Year 6 Maths: Multiplication by Partitioning

Introduction to Partitioning

Hello Year 6! Today, we’re going to learn about a method called “Multiplication by Partitioning”. This is a way to help us multiply larger numbers by breaking them into smaller, easier parts. Let’s dive in!

What is Partitioning?

Partitioning means splitting a number into smaller parts. For example, if we have the number 34, we can partition it into 30 and 4. This makes it easier to multiply!

How Does It Work?

When we multiply by partitioning, we follow these steps:

1. Partition the Numbers: Break one or both of the numbers into parts.
2. Multiply Each Part: Multiply each part separately.
3. Add the Results: Finally, add all the products together.

Example 1: Multiplying 34 by 6

1. Partition 34: We can split 34 into 30 and 4.
   • So, 34 = 30 + 4
2. Multiply Each Part by 6:
   • Multiply 30 by 6: $$30 \times 6 = 180$$
   • Multiply 4 by 6: $$4 \times 6 = 24$$
3. Add the Results:
   • Now we add 180 and 24: $$180 + 24 = 204$$

So,

Example 2: Multiplying 27 by 5

1. Partition 27: We can split 27 into 20 and 7.
   • So, 27 = 20 + 7
2. Multiply Each Part by 5:
   • Multiply 20 by 5: $$20 \times 5 = 100$$
   • Multiply 7 by 5: $$7 \times 5 = 35$$
3. Add the Results:
   • Now we add 100 and 35: $$100 + 35 = 135$$

So,

Key Rules

• Always break numbers down into tens and units when possible.
• Make sure to keep track of your addition at the end!
• Double-check your multiplication for accuracy.

Tips and Tricks

• Use a number line to help visualise the breaking down of numbers.
• Practice with different numbers to get comfortable with the process.
• Remember that partitioning can also work with larger numbers, not just two-digit numbers!

Questions

Easy Level Questions

1. What is $$12 \times 3$$ using partitioning?
2. Multiply $$25 \times 4$$ using partitioning.
3. Find $$15 \times 2$$ using partitioning.
4. Calculate $$22 \times 5$$ using partitioning.
5. What is $$30 \times 6$$ using partitioning?
6. Multiply $$14 \times 3$$ using partitioning.
7. Find $$10 \times 9$$ using partitioning.
8. Calculate $$18 \times 4$$ using partitioning.
9. What is $$20 \times 7$$ using partitioning?
10. Multiply $$36 \times 2$$ using partitioning.
11. Find $$24 \times 3$$ using partitioning.
12. Calculate $$16 \times 5$$ using partitioning.
13. What is $$28 \times 4$$ using partitioning?
14. Multiply $$32 \times 3$$ using partitioning.
15. Find $$40 \times 2$$ using partitioning.
16. Calculate $$50 \times 1$$ using partitioning.
17. What is $$12 \times 5$$ using partitioning?
18. Multiply $$15 \times 4$$ using partitioning.
19. Find $$21 \times 2$$ using partitioning.
20. Calculate $$33 \times 3$$ using partitioning.

Medium Level Questions

1. What is $$45 \times 6$$ using partitioning?
2. Multiply $$52 \times 3$$ using partitioning.
3. Find $$63 \times 4$$ using partitioning.
4. Calculate $$76 \times 5$$ using partitioning.
5. What is $$34 \times 7$$ using partitioning?
6. Multiply $$81 \times 2$$ using partitioning.
7. Find $$22 \times 8$$ using partitioning.
8. Calculate $$39 \times 6$$ using partitioning.
9. What is $$47 \times 3$$ using partitioning?
10. Multiply $$54 \times 5$$ using partitioning.
11. Find $$29 \times 7$$ using partitioning.
12. Calculate $$68 \times 4$$ using partitioning.
13. What is $$33 \times 6$$ using partitioning?
14. Multiply $$72 \times 3$$ using partitioning.
15. Find $$85 \times 2$$ using partitioning.
16. Calculate $$40 \times 9$$ using partitioning.
17. What is $$93 \times 4$$ using partitioning?
18. Multiply $$57 \times 5$$ using partitioning.
19. Find $$48 \times 3$$ using partitioning.
20. Calculate $$70 \times 2$$ using partitioning.

Hard Level Questions

1. What is $$126 \times 7$$ using partitioning?
2. Multiply $$234 \times 5$$ using partitioning.
3. Find $$167 \times 8$$ using partitioning.
4. Calculate $$312 \times 4$$ using partitioning.
5. What is $$245 \times 3$$ using partitioning?
6. Multiply $$198 \times 6$$ using partitioning.
7. Find $$275 \times 9$$ using partitioning.
8. Calculate $$384 \times 2$$ using partitioning.
9. What is $$157 \times 5$$ using partitioning?
10. Multiply $$420 \times 4$$ using partitioning.
11. Find $$289 \times 3$$ using partitioning.
12. Calculate $$395 \times 6$$ using partitioning.
13. What is $$512 \times 2$$ using partitioning?
14. Multiply $$630 \times 5$$ using partitioning.
15. Find $$726 \times 3$$ using partitioning.
16. Calculate $$842 \times 4$$ using partitioning.
17. What is $$913 \times 2$$ using partitioning?
18. Multiply $$234 \times 6$$ using partitioning.
19. Find $$178 \times 5$$ using partitioning.
20. Calculate $$834 \times 3$$ using partitioning.

Answers and Explanations

Easy Level Answers

1. $$12 \times 3 = 36$$ (Partition: 10 + 2)
2. $$25 \times 4 = 100$$ (Partition: 20 + 5)
3. $$15 \times 2 = 30$$ (Partition: 10 + 5)
4. $$22 \times 5 = 110$$ (Partition: 20 + 2)
5. $$30 \times 6 = 180$$ (Partition: 30 + 0)
6. $$14 \times 3 = 42$$ (Partition: 10 + 4)
7. $$10 \times 9 = 90$$ (Partition: 10 + 0)
8. $$18 \times 4 = 72$$ (Partition: 10 + 8)
9. $$20 \times 7 = 140$$ (Partition: 20 + 0)
10. $$36 \times 2 = 72$$ (Partition: 30 + 6)
11. $$24 \times 3 = 72$$ (Partition: 20 + 4)
12. $$16 \times 5 = 80$$ (Partition: 10 + 6)
13. $$28 \times 4 = 112$$ (Partition: 20 + 8)
14. $$32 \times 3 = 96$$ (Partition: 30 + 2)
15. $$40 \times 2 = 80$$ (Partition: 40 + 0)
16. $$50 \times 1 = 50$$ (Partition: 50 + 0)
17. $$12 \times 5 = 60$$ (Partition: 10 + 2)
18. $$15 \times 4 = 60$$ (Partition: 10 + 5)
19. $$21 \times 2 = 42$$ (Partition: 20 + 1)
20. $$33 \times 3 = 99$$ (Partition: 30 + 3)

Medium Level Answers

1. $$45 \times 6 = 270$$ (Partition: 40 + 5)
2. $$52 \times 3 = 156$$ (Partition: 50 + 2)
3. $$63 \times 4 = 252$$ (Partition: 60 + 3)
4. $$76 \times 5 = 380$$ (Partition: 70 + 6)
5. $$34 \times 7 = 238$$ (Partition: 30 + 4)
6. $$81 \times 2 = 162$$ (Partition: 80 + 1)
7. $$22 \times 8 = 176$$ (Partition: 20 + 2)
8. $$39 \times 6 = 234$$ (Partition: 30 + 9)
9. $$47 \times 3 = 141$$ (Partition: 40 + 7)
10. $$54 \times 5 = 270$$ (Partition: 50 + 4)
11. $$29 \times 7 = 203$$ (Partition: 20 + 9)
12. $$68 \times 4 = 272$$ (Partition: 60 + 8)
13. $$33 \times 6 = 198$$ (Partition: 30 + 3)
14. $$72 \times 3 = 216$$ (Partition: 70 + 2)
15. $$85 \times 2 = 170$$ (Partition: 80 + 5)
16. $$40 \times 9 = 360$$ (Partition: 40 + 0)
17. $$93 \times 4 = 372$$ (Partition: 90 + 3)
18. $$57 \times 5 = 285$$ (Partition: 50 + 7)
19. $$48 \times 3 = 144$$ (Partition: 40 + 8)
20. $$70 \times 2 = 140$$ (Partition: 70 + 0)

Hard Level Answers

1. $$126 \times 7 = 882$$ (Partition: 120 + 6)
2. $$234 \times 5 = 1170$$ (Partition: 230 + 4)
3. $$167 \times 8 = 1336$$ (Partition: 160 + 7)
4. $$312 \times 4 = 1248$$ (Partition: 300 + 12)
5. $$245 \times 3 = 735$$ (Partition: 240 + 5)
6. $$198 \times 6 = 1188$$ (Partition: 180 + 18)
7. $$275 \times 9 = 2475$$ (Partition: 270 + 5)
8. $$384 \times 2 = 768$$ (Partition: 380 + 4)
9. $$157 \times 5 = 785$$ (Partition: 150 + 7)
10. $$420 \times 4 = 1680$$ (Partition: 400 + 20)
11. $$289 \times 3 = 867$$ (Partition: 280 + 9)
12. $$395 \times 6 = 2370$$ (Partition: 390 + 5)
13. $$512 \times 2 = 1024$$ (Partition: 500 + 12)
14. $$630 \times 5 = 3150$$ (Partition: 600 + 30)
15. $$726 \times 3 = 2178$$ (Partition: 720 + 6)
16. $$842 \times 4 = 3368$$ (Partition: 840 + 2)
17. $$913 \times 2 = 1826$$ (Partition: 900 + 13)
18. $$234 \times 6 = 1404$$ (Partition: 230 + 4)
19. $$178 \times 5 = 890$$ (Partition: 170 + 8)
20. $$834 \times 3 = 2502$$ (Partition: 830 + 4)

Feel free to practice these questions and use partitioning to help with your multiplications. Keep up the great work, Year 6!