Week 13 · Division strategies and story problems · 3 lessons
2
Dividing with boxes and partial quotients
Discover Mathematics P4: Term 1, Unit 7, Lessons 11–16
GoalDivide with area boxes and partial quotients.
New words
partial quotient · one friendly part of the answer, found step by stepmultiple · a number in the times table, such as 4, 8, 12, 16 for 4area model · a rectangle whose area is the dividend and whose side is the divisor
Explanation
Division is the opposite of multiplication, so we can use the area model backwards. For 156 ÷ 4, the area is 156 and one side is 4. We look for the other side, which is the quotient. Take out friendly parts: 4 × 30 = 120, so one box has area 120 and 156 − 120 = 36 is left. Then 4 × 9 = 36, so another box has area 36 and nothing is left. The quotient is the sum of the sides we found: 30 + 9 = 39. These sides are called partial quotients. We can choose any friendly multiples, such as 10 or 100 times the divisor, and the answer is the same. When a little is left at the end, it is the remainder: in 250 ÷ 4 we take 4 × 60 = 240, then 4 × 2 = 8, and 2 is left, so 250 ÷ 4 = 62 R 2.
Step
Take out
Left
1
4 × 30 = 120
156 − 120 = 36
2
4 × 9 = 36
36 − 36 = 0
Answer
30 + 9 = 39
0
Worked examples
Take out
Left
6 × 60 = 360
372 − 360 = 12
6 × 2 = 12
12 − 12 = 0
Quotient
60 + 2 = 62
Find 372 ÷ 6. 6 × 60 = 360, and 372 − 360 = 12. 6 × 2 = 12, so nothing is left. The quotient is 60 + 2 = 62. Check: 62 × 6 = 372.
Find 250 ÷ 4. 4 × 60 = 240 and 250 − 240 = 10. 4 × 2 = 8 and 10 − 8 = 2. The quotient is 62 and the remainder is 2. Check: 4 × 62 + 2 = 250.
Class activity
Choose your own steps. Divide 252 by 6 in two different ways: first take 6 × 40 and then the rest; then take 6 × 20 twice and then the rest. Do both ways give 42?
