Discover Mathematics P5: Term 1, Unit 4, Lessons 1–7
GoalSay what division means in a story and divide with an area model and partial quotients.
New words
dividend · the number that is divideddivisor · the number we divide byquotient · the answer to a divisionpartial quotient · one part of the quotient, found by multiplying the divisor by an easy number
Explanation
Division finds how many equal groups there are, or how many are in each group. If 156 pencils are shared equally into 12 boxes, 156 ÷ 12 = 13 tells how many pencils are in each box. 156 is the dividend, 12 is the divisor and 13 is the quotient. Division undoes multiplication: 12 × 13 = 156. An area model shows it: the area is the dividend, one side is the divisor, and we look for the other side. For 252 ÷ 12 take away easy multiples of 12. 12 × 20 = 240 fits, leaving 252 − 240 = 12. Then 12 × 1 = 12. The partial quotients 20 and 1 add up to the quotient 21. In partial quotients we keep taking away easy multiples of the divisor until nothing is left, then add the multipliers.
Area 252 = 240 + 12
×
20
1
12
240
12
Worked examples
156 pencils are put equally into 12 boxes. 156 ÷ 12 = 13 because 12 × 13 = 156. Each box holds 13 pencils. If instead we put 12 pencils in each box, we need 156 ÷ 12 = 13 boxes. Division answers both “how many in each?” and “how many groups?”
×
20
3
15
300
45
Find 345 ÷ 15 with an area model. The area is 345 and one side is 15. 15 × 20 = 300, so 345 − 300 = 45 is left. 15 × 3 = 45. The other side is 20 + 3 = 23. So 345 ÷ 15 = 23. Check: 15 × 23 = 345.
Step
Take away
Left
23 × 30 = 690
874 − 690
184
23 × 8 = 184
184 − 184
0
Find 874 ÷ 23 with partial quotients. 23 × 30 = 690, so 874 − 690 = 184 is left. 23 × 8 = 184, so nothing is left. The partial quotients are 30 and 8, and 30 + 8 = 38. So 874 ÷ 23 = 38.
Class activity
Share and group. Use 48 small objects (beads, buttons or dry beans). Share them equally into 6 cups and write the division. Then make groups of 6 and count how many groups there are. Now try 96 objects and groups of 12. Write both questions each time: how many in each group, and how many groups?
Practice
1
In 63 ÷ 9 = 7, name the dividend, the divisor and the quotient.
Dividend 63, divisor 9, quotient 7.
2
Find 180 ÷ 15 with partial quotients.
15 × 10 = 150, left 30. 15 × 2 = 30. 10 + 2 = 12.
3
Find 408 ÷ 17.
17 × 20 = 340, left 68. 17 × 4 = 68. 20 + 4 = 24.
4
360 LE is shared equally among 24 workers. How much does each worker get?
360 ÷ 24 = 15, because 24 × 15 = 360. Each worker gets 15 LE.
5
Split the quotient of 252 ÷ 12 as 10 + 11 and write the two area-model boxes. Do they add up to 252?
12 × 10 = 120 and 12 × 11 = 132. 120 + 132 = 252, and 10 + 11 = 21, so 252 ÷ 12 = 21. Any split of the quotient works.
