Counting to 1000
By the end of this chapter you will be able to
- Count on and back from any number up to 1000
- Count in tens, fifties and hundreds
- Count in steps of 2, 3 and 5
- Say 1, 10 and 100 more or less than a number
You should already know
- Counting to 100 (Level 2, chapter 1)
- Counting in tens (Level 2, chapter 1)
Where this leads
- Hundreds, tens and ones (Level 3, chapter 2)
Step-by-step practice: maths (Level 3). Small steps, repeated until fluent. Content: Count forwards and backwards in ones from 0 to 1000, and from any number up to 1000, Count in tens from any number, and say 10 more and 10 less, Count in hundreds and fifties from any start, and say 100 more and 100 less, Count in steps of 2, 3 and 5, from 0 and from other numbers, forwards and backwards, Say the number that is 1 more or 1 less than any number up to 1000.
Exercise P Do you remember?
Non-calculatorMethod. Start at the number and count on or back, one number at a time.
- Start at 47. We begin with this number.47
- Count on 8. Say each new number as we go.47 + 8 = 55
- Write the answer. This is the last number we reached.55
Check. Count back 8 from 55: you reach 47.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 33. We begin with this number.33
- Count back 6. Say each number as we pass it.33 - 6 = 27
- Write the answer. This is the last number we reached.27
Check. Count on 6 from 27: you reach 33.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Change only the ones digit when we go more than the number.
- Start at 56. We begin with this number.56
- Change the ones digit. Only the ones digit changes. The others stay the same.56 + 1 = 57
- Write the answer. This is the new number.57
Check. 1 less than 57 is 56. It works.
Watch out. Only the ones digit changes. Keep the other digits the same.
Method. Find the step, then count on in that step to fill each gap.
- Find the step. Each number is 2 more than the one before.32 - 30 = 2
- Fill the first gap. Add 2 to the number before the gap.32 + 2 = 34
- Fill the next gap. Add 2 again.36 + 2 = 38
- Write the missing numbers. Read them in order.34, 38
Check. Count on in 2s from 30: 30, 32, 34, 36, 38. It fits.
Watch out. Check the step with the numbers either side of a gap.
Method. Count on in tens by adding or taking away 10 each time.
- Start at 40. We count from this number.40
- Add 10 each time. We count on in tens.40 + 10 = 50; 50 + 10 = 60
- Write the numbers in order. These are the next numbers we said.50, 60, 70
Check. Count back in tens from 70 to check. You reach 40.
Watch out. The step is 10. Each new number is 10 more than the last.
Counting on and back, one at a time
Counting on means saying the next number each time, one more at a time. Counting back means saying the number before.
Count across the hundreds too. After 399 comes 400, and after 999 comes 1000.
Key ideas
- Counting on means adding one more each time.
- Counting back means taking one away each time.
- Count across 400, 500 and other hundreds without stopping.
Method. Start at the number and count on or back, one number at a time.
- Start at 468. We begin with this number.468
- Count on 7. Say each new number as we go.468 + 7 = 475
- Write the answer. This is the last number we reached.475
Check. Count back 7 from 475: you reach 468.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 603. We begin with this number.603
- Count back 5. Say each number as we pass it.603 - 5 = 598
- Write the answer. This is the last number we reached.598
Check. Count on 5 from 598: you reach 603.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 996. We begin with this number.996
- Count on 4. Say each new number as we go.996 + 4 = 1000
- Write the answer. This is the last number we reached.1000
Check. Count back 4 from 1000: you reach 996.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Watch out
Watch out. Do not start again at 1 or at 100 when a number crosses a hundred. 398 + 4 is 402, not 302.
Exam tip
Grown-up tip. Count on from a number on a number line or in a hundred square. Ask: “What comes next?” and “What came before?”
Exercise 1A Practice: counting on and back in ones
Non-calculatorMethod. Start at the number and count on or back, one number at a time.
- Start at 766. We begin with this number.766
- Count on 4. Say each new number as we go.766 + 4 = 770
- Write the answer. This is the last number we reached.770
Check. Count back 4 from 770: you reach 766.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 924. We begin with this number.924
- Count on 10. Say each new number as we go.924 + 10 = 934
- Write the answer. This is the last number we reached.934
Check. Count back 10 from 934: you reach 924.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 312. We begin with this number.312
- Count on 11. Say each new number as we go.312 + 11 = 323
- Write the answer. This is the last number we reached.323
Check. Count back 11 from 323: you reach 312.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 306. We begin with this number.306
- Count on 7. Say each new number as we go.306 + 7 = 313
- Write the answer. This is the last number we reached.313
Check. Count back 7 from 313: you reach 306.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 258. We begin with this number.258
- Count on 3. Say each new number as we go.258 + 3 = 261
- Write the answer. This is the last number we reached.261
Check. Count back 3 from 261: you reach 258.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 524. We begin with this number.524
- Count on 10. Say each new number as we go.524 + 10 = 534
- Write the answer. This is the last number we reached.534
Check. Count back 10 from 534: you reach 524.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 168. We begin with this number.168
- Count on 11. Say each new number as we go.168 + 11 = 179
- Write the answer. This is the last number we reached.179
Check. Count back 11 from 179: you reach 168.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 540. We begin with this number.540
- Count on 4. Say each new number as we go.540 + 4 = 544
- Write the answer. This is the last number we reached.544
Check. Count back 4 from 544: you reach 540.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 724. We begin with this number.724
- Count on 6. Say each new number as we go.724 + 6 = 730
- Write the answer. This is the last number we reached.730
Check. Count back 6 from 730: you reach 724.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 264. We begin with this number.264
- Count on 12. Say each new number as we go.264 + 12 = 276
- Write the answer. This is the last number we reached.276
Check. Count back 12 from 276: you reach 264.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 758. We begin with this number.758
- Count back 13. Say each number as we pass it.758 - 13 = 745
- Write the answer. This is the last number we reached.745
Check. Count on 13 from 745: you reach 758.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 296. We begin with this number.296
- Count back 10. Say each number as we pass it.296 - 10 = 286
- Write the answer. This is the last number we reached.286
Check. Count on 10 from 286: you reach 296.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 552. We begin with this number.552
- Count back 14. Say each number as we pass it.552 - 14 = 538
- Write the answer. This is the last number we reached.538
Check. Count on 14 from 538: you reach 552.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 773. We begin with this number.773
- Count back 13. Say each number as we pass it.773 - 13 = 760
- Write the answer. This is the last number we reached.760
Check. Count on 13 from 760: you reach 773.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 786. We begin with this number.786
- Count back 3. Say each number as we pass it.786 - 3 = 783
- Write the answer. This is the last number we reached.783
Check. Count on 3 from 783: you reach 786.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 640. We begin with this number.640
- Count back 5. Say each number as we pass it.640 - 5 = 635
- Write the answer. This is the last number we reached.635
Check. Count on 5 from 635: you reach 640.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Ten more, ten less, 100 more, 100 less
When we add 10, only the tens digit changes. When we add 100, only the hundreds digit changes.
The other digits stay the same. This is quick to see if you look at the digits.
Key ideas
- 10 more changes the tens digit.
- 10 less changes the tens digit.
- 100 more changes the hundreds digit.
- The other digits stay the same.
Method. Change only the tens digit when we go more than the number.
- Start at 374. We begin with this number.374
- Change the tens digit. Only the tens digit changes. The others stay the same.374 + 10 = 384
- Write the answer. This is the new number.384
Check. 10 less than 384 is 374. It works.
Watch out. Only the tens digit changes. Keep the other digits the same.
Method. Change only the hundreds digit when we go less than the number.
- Start at 805. We begin with this number.805
- Change the hundreds digit. Only the hundreds digit changes. The others stay the same.805 - 100 = 705
- Write the answer. This is the new number.705
Check. 100 more than 705 is 805. It works.
Watch out. Only the hundreds digit changes. Keep the other digits the same.
Method. Count on in tens by adding or taking away 10 each time.
- Start at 340. We count from this number.340
- Add 10 each time. We count on in tens.340 + 10 = 350; 350 + 10 = 360
- Write the numbers in order. These are the next numbers we said.350, 360, 370
Check. Count back in tens from 370 to check. You reach 340.
Watch out. The step is 10. Each new number is 10 more than the last.
Watch out
Watch out. 10 more than 396 is 406, not 496. The 9 tens and 1 ten make 10 tens, which is 1 hundred, so the 3 hundreds becomes 4 hundreds.
Exam tip
Grown-up tip. Use base-ten blocks. Ask the child to add one ten stick, then say which digit changed.
Exercise 1B Practice: 10 and 100 more or less
Non-calculatorMethod. Change only the tens digit when we go more than the number.
- Start at 295. We begin with this number.295
- Change the tens digit. Only the tens digit changes. The others stay the same.295 + 10 = 305
- Write the answer. This is the new number.305
Check. 10 less than 305 is 295. It works.
Watch out. Only the tens digit changes. Keep the other digits the same.
Method. Change only the tens digit when we go more than the number.
- Start at 113. We begin with this number.113
- Change the tens digit. Only the tens digit changes. The others stay the same.113 + 10 = 123
- Write the answer. This is the new number.123
Check. 10 less than 123 is 113. It works.
Watch out. Only the tens digit changes. Keep the other digits the same.
Method. Change only the hundreds digit when we go more than the number.
- Start at 217. We begin with this number.217
- Change the hundreds digit. Only the hundreds digit changes. The others stay the same.217 + 100 = 317
- Write the answer. This is the new number.317
Check. 100 less than 317 is 217. It works.
Watch out. Only the hundreds digit changes. Keep the other digits the same.
Method. Change only the ones digit when we go less than the number.
- Start at 256. We begin with this number.256
- Change the ones digit. Only the ones digit changes. The others stay the same.256 - 1 = 255
- Write the answer. This is the new number.255
Check. 1 more than 255 is 256. It works.
Watch out. Only the ones digit changes. Keep the other digits the same.
Method. Change only the ones digit when we go less than the number.
- Start at 956. We begin with this number.956
- Change the ones digit. Only the ones digit changes. The others stay the same.956 - 1 = 955
- Write the answer. This is the new number.955
Check. 1 more than 955 is 956. It works.
Watch out. Only the ones digit changes. Keep the other digits the same.
Method. Change only the hundreds digit when we go less than the number.
- Start at 372. We begin with this number.372
- Change the hundreds digit. Only the hundreds digit changes. The others stay the same.372 - 100 = 272
- Write the answer. This is the new number.272
Check. 100 more than 272 is 372. It works.
Watch out. Only the hundreds digit changes. Keep the other digits the same.
Method. Change only the tens digit when we go less than the number.
- Start at 792. We begin with this number.792
- Change the tens digit. Only the tens digit changes. The others stay the same.792 - 10 = 782
- Write the answer. This is the new number.782
Check. 10 more than 782 is 792. It works.
Watch out. Only the tens digit changes. Keep the other digits the same.
Method. Change only the hundreds digit when we go less than the number.
- Start at 146. We begin with this number.146
- Change the hundreds digit. Only the hundreds digit changes. The others stay the same.146 - 100 = 46
- Write the answer. This is the new number.46
Check. 100 more than 46 is 146. It works.
Watch out. Only the hundreds digit changes. Keep the other digits the same.
Method. Change only the tens digit when we go more than the number.
- Start at 795. We begin with this number.795
- Change the tens digit. Only the tens digit changes. The others stay the same.795 + 10 = 805
- Write the answer. This is the new number.805
Check. 10 less than 805 is 795. It works.
Watch out. Only the tens digit changes. Keep the other digits the same.
Method. Change only the hundreds digit when we go more than the number.
- Start at 812. We begin with this number.812
- Change the hundreds digit. Only the hundreds digit changes. The others stay the same.812 + 100 = 912
- Write the answer. This is the new number.912
Check. 100 less than 912 is 812. It works.
Watch out. Only the hundreds digit changes. Keep the other digits the same.
Method. Change only the tens digit when we go less than the number.
- Start at 591. We begin with this number.591
- Change the tens digit. Only the tens digit changes. The others stay the same.591 - 10 = 581
- Write the answer. This is the new number.581
Check. 10 more than 581 is 591. It works.
Watch out. Only the tens digit changes. Keep the other digits the same.
Method. Change only the tens digit when we go less than the number.
- Start at 623. We begin with this number.623
- Change the tens digit. Only the tens digit changes. The others stay the same.623 - 10 = 613
- Write the answer. This is the new number.613
Check. 10 more than 613 is 623. It works.
Watch out. Only the tens digit changes. Keep the other digits the same.
Method. Change only the ones digit when we go less than the number.
- Start at 279. We begin with this number.279
- Change the ones digit. Only the ones digit changes. The others stay the same.279 - 1 = 278
- Write the answer. This is the new number.278
Check. 1 more than 278 is 279. It works.
Watch out. Only the ones digit changes. Keep the other digits the same.
Method. Change only the hundreds digit when we go more than the number.
- Start at 781. We begin with this number.781
- Change the hundreds digit. Only the hundreds digit changes. The others stay the same.781 + 100 = 881
- Write the answer. This is the new number.881
Check. 100 less than 881 is 781. It works.
Watch out. Only the hundreds digit changes. Keep the other digits the same.
Method. Change only the tens digit when we go less than the number.
- Start at 896. We begin with this number.896
- Change the tens digit. Only the tens digit changes. The others stay the same.896 - 10 = 886
- Write the answer. This is the new number.886
Check. 10 more than 886 is 896. It works.
Watch out. Only the tens digit changes. Keep the other digits the same.
Method. Change only the hundreds digit when we go more than the number.
- Start at 710. We begin with this number.710
- Change the hundreds digit. Only the hundreds digit changes. The others stay the same.710 + 100 = 810
- Write the answer. This is the new number.810
Check. 100 less than 810 is 710. It works.
Watch out. Only the hundreds digit changes. Keep the other digits the same.
Counting in fifties and hundreds
A fifty is half of a hundred. When we count in fifties we say 50, 100, 150, 200 and so on.
Count in hundreds when you add 100 each time. Find the step first, then fill the gaps.
Key ideas
- Count in fifties: 50, 100, 150, 200.
- Count in hundreds: 100, 200, 300.
- Find the step before you fill a gap.
Method. Count on in fifties by adding or taking away 50 each time.
- Start at 450. We count from this number.450
- Add 50 each time. We count on in fifties.450 + 50 = 500; 500 + 50 = 550
- Write the numbers in order. These are the next numbers we said.500, 550, 600
Check. Count back in fifties from 600 to check. You reach 450.
Watch out. The step is 50. Each new number is 50 more than the last.
Method. Find the step, then count on in that step to fill each gap.
- Find the step. Each number is 10 more than the one before.490 - 480 = 10
- Fill the first gap. Add 10 to the number before the gap.490 + 10 = 500
- Fill the next gap. Add 10 again.510 + 10 = 520
- Write the missing numbers. Read them in order.500, 520
Check. Count on in 10s from 480: 480, 490, 500, 510, 520. It fits.
Watch out. Check the step with the numbers either side of a gap.
Method. Count back in hundreds by adding or taking away 100 each time.
- Start at 700. We count from this number.700
- Take 100 each time. We count back in hundreds.700 - 100 = 600; 600 - 100 = 500
- Write the numbers in order. These are the next numbers we said.600, 500, 400
Check. Count on in hundreds from 400 to check. You reach 700.
Watch out. The step is 100. Each new number is 100 less than the last.
Watch out
Watch out. In a count of fifties, the step is 50, not 5. After 450 comes 500, not 455.
Exam tip
Grown-up tip. Ask the child to say the step out loud before counting. Clapping on each number helps.
Exercise 1C Practice: counting in fifties, hundreds and gaps
Non-calculatorMethod. Count on in hundreds by adding or taking away 100 each time.
- Start at 600. We count from this number.600
- Add 100 each time. We count on in hundreds.600 + 100 = 700; 700 + 100 = 800
- Write the numbers in order. These are the next numbers we said.700, 800, 900
Check. Count back in hundreds from 900 to check. You reach 600.
Watch out. The step is 100. Each new number is 100 more than the last.
Method. Count on in fifties by adding or taking away 50 each time.
- Start at 100. We count from this number.100
- Add 50 each time. We count on in fifties.100 + 50 = 150; 150 + 50 = 200
- Write the numbers in order. These are the next numbers we said.150, 200, 250
Check. Count back in fifties from 250 to check. You reach 100.
Watch out. The step is 50. Each new number is 50 more than the last.
Method. Count on in fifties by adding or taking away 50 each time.
- Start at 0. We count from this number.0
- Add 50 each time. We count on in fifties.0 + 50 = 50; 50 + 50 = 100
- Write the numbers in order. These are the next numbers we said.50, 100, 150
Check. Count back in fifties from 150 to check. You reach 0.
Watch out. The step is 50. Each new number is 50 more than the last.
Method. Count back in fifties by adding or taking away 50 each time.
- Start at 600. We count from this number.600
- Take 50 each time. We count back in fifties.600 - 50 = 550; 550 - 50 = 500
- Write the numbers in order. These are the next numbers we said.550, 500, 450
Check. Count on in fifties from 450 to check. You reach 600.
Watch out. The step is 50. Each new number is 50 less than the last.
Method. Count on in hundreds by adding or taking away 100 each time.
- Start at 0. We count from this number.0
- Add 100 each time. We count on in hundreds.0 + 100 = 100; 100 + 100 = 200
- Write the numbers in order. These are the next numbers we said.100, 200, 300
Check. Count back in hundreds from 300 to check. You reach 0.
Watch out. The step is 100. Each new number is 100 more than the last.
Method. Count on in hundreds by adding or taking away 100 each time.
- Start at 700. We count from this number.700
- Add 100 each time. We count on in hundreds.700 + 100 = 800; 800 + 100 = 900
- Write the numbers in order. These are the next numbers we said.800, 900, 1000
Check. Count back in hundreds from 1000 to check. You reach 700.
Watch out. The step is 100. Each new number is 100 more than the last.
Method. Count on in hundreds by adding or taking away 100 each time.
- Start at 200. We count from this number.200
- Add 100 each time. We count on in hundreds.200 + 100 = 300; 300 + 100 = 400
- Write the numbers in order. These are the next numbers we said.300, 400, 500
Check. Count back in hundreds from 500 to check. You reach 200.
Watch out. The step is 100. Each new number is 100 more than the last.
Method. Count back in hundreds by adding or taking away 100 each time.
- Start at 800. We count from this number.800
- Take 100 each time. We count back in hundreds.800 - 100 = 700; 700 - 100 = 600
- Write the numbers in order. These are the next numbers we said.700, 600, 500
Check. Count on in hundreds from 500 to check. You reach 800.
Watch out. The step is 100. Each new number is 100 less than the last.
Method. Find the step, then count on in that step to fill each gap.
- Find the step. Each number is 1 more than the one before.419 - 418 = 1
- Fill the first gap. Add 1 to the number before the gap.419 + 1 = 420
- Fill the next gap. Add 1 again.421 + 1 = 422
- Write the missing numbers. Read them in order.420, 422
Check. Count on in 1s from 418: 418, 419, 420, 421, 422. It fits.
Watch out. Check the step with the numbers either side of a gap.
Method. Find the step, then count on in that step to fill each gap.
- Find the step. Each number is 10 more than the one before.20 - 10 = 10
- Fill the first gap. Add 10 to the number before the gap.20 + 10 = 30
- Fill the next gap. Add 10 again.40 + 10 = 50
- Write the missing numbers. Read them in order.30, 50
Check. Count on in 10s from 10: 10, 20, 30, 40, 50. It fits.
Watch out. Check the step with the numbers either side of a gap.
Method. Find the step, then count on in that step to fill each gap.
- Find the step. Each number is 100 more than the one before.600 - 500 = 100
- Fill the first gap. Add 100 to the number before the gap.600 + 100 = 700
- Fill the next gap. Add 100 again.800 + 100 = 900
- Write the missing numbers. Read them in order.700, 900
Check. Count on in 100s from 500: 500, 600, 700, 800, 900. It fits.
Watch out. Check the step with the numbers either side of a gap.
Method. Find the step, then count on in that step to fill each gap.
- Find the step. Each number is 5 more than the one before.13 - 8 = 5
- Fill the first gap. Add 5 to the number before the gap.13 + 5 = 18
- Fill the next gap. Add 5 again.23 + 5 = 28
- Write the missing numbers. Read them in order.18, 28
Check. Count on in 5s from 8: 8, 13, 18, 23, 28. It fits.
Watch out. Check the step with the numbers either side of a gap.
Method. Find the step, then count on in that step to fill each gap.
- Find the step. Each number is 5 more than the one before.551 - 546 = 5
- Fill the first gap. Add 5 to the number before the gap.551 + 5 = 556
- Fill the next gap. Add 5 again.561 + 5 = 566
- Write the missing numbers. Read them in order.556, 566
Check. Count on in 5s from 546: 546, 551, 556, 561, 566. It fits.
Watch out. Check the step with the numbers either side of a gap.
Method. Find the step, then count on in that step to fill each gap.
- Find the step. Each number is 1 more than the one before.852 - 851 = 1
- Fill the first gap. Add 1 to the number before the gap.852 + 1 = 853
- Fill the next gap. Add 1 again.854 + 1 = 855
- Write the missing numbers. Read them in order.853, 855
Check. Count on in 1s from 851: 851, 852, 853, 854, 855. It fits.
Watch out. Check the step with the numbers either side of a gap.
Method. Find the step, then count on in that step to fill each gap.
- Find the step. Each number is 5 more than the one before.905 - 900 = 5
- Fill the first gap. Add 5 to the number before the gap.905 + 5 = 910
- Fill the next gap. Add 5 again.915 + 5 = 920
- Write the missing numbers. Read them in order.910, 920
Check. Count on in 5s from 900: 900, 905, 910, 915, 920. It fits.
Watch out. Check the step with the numbers either side of a gap.
Method. Find the step, then count on in that step to fill each gap.
- Find the step. Each number is 2 more than the one before.596 - 594 = 2
- Fill the first gap. Add 2 to the number before the gap.596 + 2 = 598
- Fill the next gap. Add 2 again.600 + 2 = 602
- Write the missing numbers. Read them in order.598, 602
Check. Count on in 2s from 594: 594, 596, 598, 600, 602. It fits.
Watch out. Check the step with the numbers either side of a gap.
Counting in steps of 2, 3 and 5
We can count in steps of 2, 3 or 5. Each new number is the step more than the last one.
Start from 0 or from another number. Write the new numbers one by one.
Key ideas
- Count in twos: each number is 2 more.
- Count in threes: each number is 3 more.
- Count in fives: each number is 5 more.
Method. Count on in twos by adding or taking away 2 each time.
- Start at 46. We count from this number.46
- Add 2 each time. We count on in twos.46 + 2 = 48; 48 + 2 = 50
- Write the numbers in order. These are the next numbers we said.48, 50, 52
Check. Count back in twos from 52 to check. You reach 46.
Watch out. The step is 2. Each new number is 2 more than the last.
Method. Count back in threes by adding or taking away 3 each time.
- Start at 30. We count from this number.30
- Take 3 each time. We count back in threes.30 - 3 = 27; 27 - 3 = 24
- Write the numbers in order. These are the next numbers we said.27, 24, 21
Check. Count on in threes from 21 to check. You reach 30.
Watch out. The step is 3. Each new number is 3 less than the last.
Method. Count on in tens by adding or taking away 10 each time.
- Start at 340. We count from this number.340
- Add 10 each time. We count on in tens.340 + 10 = 350; 350 + 10 = 360
- Write the numbers in order. These are the next numbers we said.350, 360, 370
Check. Count back in tens from 370 to check. You reach 340.
Watch out. The step is 10. Each new number is 10 more than the last.
Watch out
Watch out. Counting in threes from 30 gives 33, 36, 39. Do not add 1 each time.
Exam tip
Grown-up tip. Skip-count out loud with the child. Try the twos and fives on a hundred square and colour each number.
Exercise 1D Practice: counting in twos, threes and fives
Non-calculatorMethod. Count back in threes by adding or taking away 3 each time.
- Start at 36. We count from this number.36
- Take 3 each time. We count back in threes.36 - 3 = 33; 33 - 3 = 30
- Write the numbers in order. These are the next numbers we said.33, 30, 27
Check. Count on in threes from 27 to check. You reach 36.
Watch out. The step is 3. Each new number is 3 less than the last.
Method. Count back in threes by adding or taking away 3 each time.
- Start at 784. We count from this number.784
- Take 3 each time. We count back in threes.784 - 3 = 781; 781 - 3 = 778
- Write the numbers in order. These are the next numbers we said.781, 778, 775
Check. Count on in threes from 775 to check. You reach 784.
Watch out. The step is 3. Each new number is 3 less than the last.
Method. Count back in fives by adding or taking away 5 each time.
- Start at 308. We count from this number.308
- Take 5 each time. We count back in fives.308 - 5 = 303; 303 - 5 = 298
- Write the numbers in order. These are the next numbers we said.303, 298, 293
Check. Count on in fives from 293 to check. You reach 308.
Watch out. The step is 5. Each new number is 5 less than the last.
Method. Count on in twos by adding or taking away 2 each time.
- Start at 257. We count from this number.257
- Add 2 each time. We count on in twos.257 + 2 = 259; 259 + 2 = 261
- Write the numbers in order. These are the next numbers we said.259, 261, 263
Check. Count back in twos from 263 to check. You reach 257.
Watch out. The step is 2. Each new number is 2 more than the last.
Method. Count on in threes by adding or taking away 3 each time.
- Start at 211. We count from this number.211
- Add 3 each time. We count on in threes.211 + 3 = 214; 214 + 3 = 217
- Write the numbers in order. These are the next numbers we said.214, 217, 220
Check. Count back in threes from 220 to check. You reach 211.
Watch out. The step is 3. Each new number is 3 more than the last.
Method. Count on in twos by adding or taking away 2 each time.
- Start at 657. We count from this number.657
- Add 2 each time. We count on in twos.657 + 2 = 659; 659 + 2 = 661
- Write the numbers in order. These are the next numbers we said.659, 661, 663
Check. Count back in twos from 663 to check. You reach 657.
Watch out. The step is 2. Each new number is 2 more than the last.
Method. Count on in threes by adding or taking away 3 each time.
- Start at 48. We count from this number.48
- Add 3 each time. We count on in threes.48 + 3 = 51; 51 + 3 = 54
- Write the numbers in order. These are the next numbers we said.51, 54, 57
Check. Count back in threes from 57 to check. You reach 48.
Watch out. The step is 3. Each new number is 3 more than the last.
Method. Count back in twos by adding or taking away 2 each time.
- Start at 663. We count from this number.663
- Take 2 each time. We count back in twos.663 - 2 = 661; 661 - 2 = 659
- Write the numbers in order. These are the next numbers we said.661, 659, 657
Check. Count on in twos from 657 to check. You reach 663.
Watch out. The step is 2. Each new number is 2 less than the last.
Method. Count back in fives by adding or taking away 5 each time.
- Start at 834. We count from this number.834
- Take 5 each time. We count back in fives.834 - 5 = 829; 829 - 5 = 824
- Write the numbers in order. These are the next numbers we said.829, 824, 819
Check. Count on in fives from 819 to check. You reach 834.
Watch out. The step is 5. Each new number is 5 less than the last.
Method. Count back in fives by adding or taking away 5 each time.
- Start at 884. We count from this number.884
- Take 5 each time. We count back in fives.884 - 5 = 879; 879 - 5 = 874
- Write the numbers in order. These are the next numbers we said.879, 874, 869
Check. Count on in fives from 869 to check. You reach 884.
Watch out. The step is 5. Each new number is 5 less than the last.
Method. Count on in twos by adding or taking away 2 each time.
- Start at 134. We count from this number.134
- Add 2 each time. We count on in twos.134 + 2 = 136; 136 + 2 = 138
- Write the numbers in order. These are the next numbers we said.136, 138, 140
Check. Count back in twos from 140 to check. You reach 134.
Watch out. The step is 2. Each new number is 2 more than the last.
Method. Count back in twos by adding or taking away 2 each time.
- Start at 109. We count from this number.109
- Take 2 each time. We count back in twos.109 - 2 = 107; 107 - 2 = 105
- Write the numbers in order. These are the next numbers we said.107, 105, 103
Check. Count on in twos from 103 to check. You reach 109.
Watch out. The step is 2. Each new number is 2 less than the last.
Method. Count on in fives by adding or taking away 5 each time.
- Start at 205. We count from this number.205
- Add 5 each time. We count on in fives.205 + 5 = 210; 210 + 5 = 215
- Write the numbers in order. These are the next numbers we said.210, 215, 220
Check. Count back in fives from 220 to check. You reach 205.
Watch out. The step is 5. Each new number is 5 more than the last.
Method. Count back in fives by adding or taking away 5 each time.
- Start at 560. We count from this number.560
- Take 5 each time. We count back in fives.560 - 5 = 555; 555 - 5 = 550
- Write the numbers in order. These are the next numbers we said.555, 550, 545
Check. Count on in fives from 545 to check. You reach 560.
Watch out. The step is 5. Each new number is 5 less than the last.
Method. Count back in twos by adding or taking away 2 each time.
- Start at 201. We count from this number.201
- Take 2 each time. We count back in twos.201 - 2 = 199; 199 - 2 = 197
- Write the numbers in order. These are the next numbers we said.199, 197, 195
Check. Count on in twos from 195 to check. You reach 201.
Watch out. The step is 2. Each new number is 2 less than the last.
Method. Count on in threes by adding or taking away 3 each time.
- Start at 297. We count from this number.297
- Add 3 each time. We count on in threes.297 + 3 = 300; 300 + 3 = 303
- Write the numbers in order. These are the next numbers we said.300, 303, 306
Check. Count back in threes from 306 to check. You reach 297.
Watch out. The step is 3. Each new number is 3 more than the last.
Chapter summary
| Skill | Method |
|---|---|
| Count on or back in ones | Say the next (or previous) number each time, across hundreds too |
| 10 more or less | Only the tens digit changes |
| 100 more or less | Only the hundreds digit changes |
| Count in fifties | Add 50 each time: 50, 100, 150 |
| Count in steps of 2, 3 or 5 | Add the step each time, from 0 or from any number |
Can you…?
- I can count on and back in ones from any number up to 1000
- I can say 10 more and 10 less than a number
- I can say 100 more and 100 less than a number
- I can count in fifties and hundreds
- I can count in steps of 2, 3 and 5, forwards and backwards
Key terms
- count on
- say the next numbers, one step at a time
- count back
- say the numbers that come before, one step at a time
- step
- the amount added each time, for example 5 in 5, 10, 15
- hundreds digit
- the digit in the hundreds place, for example the 4 in 458
Exercise 1Z Check-up
Non-calculatorMethod. Change only the hundreds digit when we go more than the number.
- Start at 645. We begin with this number.645
- Change the hundreds digit. Only the hundreds digit changes. The others stay the same.645 + 100 = 745
- Write the answer. This is the new number.745
Check. 100 less than 745 is 645. It works.
Watch out. Only the hundreds digit changes. Keep the other digits the same.
Method. Start at the number and count on or back, one number at a time.
- Start at 255. We begin with this number.255
- Count on 8. Say each new number as we go.255 + 8 = 263
- Write the answer. This is the last number we reached.263
Check. Count back 8 from 263: you reach 255.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 156. We begin with this number.156
- Count on 6. Say each new number as we go.156 + 6 = 162
- Write the answer. This is the last number we reached.162
Check. Count back 6 from 162: you reach 156.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Count on in fifties by adding or taking away 50 each time.
- Start at 50. We count from this number.50
- Add 50 each time. We count on in fifties.50 + 50 = 100; 100 + 50 = 150
- Write the numbers in order. These are the next numbers we said.100, 150, 200
Check. Count back in fifties from 200 to check. You reach 50.
Watch out. The step is 50. Each new number is 50 more than the last.
Method. Start at the number and count on or back, one number at a time.
- Start at 391. We begin with this number.391
- Count back 11. Say each number as we pass it.391 - 11 = 380
- Write the answer. This is the last number we reached.380
Check. Count on 11 from 380: you reach 391.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Count back in hundreds by adding or taking away 100 each time.
- Start at 900. We count from this number.900
- Take 100 each time. We count back in hundreds.900 - 100 = 800; 800 - 100 = 700
- Write the numbers in order. These are the next numbers we said.800, 700, 600
Check. Count on in hundreds from 600 to check. You reach 900.
Watch out. The step is 100. Each new number is 100 less than the last.
Method. Start at the number and count on or back, one number at a time.
- Start at 648. We begin with this number.648
- Count on 6. Say each new number as we go.648 + 6 = 654
- Write the answer. This is the last number we reached.654
Check. Count back 6 from 654: you reach 648.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Count on in tens by adding or taking away 10 each time.
- Start at 960. We count from this number.960
- Add 10 each time. We count on in tens.960 + 10 = 970; 970 + 10 = 980
- Write the numbers in order. These are the next numbers we said.970, 980, 990
Check. Count back in tens from 990 to check. You reach 960.
Watch out. The step is 10. Each new number is 10 more than the last.
Method. Count on in fives by adding or taking away 5 each time.
- Start at 238. We count from this number.238
- Add 5 each time. We count on in fives.238 + 5 = 243; 243 + 5 = 248
- Write the numbers in order. These are the next numbers we said.243, 248, 253
Check. Count back in fives from 253 to check. You reach 238.
Watch out. The step is 5. Each new number is 5 more than the last.
Method. Change only the hundreds digit when we go less than the number.
- Start at 390. We begin with this number.390
- Change the hundreds digit. Only the hundreds digit changes. The others stay the same.390 - 100 = 290
- Write the answer. This is the new number.290
Check. 100 more than 290 is 390. It works.
Watch out. Only the hundreds digit changes. Keep the other digits the same.
Total 19 marks. Allow about 19 minutes.
Exercise 1X Practice test questions
Non-calculatorMethod. Count back in tens by adding or taking away 10 each time.
- Start at 800. We count from this number.800
- Take 10 each time. We count back in tens.800 - 10 = 790; 790 - 10 = 780
- Write the numbers in order. These are the next numbers we said.790, 780, 770
Check. Count on in tens from 770 to check. You reach 800.
Watch out. The step is 10. Each new number is 10 less than the last.
Method. Start at the number and count on or back, one number at a time.
- Start at 759. We begin with this number.759
- Count on 4. Say each new number as we go.759 + 4 = 763
- Write the answer. This is the last number we reached.763
Check. Count back 4 from 763: you reach 759.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 82. We begin with this number.82
- Count on 10. Say each new number as we go.82 + 10 = 92
- Write the answer. This is the last number we reached.92
Check. Count back 10 from 92: you reach 82.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Count on in twos by adding or taking away 2 each time.
- Start at 36. We count from this number.36
- Add 2 each time. We count on in twos.36 + 2 = 38; 38 + 2 = 40
- Write the numbers in order. These are the next numbers we said.38, 40, 42
Check. Count back in twos from 42 to check. You reach 36.
Watch out. The step is 2. Each new number is 2 more than the last.
Method. Count on in fives by adding or taking away 5 each time.
- Start at 84. We count from this number.84
- Add 5 each time. We count on in fives.84 + 5 = 89; 89 + 5 = 94
- Write the numbers in order. These are the next numbers we said.89, 94, 99
Check. Count back in fives from 99 to check. You reach 84.
Watch out. The step is 5. Each new number is 5 more than the last.
Method. Change only the hundreds digit when we go less than the number.
- Start at 661. We begin with this number.661
- Change the hundreds digit. Only the hundreds digit changes. The others stay the same.661 - 100 = 561
- Write the answer. This is the new number.561
Check. 100 more than 561 is 661. It works.
Watch out. Only the hundreds digit changes. Keep the other digits the same.
Method. Change only the tens digit when we go less than the number.
- Start at 774. We begin with this number.774
- Change the tens digit. Only the tens digit changes. The others stay the same.774 - 10 = 764
- Write the answer. This is the new number.764
Check. 10 more than 764 is 774. It works.
Watch out. Only the tens digit changes. Keep the other digits the same.
Method. Start at the number and count on or back, one number at a time.
- Start at 249. We begin with this number.249
- Count on 5. Say each new number as we go.249 + 5 = 254
- Write the answer. This is the last number we reached.254
Check. Count back 5 from 254: you reach 249.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Start at the number and count on or back, one number at a time.
- Start at 774. We begin with this number.774
- Count back 3. Say each number as we pass it.774 - 3 = 771
- Write the answer. This is the last number we reached.771
Check. Count on 3 from 771: you reach 774.
Watch out. Start from the number in the question. Do not start again from 1 or from 0.
Method. Count back in tens by adding or taking away 10 each time.
- Start at 170. We count from this number.170
- Take 10 each time. We count back in tens.170 - 10 = 160; 160 - 10 = 150
- Write the numbers in order. These are the next numbers we said.160, 150, 140
Check. Count on in tens from 140 to check. You reach 170.
Watch out. The step is 10. Each new number is 10 less than the last.