**Warmup**

Which one doesn’t belong? Explain your reasoning.

**Activity #1**

Model a Relationship.

- To start this activity, move both sliders to the left so you have zero coefficient, zero constant term, and zero values at the top.
- Now, move slider
**a**1 level up. Note the pattern of the numbers. - Move until you have 5 while writing down the relationships in the numbers.
- Now, move slider
**b**up by one level and repeat all the steps above. - Continue until
**b**goes up to 6.

(1.) What relationship do you see in the models when **a** increases?

(2.) What relation do you see in the models when **b** increases?

(3.) How would you describe **a** in the equation?

(4.) How would you describe **b** in the equation?

**Activity #2**

Investigate the Relationship Between the Area of the Base and the Height of a Box.

In this activity, you are going to explore the relationship between the area of a prism and the height. Then use the data you produce to draw a graph. Read the story below and then answer the questions that follow.

A cereal manufacturer needs to design a cereal box that has a volume of 225 cubic inches and a height that is no more than 15 inches. The designers know that the volume of a rectangular prism can be calculated by multiplying the area of its base and its height.

- Complete the table with pairs of values that will make the volume 225 inches cubed.

(1.) Describe how you found the missing values for the table.

(2.) Write an equation that shows how the area of the base, *A, * is affected by changes in the height, *h,* for different rectangular prisms with volume 225 in^{3}.

- Plot the ordered pairs from the table on the graph to show the relationship between the area of the base and the height for different boxes box with volume 225 inches cubed.

**Activity #3**

`Application of Relationships Between Quantities to Solve Problems.`

In this exercise, you are going to apply the relationship between quantities to solve a real world problem.

- Read the story below and answer the questions that follow.

A researcher who is studying mosquito populations collects the following data:

The researcher said that, for these five days, the number of mosquitoes, , can be found with the equation = , where *d* is the day in the study.

Explain why this equation matches the data.

- Use the ordered pairs in the table to graph the relationship between number of mosquitoes and day in the study for these five days.

(1.) Describe the graph. Compare how the data, equation, and graph illustrate the relationship between the day in the study and the number of mosquitoes.

(2.) If the pattern continues, how many mosquitoes will there be on day 6?

**Challenge #1**

Andre set up a lemonade stand last weekend. It cost him $0.15 to make each cup of lemonade, and he sold each cup for $0.35.

(1.) If Andre collects $9.80, how many cups did he sell?

(2.) How much money did it cost Andre to make this amount of lemonade?

(3.) How much money did Andre make in profit?

**Challenge #2**

Elena is designing a logo in the shape of a parallelogram. She wants the logo to have an area of 12 square inches. She draws bases of different lengths and tries to compute the height for each.

(1.) Write an equation Elena can use to find the height, for each value of the base,.

(2.) Use your equation to find the height of a parallelogram with base **1.5 ** inches.

**Challenge #3**

**Quiz Time**

https://www.ixl.com/math/grade-6/identify-proportional-relationships-by-graphing

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