Lesson 2
Introducing Proportional Relationships with Tables
Let’s solve problems involving proportional relationships using tables.
Problem 1
When Han makes chocolate milk, he mixes 2 cups of milk with 3 tablespoons of chocolate syrup. Here is a table that shows how to make batches of different sizes. Use the information in the table to complete the statements. Some terms are used more than once.
![Table with 2 columns and 4 rows of data.](https://cms-im.s3.amazonaws.com/7xwgzBW1Ao6z7xnXowb7bbEf?response-content-disposition=inline%3B%20filename%3D%227-7.2.B.PP.Image.02.png%22%3B%20filename%2A%3DUTF-8%27%277-7.2.B.PP.Image.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T234228Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ca4b9cdb16f6434d500daca4ba87c0baed1de22b192d0fa7376058dcd8270060)
- The table shows a proportional relationship between ______________ and ______________.
- The scale factor shown is ______________.
- The constant of proportionality for this relationship is______________.
- The units for the constant of proportionality are ______________ per ______________.
Bank of Terms: tablespoons of chocolate syrup, 4, cups of milk, cup of milk, \(\frac32\)
Problem 2
A certain shade of pink is created by adding 3 cups of red paint to 7 cups of white paint.
- How many cups of red paint should be added to 1 cup of white paint?
cups of white paint cups of red paint 1 7 3 - What is the constant of proportionality?
Problem 3
A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for every 30 miles.
-
What is the actual area of the park? Show how you know.
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The map needs to be reproduced at a different scale so that it has an area of 6 square inches and can fit in a brochure. At what scale should the map be reproduced so that it fits on the brochure? Show your reasoning.
Problem 4
Noah drew a scaled copy of Polygon P and labeled it Polygon Q.
![Polygon Q on a grid.](https://cms-im.s3.amazonaws.com/zkdNCwzbKYMjWz4ps74x1c9f?response-content-disposition=inline%3B%20filename%3D%227-7.1.A.PP.Image.33.png%22%3B%20filename%2A%3DUTF-8%27%277-7.1.A.PP.Image.33.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240726%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240726T234228Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=29ec4d1540f7403211262f1bb9987214f94b68b0ab90bf424259cc0a8be05e04)
If the area of Polygon P is 5 square units, what scale factor did Noah apply to Polygon P to create Polygon Q? Explain or show how you know.
Problem 5
Select all the ratios that are equivalent to each other.
\(4:7\)
\(8:15\)
\(16:28\)
\(2:3\)
\(20:35\)