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Illustrative Math
Grade 8
Let’s compare proportional relationships
Illustrative Math Unit 8.3, Lesson 4 (printable worksheets)
The following diagram shows how to compare proportional relationships represented in different ways.
The equation y = 4.2x could represent a variety of different situations.
Han and Clare are still stuffing envelopes. Han can stuff 20 envelopes in a minute, and Clare can stuff 10 envelopes in a minute. They start working together on a pile of 1,000 envelopes.
Together, they finish 30 envelopes in 1 minute. To finish 1000 envelopes, they will take 1000 ÷ 30 = 33 minutes 20 seconds
In 33 minutes 20 seconds, Han would have stuffed about 667 envelopes and Clare would have stuffed about 333 envelopes.
If they are not paid for partial amounts then Han will earn $30 and Clare would not be paid.
It might be better for Han to stuff 600 envelopes and then he will be paid $30 and Clare to stuff 400 envelopes and she would be paid $40.
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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