Line Diagrams
Let’s use number lines to represent equivalent ratios.
Problem 1
A particular shade of orange paint has 2 cups of yellow paint for every 3 cups of red paint. On the double number line, circle the numbers of cups of yellow and red paint needed for 3 batches of orange paint.
![Double number line, 7 evenly spaced tick marks. Top line, yellow paint, cups. Scale 0 to 12, by 2’s. Bottom line, red paint, cups. Scale 0 to 18, by 3’s.](https://staging-cms-im.s3.amazonaws.com/DCUNoALBzA93fo3xXrTvpp6S?response-content-disposition=inline%3B%20filename%3D%226-6.2.C.PP_Image_2.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.C.PP_Image_2.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=20240703T113238Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=fcbd40b7c38000798a2b1ac30412db33b2bdb5ecad5f2bd1b830e0006dcd73c6)
Problem 2
This double number line diagram shows the amount of flour and eggs needed for 1 batch of cookies.
![Double number line, 5 evenly spaced tick marks.](https://staging-cms-im.s3.amazonaws.com/vUq5nVQmxYnryg8RswePsKVc?response-content-disposition=inline%3B%20filename%3D%226-6.2.C1.PP.Image.Rev.0404.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.C1.PP.Image.Rev.0404.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=20240703T113238Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=18c4a463275e727fa455739d64c0a890c2f4d82fc6bef31390ecbe13b042d30c)
- Complete the diagram to show the amount of flour and eggs needed for 2, 3, and 4 batches of cookies.
- What is the ratio of cups of flour to eggs?
- How much flour and how many eggs are used in 4 batches of cookies?
- How much flour is used with 6 eggs?
- How many eggs are used with 15 cups of flour?
Problem 3
Here is a representation showing the amount of red and blue paint that make 2 batches of purple paint.
- On the double number line, label the tick marks to represent amounts of red and blue paint used to make batches of this shade of purple paint.
![a discrete diagram](https://staging-cms-im.s3.amazonaws.com/bUfrXC8nwX5HDTtCc2q6DDw7?response-content-disposition=inline%3B%20filename%3D%226-6.2.C1.PP.Image.Rev.0202.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.C1.PP.Image.Rev.0202.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=20240703T113238Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=219438f908544f71e0d97fa993240eafd8d34fb20f409051b0c12332d3ad74db)
- How many batches are made with 12 cups of red paint?
- How many batches are made with 6 cups of blue paint?
![Double number line, 5 evenly spaced tick marks. Top line, red paint, cups. Blank except for first tick mark labeled zero. Bottom line, blue paint, cups. Blank except for first tick mark labeled zero.](https://staging-cms-im.s3.amazonaws.com/Q87xs4rAMxHUuZN4cNc2UDND?response-content-disposition=inline%3B%20filename%3D%226-6.2.C1.PP.Image.Rev.0303.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.C1.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=20240703T113238Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ef17f7d8c6a6cf27a0ec7cc8a5d576634690fa1151cecadcbee68b276fd0f8ed)
Problem 4
Diego estimates that there will need to be 3 pizzas for every 7 kids at his party. Select all the statements that express this ratio.
The ratio of kids to pizzas is \(7:3\).
The ratio of pizzas to kids is 3 to 7.
The ratio of kids to pizzas is \(3:7\).
The ratio of pizzas to kids is 7 to 3.
For every 7 kids there need to be 3 pizzas.
Problem 5
- Draw a parallelogram that is not a rectangle that has an area of 24 square units. Explain or show how you know the area is 24 square units.
- Draw a triangle that has an area of 24 square units. Explain or show how you know the area is 24 square units.