الأسبوع 11 · نموذج المساحة والنواتج الجزئية · 3 دروس
1
The area model for multiplying
Discover Mathematics P4: Term 1, Unit 7, Lessons 1–5
GoalMultiply a 2-digit or 3-digit number by a 1-digit number with an area model.
New words
area model · a rectangle cut into boxes; each box shows one small multiplicationproduct · the answer of a multiplicationexpanded form · a number split by place value, such as 248 = 200 + 40 + 8
Explanation
A big multiplication is easier when we cut it into small ones. Draw a rectangle. Its height is the 1-digit factor and its width is the other factor. Split the width by place value. To find 5 × 248, split 248 into 200, 40 and 8. The rectangle now has three boxes. Their areas are 5 × 200 = 1,000, 5 × 40 = 200 and 5 × 8 = 40. Add the areas of the boxes: 1,000 + 200 + 40 = 1,240. So 5 × 248 = 1,240. Always say each small multiplication aloud and use the facts you already know, such as 5 × 2 = 10, so 5 × 200 = 1,000. A quick check: 248 is a little less than 250, and 5 × 250 = 1,250, so 1,240 is sensible.
5 × 248 = 1,000 + 200 + 40 = 1,240
5 ×
200
40
8
Area of the box
1,000
200
40
Worked examples
7 × 36 = 210 + 42 = 252
7 ×
30
6
Area of the box
210
42
Mariam buys 7 notebooks at 36 LE each. Split 36 into 30 and 6. 7 × 30 = 210 and 7 × 6 = 42. The total is 210 + 42 = 252 LE.
4 × 1,250 = 5,000
4 ×
1,000
200
50
Area of the box
4,000
800
200
A baker puts 4 trays in an oven and each tray holds 1,250 g of dough. Split 1,250 into 1,000, 200 and 50. 4 × 1,000 = 4,000, 4 × 200 = 800 and 4 × 50 = 200. Add: 4,000 + 800 + 200 = 5,000 g.
9 × 408 = 3,672
9 ×
400
0
8
Area of the box
3,600
0
72
A zero in the number gives a box with area 0. For 9 × 408, split 408 into 400, 0 and 8. 9 × 400 = 3,600 and 9 × 8 = 72. Answer: 3,600 + 72 = 3,672. We can leave out the empty box, but we must not forget that the 0 keeps the tens place.
Class activity
Draw it big. Cut a sheet of paper into a rectangle. Pick a 1-digit number and a 3-digit number, for example 6 and 235. Draw the boxes for 200, 30 and 5, write the area in each box and add. Check with a calculator.
