Lesson 13
Tables and Double Number Line Diagrams
Let’s contrast double number lines and tables.
Problem 1
The double number line shows how much water and how much lemonade powder to mix to make different amounts of lemonade.
![A double number line with 4 evenly spaced tick marks. For "water, in cups" the numbers 0, 2, 4, and 6 are indicated. For "lemonade powder, in scoops" the numbers 0, 1.5, 3, and 4.5 are indicated.](https://staging-cms-im.s3.amazonaws.com/TSYLSM2GSutkmeE7eTSymBvu?response-content-disposition=inline%3B%20filename%3D%226-6.2.D.PP_Image_0.6.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.D.PP_Image_0.6.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=20240703T112251Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0b32182a34645d72693723b600d410d52d542f99f11215cb11fa114735d848f7)
Make a table that represents the same situation.
Problem 2
A bread recipe uses 3 tablespoons of olive oil for every 2 cloves of crushed garlic.
- Complete the table to show different-sized batches of bread that taste the same as the recipe.
- Draw a double number line that represents the same situation.
- Which representation do you think works better in this situation? Explain why.
olive oil (tablespoons) | crushed garlic (cloves) |
---|---|
3 | 2 |
1 | |
2 | |
5 | |
10 |
Problem 3
Clare travels at a constant speed, as shown on the double number line.
![Double number line. Distance, miles. Elapsed time, hours.](https://staging-cms-im.s3.amazonaws.com/TdCNorzajQNVJNoiFAJCaKYL?response-content-disposition=inline%3B%20filename%3D%226-6.2.D3.PP.Image.Rev.0303.png%22%3B%20filename%2A%3DUTF-8%27%276-6.2.D3.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=20240703T112255Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=80c8aa8c56cab9de628c9fb71d672f44ce8c231f048cf1961694ff70623a90c2)
At this rate, how far does she travel in each of these intervals of time? Explain or show your reasoning. If you get stuck, consider using a table.
- 1 hour
- 3 hours
- 6.5 hours
Problem 4
Lin and Diego travel in cars on the highway at constant speeds. In each case, decide who was traveling faster and explain how you know.
- During the first half hour, Lin travels 23 miles while Diego travels 25 miles.
- After stopping for lunch, they travel at different speeds. To travel the next 60 miles, it takes Lin 65 minutes and it takes Diego 70 minutes.
Problem 5
A sports drink recipe calls for \(\frac{5}{3}\) tablespoons of powdered drink mix for every 12 ounces of water. How many batches can you make with 5 tablespoons of drink mix and 36 ounces of water? Explain your reasoning.
Problem 6
In this cube, each small square has side length 1 unit.
- What is the surface area of this cube?
- What is the volume of this cube?
![A cube with 3 faces shown. Each face has a dimension of 3 by 3 units.](https://staging-cms-im.s3.amazonaws.com/BqNyXrxYGtDr6DcdspRrMG4G?response-content-disposition=inline%3B%20filename%3D%226-6.1.F.PP_Image_4.1a.png%22%3B%20filename%2A%3DUTF-8%27%276-6.1.F.PP_Image_4.1a.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=20240703T112255Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=14e354f770159575b1495eeb63c550273ca530a97c6d4e88fb618e772fab17a3)