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Cogito

Grade 3 Math · Chapter 1 · Lesson 4

Answer Key

Division as an Unknown Factor

Every division is a multiplication with a gap in it.

10 problems · about 13 minutes · 3.OA.B.6, 3.OA.A.4

What this lesson teaches

The child solves a division by finding the unknown factor in a related multiplication.

  • A division asks for a missing factor.
  • 56 ÷ 8 means: what times 8 makes 56?
  • Your times tables are your division facts too.

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. Review — Division as Sharing: 24 ÷ 4 = ?

    Answer 6

    Why 24 ÷ 4 = 6.

  2. Review — Arrays and the Commutative Property: You know 9 × 2 = 18. What is 2 × 9?

    Answer 18

    Why The commutative property gives it free.

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. 45 ÷ 5 = ?

    Answer 9

    Why 9 × 5 = 45.

  2. What question does 24 ÷ 6 really ask?

    Answer What times 6 makes 24?

    Why A division is a multiplication with a factor missing.

  3. ? × 5 = 20. What is the missing factor?

    Answer 4

    Why Count in fives to 20.

  4. 18 ÷ 2 = ?

    Answer 9

    Why What times 2 makes 18?

Build It Up

The same ideas with more to keep track of.

2 problems

  1. 40 ÷ 10 = ?

    Answer 4

    Why What times 10 makes 40?

  2. ? × 3 = 15. What is the missing factor?

    Answer 5

    Why Count in threes.

Stretch Yourself

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

2 problems

  1. The Seating Plan: 30 chairs are put into rows of 5. How many rows are there?

    Answer 6 rows

    Why 6 × 5 = 30, so 30 ÷ 5 = 6.

  2. Checking Work: Ana says 28 ÷ 4 = 7. Check it: what is 7 × 4?

    Answer 28

    Why 7 × 4 = 28, so her answer was right.