Roots of Reason
Roots of Reason
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Multi-Digit Multiplication · Grades 4-5

Area Models: 2-Digit × 1-Digit

Name Date
ExampleWatch how 4 × 23 works. Break 23 into 20 + 3, multiply each part, then add.
4
20
3
80
12
80 + 12 = 92
so 4 × 23 = 92
1. Solve 3 × 47. The parts are done for you: 47 = 40 + 7. Fill each box, then add.
3
40
7
3 × 47 =
2. Solve 6 × 58. This time break the number apart yourself: write the parts on top, fill the boxes, add.
6 × 58 =
Roots of Reason CA CCSS 4.NBT.B.5 rootsofreason.org · Page 1 of 5
Roots of Reason
Area Models: 2-Digit × 2-Digit
Name Date
Example12 × 34: both numbers break apart, so the model gets four boxes. Add all four.
10
2
30
4
300
40
60
8
300 + 40 + 60 + 8 = 408
so 12 × 34 = 408
3. Solve 24 × 36. The parts are done: 24 = 20 + 4 and 36 = 30 + 6. Fill the four boxes, then add.
20
4
30
6
24 × 36 =
4. Solve 47 × 25. Break both numbers apart yourself: write the parts on the top and the side.
47 × 25 =
Roots of Reason CA CCSS 4.NBT.B.5 | 5.NBT.B.5 rootsofreason.org · Page 2 of 5
Roots of Reason
Area Models: 3-Digit × 2-Digit
Name Date
Example132 × 21: three parts across, two parts down. Six boxes, one sum.
20
1
100
30
2
2000
600
40
100
30
2
2000 + 600 + 40
+ 100 + 30 + 2 = 2772
5. Solve 243 × 15. Parts done: 243 = 200 + 40 + 3 and 15 = 10 + 5. Fill the six boxes, then add.
10
5
200
40
3
243 × 15 =
6. Solve 316 × 24. Break both numbers apart yourself, label the model, fill it, add.
316 × 24 =
Roots of Reason CA CCSS 5.NBT.B.5 rootsofreason.org · Page 3 of 5
Roots of Reason
Area Models: 3-Digit × 3-Digit
Name Date
Example123 × 111: nine boxes. Big models are just more of the same move.
100
10
1
100
20
3
10000
2000
300
1000
200
30
100
20
3
All nine boxes
add to 13653
7. Solve 234 × 123. Parts done for you. Fill the nine boxes, then add.
100
20
3
200
30
4
234 × 123 =
8. Solve 312 × 214. Yours from the start: label the top and side, fill the boxes, add.
312 × 214 =
Roots of Reason CA CCSS 5.NBT.B.5 rootsofreason.org · Page 4 of 5
Roots of Reason
Roots of Reason
rootsofreason.org
Answer Key
Multi-Digit Multiplication · Grades 4-5

Area Model Multiplication

2-Digit × 1-Digit
1. 3 × 40 = 120, 3 × 7 = 21, so 3 × 47 = 141
2. 58 = 50 + 8; 6 × 50 = 300, 6 × 8 = 48, so 6 × 58 = 348
2-Digit × 2-Digit
3. Boxes: 600, 120, 120, 24, so 24 × 36 = 864
4. 47 = 40 + 7, 25 = 20 + 5; boxes: 800, 200, 140, 35, so 47 × 25 = 1175
3-Digit × 2-Digit
5. Boxes: 2000, 400, 30, 1000, 200, 15, so 243 × 15 = 3645
6. 316 = 300 + 10 + 6, 24 = 20 + 4; boxes: 6000, 200, 120, 1200, 40, 24, so 316 × 24 = 7584
3-Digit × 3-Digit
7. Boxes: 20000, 3000, 400, 4000, 600, 80, 600, 90, 12, so 234 × 123 = 28782
8. 312 = 300 + 10 + 2, 214 = 200 + 10 + 4; boxes: 60000, 2000, 400, 3000, 100, 20, 1200, 40, 8, so 312 × 214 = 66768
The scaffold fades on purpose: example, then filled labels, then a bare rectangle. A student who can label the bare model owns the strategy. One who can only fill boxes is telling you where to reteach.