Year 4: Partitioning, the grid method and the distributive law
Part of the Year 4 short multiplication and short division chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Partitioning, the grid method and the distributive law
Big multiplications are easier when you partition the number. Partition means split it into parts: tens and ones, or hundreds, tens and ones. Imagine 6 packs with 34 stickers in each pack. 34 is 30 + 4. So 6 packs hold 6 lots of 30 and 6 lots of 4. 6 × 30 = 180 and 6 × 4 = 24. Add them: 180 + 24 = 204.
An area model is a rectangle split into parts. The length of each part is across the top, and the number on the side is the same for every part. The area of each part is a partial product. Add the partial products to get the total.
The distributive law. Splitting a number before you multiply always works. We write it like this:
34 × 6 = (30 + 4) × 6 = (30 × 6) + (4 × 6) = 180 + 24 = 204
That is the distributive law. You can do it in your head for two-digit numbers: multiply the tens, multiply the ones, then add.
Near a round number? If a number is just below a multiple of ten, you can multiply the round number and take some away. 29 × 6: 30 × 6 = 180, but 29 is one less than 30, so take away one lot of 6. 180 − 6 = 174.
The grid method for three-digit numbers. Do exactly the same with hundreds, tens and ones. 347 = 300 + 40 + 7. Put the parts in a grid and multiply each by 6.
| × | 300 | 40 | 7 |
| 6 | 300 × 61,800 | 40 × 6240 | 7 × 642 |
1,800 + 240 + 42 = 2,082. A zero digit makes no part: 305 = 300 + 5, so there are only two boxes.
Key words. To partition a number is to split it into parts, one for each digit. A partial product is the answer to one part of the multiplication. The grid method puts the parts in a table.
Key ideas
- Partition the number: 34 = 30 + 4 and 347 = 300 + 40 + 7.
- Multiply each part by the one-digit number. Use a times table fact and put the zeros back.
- Add the partial products: this is the distributive law, (30 + 4) × 6 = 30 × 6 + 4 × 6.
- Near a round number? 29 × 6 = 30 × 6 − 6.
- A zero digit makes no part. Never skip a part that is not zero.
Key words. The distributive law says that (30 + 4) × 6 is the same as 30 × 6 + 4 × 6. You can split a number and multiply the parts.
Method. Partition the two-digit number into tens and ones. Multiply each part by the one-digit number and add the two answers. This is called the distributive law.
- Partition the number into tens and ones. Tens and ones are easy to multiply.34 = 30 + 4
- Write it as two multiplications. This is the distributive law: multiplying a sum by 6 is the same as multiplying each part by 6 and adding.34 × 6 = (30 + 4) × 6 = (30 × 6) + (4 × 6)
- Multiply the tens part. 3 × 6 = 18, so 3 tens × 6 = 18 tens.30 × 6 = 180
- Multiply the ones part. Use a times table fact.4 × 6 = 24
- Add the two answers. 180 + 24 = 204
Check. Estimate: 34 is about 30 (to the nearest 10). 30 × 6 = 180. Our answer, 204, is a bit more than 180, which is right because we rounded down. ✓
Watch out. Both parts must be multiplied by 6. A common mistake is to multiply only the tens, or only the ones.
Key words. The distributive law says that (30 + 4) × 6 is the same as 30 × 6 + 4 × 6. You can split a number and multiply the parts.
Method. Partition the two-digit number into tens and ones. Multiply each part by the one-digit number and add the two answers. This is called the distributive law.
- Partition the number into tens and ones. Tens and ones are easy to multiply.58 = 50 + 8
- Write it as two multiplications. This is the distributive law: multiplying a sum by 7 is the same as multiplying each part by 7 and adding.58 × 7 = (50 + 8) × 7 = (50 × 7) + (8 × 7)
- Multiply the tens part. 5 × 7 = 35, so 5 tens × 7 = 35 tens.50 × 7 = 350
- Multiply the ones part. Use a times table fact.8 × 7 = 56
- Add the two answers. 350 + 56 = 406
Check. Estimate: 58 is about 60 (to the nearest 10). 60 × 7 = 420. Our answer, 406, is a bit less than 420, which is right because we rounded up. ✓
Watch out. Both parts must be multiplied by 7. A common mistake is to multiply only the tens, or only the ones.
Key words. To compensate is to make up for a change. Here we multiply an easy number, then correct the answer.
Method. 49 is close to the round number 50. Multiply 50 first, then take away the extra bit.
- Spot a round number close by. 49 is just 1 below 50.49 = 50 − 1
- Multiply the round number by 6. Round numbers are easy to multiply.50 × 6 = 300
- Work out the extra bit: 1 × 6. We multiplied 50 by 6, but 49 is 1 less, so we have to take away 1 lots of 6.1 × 6 = 6
- Fix the answer. Take it away (or add it) to get to the real answer.300 − 6 = 294
Check. Partition instead: 49 = 40 + 9, and 240 + 54 = 294. ✓
Watch out. Take away 1 lots of 6, not just 1.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Split the number into hundreds, tens and ones (partition it). Multiply each part by the one-digit number, then add the answers.
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply.47 = 40 + 7
- Draw the grid and write the parts across the top. The number on the side is 8. Every part gets multiplied by 8.
× 40 7 8 ? ? - Multiply each part. Use a times table fact, then put the zeros back.7 × 8 = 56
40 is 4 tens. 4 × 8 = 32, so 4 tens × 8 = 32 tens = 320 - Write each answer in the grid. These are the partial products.
× 40 7 8 40 × 8320 7 × 856 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.320 + 56 = 376
- Write the answer. 47 × 8 = 376
Check. Estimate: 47 is about 50 (to the nearest 10). 50 × 8 = 400. Our answer, 376, is a bit less than 400, which is right because we rounded up. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Split the number into hundreds, tens and ones (partition it). Multiply each part by the one-digit number, then add the answers.
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply.325 = 300 + 20 + 5
- Draw the grid and write the parts across the top. The number on the side is 4. Every part gets multiplied by 4.
× 300 20 5 4 ? ? ? - Multiply each part. Use a times table fact, then put the zeros back.5 × 4 = 20
20 is 2 tens. 2 × 4 = 8, so 2 tens × 4 = 8 tens = 80
300 is 3 hundreds. 3 × 4 = 12, so 3 hundreds × 4 = 12 hundreds = 1,200 - Write each answer in the grid. These are the partial products.
× 300 20 5 4 300 × 41,200 20 × 480 5 × 420 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.1,200 + 80 = 1,280
1,280 + 20 = 1,300 - Write the answer. 325 × 4 = 1,300
Check. Estimate: 325 is about 300 (to the nearest 100). 300 × 4 = 1,200. Our answer, 1,300, is a bit more than 1,200, which is right because we rounded down. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Split the number into hundreds, tens and ones (partition it). Multiply each part by the one-digit number, then add the answers.
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply. The 0 in the number means there are none of that place, so it has no part.406 = 400 + 6
- Draw the grid and write the parts across the top. The number on the side is 7. Every part gets multiplied by 7.
× 400 6 7 ? ? - Multiply each part. Use a times table fact, then put the zeros back.6 × 7 = 42
400 is 4 hundreds. 4 × 7 = 28, so 4 hundreds × 7 = 28 hundreds = 2,800 - Write each answer in the grid. These are the partial products.
× 400 6 7 400 × 72,800 6 × 742 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.2,800 + 42 = 2,842
- Write the answer. 406 × 7 = 2,842
Check. Estimate: 406 is about 400 (to the nearest 100). 400 × 7 = 2,800. Our answer, 2,842, is a bit more than 2,800, which is right because we rounded down. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Method. Partition the number into tens and ones, multiply each part by the one-digit number, and add the answers.
- Partition the number. Split 52 into tens and ones.52 = 50 + 2
- Write what each part makes. 50 × 7 = 350 and 2 × 7 = 14.(50 × 7) + (2 × 7) = 350 + 14
- Find the missing number. The tens part of 52 is 50. Multiply it by 7.50 × 7 = 350
Check. Total: 350 + 14 = 364, and 52 × 7 = 364. ✓
Watch out. Read the whole sentence with your answer in the box. It must be true.
Watch out
Multiply the whole value of each part. In 52 × 6, the 5 is worth 50, so work out 50 × 6 = 300, not 5 × 6 = 30. Also remember every part: if you only multiply the tens, you have forgotten the ones.Exercise 4B Partitioning, the grid method and the distributive law
Non-calculatorKey words. The distributive law says that (30 + 4) × 6 is the same as 30 × 6 + 4 × 6. You can split a number and multiply the parts.
Method. Partition the two-digit number into tens and ones. Multiply each part by the one-digit number and add the two answers. This is called the distributive law.
- Partition the number into tens and ones. Tens and ones are easy to multiply.23 = 20 + 3
- Write it as two multiplications. This is the distributive law: multiplying a sum by 3 is the same as multiplying each part by 3 and adding.23 × 3 = (20 + 3) × 3 = (20 × 3) + (3 × 3)
- Multiply the tens part. 2 × 3 = 6, so 2 tens × 3 = 6 tens.20 × 3 = 60
- Multiply the ones part. Use a times table fact.3 × 3 = 9
- Add the two answers. 60 + 9 = 69
Check. Estimate: 23 is about 20 (to the nearest 10). 20 × 3 = 60. Our answer, 69, is a bit more than 60, which is right because we rounded down. ✓
Watch out. Both parts must be multiplied by 3. A common mistake is to multiply only the tens, or only the ones.
Key words. The distributive law says that (30 + 4) × 6 is the same as 30 × 6 + 4 × 6. You can split a number and multiply the parts.
Method. Partition the two-digit number into tens and ones. Multiply each part by the one-digit number and add the two answers. This is called the distributive law.
- Partition the number into tens and ones. Tens and ones are easy to multiply.41 = 40 + 1
- Write it as two multiplications. This is the distributive law: multiplying a sum by 5 is the same as multiplying each part by 5 and adding.41 × 5 = (40 + 1) × 5 = (40 × 5) + (1 × 5)
- Multiply the tens part. 4 × 5 = 20, so 4 tens × 5 = 20 tens.40 × 5 = 200
- Multiply the ones part. Use a times table fact.1 × 5 = 5
- Add the two answers. 200 + 5 = 205
Check. Estimate: 41 is about 40 (to the nearest 10). 40 × 5 = 200. Our answer, 205, is a bit more than 200, which is right because we rounded down. ✓
Watch out. Both parts must be multiplied by 5. A common mistake is to multiply only the tens, or only the ones.
Key words. The distributive law says that (30 + 4) × 6 is the same as 30 × 6 + 4 × 6. You can split a number and multiply the parts.
Method. Partition the two-digit number into tens and ones. Multiply each part by the one-digit number and add the two answers. This is called the distributive law.
- Partition the number into tens and ones. Tens and ones are easy to multiply.32 = 30 + 2
- Write it as two multiplications. This is the distributive law: multiplying a sum by 4 is the same as multiplying each part by 4 and adding.32 × 4 = (30 + 2) × 4 = (30 × 4) + (2 × 4)
- Multiply the tens part. 3 × 4 = 12, so 3 tens × 4 = 12 tens.30 × 4 = 120
- Multiply the ones part. Use a times table fact.2 × 4 = 8
- Add the two answers. 120 + 8 = 128
Check. Estimate: 32 is about 30 (to the nearest 10). 30 × 4 = 120. Our answer, 128, is a bit more than 120, which is right because we rounded down. ✓
Watch out. Both parts must be multiplied by 4. A common mistake is to multiply only the tens, or only the ones.
Key words. The distributive law says that (30 + 4) × 6 is the same as 30 × 6 + 4 × 6. You can split a number and multiply the parts.
Method. Partition the two-digit number into tens and ones. Multiply each part by the one-digit number and add the two answers. This is called the distributive law.
- Partition the number into tens and ones. Tens and ones are easy to multiply.54 = 50 + 4
- Write it as two multiplications. This is the distributive law: multiplying a sum by 6 is the same as multiplying each part by 6 and adding.54 × 6 = (50 + 4) × 6 = (50 × 6) + (4 × 6)
- Multiply the tens part. 5 × 6 = 30, so 5 tens × 6 = 30 tens.50 × 6 = 300
- Multiply the ones part. Use a times table fact.4 × 6 = 24
- Add the two answers. 300 + 24 = 324
Check. Estimate: 54 is about 50 (to the nearest 10). 50 × 6 = 300. Our answer, 324, is a bit more than 300, which is right because we rounded down. ✓
Watch out. Both parts must be multiplied by 6. A common mistake is to multiply only the tens, or only the ones.
Key words. The distributive law says that (30 + 4) × 6 is the same as 30 × 6 + 4 × 6. You can split a number and multiply the parts.
Method. Partition the two-digit number into tens and ones. Multiply each part by the one-digit number and add the two answers. This is called the distributive law.
- Partition the number into tens and ones. Tens and ones are easy to multiply.67 = 60 + 7
- Write it as two multiplications. This is the distributive law: multiplying a sum by 3 is the same as multiplying each part by 3 and adding.67 × 3 = (60 + 7) × 3 = (60 × 3) + (7 × 3)
- Multiply the tens part. 6 × 3 = 18, so 6 tens × 3 = 18 tens.60 × 3 = 180
- Multiply the ones part. Use a times table fact.7 × 3 = 21
- Add the two answers. 180 + 21 = 201
Check. Estimate: 67 is about 70 (to the nearest 10). 70 × 3 = 210. Our answer, 201, is a bit less than 210, which is right because we rounded up. ✓
Watch out. Both parts must be multiplied by 3. A common mistake is to multiply only the tens, or only the ones.
Key words. The distributive law says that (30 + 4) × 6 is the same as 30 × 6 + 4 × 6. You can split a number and multiply the parts.
Method. Partition the two-digit number into tens and ones. Multiply each part by the one-digit number and add the two answers. This is called the distributive law.
- Partition the number into tens and ones. Tens and ones are easy to multiply.76 = 70 + 6
- Write it as two multiplications. This is the distributive law: multiplying a sum by 8 is the same as multiplying each part by 8 and adding.76 × 8 = (70 + 6) × 8 = (70 × 8) + (6 × 8)
- Multiply the tens part. 7 × 8 = 56, so 7 tens × 8 = 56 tens.70 × 8 = 560
- Multiply the ones part. Use a times table fact.6 × 8 = 48
- Add the two answers. 560 + 48 = 608
Check. Estimate: 76 is about 80 (to the nearest 10). 80 × 8 = 640. Our answer, 608, is a bit less than 640, which is right because we rounded up. ✓
Watch out. Both parts must be multiplied by 8. A common mistake is to multiply only the tens, or only the ones.
Method. Partition the number into tens and ones, multiply each part by the one-digit number, and add the answers.
- Partition the number. Split 27 into tens and ones.27 = 20 + 7
- Write what each part makes. 20 × 4 = 80 and 7 × 4 = 28.(20 × 4) + (7 × 4) = 80 + 28
- Find the missing number. 27 = 20 + 7, so the missing part is the ones digit.27 = 20 + 7
Check. Total: 80 + 28 = 108, and 27 × 4 = 108. ✓
Watch out. Read the whole sentence with your answer in the box. It must be true.
Method. Partition the number into tens and ones, multiply each part by the one-digit number, and add the answers.
- Partition the number. Split 36 into tens and ones.36 = 30 + 6
- Write what each part makes. 30 × 5 = 150 and 6 × 5 = 30.(30 × 5) + (6 × 5) = 150 + 30
- Find the missing number. The tens part of 36 is 30. Multiply it by 5.30 × 5 = 150
Check. Total: 150 + 30 = 180, and 36 × 5 = 180. ✓
Watch out. Read the whole sentence with your answer in the box. It must be true.
Method. Partition the number into tens and ones, multiply each part by the one-digit number, and add the answers.
- Partition the number. Split 58 into tens and ones.58 = 50 + 8
- Write what each part makes. 50 × 6 = 300 and 8 × 6 = 48.(50 × 6) + (8 × 6) = 300 + 48
- Find the missing number. The ones part of 58 is 8. Multiply it by 6.8 × 6 = 48
Check. Total: 300 + 48 = 348, and 58 × 6 = 348. ✓
Watch out. Read the whole sentence with your answer in the box. It must be true.
Method. Partition the number into tens and ones, multiply each part by the one-digit number, and add the answers.
- Partition the number. Split 43 into tens and ones.43 = 40 + 3
- Write what each part makes. 40 × 7 = 280 and 3 × 7 = 21.(40 × 7) + (3 × 7) = 280 + 21
- Find the missing number. Add the two partial products.280 + 21 = 301
Check. Total: 280 + 21 = 301, and 43 × 7 = 301. ✓
Watch out. Read the whole sentence with your answer in the box. It must be true.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Split the number into hundreds, tens and ones (partition it). Multiply each part by the one-digit number, then add the answers.
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply.52 = 50 + 2
- Draw the grid and write the parts across the top. The number on the side is 4. Every part gets multiplied by 4.
× 50 2 4 ? ? - Multiply each part. Use a times table fact, then put the zeros back.2 × 4 = 8
50 is 5 tens. 5 × 4 = 20, so 5 tens × 4 = 20 tens = 200 - Write each answer in the grid. These are the partial products.
× 50 2 4 50 × 4200 2 × 48 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.200 + 8 = 208
- Write the answer. 52 × 4 = 208
Check. Estimate: 52 is about 50 (to the nearest 10). 50 × 4 = 200. Our answer, 208, is a bit more than 200, which is right because we rounded down. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Split the number into hundreds, tens and ones (partition it). Multiply each part by the one-digit number, then add the answers.
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply.34 = 30 + 4
- Draw the grid and write the parts across the top. The number on the side is 5. Every part gets multiplied by 5.
× 30 4 5 ? ? - Multiply each part. Use a times table fact, then put the zeros back.4 × 5 = 20
30 is 3 tens. 3 × 5 = 15, so 3 tens × 5 = 15 tens = 150 - Write each answer in the grid. These are the partial products.
× 30 4 5 30 × 5150 4 × 520 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.150 + 20 = 170
- Write the answer. 34 × 5 = 170
Check. Estimate: 34 is about 30 (to the nearest 10). 30 × 5 = 150. Our answer, 170, is a bit more than 150, which is right because we rounded down. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Split the number into hundreds, tens and ones (partition it). Multiply each part by the one-digit number, then add the answers.
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply.63 = 60 + 3
- Draw the grid and write the parts across the top. The number on the side is 7. Every part gets multiplied by 7.
× 60 3 7 ? ? - Multiply each part. Use a times table fact, then put the zeros back.3 × 7 = 21
60 is 6 tens. 6 × 7 = 42, so 6 tens × 7 = 42 tens = 420 - Write each answer in the grid. These are the partial products.
× 60 3 7 60 × 7420 3 × 721 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.420 + 21 = 441
- Write the answer. 63 × 7 = 441
Check. Estimate: 63 is about 60 (to the nearest 10). 60 × 7 = 420. Our answer, 441, is a bit more than 420, which is right because we rounded down. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To compensate is to make up for a change. Here we multiply an easy number, then correct the answer.
Method. 39 is close to the round number 40. Multiply 40 first, then take away the extra bit.
- Spot a round number close by. 39 is just 1 below 40.39 = 40 − 1
- Multiply the round number by 5. Round numbers are easy to multiply.40 × 5 = 200
- Work out the extra bit: 1 × 5. We multiplied 40 by 5, but 39 is 1 less, so we have to take away 1 lots of 5.1 × 5 = 5
- Fix the answer. Take it away (or add it) to get to the real answer.200 − 5 = 195
Check. Partition instead: 39 = 30 + 9, and 150 + 45 = 195. ✓
Watch out. Take away 1 lots of 5, not just 1.
Key words. To compensate is to make up for a change. Here we multiply an easy number, then correct the answer.
Method. 49 is close to the round number 50. Multiply 50 first, then take away the extra bit.
- Spot a round number close by. 49 is just 1 below 50.49 = 50 − 1
- Multiply the round number by 6. Round numbers are easy to multiply.50 × 6 = 300
- Work out the extra bit: 1 × 6. We multiplied 50 by 6, but 49 is 1 less, so we have to take away 1 lots of 6.1 × 6 = 6
- Fix the answer. Take it away (or add it) to get to the real answer.300 − 6 = 294
Check. Partition instead: 49 = 40 + 9, and 240 + 54 = 294. ✓
Watch out. Take away 1 lots of 6, not just 1.
Key words. To compensate is to make up for a change. Here we multiply an easy number, then correct the answer.
Method. 28 is close to the round number 30. Multiply 30 first, then take away the extra bit.
- Spot a round number close by. 28 is just 2 below 30.28 = 30 − 2
- Multiply the round number by 4. Round numbers are easy to multiply.30 × 4 = 120
- Work out the extra bit: 2 × 4. We multiplied 30 by 4, but 28 is 2 less, so we have to take away 2 lots of 4.2 × 4 = 8
- Fix the answer. Take it away (or add it) to get to the real answer.120 − 8 = 112
Check. Partition instead: 28 = 20 + 8, and 80 + 32 = 112. ✓
Watch out. Take away 2 lots of 4, not just 2.
Key words. To compensate is to make up for a change. Here we multiply an easy number, then correct the answer.
Method. 98 is close to the round number 100. Multiply 100 first, then take away the extra bit.
- Spot a round number close by. 98 is just 2 below 100.98 = 100 − 2
- Multiply the round number by 3. Round numbers are easy to multiply.100 × 3 = 300
- Work out the extra bit: 2 × 3. We multiplied 100 by 3, but 98 is 2 less, so we have to take away 2 lots of 3.2 × 3 = 6
- Fix the answer. Take it away (or add it) to get to the real answer.300 − 6 = 294
Check. Partition instead: 98 = 90 + 8, and 270 + 24 = 294. ✓
Watch out. Take away 2 lots of 3, not just 2.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Split the number into hundreds, tens and ones (partition it). Multiply each part by the one-digit number, then add the answers.
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply.46 = 40 + 6
- Draw the grid and write the parts across the top. The number on the side is 3. Every part gets multiplied by 3.
× 40 6 3 ? ? - Multiply each part. Use a times table fact, then put the zeros back.6 × 3 = 18
40 is 4 tens. 4 × 3 = 12, so 4 tens × 3 = 12 tens = 120 - Write each answer in the grid. These are the partial products.
× 40 6 3 40 × 3120 6 × 318 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.120 + 18 = 138
- Write the answer. 46 × 3 = 138
Check. Estimate: 46 is about 50 (to the nearest 10). 50 × 3 = 150. Our answer, 138, is a bit less than 150, which is right because we rounded up. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Split the number into hundreds, tens and ones (partition it). Multiply each part by the one-digit number, then add the answers.
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply.73 = 70 + 3
- Draw the grid and write the parts across the top. The number on the side is 4. Every part gets multiplied by 4.
× 70 3 4 ? ? - Multiply each part. Use a times table fact, then put the zeros back.3 × 4 = 12
70 is 7 tens. 7 × 4 = 28, so 7 tens × 4 = 28 tens = 280 - Write each answer in the grid. These are the partial products.
× 70 3 4 70 × 4280 3 × 412 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.280 + 12 = 292
- Write the answer. 73 × 4 = 292
Check. Estimate: 73 is about 70 (to the nearest 10). 70 × 4 = 280. Our answer, 292, is a bit more than 280, which is right because we rounded down. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Split the number into hundreds, tens and ones (partition it). Multiply each part by the one-digit number, then add the answers.
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply.58 = 50 + 8
- Draw the grid and write the parts across the top. The number on the side is 7. Every part gets multiplied by 7.
× 50 8 7 ? ? - Multiply each part. Use a times table fact, then put the zeros back.8 × 7 = 56
50 is 5 tens. 5 × 7 = 35, so 5 tens × 7 = 35 tens = 350 - Write each answer in the grid. These are the partial products.
× 50 8 7 50 × 7350 8 × 756 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.350 + 56 = 406
- Write the answer. 58 × 7 = 406
Check. Estimate: 58 is about 60 (to the nearest 10). 60 × 7 = 420. Our answer, 406, is a bit less than 420, which is right because we rounded up. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Split the number into hundreds, tens and ones (partition it). Multiply each part by the one-digit number, then add the answers.
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply.84 = 80 + 4
- Draw the grid and write the parts across the top. The number on the side is 9. Every part gets multiplied by 9.
× 80 4 9 ? ? - Multiply each part. Use a times table fact, then put the zeros back.4 × 9 = 36
80 is 8 tens. 8 × 9 = 72, so 8 tens × 9 = 72 tens = 720 - Write each answer in the grid. These are the partial products.
× 80 4 9 80 × 9720 4 × 936 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.720 + 36 = 756
- Write the answer. 84 × 9 = 756
Check. Estimate: 84 is about 80 (to the nearest 10). 80 × 9 = 720. Our answer, 756, is a bit more than 720, which is right because we rounded down. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Split the number into hundreds, tens and ones (partition it). Multiply each part by the one-digit number, then add the answers.
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply.213 = 200 + 10 + 3
- Draw the grid and write the parts across the top. The number on the side is 4. Every part gets multiplied by 4.
× 200 10 3 4 ? ? ? - Multiply each part. Use a times table fact, then put the zeros back.3 × 4 = 12
10 is 1 ten. 1 × 4 = 4, so 1 ten × 4 = 4 tens = 40
200 is 2 hundreds. 2 × 4 = 8, so 2 hundreds × 4 = 8 hundreds = 800 - Write each answer in the grid. These are the partial products.
× 200 10 3 4 200 × 4800 10 × 440 3 × 412 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.800 + 40 = 840
840 + 12 = 852 - Write the answer. 213 × 4 = 852
Check. Estimate: 213 is about 200 (to the nearest 100). 200 × 4 = 800. Our answer, 852, is a bit more than 800, which is right because we rounded down. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Split the number into hundreds, tens and ones (partition it). Multiply each part by the one-digit number, then add the answers.
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply.325 = 300 + 20 + 5
- Draw the grid and write the parts across the top. The number on the side is 3. Every part gets multiplied by 3.
× 300 20 5 3 ? ? ? - Multiply each part. Use a times table fact, then put the zeros back.5 × 3 = 15
20 is 2 tens. 2 × 3 = 6, so 2 tens × 3 = 6 tens = 60
300 is 3 hundreds. 3 × 3 = 9, so 3 hundreds × 3 = 9 hundreds = 900 - Write each answer in the grid. These are the partial products.
× 300 20 5 3 300 × 3900 20 × 360 5 × 315 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.900 + 60 = 960
960 + 15 = 975 - Write the answer. 325 × 3 = 975
Check. Estimate: 325 is about 300 (to the nearest 100). 300 × 3 = 900. Our answer, 975, is a bit more than 900, which is right because we rounded down. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Split the number into hundreds, tens and ones (partition it). Multiply each part by the one-digit number, then add the answers.
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply.452 = 400 + 50 + 2
- Draw the grid and write the parts across the top. The number on the side is 6. Every part gets multiplied by 6.
× 400 50 2 6 ? ? ? - Multiply each part. Use a times table fact, then put the zeros back.2 × 6 = 12
50 is 5 tens. 5 × 6 = 30, so 5 tens × 6 = 30 tens = 300
400 is 4 hundreds. 4 × 6 = 24, so 4 hundreds × 6 = 24 hundreds = 2,400 - Write each answer in the grid. These are the partial products.
× 400 50 2 6 400 × 62,400 50 × 6300 2 × 612 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.2,400 + 300 = 2,700
2,700 + 12 = 2,712 - Write the answer. 452 × 6 = 2,712
Check. Estimate: 452 is about 500 (to the nearest 100). 500 × 6 = 3,000. Our answer, 2,712, is a bit less than 3,000, which is right because we rounded up. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Split the number into hundreds, tens and ones (partition it). Multiply each part by the one-digit number, then add the answers.
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply.678 = 600 + 70 + 8
- Draw the grid and write the parts across the top. The number on the side is 5. Every part gets multiplied by 5.
× 600 70 8 5 ? ? ? - Multiply each part. Use a times table fact, then put the zeros back.8 × 5 = 40
70 is 7 tens. 7 × 5 = 35, so 7 tens × 5 = 35 tens = 350
600 is 6 hundreds. 6 × 5 = 30, so 6 hundreds × 5 = 30 hundreds = 3,000 - Write each answer in the grid. These are the partial products.
× 600 70 8 5 600 × 53,000 70 × 5350 8 × 540 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.3,000 + 350 = 3,350
3,350 + 40 = 3,390 - Write the answer. 678 × 5 = 3,390
Check. Estimate: 678 is about 700 (to the nearest 100). 700 × 5 = 3,500. Our answer, 3,390, is a bit less than 3,500, which is right because we rounded up. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Split the number into hundreds, tens and ones (partition it). Multiply each part by the one-digit number, then add the answers.
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply. The 0 in the number means there are none of that place, so it has no part.305 = 300 + 5
- Draw the grid and write the parts across the top. The number on the side is 4. Every part gets multiplied by 4.
× 300 5 4 ? ? - Multiply each part. Use a times table fact, then put the zeros back.5 × 4 = 20
300 is 3 hundreds. 3 × 4 = 12, so 3 hundreds × 4 = 12 hundreds = 1,200 - Write each answer in the grid. These are the partial products.
× 300 5 4 300 × 41,200 5 × 420 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.1,200 + 20 = 1,220
- Write the answer. 305 × 4 = 1,220
Check. Estimate: 305 is about 300 (to the nearest 100). 300 × 4 = 1,200. Our answer, 1,220, is a bit more than 1,200, which is right because we rounded down. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Split the number into hundreds, tens and ones (partition it). Multiply each part by the one-digit number, then add the answers.
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply. The 0 in the number means there are none of that place, so it has no part.620 = 600 + 20
- Draw the grid and write the parts across the top. The number on the side is 3. Every part gets multiplied by 3.
× 600 20 3 ? ? - Multiply each part. Use a times table fact, then put the zeros back.20 is 2 tens. 2 × 3 = 6, so 2 tens × 3 = 6 tens = 60
600 is 6 hundreds. 6 × 3 = 18, so 6 hundreds × 3 = 18 hundreds = 1,800 - Write each answer in the grid. These are the partial products.
× 600 20 3 600 × 31,800 20 × 360 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.1,800 + 60 = 1,860
- Write the answer. 620 × 3 = 1,860
Check. Estimate: 620 is about 600 (to the nearest 100). 600 × 3 = 1,800. Our answer, 1,860, is a bit more than 1,800, which is right because we rounded down. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Split the number into hundreds, tens and ones (partition it). Multiply each part by the one-digit number, then add the answers.
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply. The 0 in the number means there are none of that place, so it has no part.804 = 800 + 4
- Draw the grid and write the parts across the top. The number on the side is 5. Every part gets multiplied by 5.
× 800 4 5 ? ? - Multiply each part. Use a times table fact, then put the zeros back.4 × 5 = 20
800 is 8 hundreds. 8 × 5 = 40, so 8 hundreds × 5 = 40 hundreds = 4,000 - Write each answer in the grid. These are the partial products.
× 800 4 5 800 × 54,000 4 × 520 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.4,000 + 20 = 4,020
- Write the answer. 804 × 5 = 4,020
Check. Estimate: 804 is about 800 (to the nearest 100). 800 × 5 = 4,000. Our answer, 4,020, is a bit more than 4,000, which is right because we rounded down. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Draw a bar model, choose the operation, then use the grid method: split the number into parts, multiply each part and add.
- Draw a bar model. A bar model shows the equal groups.
- Choose the operation. There are 6 trays with 34 rolls on each, so multiply 34 by 6.34 × 6
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply.34 = 30 + 4
- Draw the grid and write the parts across the top. The number on the side is 6. Every part gets multiplied by 6.
× 30 4 6 ? ? - Multiply each part. Use a times table fact, then put the zeros back.4 × 6 = 24
30 is 3 tens. 3 × 6 = 18, so 3 tens × 6 = 18 tens = 180 - Write each answer in the grid. These are the partial products.
× 30 4 6 30 × 6180 4 × 624 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.180 + 24 = 204
- Write the answer. Include the unit.204 rolls
Check. Estimate: 34 is about 30 (to the nearest 10). 30 × 6 = 180. Our answer, 204, is a bit more than 180, which is right because we rounded down. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Draw a bar model, choose the operation, then use the grid method: split the number into parts, multiply each part and add.
- Draw a bar model. A bar model shows the equal groups.
- Choose the operation. Each ticket costs £47, so multiply 47 by 6.£47 × 6
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply.47 = 40 + 7
- Draw the grid and write the parts across the top. The number on the side is 6. Every part gets multiplied by 6.
× 40 7 6 ? ? - Multiply each part. Use a times table fact, then put the zeros back.7 × 6 = 42
40 is 4 tens. 4 × 6 = 24, so 4 tens × 6 = 24 tens = 240 - Write each answer in the grid. These are the partial products.
× 40 7 6 40 × 6240 7 × 642 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.240 + 42 = 282
- Write the answer. Include the unit.£282
Check. Estimate: 47 is about 50 (to the nearest 10). 50 × 6 = 300. Our answer, 282, is a bit less than 300, which is right because we rounded up. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Key words. To partition a number is to split it into parts, one for each digit (347 = 300 + 40 + 7). A partial product is the answer to one part of a multiplication. The grid method (or area method) puts the parts in a table and multiplies each part.
Method. Draw a bar model, choose the operation, then use the grid method: split the number into parts, multiply each part and add.
- Draw a bar model. A bar model shows the equal groups.
- Choose the operation. Leo reads 28 pages each day for 7 days, so multiply 28 by 7.28 × 7
- Partition the number you are multiplying. Split it into hundreds, tens and ones. Each part is easy to multiply.28 = 20 + 8
- Draw the grid and write the parts across the top. The number on the side is 7. Every part gets multiplied by 7.
× 20 8 7 ? ? - Multiply each part. Use a times table fact, then put the zeros back.8 × 7 = 56
20 is 2 tens. 2 × 7 = 14, so 2 tens × 7 = 14 tens = 140 - Write each answer in the grid. These are the partial products.
× 20 8 7 20 × 7140 8 × 756 - Add the partial products. Add them one at a time, from the biggest. Keep a running total.140 + 56 = 196
- Write the answer. Include the unit.196 pages
Check. Estimate: 28 is about 30 (to the nearest 10). 30 × 7 = 210. Our answer, 196, is a bit less than 210, which is right because we rounded up. ✓
Watch out. Do not forget a part. Count the parts: every digit that is not 0 needs its own box. And keep the zeros: 40 × 6 is 240, not 24.
Method. Estimate first. Then work out the correct answer and find what Jack did wrong.
- Estimate 52 × 6. 52 is about 50. 50 × 6 is easy: 5 × 6 = 30, so 5 tens × 6 = 30 tens.50 × 6 = 300
- Compare with Jack’s answer. The answer should be a bit more than 300.Jack’s answer, 42, is much smaller than 300. It cannot be right.
- Find Jack’s mistake. He used 5 × 6 = 30 instead of 50 × 6 = 300. He forgot that the 5 means 5 tens.5 × 6 = 30 and 2 × 6 = 12, and 30 + 12 = 42
- Work out the correct answer. Multiply the whole value of each part.50 × 6 = 300, 2 × 6 = 12, 300 + 12 = 312
Check. Estimate: 52 is about 50 (to the nearest 10). 50 × 6 = 300. Our answer, 312, is a bit more than 300, which is right because we rounded down. ✓
Watch out. In 52, the 5 is worth 50. Always multiply the whole value of the part.
Method. Try some two-digit numbers. Look for one that gives a 2-digit answer and one that gives a 3-digit answer.
- Try a small number. Use the partition method or the 5 times table.12 × 5 = 60 (2 digits)
- Try a bigger number. 24 × 5 = 120 (3 digits) 47 × 5 = 235 (3 digits)
- Find the turning point. 19 × 5 = 95 is still 2 digits, but 20 × 5 = 100 has 3 digits.19 × 5 = 95 20 × 5 = 100
- Decide. We found one that does and one that does not.Sometimes
Check. Numbers up to 19 give a 2-digit answer. Numbers from 20 to 99 give a 3-digit answer. ✓
Watch out. “Sometimes” needs an example that works and an example that does not.
Method. Work out both answers using the distributive law, then compare them.
- Work out 28 × 6. Partition 28 into 20 + 8.20 × 6 = 120 8 × 6 = 48 120 + 48 = 168
- Work out 34 × 5. Partition 34 into 30 + 4.30 × 5 = 150 4 × 5 = 20 150 + 20 = 170
- Compare. 170 is bigger than 168.170 > 168
- Answer. 34 × 5 is greater. It is only 2 more.
Check. Estimate: 30 × 6 = 180 and 30 × 5 = 150. The estimates are not enough to decide, so we needed the exact answers. ✓
Watch out. The numbers are very close, so an estimate is not enough. Work out both exactly.
Method. Try every way of using the three cards. Each card is used once: two make the two-digit number and one is the multiplier.
- List the possibilities. There are 6 ways: pick which card is the multiplier, then the order of the other two.57 × 3 = 171
37 × 5 = 185
75 × 3 = 225
35 × 7 = 245
73 × 5 = 365
53 × 7 = 371 - Find the biggest. Compare the answers.The biggest answer is 371, from 53 × 7.
Check. Work out 53 × 7 again: 50 × 7 = 350 and 3 × 7 = 21, so 350 + 21 = 371. ✓
Watch out. Check every possibility, not just the one that looks biggest. A smaller multiplier does not always lose.