Multiplying with powers of ten, area models and partial products
Week 6 · Multiplying with powers of ten, area models and partial products · 3 lessons
3
Partial products, step by step
Discover Mathematics P5: Term 1, Unit 3, Lessons 1–4
GoalMultiply by writing partial products, one for every digit of the second factor.
New words
partial product · one of the smaller products that add up to the final productplace value · what a digit is worth because of its place
Explanation
Partial products are the area-model boxes written as a list. To multiply 346 × 27, multiply 346 by the 7 ones first, and then by the 2 tens, which is 20. 346 × 7 = 2,422 and 346 × 20 = 6,920. Then add the partial products: 2,422 + 6,920 = 9,342. You can go deeper and multiply every digit of 346 separately: 6 × 7 = 42, 40 × 7 = 280, 300 × 7 = 2,100, and then 6 × 20 = 120, 40 × 20 = 800, 300 × 20 = 6,000. The six partial products add up to 9,342 as well. Always give each digit its true value: the 2 in 27 is worth 20, not 2. Estimate to check: 350 × 30 is about 10,500, close to 9,342.
Multiply 346 × 27. 346 × 7 = 2,422 and 346 × 20 = 6,920. The sum is 2,422 + 6,920 = 9,342. Estimate: 350 × 30 = 10,500. The answer is a little less, which makes sense because both numbers were rounded up.
A school has 28 classes with 35 pupils in each. The partial products are 8 × 5 = 40, 20 × 5 = 100, 8 × 30 = 240 and 20 × 30 = 600. Together 40 + 100 + 240 + 600 = 980 pupils.
Class activity
Partial product cards. Choose two numbers, one with three digits and one with two digits (for example 213 × 14). Write each partial product on its own card. Shuffle the cards, then put them back in order and add them. Check with a calculator or with the area model.
