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Cogito

Grade 6 Math · Chapter 1 · Lesson 3

Practice Worksheet

Why You Multiply and Not Add

The most common mistake in all of middle school.

10 problems · about 18 minutes · 6.RP.A.1, 6.RP.A.3

NameDate

Figure — use these to answer the problems

Compare multiplying both with adding the same amount to both.
A ratio table for 4 to 6
FirstSecond
46
812
FirstSecond0046812
Multiplied: 8 to 12Same comparison.
Added 4 to each: 8 to 10A different comparison.
First quantity4
Second quantity6
Scale it up by2
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Equivalent Ratios”

    4 : 5. With 16 of the first, how many of the second?

    Answer

  2. From “What a Ratio Says”

    6 pens and 9 pencils. Pens to total: what is the second number?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. 6 : 9 scaled so the first is 12. What is the second?

    Answer

  2. How does a ratio compare two numbers?

    • By how many times bigger one is.
    • By the difference between them.

  3. 2 : 5 scaled so the first is 6. What is the second?

    Answer

  4. 3 : 4 scaled so the first is 12. What is the second?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. 5 : 8 scaled so the first is 10. What is the second?

    Answer

  2. Is 3 : 5 the same comparison as 6 : 8?

    • No. 6 : 10 would be.
    • Yes.

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

2 problems

  1. The Right Answer

    4 : 6 scaled so the first is 6. What is the second?

    Answer

  2. The Squash

    1 : 4 squash to water. With 3 squash, how much water?

    Answerwater