Year 4: Counting in steps of 6, 7, 9, 25 and 1000
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Counting in steps of 6, 7, 9, 25 and 1000
Counting in steps means adding the same number again and again. When you start at 0 and count in 6s, you say 6, 12, 18, 24, 30… These numbers are the multiples of 6. They are the answers in the 6 times table. Here is a hundred square with the multiples of 6 coloured in. Can you see the pattern?
Counting in 7s. When a jump crosses a tens number, jump to the tens number first. For 28 + 7: 28 + 2 = 30, then 30 + 5 = 35.
Counting in 9s. Adding 9 is the same as adding 10 and then taking away 1. So 36 + 9 is 36 + 10 = 46, then 46 − 1 = 45. The multiples of 9 go 9, 18, 27, 36, 45… The tens digit goes up by 1 and the ones digit goes down by 1.
Counting in 25s. Think of 25p coins. Four 25p coins make 100p, which is £1. So the last two digits go 25, 50, 75, 00, and then they start again.
Counting in 1000s. Only the thousands digit changes. Counting on from 2,350 we say 3,350, 4,350, 5,350… Counting back from 2,350 we say 1,350 and then 350. You can count back in every step too: take away the step each time.
Key words. A step is the jump you make each time. A multiple of a number is a number you get when you count in steps of that number from 0.
Key ideas
- Counting on means adding the step each time. Counting back means taking it away.
- Multiples of 9: add 10 and take away 1.
- Multiples of 25 end in 25, 50, 75 or 00.
- Counting in 1000s: only the thousands digit changes.
- A number is a multiple of 7 if you say it when you count in 7s from 0.
Key words. Counting in steps of 6 means adding 6 again and again. The numbers you say are multiples of 6 if you start from 0.
Method. Counting on in 6s means adding 6 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting on in steps of 6.Each jump is +6.
- Work out the numbers one jump at a time. Always start from the number you have just found.18 + 2 = 20 (a tens number), then + 4 more = 24
24 + 6 = 30
30 + 6 = 36
36 + 4 = 40 (a tens number), then + 2 more = 42 - Write the numbers in order. 24, 30, 36, 42
Check. Go the other way from the last number: 42 − 6 = 36. ✓
Watch out. Take care when you cross a tens number. Jump to the next ten first, then add the rest.
Key words. Counting in steps of 9 means taking away 9 again and again. The numbers you say are multiples of 9 if you start from 0.
Method. Counting back in 9s means taking away 9 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting back in steps of 9.Each jump is −9.
- Work out the numbers one jump at a time. Always start from the number you have just found.90 − 10 = 80, then add 1 back = 81
81 − 10 = 71, then add 1 back = 72
72 − 10 = 62, then add 1 back = 63
63 − 10 = 53, then add 1 back = 54 - Write the numbers in order. 81, 72, 63, 54
Check. Go the other way from the last number: 54 + 9 = 63. ✓
Watch out. Adding 9 is the same as adding 10 and then taking away 1. Taking away 9 is taking away 10 and adding 1 back.
Method. Find the size of one jump from two numbers you can see. Then use it to fill the gaps.
- Find two numbers you know and count the jumps between them. Each jump in the sequence is the same size.From 4,350 to 7,350 is 3 jumps.
The difference is 3,000.
3,000 ÷ 3 = 1,000 - Say which way and how big each jump is. The numbers are getting bigger, so we count on.Each jump is +1,000.
- Fill in the missing numbers. Add (or take away) one jump from a number you know.Number 2: 4,350 + 1,000 = 5,350
Number 3: 7,350 − 1,000 = 6,350 - Write the missing numbers. 5,350, 6,350
Check. Read the whole sequence again and check every jump is +1,000: 4,350, 5,350, 6,350, 7,350. ✓
Watch out. Do not just look at the first two numbers. Check the jump is the same all the way along.
Method. Find the size of one jump from two numbers you can see. Then use it to fill the gaps.
- Find two numbers you know and count the jumps between them. Each jump in the sequence is the same size.From 175 to 225 is 2 jumps.
The difference is 50.
50 ÷ 2 = 25 - Say which way and how big each jump is. The numbers are getting bigger, so we count on.Each jump is +25.
- Fill in the missing numbers. Add (or take away) one jump from a number you know.Number 2: 175 + 25 = 200
Number 5: 250 + 25 = 275 - Write the missing numbers. 200, 275
Check. Read the whole sequence again and check every jump is +25: 175, 200, 225, 250, 275. ✓
Watch out. Do not just look at the first two numbers. Check the jump is the same all the way along.
Method. A multiple of 6 is a number you say when you count in 6s. Count in 6s until you reach or pass 52.
- Count in 6s. Stop when you get to 52 or go past it.6, 12, 18, 24, 30, 36, 42, 48, 54
- Did we land exactly on 52? If we land on it, it is a multiple. If we jump over it, it is not.We reached 54. We jumped from 48 to 54 and missed 52, so no.
- Write the answer. Is 52 a multiple of 6? No
Check. 6 × 8 = 48 and 6 × 9 = 54. 52 is in between. ✓
Watch out
The first number you say is the first jump, not the number you start on. If you count on in 6s from 18, the first number you say is 24, not 18. Also take extra care when a jump crosses a tens or hundreds number, like 98 + 7.Exercise 1A Counting in steps
Non-calculatorKey words. Counting in steps of 6 means adding 6 again and again. The numbers you say are multiples of 6 if you start from 0.
Method. Counting on in 6s means adding 6 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting on in steps of 6.Each jump is +6.
- Work out the numbers one jump at a time. Always start from the number you have just found.12 + 6 = 18
18 + 2 = 20 (a tens number), then + 4 more = 24
24 + 6 = 30 - Write the numbers in order. 18, 24, 30
Check. Go the other way from the last number: 30 − 6 = 24. ✓
Watch out. Take care when you cross a tens number. Jump to the next ten first, then add the rest.
Key words. Counting in steps of 6 means adding 6 again and again. The numbers you say are multiples of 6 if you start from 0.
Method. Counting on in 6s means adding 6 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting on in steps of 6.Each jump is +6.
- Work out the numbers one jump at a time. Always start from the number you have just found.30 + 6 = 36
36 + 4 = 40 (a tens number), then + 2 more = 42
42 + 6 = 48 - Write the numbers in order. 36, 42, 48
Check. Go the other way from the last number: 48 − 6 = 42. ✓
Watch out. Take care when you cross a tens number. Jump to the next ten first, then add the rest.
Key words. Counting in steps of 6 means adding 6 again and again. The numbers you say are multiples of 6 if you start from 0.
Method. Counting on in 6s means adding 6 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting on in steps of 6.Each jump is +6.
- Work out the numbers one jump at a time. Always start from the number you have just found.48 + 2 = 50 (a tens number), then + 4 more = 54
54 + 6 = 60
60 + 6 = 66 - Write the numbers in order. 54, 60, 66
Check. Go the other way from the last number: 66 − 6 = 60. ✓
Watch out. Take care when you cross a tens number. Jump to the next ten first, then add the rest.
Key words. Counting in steps of 6 means adding 6 again and again. The numbers you say are multiples of 6 if you start from 0.
Method. Counting on in 6s means adding 6 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting on in steps of 6.Each jump is +6.
- Work out the numbers one jump at a time. Always start from the number you have just found.54 + 6 = 60
60 + 6 = 66
66 + 4 = 70 (a tens number), then + 2 more = 72 - Write the numbers in order. 60, 66, 72
Check. Go the other way from the last number: 72 − 6 = 66. ✓
Watch out. Take care when you cross a tens number. Jump to the next ten first, then add the rest.
Key words. Counting in steps of 7 means adding 7 again and again. The numbers you say are multiples of 7 if you start from 0.
Method. Counting on in 7s means adding 7 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting on in steps of 7.Each jump is +7.
- Work out the numbers one jump at a time. Always start from the number you have just found.14 + 6 = 20 (a tens number), then + 1 more = 21
21 + 7 = 28
28 + 2 = 30 (a tens number), then + 5 more = 35 - Write the numbers in order. 21, 28, 35
Check. Go the other way from the last number: 35 − 7 = 28. ✓
Watch out. Take care when you cross a tens number. Jump to the next ten first, then add the rest.
Key words. Counting in steps of 7 means adding 7 again and again. The numbers you say are multiples of 7 if you start from 0.
Method. Counting on in 7s means adding 7 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting on in steps of 7.Each jump is +7.
- Work out the numbers one jump at a time. Always start from the number you have just found.35 + 5 = 40 (a tens number), then + 2 more = 42
42 + 7 = 49
49 + 1 = 50 (a tens number), then + 6 more = 56 - Write the numbers in order. 42, 49, 56
Check. Go the other way from the last number: 56 − 7 = 49. ✓
Watch out. Take care when you cross a tens number. Jump to the next ten first, then add the rest.
Key words. Counting in steps of 7 means adding 7 again and again. The numbers you say are multiples of 7 if you start from 0.
Method. Counting on in 7s means adding 7 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting on in steps of 7.Each jump is +7.
- Work out the numbers one jump at a time. Always start from the number you have just found.49 + 1 = 50 (a tens number), then + 6 more = 56
56 + 4 = 60 (a tens number), then + 3 more = 63
63 + 7 = 70 - Write the numbers in order. 56, 63, 70
Check. Go the other way from the last number: 70 − 7 = 63. ✓
Watch out. Take care when you cross a tens number. Jump to the next ten first, then add the rest.
Key words. Counting in steps of 7 means adding 7 again and again. The numbers you say are multiples of 7 if you start from 0.
Method. Counting on in 7s means adding 7 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting on in steps of 7.Each jump is +7.
- Work out the numbers one jump at a time. Always start from the number you have just found.63 + 7 = 70
70 + 7 = 77
77 + 3 = 80 (a tens number), then + 4 more = 84 - Write the numbers in order. 70, 77, 84
Check. Go the other way from the last number: 84 − 7 = 77. ✓
Watch out. Take care when you cross a tens number. Jump to the next ten first, then add the rest.
Key words. Counting in steps of 9 means adding 9 again and again. The numbers you say are multiples of 9 if you start from 0.
Method. Counting on in 9s means adding 9 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting on in steps of 9.Each jump is +9.
- Work out the numbers one jump at a time. Always start from the number you have just found.18 + 10 = 28, then take away 1 = 27
27 + 10 = 37, then take away 1 = 36
36 + 10 = 46, then take away 1 = 45 - Write the numbers in order. 27, 36, 45
Check. Go the other way from the last number: 45 − 9 = 36. ✓
Watch out. Adding 9 is the same as adding 10 and then taking away 1. Taking away 9 is taking away 10 and adding 1 back.
Key words. Counting in steps of 9 means adding 9 again and again. The numbers you say are multiples of 9 if you start from 0.
Method. Counting on in 9s means adding 9 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting on in steps of 9.Each jump is +9.
- Work out the numbers one jump at a time. Always start from the number you have just found.45 + 10 = 55, then take away 1 = 54
54 + 10 = 64, then take away 1 = 63
63 + 10 = 73, then take away 1 = 72 - Write the numbers in order. 54, 63, 72
Check. Go the other way from the last number: 72 − 9 = 63. ✓
Watch out. Adding 9 is the same as adding 10 and then taking away 1. Taking away 9 is taking away 10 and adding 1 back.
Key words. Counting in steps of 9 means adding 9 again and again. The numbers you say are multiples of 9 if you start from 0.
Method. Counting on in 9s means adding 9 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting on in steps of 9.Each jump is +9.
- Work out the numbers one jump at a time. Always start from the number you have just found.72 + 10 = 82, then take away 1 = 81
81 + 10 = 91, then take away 1 = 90
90 + 10 = 100, then take away 1 = 99 - Write the numbers in order. 81, 90, 99
Check. Go the other way from the last number: 99 − 9 = 90. ✓
Watch out. Adding 9 is the same as adding 10 and then taking away 1. Taking away 9 is taking away 10 and adding 1 back.
Key words. Counting in steps of 9 means adding 9 again and again. The numbers you say are multiples of 9 if you start from 0.
Method. Counting on in 9s means adding 9 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting on in steps of 9.Each jump is +9.
- Work out the numbers one jump at a time. Always start from the number you have just found.81 + 10 = 91, then take away 1 = 90
90 + 10 = 100, then take away 1 = 99
99 + 10 = 109, then take away 1 = 108 - Write the numbers in order. 90, 99, 108
Check. Go the other way from the last number: 108 − 9 = 99. ✓
Watch out. Adding 9 is the same as adding 10 and then taking away 1. Taking away 9 is taking away 10 and adding 1 back.
Key words. Counting in steps of 6 means taking away 6 again and again. The numbers you say are multiples of 6 if you start from 0.
Method. Counting back in 6s means taking away 6 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting back in steps of 6.Each jump is −6.
- Work out the numbers one jump at a time. Always start from the number you have just found.60 − 6 = 54
54 − 4 = 50 (a tens number), then − 2 more = 48
48 − 6 = 42 - Write the numbers in order. 54, 48, 42
Check. Go the other way from the last number: 42 + 6 = 48. ✓
Watch out. Take care when you cross a tens number. Jump to the next ten first, then add the rest.
Key words. Counting in steps of 7 means taking away 7 again and again. The numbers you say are multiples of 7 if you start from 0.
Method. Counting back in 7s means taking away 7 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting back in steps of 7.Each jump is −7.
- Work out the numbers one jump at a time. Always start from the number you have just found.70 − 7 = 63
63 − 3 = 60 (a tens number), then − 4 more = 56
56 − 6 = 50 (a tens number), then − 1 more = 49 - Write the numbers in order. 63, 56, 49
Check. Go the other way from the last number: 49 + 7 = 56. ✓
Watch out. Take care when you cross a tens number. Jump to the next ten first, then add the rest.
Key words. Counting in steps of 9 means taking away 9 again and again. The numbers you say are multiples of 9 if you start from 0.
Method. Counting back in 9s means taking away 9 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting back in steps of 9.Each jump is −9.
- Work out the numbers one jump at a time. Always start from the number you have just found.99 − 10 = 89, then add 1 back = 90
90 − 10 = 80, then add 1 back = 81
81 − 10 = 71, then add 1 back = 72 - Write the numbers in order. 90, 81, 72
Check. Go the other way from the last number: 72 + 9 = 81. ✓
Watch out. Adding 9 is the same as adding 10 and then taking away 1. Taking away 9 is taking away 10 and adding 1 back.
Key words. Counting in steps of 25 means taking away 25 again and again. The numbers you say are multiples of 25 if you start from 0.
Method. Counting back in 25s means taking away 25 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting back in steps of 25.Each jump is −25.
- Work out the numbers one jump at a time. Always start from the number you have just found.300 − 20 = 280, then − 5 = 275
275 − 20 = 255, then − 5 = 250
250 − 20 = 230, then − 5 = 225 - Write the numbers in order. 275, 250, 225
Check. Go the other way from the last number: 225 + 25 = 250. ✓
Watch out. In the 25 sequence the last two digits go 25, 50, 75, 00, then repeat.
Method. Find the size of one jump from two numbers you can see. Then use it to fill the gaps.
- Find two numbers you know and count the jumps between them. Each jump in the sequence is the same size.From 0 to 100 is 4 jumps.
The difference is 100.
100 ÷ 4 = 25 - Say which way and how big each jump is. The numbers are getting bigger, so we count on.Each jump is +25.
- Fill in the missing numbers. Add (or take away) one jump from a number you know.Number 2: 0 + 25 = 25
Number 3: 75 − 25 = 50
Number 4: 100 − 25 = 75
Number 6: 100 + 25 = 125
Number 7: 175 − 25 = 150
Number 8: 200 − 25 = 175 - Write the missing numbers. 25, 50, 75, 125, 150, 175
Check. Read the whole sequence again and check every jump is +25: 0, 25, 50, 75, 100, 125, 150, 175, 200. ✓
Watch out. Do not just look at the first two numbers. Check the jump is the same all the way along.
Key words. Counting in steps of 1,000 means adding 1,000 again and again. The numbers you say are multiples of 1,000 if you start from 0.
Method. Counting on in 1,000s means adding 1,000 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting on in steps of 1,000.Each jump is +1,000.
- Work out the numbers one jump at a time. Always start from the number you have just found.2,350 + 1,000 = 3,350 (the thousands digit goes up by 1)
3,350 + 1,000 = 4,350 (the thousands digit goes up by 1)
4,350 + 1,000 = 5,350 (the thousands digit goes up by 1)
5,350 + 1,000 = 6,350 (the thousands digit goes up by 1) - Write the numbers in order. 3,350, 4,350, 5,350, 6,350
Check. Go the other way from the last number: 6,350 − 1,000 = 5,350. ✓
Watch out. Only the thousands digit changes. The hundreds, tens and ones digits stay the same.
Key words. Counting in steps of 1,000 means taking away 1,000 again and again. The numbers you say are multiples of 1,000 if you start from 0.
Method. Counting back in 1,000s means taking away 1,000 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting back in steps of 1,000.Each jump is −1,000.
- Work out the numbers one jump at a time. Always start from the number you have just found.9,125 − 1,000 = 8,125 (the thousands digit goes down by 1)
8,125 − 1,000 = 7,125 (the thousands digit goes down by 1)
7,125 − 1,000 = 6,125 (the thousands digit goes down by 1)
6,125 − 1,000 = 5,125 (the thousands digit goes down by 1) - Write the numbers in order. 8,125, 7,125, 6,125, 5,125
Check. Go the other way from the last number: 5,125 + 1,000 = 6,125. ✓
Watch out. Only the thousands digit changes. The hundreds, tens and ones digits stay the same.
Key words. Counting in steps of 1,000 means adding 1,000 again and again. The numbers you say are multiples of 1,000 if you start from 0.
Method. Counting on in 1,000s means adding 1,000 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting on in steps of 1,000.Each jump is +1,000.
- Work out the numbers one jump at a time. Always start from the number you have just found.5,008 + 1,000 = 6,008 (the thousands digit goes up by 1)
6,008 + 1,000 = 7,008 (the thousands digit goes up by 1)
7,008 + 1,000 = 8,008 (the thousands digit goes up by 1)
8,008 + 1,000 = 9,008 (the thousands digit goes up by 1) - Write the numbers in order. 6,008, 7,008, 8,008, 9,008
Check. Go the other way from the last number: 9,008 − 1,000 = 8,008. ✓
Watch out. Only the thousands digit changes. The hundreds, tens and ones digits stay the same.
Key words. Counting in steps of 1,000 means taking away 1,000 again and again. The numbers you say are multiples of 1,000 if you start from 0.
Method. Counting back in 1,000s means taking away 1,000 each time. Use each new number to start the next jump.
- Find the size of each jump. We are counting back in steps of 1,000.Each jump is −1,000.
- Work out the numbers one jump at a time. Always start from the number you have just found.10,000 − 1,000 = 9,000 (the thousands digit goes down by 1)
9,000 − 1,000 = 8,000 (the thousands digit goes down by 1)
8,000 − 1,000 = 7,000 (the thousands digit goes down by 1)
7,000 − 1,000 = 6,000 (the thousands digit goes down by 1) - Write the numbers in order. 9,000, 8,000, 7,000, 6,000
Check. Go the other way from the last number: 6,000 + 1,000 = 7,000. ✓
Watch out. Only the thousands digit changes. The hundreds, tens and ones digits stay the same.
Method. Find the size of one jump from two numbers you can see. Then use it to fill the gaps.
- Find two numbers you know and count the jumps between them. Each jump in the sequence is the same size.From 7 to 14 is 1 jump.
The difference is 7. - Say which way and how big each jump is. The numbers are getting bigger, so we count on.Each jump is +7.
- Fill in the missing numbers. Add (or take away) one jump from a number you know.Number 3: 14 + 7 = 21
Number 6: 35 + 7 = 42 - Write the missing numbers. 21, 42
Check. Read the whole sequence again and check every jump is +7: 7, 14, 21, 28, 35, 42. ✓
Watch out. Do not just look at the first two numbers. Check the jump is the same all the way along.
Method. Find the size of one jump from two numbers you can see. Then use it to fill the gaps.
- Find two numbers you know and count the jumps between them. Each jump in the sequence is the same size.From 81 to 63 is 2 jumps.
The difference is 18.
18 ÷ 2 = 9 - Say which way and how big each jump is. The numbers are getting smaller, so we count back.Each jump is −9.
- Fill in the missing numbers. Add (or take away) one jump from a number you know.Number 2: 81 − 9 = 72
Number 4: 63 − 9 = 54 - Write the missing numbers. 72, 54
Check. Read the whole sequence again and check every jump is −9: 81, 72, 63, 54, 45. ✓
Watch out. Do not just look at the first two numbers. Check the jump is the same all the way along.
Method. Find the size of one jump from two numbers you can see. Then use it to fill the gaps.
- Find two numbers you know and count the jumps between them. Each jump in the sequence is the same size.From 375 to 400 is 1 jump.
The difference is 25. - Say which way and how big each jump is. The numbers are getting bigger, so we count on.Each jump is +25.
- Fill in the missing numbers. Add (or take away) one jump from a number you know.Number 1: 375 − 25 = 350
Number 4: 400 + 25 = 425 - Write the missing numbers. 350, 425
Check. Read the whole sequence again and check every jump is +25: 350, 375, 400, 425, 450. ✓
Watch out. Do not just look at the first two numbers. Check the jump is the same all the way along.
Method. Find the size of one jump from two numbers you can see. Then use it to fill the gaps.
- Find two numbers you know and count the jumps between them. Each jump in the sequence is the same size.From 3,600 to 6,600 is 3 jumps.
The difference is 3,000.
3,000 ÷ 3 = 1,000 - Say which way and how big each jump is. The numbers are getting bigger, so we count on.Each jump is +1,000.
- Fill in the missing numbers. Add (or take away) one jump from a number you know.Number 2: 3,600 + 1,000 = 4,600
Number 3: 6,600 − 1,000 = 5,600
Number 5: 6,600 + 1,000 = 7,600 - Write the missing numbers. 4,600, 5,600, 7,600
Check. Read the whole sequence again and check every jump is +1,000: 3,600, 4,600, 5,600, 6,600, 7,600. ✓
Watch out. Do not just look at the first two numbers. Check the jump is the same all the way along.
Method. Find the size of one jump from two numbers you can see. Then use it to fill the gaps.
- Find two numbers you know and count the jumps between them. Each jump in the sequence is the same size.From 60 to 48 is 2 jumps.
The difference is 12.
12 ÷ 2 = 6 - Say which way and how big each jump is. The numbers are getting smaller, so we count back.Each jump is −6.
- Fill in the missing numbers. Add (or take away) one jump from a number you know.Number 2: 60 − 6 = 54
Number 4: 48 − 6 = 42 - Write the missing numbers. 54, 42
Check. Read the whole sequence again and check every jump is −6: 60, 54, 48, 42, 36. ✓
Watch out. Do not just look at the first two numbers. Check the jump is the same all the way along.
Method. A multiple of 6 is a number you say when you count in 6s. Count in 6s until you reach or pass 42.
- Count in 6s. Stop when you get to 42 or go past it.6, 12, 18, 24, 30, 36, 42
- Did we land exactly on 42? If we land on it, it is a multiple. If we jump over it, it is not.We reached 42. That is 42, so yes.
- Write the answer. Is 42 a multiple of 6? Yes
Check. Times table fact: 6 × 7 = 42. ✓
Method. A multiple of 7 is a number you say when you count in 7s. Count in 7s until you reach or pass 52.
- Count in 7s. Stop when you get to 52 or go past it.7, 14, 21, 28, 35, 42, 49, 56
- Did we land exactly on 52? If we land on it, it is a multiple. If we jump over it, it is not.We reached 56. We jumped from 49 to 56 and missed 52, so no.
- Write the answer. Is 52 a multiple of 7? No
Check. 7 × 7 = 49 and 7 × 8 = 56. 52 is in between. ✓
Method. A multiple of 9 is a number you say when you count in 9s. Count in 9s until you reach or pass 81.
- Count in 9s. Stop when you get to 81 or go past it.9, 18, 27, 36, 45, 54, 63, 72, 81
- Did we land exactly on 81? If we land on it, it is a multiple. If we jump over it, it is not.We reached 81. That is 81, so yes.
- Write the answer. Is 81 a multiple of 9? Yes
Check. Times table fact: 9 × 9 = 81. ✓
Watch out. Counting in 9s? Add the digits of a multiple of 9 (up to 99): they always make 9 (e.g. 63: 6 + 3 = 9).
Method. A multiple of 7 is a number you say when you count in 7s. Count in 7s until you reach or pass 77.
- Count in 7s. Stop when you get to 77 or go past it.7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77
- Did we land exactly on 77? If we land on it, it is a multiple. If we jump over it, it is not.We reached 77. That is 77, so yes.
- Write the answer. Is 77 a multiple of 7? Yes
Check. Times table fact: 7 × 11 = 77. ✓
Method. A multiple of 25 is a number you say when you count in 25s. Count in 25s until you reach or pass 175.
- Count in 25s. Stop when you get to 175 or go past it.25, 50, 75, 100, 125, 150, 175
- Did we land exactly on 175? If we land on it, it is a multiple. If we jump over it, it is not.We reached 175. That is 175, so yes.
- Write the answer. Is 175 a multiple of 25? Yes
Check. Times table fact: 25 × 7 = 175. ✓
Method. A multiple of 1,000 is a number you say when you count in 1,000s. Count in 1,000s until you reach or pass 7,000.
- Count in 1,000s. Stop when you get to 7,000 or go past it.1,000, 2,000, 3,000, 4,000, 5,000, 6,000, 7,000
- Did we land exactly on 7,000? If we land on it, it is a multiple. If we jump over it, it is not.We reached 7,000. That is 7,000, so yes.
- Write the answer. Is 7,000 a multiple of 1,000? Yes
Check. Times table fact: 1,000 × 7 = 7,000. ✓
Method. £2 is 200p. Count in 25s until you reach 200, and count how many 25p coins that takes.
- Change £2 to pence. The coins are in pence, so we want both amounts in pence.£2 = 200p
- Count in 25s and number each jump. Each jump is one day.Day 1: 25p
Day 2: 50p
Day 3: 75p
Day 4: 100p
Day 5: 125p
Day 6: 150p
Day 7: 175p
Day 8: 200p - Write the answer. 200p is reached on day 8.8 days
Check. 25 × 8 = 200. ✓
Watch out. Four 25p coins make £1, so £2 needs 8 coins.
Method. Count on in 6s, one jump at a time. Each jump is one box.
- Decide what each jump means. Every box adds 6, so we count on in 6s. We start at 0.Jump = +6
- Count on 9 times. Use the new number as the start of the next jump.0 + 6 = 6
6 + 4 = 10 (a tens number), then + 2 more = 12
12 + 6 = 18
18 + 2 = 20 (a tens number), then + 4 more = 24
24 + 6 = 30
30 + 6 = 36
36 + 4 = 40 (a tens number), then + 2 more = 42
42 + 6 = 48
48 + 2 = 50 (a tens number), then + 4 more = 54 - Write the answer. There are 9 boxes with 6 eggs in each.54 eggs
Check. Check with a times fact: 6 × 9 = 54. ✓
Watch out. Count the jumps carefully. Using your fingers or tally marks helps you keep track of how many you have made.
Method. Count on in 1,000s, one jump at a time. Each jump is one month.
- Decide what each jump means. Every month adds 1,000, so we count on in 1,000s. We start at 4,250.Jump = +1,000
- Count on 5 times. Use the new number as the start of the next jump.4,250 + 1,000 = 5,250 (the thousands digit goes up by 1)
5,250 + 1,000 = 6,250 (the thousands digit goes up by 1)
6,250 + 1,000 = 7,250 (the thousands digit goes up by 1)
7,250 + 1,000 = 8,250 (the thousands digit goes up by 1)
8,250 + 1,000 = 9,250 (the thousands digit goes up by 1) - Write the answer. Each month 1,000 new books arrive.9,250 books
Check. Check with a times fact: 1,000 × 5 = 5,000, and 4,250 + 5,000 = 9,250. ✓
Watch out. Count the jumps carefully. Using your fingers or tally marks helps you keep track of how many you have made.
Method. Count in 7s from 7 and find the first number that is wrong.
- Count in 7s. Each number should be 7 more than the one before.7, 14, 21, 28, 35, 42
- Compare with Jack’s numbers. Check every jump.7 + 3 = 10 (a tens number), then + 4 more = 14
14 + 6 = 20 (a tens number), then + 1 more = 21
21 + 7 = 28 but Jack wrote 27
Jack’s next jumps: 27 + 7 = 34, but he wrote 35. - Say what went wrong. He added 6 by mistake, then went back to adding 7 from the right number.Jack wrote 27, but 27 should be 28.
Check. 28 + 7 = 35, so the numbers after 28 were right. ✓
Watch out. One wrong number can make the next jump look wrong too. Check them one at a time.
Method. Count in 9s and see which number is missed out.
- Count in 9s up to 63. These are the multiples of 9.9, 18, 27, 36, 45, 54, 63, 72
- Look for each number in the list. A number that is not in the list is not a multiple.36: yes, it is in the list
45: yes, it is in the list
56: no, the list goes 54, 63 and jumps over it
63: yes, it is in the list - Write the odd one out. 56
Check. 56 ÷ 9 = 6 remainder 2, so it does not divide exactly. The others do. ✓
Method. Write out both lists, then look for the first number that is in both.
- Zainab counts in 9s. Add 9 each time.9, 18, 27, 36, 45, 54
- Leo counts in 6s. Add 6 each time.6, 12, 18, 24, 30, 36, 42, 48, 54
- Find the first number in both lists. Look for the smallest match.18 is in both lists.
Check. 18 ÷ 9 = 2 and 18 ÷ 6 = 3. It divides by both exactly. ✓
Watch out. The answer is not 0. The question asks for a number above 0.