A focused Grade 3 learning session for Division as an Unknown-Factor Problem using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can use a related multiplication fact to solve a division problem.
Division as an Unknown-Factor Problem means choosing a model, naming what each number means, and explaining the strategy.
Question: Complete the fact family for 5, 9, and 45: What are the missing numbers?
| Multiplication | Division |
|---|---|
| \(5\times9=45\) | \(45\div5=\square\) |
| \(9\times5=45\) | \(45\div9=\square\) |
Why it works: In a fact family, \(45\div5=9\) and \(45\div9=5\). Division reverses multiplication.
Answer: 9 and 5
Question: Look at the fact-family triangle below. If \(4\times6=24\), what is \(24\div4\)?
Answer: 6
Question: Which division equation matches this bar model showing 30 split into 5 equal parts?
Answer: \(30\div5=6\)
Question: Noah has 16 pencils. He puts them into 4 boxes equally. Which division equation shows this?
Why it works: Dividing 16 pencils into 4 equal boxes means \(16\div4=\square\). Since \(4\times4=16\), each box has 4 pencils.
Answer: \(16\div4=4\)
Division as an Unknown-Factor Problem becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
Which multiplication fact helps you solve \(32\div8\)?
Answer 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.
Ben has 24 crackers to share equally among 6 friends. How many crackers does each friend get?
Answer 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.
Complete the fact family: \(\)5\times7=35 \quad 7\times5=35 \quad 35\div5=\square \quad 35\div7=\square\(\)
Answer 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.
What is the missing number? \(\square\times8=48\)
Answer 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 \(6\times8=48\).
Lily has 20 stickers. She puts them in 4 equal groups. How many stickers are in each group?
Answer 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.
Use the multiplication fact \(6\times9=54\) to write a division equation.
Answer 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.
Which pair of divisions belongs to the same fact family as \(3\times8=24\)?
Answer A: \(24\div3=8\) and \(24\div8=3\)
The fact family for \(3\times8=24\) includes the related divisions \(24\div3=8\) and \(24\div8=3\).
What is \(28\div4\)?
Answer B: 7
\(28\div4=\square\) means \(\square\times4=28\). Since \(7\times4=28\), the answer is 7. Option A (\(6\times4=24\)) is off-by-one. Option D confuses the divisor with the quotient.
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?
Answer D: 6 points
\(36\div6=\square\) means \(\square\times6=36\). Since \(6\times6=36\), Sam earned 6 points per game.
Complete the fact family for 5, 9, and 45: What are the missing numbers?
Answer D: 9 and 5
In a fact family, \(45\div5=9\) and \(45\div9=5\). Division reverses multiplication.
Which multiplication fact helps solve \(42\div7\)?
Answer A: \(6\times7=42\)
To solve \(42\div7=\square\) using the unknown-factor strategy, we ask: \(\square\times7=42\). Since \(6\times7=42\), the missing factor is 6. Options B, C, D produce different products, not 42.
