Grade 07 Mathematics - EC: M07.A-R.1.1.4

Continuum of Activities

The list below represents a continuum of activities: resources categorized by Standard/Eligible Content that teachers may use to move students toward proficiency. Using LEA curriculum and available materials and resources, teachers can customize the activity statements/questions for classroom use.

This continuum of activities offers:

Instructional activities designed to be integrated into planned lessons
Questions/activities that grow in complexity
Opportunities for differentiation for each student’s level of performance

Related Academic Standards / Eligible Content

M07.A-R.1.1.4 M07.A-R.1.1.4

Represent proportional relationships by equations. Example: If total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

Activities

Find the total height of a stack of firewood t that is proportional to the number of logs n with a constant height of h.

Find the weight of water w that is proportional to the number of gallons g of water that each weigh p pounds per gallon.

X and Y are proportional with A and B. If A = 6 and B = 7, and X is twice as much as A, what is the value of Y? Show your work

There is a proportional relationship between the cost of your cell phone bill and the amount of text messages that you use. The cost to send 500 text messages is $75.00 Write an equation to show the total cost T of the monthly bill if you send X messages. Show your work.

The length of a shadow made by a tree is proportional to the height of the tree. Use the information in the table below to write an equation to show the length of a trees shadow L that is proportional to its height. Show your work.

Part B – If these height represent trees, find the length of a shadow from a tree that is 58 feet tall. Show your work.

The commission that Henry, a salesman, makes is proportional to the cost of the items that he is selling. He earns $25 for every $250 that he sells. Write an equation that gives the total commission C, that Henry will make is he sells $S of merchandise.

Part B – If Henry sells $2750 in merchandise this month, what would his commission be? Show your work.

Answer Key/Rubric

T = NH

W = GP

The value of Y = 14. Student work might include but is not limited to

I set up a proportion and filled in the values given for a and b. The problem stated that x was twice as much as a. I know that twice as much means to multiply by 2.

6 x 2 = 12

7 x 2 = 14

T = 0.15X Student work might include but is not limited to,

Find the cost per text message by diving the total cost by the amount of text messages
$75.00 ÷ 500 = 0.15
$0.15 per text message

L = 0.75H or Student work might include but is not limited to,

Finding what the proportional relationship is between the tree height and the shadow length by diving the shadow length by the tree height. You can use any set of values in the chart
11.25 ÷ 15 = 0.75 18.75 ÷ 25 = 0.75 30 ÷ 40 = 0.75
Part B – The length of the shadow from a tree that is 58 ft tall would be found by multiply the tree height by 0.75
58 x 0.75 = 43.5 feet

C = 0.10S or C=0.1S Student work might include but is not limited to,

Find his commission rate by dividing the amount of money he earned by the amount of money he sold.
$25 ÷ $250 = 0.10 ≈ 10%
He earns 10% commission on all of his sales.
Part B – Find commission on $2750
C = 0.10 • 2750
C = $275
Henry would earn a commission of $275