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Two-digit multiplication and remainders

الأسبوع 12 · الضرب في عددين من رقمين والباقي · 3 دروس
1

Two-digit times two-digit with boxes

Discover Mathematics P4: Term 1, Unit 7, Lessons 6–10
GoalMultiply two 2-digit numbers with an area model.
New words
multiple of 10 · a number such as 20, 30 or 40 that has 0 in the ones placefactor · a number we multiplyestimate · to find an answer that is close, using friendly numbers
Explanation

First we multiply by a multiple of 10. For 36 × 30, split 36 into 30 and 6. Then 30 × 30 = 900 and 6 × 30 = 180, and 900 + 180 = 1,080. Now two 2-digit factors. To find 23 × 14, split both numbers by place value: 23 = 20 + 3 and 14 = 10 + 4. The rectangle now has four boxes: 20 × 10 = 200, 20 × 4 = 80, 3 × 10 = 30 and 3 × 4 = 12. Add all four boxes: 200 + 80 + 30 + 12 = 322. Do not stop after two boxes: every part of the first factor must meet every part of the second one. Estimate first: 23 × 14 is about 20 × 15 = 300, so 322 is sensible.

23 × 14 = 200 + 80 + 30 + 12 = 322
×104
2020080
33012
Worked examples
36 × 30 = 1,080
×306
30900180
Find 36 × 30. 30 × 30 = 900 and 6 × 30 = 180. 900 + 180 = 1,080. A class trip for 36 children at 30 LE each costs 1,080 LE.
46 × 35 = 1,610
×305
401,200200
618030
Find 46 × 35 with four boxes. 40 × 30 = 1,200; 40 × 5 = 200; 6 × 30 = 180; 6 × 5 = 30. Add: 1,200 + 200 + 180 + 30 = 1,610.
Estimate to check 46 × 35. Round 46 up to 50: 50 × 35 = 1,750. Round 35 down to 30 as well: 50 × 30 = 1,500. The exact answer 1,610 is between 1,500 and 1,750, so it is sensible.
Class activity

Box race. Roll or pick two 2-digit numbers. The child draws the four boxes and the grown-up uses the short way on paper. Who finishes first? Do the answers match?

Practice
1
Find 40 × 62.
2
Find 54 × 30.
3
Find 27 × 43 with four boxes.
×403
20??
7??
4
45 pupils each pay 20 LE for a school trip. How much do they pay together?
5
Aya finds 25 × 12 = 20 × 10 + 5 × 2 = 210. What is missing? What is the right answer?