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Illustrative Math
Grade 7
Let’s solve problems involving proportional relationships using tables.
Illustrative Math Unit 7.2, Lesson 2 (printable worksheets)
The following diagram shows how to use a table to reason about two quantities that are in a proportional relationship and understand the terms proportional relationship and constant of proportionality.
Here is a table that shows how many rolls of paper towels a store receives when they order different numbers of cases.
What do you notice about the table? What do you wonder?
A bakery uses 8 tablespoons of honey for every 10 cups of flour to make bread dough. Some days they bake bigger batches and some days they bake smaller batches, but they always use the same ratio of honey to flour. Complete the table as you answer the questions. Be prepared to explain your reasoning.
4 quarters are equal in value to 10 dimes.
Pennies made before 1982 are 95% copper and weigh about 3.11 grams each. (Pennies made after that date are primarily made of zinc). Some people claim that the value of the copper in one of these pennies is greater than the face value of the penny. Find out how much copper is worth right now, and decide if this claim is true.
If we take the copper price to be $3.5170 per pound.
95% · 3.11 g = 2.9545 g = 0.0065136 pounds
The copper in the penny is now worth $3.5170 · 0.0065136 = $0.022908 which is more than than the face value of $0.01
constant of proportionality
In a proportional relationship, the values for one quantity are each multiplied by the same number to get the values for the other quantity. This number is called the constant of proportionality.
In this example, the constant of proportionality is 3, because 2 · 3 = 6, 3 · 3 = 9, and 5 · 3 = 15. This means that there are 3 apples for every 1 orange in the fruit salad.
proportional relationship
In a proportional relationship, the values for one quantity are each multiplied by the same number to get the values for the other quantity.
For example, in this table every value of p is equal to 4 times the value of s on the same row.
We can write this relationship as p = 4s. This equation shows that p is proportional to s.
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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