Year 4: Scaling, correspondence and multiplying three numbers
Part of the Year 4 short multiplication and short division chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Scaling, correspondence and multiplying three numbers
Scaling. Alex has 6 marbles. Ben has 4 times as many marbles as Alex. “4 times as many” means 4 equal groups, and each group is the same size as Alex’s 6. So Ben has 4 × 6 = 24 marbles. We can draw it as a bar model: Alex has one box, and Ben has four boxes the same size.
The same picture helps you go backwards. If Ben has 24 marbles, which is 4 times as many as Alex, then 4 boxes make 24, so one box is 24 ÷ 4 = 6. Alex has 6.
Be careful: “4 times as many” is multiplying by 4. “4 more” is adding 4. They are very different! Alex has 6, so 4 more is 10 but 4 times as many is 24. We use scaling for lengths, heights, masses and money too: “3 times as long”, “5 times as heavy”, “twice the price”.
Correspondence. Priya has 3 hats and 5 tops. She picks one hat and one top. How many different outfits can she make? Each hat can go with any of the 5 tops. That is 5 outfits for the first hat, 5 for the second and 5 for the third. Make a table: each box is one outfit.
| hat \ top | stripy | spotty | plain | checked | yellow |
| red hat | 1 | 2 | 3 | 4 | 5 |
| blue hat | 6 | 7 | 8 | 9 | 10 |
| green hat | 11 | 12 | 13 | 14 | 15 |
There are 3 rows of 5 boxes. It is an array! So the number of outfits is 3 × 5 = 15. We say that 3 objects are connected to 5 objects in 3 × 5 ways. It works for roads, meals, sandwiches and lots more. If Priya also has 2 scarves, each of the 15 outfits can have either scarf: 15 × 2 = 30.
Multiplying three numbers. You can multiply three numbers in any order. Look for two numbers that make an easy answer, like a pair that makes 10 or 100, and multiply those first. 5 × 17 × 2: 5 × 2 = 10, then 17 × 10 = 170. Much easier than 5 × 17 first!
Key words. Scaling means making an amount a number of times bigger or smaller. A combination is one choice from each group put together.
Key ideas
- “n times as many” means n equal groups: multiply the small amount by n.
- To find the small amount, divide the big amount by n.
- “More than” means add. “Times as many” means multiply.
- If every one of n things can go with every one of m things, there are n × m combinations.
- Three groups of choices: multiply all three numbers.
- You can multiply three numbers in any order. Make 10 or 100 first if you can.
Key words. Scaling means making something a number of times bigger. “3 times as many” means 3 equal groups, so you multiply by 3. To go back, divide by 3.
Method. 6 times as many means 6 equal groups, each the same size as the smaller amount. Multiply the smaller amount by 6.
- Draw a bar model. Maya has one box. Dad has 6 boxes the same size.
- Choose the operation. 6 equal boxes: multiply the size of one box by 6.14 × 6
- Work it out. Use a written method if you need to.14 × 6 = 84
T O 1 4 × 6 8 4 2 - Write the answer. Include the unit.84 stickers
Check. Divide back: 84 ÷ 6 = 14. ✓
Watch out. “6 times as many” is multiplying by 6. It is not adding 6.
Key words. Scaling means making something a number of times bigger. “3 times as many” means 3 equal groups, so you multiply by 3. To go back, divide by 3.
Method. 4 times as many means 4 equal groups, each the same size as the smaller amount. Multiply the smaller amount by 4.
- Draw a bar model. Zainab has one box. Liam has 4 boxes the same size.
- Choose the operation. 4 equal boxes: multiply the size of one box by 4.£25 × 4
- Work it out. Use a written method if you need to.£25 × 4 = £100
H T O 2 5 × 4 1 0 0 1 2 - Write the answer. Include the unit.£100
Check. Divide back: £100 ÷ 4 = £25. ✓
Watch out. “4 times as many” is multiplying by 4. It is not adding 4.
Key words. Scaling means making something a number of times bigger. “3 times as many” means 3 equal groups, so you multiply by 3. To go back, divide by 3.
Method. Noah has 4 times as many as Priya. So Noah’s amount is split into 4 equal boxes and Priya has one box. Divide by 4.
- Draw a bar model. Noah has 4 equal boxes. Priya has one box the same size.
- Choose the operation. We know the total of the 4 boxes and want the size of one box: divide by 4.96 ÷ 4
- Work it out. Use the bus stop method.96 ÷ 4 = 24
2 4 4 9 16 - Write the answer. Include the unit.24 books
Check. Multiply back: 24 × 4 = 96. ✓
Watch out. The one with “times as many” has the bigger amount. To find the smaller amount, divide, do not multiply.
Key words. A combination is one choice from each group put together. To find how many combinations there are, multiply the numbers of choices.
Method. Each choice from one group can be paired with every choice from the other group. So multiply the numbers of choices together.
- Take just one hat. Pick the first hat. It can go with any of the 5 tops, so that makes 5 outfits.1 hat → 5 outfits
- Do the same for every hat. All the hats have the same choices. There are 3 hats, so there are 3 groups of 5 outfits.5 + 5 + 5 = 15
- Show every choice in a table. Each box is one outfit: one hat with one top. Count the boxes: it is an array.
hat \ top top 1 top 2 top 3 top 4 top 5 hat 1 1 2 3 4 5 hat 2 6 7 8 9 10 hat 3 11 12 13 14 15 - Multiply. 3 rows of 5 is a multiplication.3 × 5 = 15
- Write the answer. Say what the number means.15 different outfits
Check. Swap the numbers: 5 × 3 = 15. ✓
Watch out. Do not add the numbers. 3 + 5 = 8 would only count each item once. Every hat goes with every top, so multiply.
Key words. A combination is one choice from each group put together. To find how many combinations there are, multiply the numbers of choices.
Method. Each choice from one group can be paired with every choice from the other group. So multiply the numbers of choices together.
- Take just one flavour. Pick the first flavour. It can go with any of the 6 toppings, so that makes 6 ice creams.1 flavour → 6 ice creams
- Do the same for every flavour. All the flavours have the same choices. There are 4 flavours, so there are 4 groups of 6 ice creams.6 + 6 + 6 + 6 = 24
- Show every choice in a table. Each box is one ice cream: one flavour with one topping. Count the boxes: it is an array.
flavour \ topping topping 1 topping 2 topping 3 topping 4 topping 5 topping 6 flavour 1 1 2 3 4 5 6 flavour 2 7 8 9 10 11 12 flavour 3 13 14 15 16 17 18 flavour 4 19 20 21 22 23 24 - Multiply. 4 rows of 6 is a multiplication.4 × 6 = 24
- Write the answer. Say what the number means.24 different ice creams
Check. Swap the numbers: 6 × 4 = 24. ✓
Watch out. Do not add the numbers. 3 + 5 = 8 would only count each item once. Every flavour goes with every topping, so multiply.
Key words. A combination is one choice from each group put together. To find how many combinations there are, multiply the numbers of choices.
Method. Each choice from one group can be paired with every choice from the other group. So multiply the numbers of choices together.
- Take just one road. Pick the first road. It can go with any of the 4 roads, so that makes 4 routes.1 road → 4 routes
- Do the same for every road. All the roads have the same choices. There are 3 roads, so there are 3 groups of 4 routes.4 + 4 + 4 = 12
- Multiply. 3 rows of 4 is a multiplication.3 × 4 = 12
- Write the answer. Say what the number means.12 different routes
Check. Swap the numbers: 4 × 3 = 12. ✓
Watch out. Do not add the numbers. 3 + 5 = 8 would only count each item once. Every road goes with every road, so multiply.
Key words. A combination is one choice from each group put together. To find how many combinations there are, multiply the numbers of choices.
Method. Each choice from one group can be paired with every choice from the other group. So multiply the numbers of choices together.
- Find how many choices there are for the first two. Each of the 3 skirts can go with each of the 4 tops.3 × 4 = 12
- Now bring in the pairs of shoes. Each of those 12 choices can go with each of the 2 pairs of shoes.12 × 2 = 24
- Write the answer. Say what the number means.24 different outfits
Check. Multiply in a different order: 4 × 2 = 8, then 8 × 3 = 24. ✓
Watch out. Do not add the numbers. 3 + 5 = 8 would only count each item once. Every skirt goes with every top, so multiply.
Method. Each of the 4 starters goes with every main, so the 36 meals are 4 equal groups. Division undoes multiplication.
- Write it as a multiplication with a missing number. 4 starters × the number of mains = 36 meals.4 × ? = 36
- Divide to find the missing number. Share the 36 meals between the 4 starters.36 ÷ 4 = 9
0 9 4 3 36 - Write the answer. 9 mains
Check. Multiply back: 4 × 9 = 36. ✓
Watch out. Use the opposite operation: if the total is known, divide by the number you know.
Key words. You can multiply three numbers in any order and the answer is the same.
Method. You can multiply three numbers in any order. Look for two numbers that make an easy answer (like a pair that makes 10 or 100) and multiply those first.
- Look for a pair that is easy to multiply. 5 × 2 = 10, and multiplying by 10 is easy.5 × 2 = 10
- Multiply by the last number, 17. Multiplying by 10 moves every digit 1 place to the left.10 × 17: move the digits of 17 1 place to the left.
10 × 17 = 170 - Write the answer. 5 × 17 × 2 = 170
Check. Try a different order: 34 × 5 = 170. ✓
Watch out. You can multiply in any order. Pick the pair that gives an easy answer first.
Key words. You can multiply three numbers in any order and the answer is the same.
Method. You can multiply three numbers in any order. Look for two numbers that make an easy answer (like a pair that makes 10 or 100) and multiply those first.
- Look for a pair that is easy to multiply. 25 × 4 = 100, and multiplying by 100 is easy.25 × 4 = 100
- Multiply by the last number, 6. Multiplying by 100 moves every digit 2 places to the left.100 × 6: move the digits of 6 2 places to the left.
100 × 6 = 600 - Write the answer. 25 × 4 × 6 = 600
Check. Try a different order: 24 × 25 = 600. ✓
Watch out. You can multiply in any order. Pick the pair that gives an easy answer first.
Watch out
“Times as many” is not “more”. 4 times as many as 6 is 24 (multiply). 4 more than 6 is 10 (add). For outfits, do not add the numbers: 3 hats and 5 tops make 3 × 5 = 15 outfits, not 3 + 5 = 8, because every hat goes with every top.Exercise 4F Scaling, correspondence and three numbers
Non-calculatorKey words. Scaling means making something a number of times bigger. “3 times as many” means 3 equal groups, so you multiply by 3. To go back, divide by 3.
Method. 5 times as many means 5 equal groups, each the same size as the smaller amount. Multiply the smaller amount by 5.
- Draw a bar model. Ella has one box. Omar has 5 boxes the same size.
- Choose the operation. 5 equal boxes: multiply the size of one box by 5.18 × 5
- Work it out. Use a written method if you need to.18 × 5 = 90
T O 1 8 × 5 9 0 4 - Write the answer. Include the unit.90 stickers
Check. Divide back: 90 ÷ 5 = 18. ✓
Watch out. “5 times as many” is multiplying by 5. It is not adding 5.
Key words. Scaling means making something a number of times bigger. “3 times as many” means 3 equal groups, so you multiply by 3. To go back, divide by 3.
Method. 3 times as many means 3 equal groups, each the same size as the smaller amount. Multiply the smaller amount by 3.
- Draw a bar model. Pencil has one box. Ruler has 3 boxes the same size.
- Choose the operation. 3 equal boxes: multiply the size of one box by 3.17 × 3
- Work it out. Use a written method if you need to.17 × 3 = 51
T O 1 7 × 3 5 1 2 - Write the answer. Include the unit.51 cm
Check. Divide back: 51 ÷ 3 = 17. ✓
Watch out. “3 times as many” is multiplying by 3. It is not adding 3.
Key words. Scaling means making something a number of times bigger. “3 times as many” means 3 equal groups, so you multiply by 3. To go back, divide by 3.
Method. 4 times as many means 4 equal groups, each the same size as the smaller amount. Multiply the smaller amount by 4.
- Draw a bar model. Apples has one box. Melon has 4 boxes the same size.
- Choose the operation. 4 equal boxes: multiply the size of one box by 4.125 × 4
- Work it out. Use a written method if you need to.125 × 4 = 500
H T O 1 2 5 × 4 5 0 0 1 2 - Write the answer. Include the unit.500 g
Check. Divide back: 500 ÷ 4 = 125. ✓
Watch out. “4 times as many” is multiplying by 4. It is not adding 4.
Key words. Scaling means making something a number of times bigger. “3 times as many” means 3 equal groups, so you multiply by 3. To go back, divide by 3.
Method. 6 times as many means 6 equal groups, each the same size as the smaller amount. Multiply the smaller amount by 6.
- Draw a bar model. Pen has one box. Book has 6 boxes the same size.
- Choose the operation. 6 equal boxes: multiply the size of one box by 6.45p × 6
- Work it out. Use a written method if you need to.45p × 6 = 270p
H T O 4 5 × 6 2 7 0 2 3 - Write the answer. Include the unit.270p
Check. Divide back: 270p ÷ 6 = 45p. ✓
Watch out. “6 times as many” is multiplying by 6. It is not adding 6.
Key words. Scaling means making something a number of times bigger. “3 times as many” means 3 equal groups, so you multiply by 3. To go back, divide by 3.
Method. Dad has 6 times as many as Ben. So Dad’s amount is split into 6 equal boxes and Ben has one box. Divide by 6.
- Draw a bar model. Dad has 6 equal boxes. Ben has one box the same size.
- Choose the operation. We know the total of the 6 boxes and want the size of one box: divide by 6.84 ÷ 6
- Work it out. Use the bus stop method.84 ÷ 6 = 14
1 4 6 8 24 - Write the answer. Include the unit.14 stamps
Check. Multiply back: 14 × 6 = 84. ✓
Watch out. The one with “times as many” has the bigger amount. To find the smaller amount, divide, do not multiply.
Key words. Scaling means making something a number of times bigger. “3 times as many” means 3 equal groups, so you multiply by 3. To go back, divide by 3.
Method. Tree has 4 times as many as Shed. So Tree’s amount is split into 4 equal boxes and Shed has one box. Divide by 4.
- Draw a bar model. Tree has 4 equal boxes. Shed has one box the same size.
- Choose the operation. We know the total of the 4 boxes and want the size of one box: divide by 4.96 ÷ 4
- Work it out. Use the bus stop method.96 ÷ 4 = 24
2 4 4 9 16 - Write the answer. Include the unit.24 m
Check. Multiply back: 24 × 4 = 96. ✓
Watch out. The one with “times as many” has the bigger amount. To find the smaller amount, divide, do not multiply.
Key words. Scaling means making something a number of times bigger. “3 times as many” means 3 equal groups, so you multiply by 3. To go back, divide by 3.
Method. Bike has 4 times as many as Helmet. So Bike’s amount is split into 4 equal boxes and Helmet has one box. Divide by 4.
- Draw a bar model. Bike has 4 equal boxes. Helmet has one box the same size.
- Choose the operation. We know the total of the 4 boxes and want the size of one box: divide by 4.£192 ÷ 4
- Work it out. Use the bus stop method.£192 ÷ 4 = £48
0 4 8 4 1 19 32 - Write the answer. Include the unit.£48
Check. Multiply back: £48 × 4 = £192. ✓
Watch out. The one with “times as many” has the bigger amount. To find the smaller amount, divide, do not multiply.
Key words. Scaling means making something a number of times bigger. “3 times as many” means 3 equal groups, so you multiply by 3. To go back, divide by 3.
Method. Lorry has 5 times as many as Van. So Lorry’s amount is split into 5 equal boxes and Van has one box. Divide by 5.
- Draw a bar model. Lorry has 5 equal boxes. Van has one box the same size.
- Choose the operation. We know the total of the 5 boxes and want the size of one box: divide by 5.135 ÷ 5
- Work it out. Use the bus stop method.135 ÷ 5 = 27
0 2 7 5 1 13 35 - Write the answer. Include the unit.27 boxes
Check. Multiply back: 27 × 5 = 135. ✓
Watch out. The one with “times as many” has the bigger amount. To find the smaller amount, divide, do not multiply.
Key words. Scaling means making something a number of times bigger. “3 times as many” means 3 equal groups, so you multiply by 3. To go back, divide by 3.
Method. 6 times as many means 6 equal groups, each the same size as the smaller amount. Multiply the smaller amount by 6.
- Draw a bar model. Sam has one box. Tia has 6 boxes the same size.
- Choose the operation. 6 equal boxes: multiply the size of one box by 6.8 × 6
- Work it out. Use a written method if you need to.8 × 6 = 48
- Write the answer. Include the unit.48 books
Check. Divide back: 48 ÷ 6 = 8. ✓
Watch out. “6 times as many” is multiplying by 6. It is not adding 6.
Key words. Scaling means making something a number of times bigger. “3 times as many” means 3 equal groups, so you multiply by 3. To go back, divide by 3.
Method. Tia has 6 times as many as Sam. So Tia’s amount is split into 6 equal boxes and Sam has one box. Divide by 6.
- Draw a bar model. Tia has 6 equal boxes. Sam has one box the same size.
- Choose the operation. We know the total of the 6 boxes and want the size of one box: divide by 6.48 ÷ 6
- Work it out. Use the bus stop method.48 ÷ 6 = 8
0 8 6 4 48 - Write the answer. Include the unit.8 books
Check. Multiply back: 8 × 6 = 48. ✓
Watch out. The one with “times as many” has the bigger amount. To find the smaller amount, divide, do not multiply.
Key words. Scaling means making something a number of times bigger. “3 times as many” means 3 equal groups, so you multiply by 3. To go back, divide by 3.
Method. 7 times as many means 7 equal groups, each the same size as the smaller amount. Multiply the smaller amount by 7.
- Draw a bar model. Kai has one box. Jo has 7 boxes the same size.
- Choose the operation. 7 equal boxes: multiply the size of one box by 7.9 × 7
- Work it out. Use a written method if you need to.9 × 7 = 63
- Write the answer. Include the unit.63 marbles
Check. Divide back: 63 ÷ 7 = 9. ✓
Watch out. “7 times as many” is multiplying by 7. It is not adding 7.
Key words. Scaling means making something a number of times bigger. “3 times as many” means 3 equal groups, so you multiply by 3. To go back, divide by 3.
Method. Jo has 7 times as many as Kai. So Jo’s amount is split into 7 equal boxes and Kai has one box. Divide by 7.
- Draw a bar model. Jo has 7 equal boxes. Kai has one box the same size.
- Choose the operation. We know the total of the 7 boxes and want the size of one box: divide by 7.63 ÷ 7
- Work it out. Use the bus stop method.63 ÷ 7 = 9
0 9 7 6 63 - Write the answer. Include the unit.9 marbles
Check. Multiply back: 9 × 7 = 63. ✓
Watch out. The one with “times as many” has the bigger amount. To find the smaller amount, divide, do not multiply.
Key words. A combination is one choice from each group put together. To find how many combinations there are, multiply the numbers of choices.
Method. Each choice from one group can be paired with every choice from the other group. So multiply the numbers of choices together.
- Take just one T-shirt. Pick the first T-shirt. It can go with any of the 6 pairs of shorts, so that makes 6 outfits.1 T-shirt → 6 outfits
- Do the same for every T-shirt. All the T-shirts have the same choices. There are 4 T-shirts, so there are 4 groups of 6 outfits.6 + 6 + 6 + 6 = 24
- Show every choice in a table. Each box is one outfit: one T-shirt with one pair of shorts. Count the boxes: it is an array.
T-shirt \ pair of shorts pair of shorts 1 pair of shorts 2 pair of shorts 3 pair of shorts 4 pair of shorts 5 pair of shorts 6 T-shirt 1 1 2 3 4 5 6 T-shirt 2 7 8 9 10 11 12 T-shirt 3 13 14 15 16 17 18 T-shirt 4 19 20 21 22 23 24 - Multiply. 4 rows of 6 is a multiplication.4 × 6 = 24
- Write the answer. Say what the number means.24 different outfits
Check. Swap the numbers: 6 × 4 = 24. ✓
Watch out. Do not add the numbers. 3 + 5 = 8 would only count each item once. Every T-shirt goes with every pair of shorts, so multiply.
Key words. A combination is one choice from each group put together. To find how many combinations there are, multiply the numbers of choices.
Method. Each choice from one group can be paired with every choice from the other group. So multiply the numbers of choices together.
- Take just one starter. Pick the first starter. It can go with any of the 4 mains, so that makes 4 meals.1 starter → 4 meals
- Do the same for every starter. All the starters have the same choices. There are 5 starters, so there are 5 groups of 4 meals.4 + 4 + 4 + 4 + 4 = 20
- Show every choice in a table. Each box is one meal: one starter with one main. Count the boxes: it is an array.
starter \ main main 1 main 2 main 3 main 4 starter 1 1 2 3 4 starter 2 5 6 7 8 starter 3 9 10 11 12 starter 4 13 14 15 16 starter 5 17 18 19 20 - Multiply. 5 rows of 4 is a multiplication.5 × 4 = 20
- Write the answer. Say what the number means.20 different meals
Check. Swap the numbers: 4 × 5 = 20. ✓
Watch out. Do not add the numbers. 3 + 5 = 8 would only count each item once. Every starter goes with every main, so multiply.
Key words. A combination is one choice from each group put together. To find how many combinations there are, multiply the numbers of choices.
Method. Each choice from one group can be paired with every choice from the other group. So multiply the numbers of choices together.
- Take just one type of bread. Pick the first type of bread. It can go with any of the 5 fillings, so that makes 5 sandwiches.1 type of bread → 5 sandwiches
- Do the same for every type of bread. All the types of bread have the same choices. There are 6 types of bread, so there are 6 groups of 5 sandwiches.5 + 5 + 5 + 5 + 5 + 5 = 30
- Show every choice in a table. Each box is one sandwich: one type of bread with one filling. Count the boxes: it is an array.
type of bread \ filling filling 1 filling 2 filling 3 filling 4 filling 5 type of bread 1 1 2 3 4 5 type of bread 2 6 7 8 9 10 type of bread 3 11 12 13 14 15 type of bread 4 16 17 18 19 20 type of bread 5 21 22 23 24 25 type of bread 6 26 27 28 29 30 - Multiply. 6 rows of 5 is a multiplication.6 × 5 = 30
- Write the answer. Say what the number means.30 different sandwiches
Check. Swap the numbers: 5 × 6 = 30. ✓
Watch out. Do not add the numbers. 3 + 5 = 8 would only count each item once. Every type of bread goes with every filling, so multiply.
Key words. A combination is one choice from each group put together. To find how many combinations there are, multiply the numbers of choices.
Method. Each choice from one group can be paired with every choice from the other group. So multiply the numbers of choices together.
- Take just one drink. Pick the first drink. It can go with any of the 3 cakes, so that makes 3 pairs.1 drink → 3 pairs
- Do the same for every drink. All the drinks have the same choices. There are 7 drinks, so there are 7 groups of 3 pairs.7 groups of 3
- Multiply. 7 rows of 3 is a multiplication.7 × 3 = 21
- Write the answer. Say what the number means.21 different pairs
Check. Swap the numbers: 3 × 7 = 21. ✓
Watch out. Do not add the numbers. 3 + 5 = 8 would only count each item once. Every drink goes with every cake, so multiply.
Key words. A combination is one choice from each group put together. To find how many combinations there are, multiply the numbers of choices.
Method. Each choice from one group can be paired with every choice from the other group. So multiply the numbers of choices together.
- Find how many choices there are for the first two. Each of the 3 skirts can go with each of the 4 tops.3 × 4 = 12
- Now bring in the scarves. Each of those 12 choices can go with each of the 2 scarves.12 × 2 = 24
- Write the answer. Say what the number means.24 different outfits
Check. Multiply in a different order: 4 × 2 = 8, then 8 × 3 = 24. ✓
Watch out. Do not add the numbers. 3 + 5 = 8 would only count each item once. Every skirt goes with every top, so multiply.
Key words. A combination is one choice from each group put together. To find how many combinations there are, multiply the numbers of choices.
Method. Each choice from one group can be paired with every choice from the other group. So multiply the numbers of choices together.
- Find how many choices there are for the first two. Each of the 2 starters can go with each of the 5 mains.2 × 5 = 10
- Now bring in the puddings. Each of those 10 choices can go with each of the 4 puddings.10 × 4 = 40
- Write the answer. Say what the number means.40 different meals
Check. Multiply in a different order: 5 × 4 = 20, then 20 × 2 = 40. ✓
Watch out. Do not add the numbers. 3 + 5 = 8 would only count each item once. Every starter goes with every main, so multiply.
Method. Each of the 4 starters goes with every main, so the 36 meals are 4 equal groups. Division undoes multiplication.
- Write it as a multiplication with a missing number. 4 starters × the number of mains = 36 meals.4 × ? = 36
- Divide to find the missing number. Share the 36 meals between the 4 starters.36 ÷ 4 = 9
0 9 4 3 36 - Write the answer. 9 mains
Check. Multiply back: 4 × 9 = 36. ✓
Watch out. Use the opposite operation: if the total is known, divide by the number you know.
Method. Each of the 4 skirts goes with every top, so the 28 outfits are 4 equal groups. Division undoes multiplication.
- Write it as a multiplication with a missing number. 4 skirts × the number of tops = 28 outfits.4 × ? = 28
- Divide to find the missing number. Share the 28 outfits between the 4 skirts.28 ÷ 4 = 7
0 7 4 2 28 - Write the answer. 7 tops
Check. Multiply back: 4 × 7 = 28. ✓
Watch out. Use the opposite operation: if the total is known, divide by the number you know.
Method. Each of the 5 flavours goes with every cone, so the 45 ice creams are 5 equal groups. Division undoes multiplication.
- Write it as a multiplication with a missing number. 5 flavours × the number of cones = 45 ice creams.5 × ? = 45
- Divide to find the missing number. Share the 45 ice creams between the 5 flavours.45 ÷ 5 = 9
0 9 5 4 45 - Write the answer. 9 cones
Check. Multiply back: 5 × 9 = 45. ✓
Watch out. Use the opposite operation: if the total is known, divide by the number you know.
Key words. You can multiply three numbers in any order and the answer is the same.
Method. You can multiply three numbers in any order. Look for two numbers that make an easy answer (like a pair that makes 10 or 100) and multiply those first.
- Look for a pair that is easy to multiply. 2 × 5 = 10, and multiplying by 10 is easy.2 × 5 = 10
- Multiply by the last number, 17. Multiplying by 10 moves every digit 1 place to the left.10 × 17: move the digits of 17 1 place to the left.
10 × 17 = 170 - Write the answer. 2 × 5 × 17 = 170
Check. Try a different order: 85 × 2 = 170. ✓
Watch out. You can multiply in any order. Pick the pair that gives an easy answer first.
Key words. You can multiply three numbers in any order and the answer is the same.
Method. You can multiply three numbers in any order. Look for two numbers that make an easy answer (like a pair that makes 10 or 100) and multiply those first.
- Look for a pair that is easy to multiply. 4 × 25 = 100, and multiplying by 100 is easy.4 × 25 = 100
- Multiply by the last number, 3. Multiplying by 100 moves every digit 2 places to the left.100 × 3: move the digits of 3 2 places to the left.
100 × 3 = 300 - Write the answer. 4 × 25 × 3 = 300
Check. Try a different order: 75 × 4 = 300. ✓
Watch out. You can multiply in any order. Pick the pair that gives an easy answer first.
Key words. You can multiply three numbers in any order and the answer is the same.
Method. You can multiply three numbers in any order. Look for two numbers that make an easy answer (like a pair that makes 10 or 100) and multiply those first.
- Look for a pair that is easy to multiply. 5 × 8 = 40, which we can work out easily.5 × 8 = 40
- Multiply by the last number, 7. Multiply the answer, 40, by the last number, 7.4 × 7 = 28, so 4 tens × 7 = 28 tens
40 × 7 = 280 - Write the answer. 5 × 8 × 7 = 280
Check. Try a different order: 56 × 5 = 280. ✓
Watch out. You can multiply in any order. Pick the pair that gives an easy answer first.
Key words. You can multiply three numbers in any order and the answer is the same.
Method. You can multiply three numbers in any order. Look for two numbers that make an easy answer (like a pair that makes 10 or 100) and multiply those first.
- Look for a pair that is easy to multiply. 20 × 5 = 100, and multiplying by 100 is easy.20 × 5 = 100
- Multiply by the last number, 9. Multiplying by 100 moves every digit 2 places to the left.100 × 9: move the digits of 9 2 places to the left.
100 × 9 = 900 - Write the answer. 20 × 5 × 9 = 900
Check. Try a different order: 45 × 20 = 900. ✓
Watch out. You can multiply in any order. Pick the pair that gives an easy answer first.
Key words. You can multiply three numbers in any order and the answer is the same.
Method. You can multiply three numbers in any order. Look for two numbers that make an easy answer (like a pair that makes 10 or 100) and multiply those first.
- Look for a pair that is easy to multiply. 2 × 5 = 10, and multiplying by 10 is easy.2 × 5 = 10
- Multiply by the last number, 45. Multiplying by 10 moves every digit 1 place to the left.10 × 45: move the digits of 45 1 place to the left.
10 × 45 = 450 - Write the answer. 2 × 45 × 5 = 450
Check. Try a different order: 225 × 2 = 450. ✓
Watch out. You can multiply in any order. Pick the pair that gives an easy answer first.
Key words. You can multiply three numbers in any order and the answer is the same.
Method. You can multiply three numbers in any order. Look for two numbers that make an easy answer (like a pair that makes 10 or 100) and multiply those first.
- Look for a pair that is easy to multiply. 50 × 2 = 100, and multiplying by 100 is easy.50 × 2 = 100
- Multiply by the last number, 3. Multiplying by 100 moves every digit 2 places to the left.100 × 3: move the digits of 3 2 places to the left.
100 × 3 = 300 - Write the answer. 50 × 3 × 2 = 300
Check. Try a different order: 6 × 50 = 300. ✓
Watch out. You can multiply in any order. Pick the pair that gives an easy answer first.
Key words. You can multiply three numbers in any order and the answer is the same.
Method. You can multiply three numbers in any order. Look for two numbers that make an easy answer (like a pair that makes 10 or 100) and multiply those first.
- Look for a pair that is easy to multiply. 5 × 20 = 100, and multiplying by 100 is easy.5 × 20 = 100
- Multiply by the last number, 4. Multiplying by 100 moves every digit 2 places to the left.100 × 4: move the digits of 4 2 places to the left.
100 × 4 = 400 - Write the answer. 4 × 5 × 20 = 400
Check. Try a different order: 100 × 4 = 400. ✓
Watch out. You can multiply in any order. Pick the pair that gives an easy answer first.
Method. Read the problem, draw a bar model, then decide which operations to use. Work out one step at a time.
- Step 1: Find how many marbles Amir has. Amir has 4 times as many as Leo, so multiply 7 by 4.7 × 4 = 28
- Step 2: Find how many marbles Jo has. Jo has 3 times as many as Amir, so multiply the answer by 3.28 × 3 = 84
T O 2 8 × 3 8 4 2 - Write the answer. Include the unit and make sure it answers the question.84 marbles
Check. Another way: Jo has 4 × 3 = 12 times as many as Leo. 7 × 12 = 84. ✓
Watch out. Jo has 3 times as many as Amir, not 3 times as many as Leo.
Method. Read the problem, draw a bar model, then decide which operations to use. Work out one step at a time.
- Step 1: Find how many apples Dad picks. Dad picks 4 times as many as Ali, so multiply 35 by 4.35 × 4 = 140
H T O 3 5 × 4 1 4 0 1 2 - Step 2: Find the total. Add the apples Ali picks and the apples Dad picks.35 + 140 = 175
H T O 3 5 + 1 4 0 1 7 5 - Write the answer. Include the unit and make sure it answers the question.175 apples
Check. Another way: Ali has 1 box and Dad has 4 boxes of 35. 5 boxes × 35 = 175. ✓
Watch out. The question asks for the apples picked altogether. Do not stop after step 1.
Method. Work out how many sweets Ben and Cara each have, then compare.
- Find how many sweets Ben has. Ben has 5 more than Aisha, so add.8 + 5 = 13
- Find how many sweets Cara has. Cara has 5 times as many as Aisha, so multiply.8 × 5 = 40
- Compare. 40 is greater than 13.40 > 13
- Answer. Cara has more. She has 40 sweets and Ben has 13.
Check. Cara has 27 more than Ben: 40 − 13 = 27. ✓
Watch out. “5 more” means add 5. “5 times as many” means multiply by 5.
Method. Try some starting numbers. Compare adding 4 with multiplying by 4.
- Try the numbers. Work out both for each number.1: add 4 gives 5, multiply by 4 gives 4
2: add 4 gives 6, multiply by 4 gives 8
3: add 4 gives 7, multiply by 4 gives 12
10: add 4 gives 14, multiply by 4 gives 40 - Compare. For 1, adding is bigger (5 > 4). For 2, multiplying is bigger (8 > 6). For 3 and 10, multiplying is bigger.It changes depending on the number.
- Decide. One example works and others do not.Sometimes
Check. Only for 1 does adding 4 beat multiplying by 4 (1 + 4 = 5 and 1 × 4 = 4). ✓
Watch out. Give an example that works and one that does not. For “sometimes”, one of each is enough.
Method. Draw the table of 3 hats and 5 tops. A new hat is a new row. Count the boxes in the new row.
- Picture the 15 outfits. 3 rows (hats) of 5 boxes (tops).
hat \ top top 1 top 2 top 3 top 4 top 5 hat 1 1 2 3 4 5 hat 2 6 7 8 9 10 hat 3 11 12 13 14 15 - Add the new hat. The new hat can go with all 5 tops, so it makes a new row of 5 outfits.1 × 5 = 5 new outfits
- Check with the new total. 4 hats and 5 tops.4 × 5 = 20 outfits, and 20 − 15 = 5
Check. 3 × 5 = 15 and 4 × 5 = 20, so there are 5 more. ✓
Watch out. One more hat gives 5 more outfits (one for each top), not just 1 more.
A 3 hats and 5 tops. How many outfits?
B Sam has 5 stickers. Tom has 3 more. How many does Tom have?
C Ali has 5 books. Bea has 3 times as many. How many does Bea have?
D 15 sweets are shared between 3 children. How many does each child get?
Method. Work out the answer to each problem. The two that make 15 can be solved with 3 × 5.
- Work out A. Every hat goes with every top: multiply.3 × 5 = 15
- Work out B. “3 more” means add.5 + 3 = 8
- Work out C. “3 times as many” means multiply.5 × 3 = 15
- Work out D. Sharing means divide.15 ÷ 3 = 5
- Choose. A and C
Check. Both A and C are multiplication problems with the numbers 3 and 5. ✓
Watch out. Read each problem. B is an addition, and D is a division.
Method. Each three-course meal is one starter, one main and one pudding. Use what you know about the starters and puddings to find the mains.
- Find the number of starter-and-pudding pairs. Every starter goes with every pudding.3 × 2 = 6
- Write the missing-number sentence. The number of mains times 6 is the total.6 × ? = 30
- Divide to find the mains. Division is the opposite of multiplication.30 ÷ 6 = 5
Check. 3 × 5 × 2 = 15 × 2 = 30. ✓
Watch out. Multiply the numbers you know first, then divide the total by the result.