☰ Year plan · Mathematics

Area models and partial products

Week 11 · Area model and partial products · 3 lessons
2

Breaking apart with the distributive property

Discover Mathematics P4: Term 1, Unit 7, Lessons 1–5
GoalUse the distributive property to break a multiplication into easier parts.
New words
distributive property · multiplying a sum is the same as multiplying each part and addingparentheses · the curved marks ( ) that show what to do firstbreak apart · split a number into two or more easier numbers
Explanation

The area model works because of the distributive property. It says that a × (b + c) = a × b + a × c. We multiply the number outside the parentheses by each part inside, then add. For 6 × 14, write 14 as 10 + 4. Then 6 × 14 = 6 × (10 + 4) = 6 × 10 + 6 × 4 = 60 + 24 = 84. We may break apart either factor and choose parts that make friendly facts, such as tens and hundreds. For 8 × 125 we can use 100 + 25: 8 × 100 = 800 and 8 × 25 = 200, so the answer is 1,000. Be careful: every part must be multiplied. Writing 6 × 10 + 4 forgets to multiply the 4.

Break apartMultiply each partAdd
6 × (10 + 4)6 × 10 = 60, 6 × 4 = 2460 + 24 = 84
7 × (50 + 2)7 × 50 = 350, 7 × 2 = 14350 + 14 = 364
Worked examples
6 × 14 = 84
6 ×104
Area of the box6024
Find 6 × 14. Break 14 into 10 + 4. 6 × 10 = 60 and 6 × 4 = 24. The sum is 84. The area model shows the same two boxes.
Find 7 × 52. Break 52 into 50 + 2. 7 × 50 = 350 and 7 × 2 = 14. 350 + 14 = 364. Write it in one line: 7 × 52 = 7 × (50 + 2) = 350 + 14 = 364.
8 × 125 = 1,000
8 ×10025
Area of the box800200
Find 8 × 125 in your head. Break 125 into 100 + 25. 8 × 100 = 800 and 8 × 25 = 200 (eight quarters of a hundred are two hundred). 800 + 200 = 1,000.
Class activity

Two ways to break. Take the product 7 × 24. First break 24 into 20 + 4, then break 7 into 5 + 2 and use 24 for both parts. Do both ways with a grown-up. Do you get the same answer? (It must be 168.)

Practice
1
Find 5 × (20 + 3).
2
Fill the blank: 4 × 36 = 4 × 30 + 4 × __ = 120 + __ = __.
3
Find 9 × 47 by breaking 47 into 40 + 7.
4
A bakery bakes 6 trays with 45 rolls on each tray. How many rolls is that? Use the distributive property.
5
Nour writes 3 × (10 + 4) = 30 + 4 = 34. What is wrong? Give the right answer.