Testinar Grade 3 math

Division as an Unknown-Factor Problem

Students will connect division to multiplication by treating division as an unknown-factor problem.

CH01-06 Operations and Algebraic Thinking
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. Which multiplication fact helps you solve \(32\div8\)?

    1. \(4\times8=32\)
    2. \(5\times8=40\)
    3. \(8\times8=64\)
    4. \(3\times8=24\)

  2. Ben has 24 crackers to share equally among 6 friends. How many crackers does each friend get?

    1. 4
    2. 6
    3. 3
    4. 5

  3. Complete the fact family: \(\)5\times7=35 \quad 7\times5=35 \quad 35\div5=\square \quad 35\div7=\square\(\)

    1. 7 and 5
    2. 5 and 7
    3. 35 and 35
    4. 10 and 10

  4. What is the missing number? \(\square\times8=48\)

    1. 5
    2. 8
    3. 7
    4. 6

  5. Lily has 20 stickers. She puts them in 4 equal groups. How many stickers are in each group?

    1. 5
    2. 4
    3. 6
    4. 24

  6. Use the multiplication fact \(6\times9=54\) to write a division equation.

    1. \(54\div6=9\)
    2. \(54\div9=6\)
    3. \(9\div6=1\)
    4. \(54+6=60\)

  7. Which pair of divisions belongs to the same fact family as \(3\times8=24\)?

    1. \(24\div3=8\) and \(24\div8=3\)
    2. \(24\div4=6\) and \(24\div6=4\)
    3. \(24-3=21\) and \(24-8=16\)
    4. \(24+3=27\) and \(24+8=32\)

  8. Sam earned 36 points in 6 games. If he earned the same number of points in each game, how many points did he earn per game?

    1. 5 points
    2. 8 points
    3. 7 points
    4. 6 points
Teacher and parent reference

Answer key and explanations

  1. A. \(4\times8=32\)

    Division is an unknown-factor problem. \(32\div8=\square\) is the same as finding \(\square\times8=32\), which gives \(\square=4\). Distractors B, C, D are off-by-one or incorrect products.

  2. A. 4

    \(24\div6=\square\) means \(\square\times6=24\). Since \(4\times6=24\), each friend gets 4 crackers. We use a multiplication fact to solve the division problem.

  3. A. 7 and 5

    In a fact family, if \(5\times7=35\), then \(35\div5=7\) (because \(7\times5=35\)) and \(35\div7=5\) (because \(5\times7=35\)). In division, we find the missing factor from the multiplication fact. Options C and D incorrectly repeat the same number.

  4. D. 6

    Finding the missing factor: \(6\times8=48\). This is the same as asking \(48\div8=\square\). We think: what times 8 makes 48? The answer is 6 because \(6\times8=48\).

  5. A. 5

    \(20\div4=\square\) means \(\square\times4=20\). Since \(5\times4=20\), there are 5 stickers in each group. Option B (confuses divisor with quotient); Option D adds instead of divides.

  6. A. \(54\div6=9\)

    From \(6\times9=54\), one related division equation is \(54\div6=9\) (the answer is the factor 9). Option B reverses correctly but is also valid; A is the expected answer. Options C and D use wrong operations.

  7. A. \(24\div3=8\) and \(24\div8=3\)

    The fact family for \(3\times8=24\) includes the related divisions \(24\div3=8\) and \(24\div8=3\).

  8. D. 6 points

    \(36\div6=\square\) means \(\square\times6=36\). Since \(6\times6=36\), Sam earned 6 points per game.

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