Multiplying decimals to thousandths and the metric system
Week 10 · Multiplying decimals to thousandths and the metric system · 3 lessons
1
Area models for decimal products
Discover Mathematics P5: Term 1, Unit 5, Lessons 5–10
GoalMultiply two decimals with an area model by splitting each into its whole part and its decimal part.
New words
area model · a rectangle cut into boxes, one box for each partial productpartial product · one of the smaller products that add up to the full productsquare metre · the area of a square with sides of 1 metre, written m²
Explanation
An area model works with decimals just as it does with whole numbers. Split each factor into its parts: 2.4 = 2 + 0.4 and 1.3 = 1 + 0.3. The four boxes are 2 × 1 = 2, 0.4 × 1 = 0.4, 2 × 0.3 = 0.6 and 0.4 × 0.3 = 0.12 (remember that 4 × 3 = 12 and two decimal places). Add the four partial products: 2 + 0.4 + 0.6 + 0.12 = 3.12. So 2.4 × 1.3 = 3.12. The area of a rectangle with sides of 2.4 m and 1.3 m is 3.12 square metres. Estimate to check: 2 × 1 = 2 is too small and 3 × 2 = 6 is too big, so about 3 makes sense.
×
2
0.4
1
2
0.4
0.3
0.6
0.12
Worked examples
Work out 2.4 × 1.3 with boxes: 2, 0.4, 0.6 and 0.12. The sum is 2 + 0.4 + 0.6 + 0.12 = 3.12. A rectangular garden bed 2.4 m long and 1.3 m wide has an area of 3.12 m².
×
3
0.6
2
6
1.2
0.5
1.5
0.3
Work out 3.6 × 2.5. 3 × 2 = 6, 0.6 × 2 = 1.2, 3 × 0.5 = 1.5 and 0.6 × 0.5 = 0.3. The sum is 6 + 1.2 + 1.5 + 0.3 = 9. So 3.6 × 2.5 = 9.
Work out 1.7 × 4.2. 1 × 4 = 4, 0.7 × 4 = 2.8, 1 × 0.2 = 0.2 and 0.7 × 0.2 = 0.14. The sum is 4 + 2.8 + 0.2 + 0.14 = 7.14. Estimate: 2 × 4 = 8, and 7.14 is a bit smaller, which fits because 1.7 is less than 2.
Class activity
Cover the floor. Draw a rectangle on squared paper for a rug 1.5 m by 1.4 m, using 1 square for 0.1 m. Split it into four boxes (1 × 1, 0.4 × 1, 1 × 0.5, 0.4 × 0.5) and add their areas. Check by counting all the small squares: each one is 0.01 m².
