Counting and place value to 10000
By the end of this chapter you will be able to
- Count on and back in hundreds, thousands and fifties
- Say the value of each digit in a four-digit number
- Partition a number in more than one way
- Read and write four-digit numbers in figures and words
- Say 1000 more and 1000 less than any number
You should already know
- Counting and place value to 1000 (Level 3, chapter 2)
- Counting in tens and hundreds (Level 3, chapter 1)
Where this leads
- Comparing, ordering and rounding four-digit numbers (chapter 2)
Step-by-step practice: maths (Level 4). Small steps, repeated until fluent. Content: Count in steps of 50, 100 and 1000 from any number, forwards and backwards (PV1), Recognise the place value of each digit in a four-digit number (PV2), Read and write numbers to 10000 in figures and in words (PV5), Count in 1000s and find 1000 more or less than a given number (Year 4 paraphrase).
Exercise P Do you remember?
Non-calculatorMethod. Count on in tens, four times.
- Start at 340. It is where we begin.340
- Add 10 four times. Each count adds 10.340 + 40 = 380
- Write the answer. This is the last number.380
Check. Check: 380 - 40 = 340.
Watch out. Adding ten changes only the tens digit.
Method. Add 100 by changing the hundreds digit.
- Look at the hundreds digit. It is 6 hundreds.645: 6 hundreds
- Add one hundred. The hundreds digit goes up by 1.6 + 1 = 7 hundreds
- Write the answer. The tens and ones stay the same.745
Check. Check: 745 - 645 = 100.
Watch out. Only the hundreds digit changes.
Method. Read the hundreds first, then the tens and ones.
- Say the hundreds. There are five hundred.five hundred
- Say the tens and ones. Use and before them.and seven
- Write the answer in words. Join the parts.five hundred and seven
Check. Check: 500 + 7 = 507.
Watch out. Keep the zero in the tens place in your mind: no tens.
Method. Compare the hundreds first, then the tens, then the ones.
- Compare the hundreds. Both have 4 hundreds.4 and 4 are the same
- Compare the tens. The tens digits are 1 and 2. Two tens is more than one ten.1 ten and 2 tens
- Write the greater number. It has more tens, so it is greater.421
Check. Check: 421 - 412 = 9, so 421 is greater.
Watch out. Start at the left: the greater hundreds digit wins.
Method. Add the same number four times.
- Count the groups. There are four 2s.4 groups of 2
- Add the groups. Count in twos four times.2, 4, 6, 8
- Write the answer. This is the total.8
Check. Check: 4 × 2 = 8.
Watch out. Repeated addition is the same as multiplying.
Counting in hundreds
Counting in hundreds means each number is 100 more than the one before. Only the hundreds digit goes up by 1 each time, until the hundreds go past 9. Then the thousands digit goes up by 1.
Counting back in hundreds means each number is 100 less than the one before.
Key ideas
- Counting on in hundreds adds 100 each time.
- Counting back in hundreds takes away 100 each time.
- Find the step first, then count in that step.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.2350
- Add 100 each time. Each count moves by the same step.2350 + 100 = 2450
- Add 100 each time. Each count moves by the same step.2450 + 100 = 2550
- Add 100 each time. Each count moves by the same step.2550 + 100 = 2650
- Write the answer. This is the last number we reached.2650
Check. Count the steps back: 2650 - 300 = 2350.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.4100
- Take 100 each time. Each count moves by the same step.4100 - 100 = 4000
- Take 100 each time. Each count moves by the same step.4000 - 100 = 3900
- Write the answer. This is the last number we reached.3900
Check. Count the steps back: 3900 + 200 = 4100.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Find the step between the numbers, then count on to fill the gap.
- Find the step. The numbers go up by the same amount each time.6300 - 6200 = 100
- Count on from 6300. Add the step to the number before the gap.6300 + 100 = 6400
- Write the missing number. It fits the pattern.6400
Check. Check: 6400 + 100 = 6500, the next number.
Watch out. Look at the numbers either side of the gap.
Watch out
Watch out. 2950 + 100 is 3050, not 2960. The hundreds go past 9, so the thousands digit goes up.
Exam tip
Grown-up tip. Ask the child to say the step out loud as they go: “2350, 2450, 2550.” Aim to count in hundreds from any number in under 10 seconds.
Exercise 1A Practice: counting in hundreds
Non-calculatorMethod. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.3009
- Add 100 each time. Each count moves by the same step.3009 + 100 = 3109
- Add 100 each time. Each count moves by the same step.3109 + 100 = 3209
- Add 100 each time. Each count moves by the same step.3209 + 100 = 3309
- Add 100 each time. Each count moves by the same step.3309 + 100 = 3409
- Add 100 each time. Each count moves by the same step.3409 + 100 = 3509
- Write the answer. This is the last number we reached.3509
Check. Count the steps back: 3509 - 500 = 3009.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.1290
- Take 100 each time. Each count moves by the same step.1290 - 100 = 1190
- Take 100 each time. Each count moves by the same step.1190 - 100 = 1090
- Write the answer. This is the last number we reached.1090
Check. Count the steps back: 1090 + 200 = 1290.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.2082
- Add 100 each time. Each count moves by the same step.2082 + 100 = 2182
- Add 100 each time. Each count moves by the same step.2182 + 100 = 2282
- Add 100 each time. Each count moves by the same step.2282 + 100 = 2382
- Add 100 each time. Each count moves by the same step.2382 + 100 = 2482
- Add 100 each time. Each count moves by the same step.2482 + 100 = 2582
- Write the answer. This is the last number we reached.2582
Check. Count the steps back: 2582 - 500 = 2082.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.1910
- Take 100 each time. Each count moves by the same step.1910 - 100 = 1810
- Take 100 each time. Each count moves by the same step.1810 - 100 = 1710
- Take 100 each time. Each count moves by the same step.1710 - 100 = 1610
- Take 100 each time. Each count moves by the same step.1610 - 100 = 1510
- Write the answer. This is the last number we reached.1510
Check. Count the steps back: 1510 + 400 = 1910.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.1478
- Add 100 each time. Each count moves by the same step.1478 + 100 = 1578
- Add 100 each time. Each count moves by the same step.1578 + 100 = 1678
- Add 100 each time. Each count moves by the same step.1678 + 100 = 1778
- Add 100 each time. Each count moves by the same step.1778 + 100 = 1878
- Write the answer. This is the last number we reached.1878
Check. Count the steps back: 1878 - 400 = 1478.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.7174
- Add 100 each time. Each count moves by the same step.7174 + 100 = 7274
- Add 100 each time. Each count moves by the same step.7274 + 100 = 7374
- Add 100 each time. Each count moves by the same step.7374 + 100 = 7474
- Write the answer. This is the last number we reached.7474
Check. Count the steps back: 7474 - 300 = 7174.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.8726
- Add 100 each time. Each count moves by the same step.8726 + 100 = 8826
- Add 100 each time. Each count moves by the same step.8826 + 100 = 8926
- Add 100 each time. Each count moves by the same step.8926 + 100 = 9026
- Add 100 each time. Each count moves by the same step.9026 + 100 = 9126
- Add 100 each time. Each count moves by the same step.9126 + 100 = 9226
- Write the answer. This is the last number we reached.9226
Check. Count the steps back: 9226 - 500 = 8726.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Find the step between the numbers, then count on to fill the gap.
- Find the step size from two numbers that are next to each other. The step is the same all the way along.5164 - 5064 = 100
- Count from the number before the gap. Add the step to get the missing number.4964 + 100 = 5064
- Write the missing number. It fits the pattern.5064
Check. Check: 5064 + 100 is the next number, 5164.
Watch out. Look at the numbers either side of the gap. The step is the same each time.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.7878
- Add 100 each time. Each count moves by the same step.7878 + 100 = 7978
- Add 100 each time. Each count moves by the same step.7978 + 100 = 8078
- Add 100 each time. Each count moves by the same step.8078 + 100 = 8178
- Add 100 each time. Each count moves by the same step.8178 + 100 = 8278
- Add 100 each time. Each count moves by the same step.8278 + 100 = 8378
- Write the answer. This is the last number we reached.8378
Check. Count the steps back: 8378 - 500 = 7878.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.7424
- Take 100 each time. Each count moves by the same step.7424 - 100 = 7324
- Take 100 each time. Each count moves by the same step.7324 - 100 = 7224
- Take 100 each time. Each count moves by the same step.7224 - 100 = 7124
- Take 100 each time. Each count moves by the same step.7124 - 100 = 7024
- Take 100 each time. Each count moves by the same step.7024 - 100 = 6924
- Write the answer. This is the last number we reached.6924
Check. Count the steps back: 6924 + 500 = 7424.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.9961
- Take 100 each time. Each count moves by the same step.9961 - 100 = 9861
- Take 100 each time. Each count moves by the same step.9861 - 100 = 9761
- Take 100 each time. Each count moves by the same step.9761 - 100 = 9661
- Write the answer. This is the last number we reached.9661
Check. Count the steps back: 9661 + 300 = 9961.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.4069
- Take 100 each time. Each count moves by the same step.4069 - 100 = 3969
- Take 100 each time. Each count moves by the same step.3969 - 100 = 3869
- Write the answer. This is the last number we reached.3869
Check. Count the steps back: 3869 + 200 = 4069.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.8581
- Add 100 each time. Each count moves by the same step.8581 + 100 = 8681
- Add 100 each time. Each count moves by the same step.8681 + 100 = 8781
- Add 100 each time. Each count moves by the same step.8781 + 100 = 8881
- Add 100 each time. Each count moves by the same step.8881 + 100 = 8981
- Add 100 each time. Each count moves by the same step.8981 + 100 = 9081
- Write the answer. This is the last number we reached.9081
Check. Count the steps back: 9081 - 500 = 8581.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Find the step between the numbers, then count on to fill the gap.
- Find the step size from two numbers that are next to each other. The step is the same all the way along.4871 - 4771 = 100
- Count from the number before the gap. Add the step to get the missing number.4771 + 100 = 4871
- Write the missing number. It fits the pattern.4871
Check. Check: 4871 + 100 is the next number, 4971.
Watch out. Look at the numbers either side of the gap. The step is the same each time.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.4363
- Take 100 each time. Each count moves by the same step.4363 - 100 = 4263
- Take 100 each time. Each count moves by the same step.4263 - 100 = 4163
- Write the answer. This is the last number we reached.4163
Check. Count the steps back: 4163 + 200 = 4363.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Find the step between the numbers, then count on to fill the gap.
- Find the step size from two numbers that are next to each other. The step is the same all the way along.7233 - 7133 = 100
- Count from the number before the gap. Add the step to get the missing number.7133 + 100 = 7233
- Write the missing number. It fits the pattern.7233
Check. Check: 7233 + 100 is the next number, 7333.
Watch out. Look at the numbers either side of the gap. The step is the same each time.
Counting in thousands; 1000 more and 1000 less
Adding 1000 changes only the thousands digit: it goes up by 1. Taking away 1000 changes the thousands digit: it goes down by 1.
The hundreds, tens and ones stay the same.
Key ideas
- 1000 more: the thousands digit goes up by 1.
- 1000 less: the thousands digit goes down by 1.
- The other digits do not change.
Method. Change the thousands digit by one; the other digits stay the same.
- Look at the thousands digit. Only the thousands digit changes.4826 has 4 thousands
- Add one thousand. The thousands digit goes up by 1.4 + 1 = 5 thousands
- Write the answer. The hundreds, tens and ones stay the same.5826
Check. Check: 5826 - 4826 = 1000.
Watch out. Do not change the hundreds, tens or ones.
Method. Change the thousands digit by one; the other digits stay the same.
- Look at the thousands digit. Only the thousands digit changes.7060 has 7 thousands
- Take away one thousand. The thousands digit goes down by 1.7 - 1 = 6 thousands
- Write the answer. The hundreds, tens and ones stay the same.6060
Check. Check: 6060 + 1000 = 7060.
Watch out. The 0 in the hundreds place stays a 0.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.2415
- Add 1000 each time. Each count moves by the same step.2415 + 1000 = 3415
- Add 1000 each time. Each count moves by the same step.3415 + 1000 = 4415
- Add 1000 each time. Each count moves by the same step.4415 + 1000 = 5415
- Write the answer. This is the last number we reached.5415
Check. Count the steps back: 5415 - 3000 = 2415.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Watch out
Watch out. 1000 more than 4826 is 5826, not 4836. Change the thousands, not the tens.
Exam tip
Grown-up tip. Point to the thousands digit before each answer. Ask: “Which digit changes, and by how much?”
Exercise 1B Practice: counting in thousands
Non-calculatorMethod. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.3334
- Add 1000 each time. Each count moves by the same step.3334 + 1000 = 4334
- Add 1000 each time. Each count moves by the same step.4334 + 1000 = 5334
- Add 1000 each time. Each count moves by the same step.5334 + 1000 = 6334
- Add 1000 each time. Each count moves by the same step.6334 + 1000 = 7334
- Write the answer. This is the last number we reached.7334
Check. Count the steps back: 7334 - 4000 = 3334.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.1128
- Add 1000 each time. Each count moves by the same step.1128 + 1000 = 2128
- Add 1000 each time. Each count moves by the same step.2128 + 1000 = 3128
- Add 1000 each time. Each count moves by the same step.3128 + 1000 = 4128
- Add 1000 each time. Each count moves by the same step.4128 + 1000 = 5128
- Write the answer. This is the last number we reached.5128
Check. Count the steps back: 5128 - 4000 = 1128.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Change the thousands digit by one; the other digits stay the same.
- Look at the thousands digit. Only the thousands digit changes when we add or take away 1000.3054 has 3 thousands
- Take away one thousand. The thousands digit goes up or down by 1.3 - 1 = 2 thousands
- Write the answer. The hundreds, tens and ones stay the same.2054
Check. Check: 2054 and 3054 differ by exactly 1000.
Watch out. Do not change the hundreds, tens or ones when you add or take away 1000.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.1867
- Add 1000 each time. Each count moves by the same step.1867 + 1000 = 2867
- Add 1000 each time. Each count moves by the same step.2867 + 1000 = 3867
- Add 1000 each time. Each count moves by the same step.3867 + 1000 = 4867
- Add 1000 each time. Each count moves by the same step.4867 + 1000 = 5867
- Write the answer. This is the last number we reached.5867
Check. Count the steps back: 5867 - 4000 = 1867.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.4441
- Add 1000 each time. Each count moves by the same step.4441 + 1000 = 5441
- Add 1000 each time. Each count moves by the same step.5441 + 1000 = 6441
- Write the answer. This is the last number we reached.6441
Check. Count the steps back: 6441 - 2000 = 4441.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.3427
- Add 1000 each time. Each count moves by the same step.3427 + 1000 = 4427
- Add 1000 each time. Each count moves by the same step.4427 + 1000 = 5427
- Add 1000 each time. Each count moves by the same step.5427 + 1000 = 6427
- Add 1000 each time. Each count moves by the same step.6427 + 1000 = 7427
- Add 1000 each time. Each count moves by the same step.7427 + 1000 = 8427
- Write the answer. This is the last number we reached.8427
Check. Count the steps back: 8427 - 5000 = 3427.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.1370
- Add 1000 each time. Each count moves by the same step.1370 + 1000 = 2370
- Add 1000 each time. Each count moves by the same step.2370 + 1000 = 3370
- Write the answer. This is the last number we reached.3370
Check. Count the steps back: 3370 - 2000 = 1370.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.1436
- Add 1000 each time. Each count moves by the same step.1436 + 1000 = 2436
- Add 1000 each time. Each count moves by the same step.2436 + 1000 = 3436
- Write the answer. This is the last number we reached.3436
Check. Count the steps back: 3436 - 2000 = 1436.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Change the thousands digit by one; the other digits stay the same.
- Look at the thousands digit. Only the thousands digit changes when we add or take away 1000.3745 has 3 thousands
- Take away one thousand. The thousands digit goes up or down by 1.3 - 1 = 2 thousands
- Write the answer. The hundreds, tens and ones stay the same.2745
Check. Check: 2745 and 3745 differ by exactly 1000.
Watch out. Do not change the hundreds, tens or ones when you add or take away 1000.
Method. Change the thousands digit by one; the other digits stay the same.
- Look at the thousands digit. Only the thousands digit changes when we add or take away 1000.1910 has 1 thousands
- Add one thousand. The thousands digit goes up or down by 1.1 + 1 = 2 thousands
- Write the answer. The hundreds, tens and ones stay the same.2910
Check. Check: 2910 and 1910 differ by exactly 1000.
Watch out. Do not change the hundreds, tens or ones when you add or take away 1000.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.5514
- Add 1000 each time. Each count moves by the same step.5514 + 1000 = 6514
- Add 1000 each time. Each count moves by the same step.6514 + 1000 = 7514
- Add 1000 each time. Each count moves by the same step.7514 + 1000 = 8514
- Add 1000 each time. Each count moves by the same step.8514 + 1000 = 9514
- Write the answer. This is the last number we reached.9514
Check. Count the steps back: 9514 - 4000 = 5514.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.9613
- Take 1000 each time. Each count moves by the same step.9613 - 1000 = 8613
- Take 1000 each time. Each count moves by the same step.8613 - 1000 = 7613
- Take 1000 each time. Each count moves by the same step.7613 - 1000 = 6613
- Take 1000 each time. Each count moves by the same step.6613 - 1000 = 5613
- Take 1000 each time. Each count moves by the same step.5613 - 1000 = 4613
- Write the answer. This is the last number we reached.4613
Check. Count the steps back: 4613 + 5000 = 9613.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.3901
- Add 1000 each time. Each count moves by the same step.3901 + 1000 = 4901
- Add 1000 each time. Each count moves by the same step.4901 + 1000 = 5901
- Add 1000 each time. Each count moves by the same step.5901 + 1000 = 6901
- Add 1000 each time. Each count moves by the same step.6901 + 1000 = 7901
- Add 1000 each time. Each count moves by the same step.7901 + 1000 = 8901
- Write the answer. This is the last number we reached.8901
Check. Count the steps back: 8901 - 5000 = 3901.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.4738
- Take 1000 each time. Each count moves by the same step.4738 - 1000 = 3738
- Take 1000 each time. Each count moves by the same step.3738 - 1000 = 2738
- Write the answer. This is the last number we reached.2738
Check. Count the steps back: 2738 + 2000 = 4738.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.7752
- Take 1000 each time. Each count moves by the same step.7752 - 1000 = 6752
- Take 1000 each time. Each count moves by the same step.6752 - 1000 = 5752
- Take 1000 each time. Each count moves by the same step.5752 - 1000 = 4752
- Take 1000 each time. Each count moves by the same step.4752 - 1000 = 3752
- Take 1000 each time. Each count moves by the same step.3752 - 1000 = 2752
- Write the answer. This is the last number we reached.2752
Check. Count the steps back: 2752 + 5000 = 7752.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Change the thousands digit by one; the other digits stay the same.
- Look at the thousands digit. Only the thousands digit changes when we add or take away 1000.4496 has 4 thousands
- Add one thousand. The thousands digit goes up or down by 1.4 + 1 = 5 thousands
- Write the answer. The hundreds, tens and ones stay the same.5496
Check. Check: 5496 and 4496 differ by exactly 1000.
Watch out. Do not change the hundreds, tens or ones when you add or take away 1000.
Counting in fifties
Fifty is half of a hundred. Counting in fifties gives 50, 100, 150, 200 and so on.
Each hundred has two fifties in it: the number ends in 50 or 00.
Key ideas
- Each fifty ends in 50 or 00.
- Fifty is half of a hundred.
- Count in steps of 50 to find the answer.
Method. Find the step between the numbers, then count on to fill the gap.
- Find the step. The numbers go up by 50 each time.1900 - 1850 = 50
- Count on from 1900. Add 50 to get the missing number.1900 + 50 = 1950
- Write the missing number. It fits the pattern.1950
Check. Check: 1950 + 50 = 2000.
Watch out. Fifties go up in steps of 50, so the ones and tens count in fifties.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.3250
- Add 50 each time. Each count moves by the same step.3250 + 50 = 3300
- Add 50 each time. Each count moves by the same step.3300 + 50 = 3350
- Add 50 each time. Each count moves by the same step.3350 + 50 = 3400
- Add 50 each time. Each count moves by the same step.3400 + 50 = 3450
- Write the answer. This is the last number we reached.3450
Check. Count the steps back: 3450 - 200 = 3250.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.6000
- Take 50 each time. Each count moves by the same step.6000 - 50 = 5950
- Take 50 each time. Each count moves by the same step.5950 - 50 = 5900
- Take 50 each time. Each count moves by the same step.5900 - 50 = 5850
- Write the answer. This is the last number we reached.5850
Check. Count the steps back: 5850 + 150 = 6000.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Watch out
Watch out. After 1950 comes 2000, not 1960. Fifties always end in 00 or 50.
Exam tip
Grown-up tip. Ask the child to count in fifties from a multiple of 50, such as 3250, then say the next number before you do.
Exercise 1C Practice: counting in fifties
Non-calculatorMethod. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.2000
- Add 50 each time. Each count moves by the same step.2000 + 50 = 2050
- Add 50 each time. Each count moves by the same step.2050 + 50 = 2100
- Add 50 each time. Each count moves by the same step.2100 + 50 = 2150
- Add 50 each time. Each count moves by the same step.2150 + 50 = 2200
- Write the answer. This is the last number we reached.2200
Check. Count the steps back: 2200 - 200 = 2000.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.4200
- Add 50 each time. Each count moves by the same step.4200 + 50 = 4250
- Add 50 each time. Each count moves by the same step.4250 + 50 = 4300
- Add 50 each time. Each count moves by the same step.4300 + 50 = 4350
- Write the answer. This is the last number we reached.4350
Check. Count the steps back: 4350 - 150 = 4200.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.2950
- Add 50 each time. Each count moves by the same step.2950 + 50 = 3000
- Add 50 each time. Each count moves by the same step.3000 + 50 = 3050
- Add 50 each time. Each count moves by the same step.3050 + 50 = 3100
- Write the answer. This is the last number we reached.3100
Check. Count the steps back: 3100 - 150 = 2950.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.6350
- Take 50 each time. Each count moves by the same step.6350 - 50 = 6300
- Take 50 each time. Each count moves by the same step.6300 - 50 = 6250
- Take 50 each time. Each count moves by the same step.6250 - 50 = 6200
- Write the answer. This is the last number we reached.6200
Check. Count the steps back: 6200 + 150 = 6350.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.7250
- Take 50 each time. Each count moves by the same step.7250 - 50 = 7200
- Take 50 each time. Each count moves by the same step.7200 - 50 = 7150
- Take 50 each time. Each count moves by the same step.7150 - 50 = 7100
- Write the answer. This is the last number we reached.7100
Check. Count the steps back: 7100 + 150 = 7250.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.4650
- Take 50 each time. Each count moves by the same step.4650 - 50 = 4600
- Take 50 each time. Each count moves by the same step.4600 - 50 = 4550
- Write the answer. This is the last number we reached.4550
Check. Count the steps back: 4550 + 100 = 4650.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.4000
- Add 50 each time. Each count moves by the same step.4000 + 50 = 4050
- Add 50 each time. Each count moves by the same step.4050 + 50 = 4100
- Add 50 each time. Each count moves by the same step.4100 + 50 = 4150
- Write the answer. This is the last number we reached.4150
Check. Count the steps back: 4150 - 150 = 4000.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Find the step between the numbers, then count on to fill the gap.
- Find the step size from two numbers that are next to each other. The step is the same all the way along.6650 - 6600 = 50
- Count from the number before the gap. Add the step to get the missing number.6550 + 50 = 6600
- Write the missing number. It fits the pattern.6600
Check. Check: 6600 + 50 is the next number, 6650.
Watch out. Look at the numbers either side of the gap. The step is the same each time.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.3700
- Add 50 each time. Each count moves by the same step.3700 + 50 = 3750
- Add 50 each time. Each count moves by the same step.3750 + 50 = 3800
- Add 50 each time. Each count moves by the same step.3800 + 50 = 3850
- Add 50 each time. Each count moves by the same step.3850 + 50 = 3900
- Add 50 each time. Each count moves by the same step.3900 + 50 = 3950
- Write the answer. This is the last number we reached.3950
Check. Count the steps back: 3950 - 250 = 3700.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.8000
- Add 50 each time. Each count moves by the same step.8000 + 50 = 8050
- Add 50 each time. Each count moves by the same step.8050 + 50 = 8100
- Write the answer. This is the last number we reached.8100
Check. Count the steps back: 8100 - 100 = 8000.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Find the step between the numbers, then count on to fill the gap.
- Find the step size from two numbers that are next to each other. The step is the same all the way along.5950 - 5900 = 50
- Count from the number before the gap. Add the step to get the missing number.5900 + 50 = 5950
- Write the missing number. It fits the pattern.5950
Check. Check: 5950 + 50 is the next number, 6000.
Watch out. Look at the numbers either side of the gap. The step is the same each time.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.2400
- Take 50 each time. Each count moves by the same step.2400 - 50 = 2350
- Take 50 each time. Each count moves by the same step.2350 - 50 = 2300
- Take 50 each time. Each count moves by the same step.2300 - 50 = 2250
- Take 50 each time. Each count moves by the same step.2250 - 50 = 2200
- Take 50 each time. Each count moves by the same step.2200 - 50 = 2150
- Write the answer. This is the last number we reached.2150
Check. Count the steps back: 2150 + 250 = 2400.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Find the step between the numbers, then count on to fill the gap.
- Find the step size from two numbers that are next to each other. The step is the same all the way along.7500 - 7450 = 50
- Count from the number before the gap. Add the step to get the missing number.7400 + 50 = 7450
- Write the missing number. It fits the pattern.7450
Check. Check: 7450 + 50 is the next number, 7500.
Watch out. Look at the numbers either side of the gap. The step is the same each time.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.8900
- Take 50 each time. Each count moves by the same step.8900 - 50 = 8850
- Take 50 each time. Each count moves by the same step.8850 - 50 = 8800
- Write the answer. This is the last number we reached.8800
Check. Count the steps back: 8800 + 100 = 8900.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.5850
- Take 50 each time. Each count moves by the same step.5850 - 50 = 5800
- Take 50 each time. Each count moves by the same step.5800 - 50 = 5750
- Take 50 each time. Each count moves by the same step.5750 - 50 = 5700
- Take 50 each time. Each count moves by the same step.5700 - 50 = 5650
- Write the answer. This is the last number we reached.5650
Check. Count the steps back: 5650 + 200 = 5850.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Find the step between the numbers, then count on to fill the gap.
- Find the step size from two numbers that are next to each other. The step is the same all the way along.8350 - 8300 = 50
- Count from the number before the gap. Add the step to get the missing number.8300 + 50 = 8350
- Write the missing number. It fits the pattern.8350
Check. Check: 8350 + 50 is the next number, 8400.
Watch out. Look at the numbers either side of the gap. The step is the same each time.
Place value in four-digit numbers
A four-digit number has four columns: thousands, hundreds, tens and ones. The value of a digit depends on its column.
In 4826 the 4 is worth 4000, the 8 is worth 800, the 2 is worth 20 and the 6 is worth 6.
Key ideas
- Thousands, hundreds, tens and ones.
- The value of a digit = the digit × the place value.
- Place values: 1000, 100, 10 and 1.
Method. The value of a digit depends on its place. Multiply the digit by the place value.
- Find the digit in the hundreds place. Read the digit in that column.8 is in the hundreds place
- Multiply the digit by its place value. Each hundred is worth 100.8 × 100 = 800
- Write the value. This is what the digit is worth in this number.800
Check. Check: 800 is eight hundreds.
Watch out. Say what the digit is worth, such as 800 not 8.
Method. Read the number from the right, column by column.
- Count from the right to the tens column. Ones are on the right, then tens.5271: ones 1, tens 7
- Read the digit in the tens column. It is the digit that stands in that place.the tens digit is 7
- Write the digit. Write only the digit.7
Check. Check: 70 is the value of the 7 in the tens place.
Watch out. Count the columns from the right, not from the left.
Method. The thousands digit tells how many thousands.
- Look at the thousands digit. It is the first digit in 9034.9034: thousands digit is 9
- Read the number of thousands. Nine thousands.9 thousands
- Write the answer. This is how many thousands there are.9
Check. Check: 9000 is 9 thousands.
Watch out. The number of thousands is not the same as the whole number.
Watch out
Watch out. The 2 in 5271 is worth 200 (hundreds), not 2. The digit and its value are different.
Exam tip
Grown-up tip. Ask: “What is the value of the digit, not just the digit?” Get the child to say the place value as a number.
Exercise 1D Practice: place value
Non-calculatorMethod. Read the number from the right, column by column.
- Count from the right to the ones column. Ones are on the right, then tens, hundreds and thousands.1822: thousands, hundreds, tens, ones
- Read the digit in that column. It is the digit that stands in that place.the ones digit is 2
- Write the digit. Write only the digit.2
Check. Check: the picture shows 2 squares in the ones column.
Watch out. Count the place columns from the right, not from the left.
Method. Read the number from the right, column by column.
- Count from the right to the ones column. Ones are on the right, then tens, hundreds and thousands.1961: thousands, hundreds, tens, ones
- Read the digit in that column. It is the digit that stands in that place.the ones digit is 1
- Write the digit. Write only the digit.1
Check. Check: the picture shows 1 squares in the ones column.
Watch out. Count the place columns from the right, not from the left.
Method. The value of a digit depends on its place. Multiply the digit by the place value.
- Find the digit in the ones place. Read the digit in that column.4 is in the ones place
- Multiply the digit by its place value. Each one is worth 1.4 × 1 = 4
- Write the value. This is what the digit is worth in this number.4
Check. Check: 4 is 4 ones written as a number.
Watch out. Do not give just the digit. Say what it is worth, such as 300 not 3.
Method. The value of a digit depends on its place. Multiply the digit by the place value.
- Find the digit in the thousands place. Read the digit in that column.6 is in the thousands place
- Multiply the digit by its place value. Each thousand is worth 1000.6 × 1000 = 6000
- Write the value. This is what the digit is worth in this number.6000
Check. Check: 6000 is 6 thousands written as a number.
Watch out. Do not give just the digit. Say what it is worth, such as 300 not 3.
Method. The value of a digit depends on its place. Multiply the digit by the place value.
- Find the digit in the tens place. Read the digit in that column.1 is in the tens place
- Multiply the digit by its place value. Each ten is worth 10.1 × 10 = 10
- Write the value. This is what the digit is worth in this number.10
Check. Check: 10 is 1 tens written as a number.
Watch out. Do not give just the digit. Say what it is worth, such as 300 not 3.
Method. Read the number from the right, column by column.
- Count from the right to the hundreds column. Ones are on the right, then tens, hundreds and thousands.4608: thousands, hundreds, tens, ones
- Read the digit in that column. It is the digit that stands in that place.the hundreds digit is 6
- Write the digit. Write only the digit.6
Check. Check: the picture shows 6 squares in the hundreds column.
Watch out. Count the place columns from the right, not from the left.
Method. Read the number from the right, column by column.
- Count from the right to the thousands column. Ones are on the right, then tens, hundreds and thousands.1428: thousands, hundreds, tens, ones
- Read the digit in that column. It is the digit that stands in that place.the thousands digit is 1
- Write the digit. Write only the digit.1
Check. Check: the picture shows 1 squares in the thousands column.
Watch out. Count the place columns from the right, not from the left.
Method. The value of a digit depends on its place. Multiply the digit by the place value.
- Find the digit in the ones place. Read the digit in that column.7 is in the ones place
- Multiply the digit by its place value. Each one is worth 1.7 × 1 = 7
- Write the value. This is what the digit is worth in this number.7
Check. Check: 7 is 7 ones written as a number.
Watch out. Do not give just the digit. Say what it is worth, such as 300 not 3.
Method. Read the number from the right, column by column.
- Count from the right to the hundreds column. Ones are on the right, then tens, hundreds and thousands.3131: thousands, hundreds, tens, ones
- Read the digit in that column. It is the digit that stands in that place.the hundreds digit is 1
- Write the digit. Write only the digit.1
Check. Check: the picture shows 1 squares in the hundreds column.
Watch out. Count the place columns from the right, not from the left.
Method. The value of a digit depends on its place. Multiply the digit by the place value.
- Find the digit in the ones place. Read the digit in that column.4 is in the ones place
- Multiply the digit by its place value. Each one is worth 1.4 × 1 = 4
- Write the value. This is what the digit is worth in this number.4
Check. Check: 4 is 4 ones written as a number.
Watch out. Do not give just the digit. Say what it is worth, such as 300 not 3.
Method. Read the number from the right, column by column.
- Count from the right to the ones column. Ones are on the right, then tens, hundreds and thousands.8865: thousands, hundreds, tens, ones
- Read the digit in that column. It is the digit that stands in that place.the ones digit is 5
- Write the digit. Write only the digit.5
Check. Check: the picture shows 5 squares in the ones column.
Watch out. Count the place columns from the right, not from the left.
Method. The value of a digit depends on its place. Multiply the digit by the place value.
- Find the digit in the thousands place. Read the digit in that column.9 is in the thousands place
- Multiply the digit by its place value. Each thousand is worth 1000.9 × 1000 = 9000
- Write the value. This is what the digit is worth in this number.9000
Check. Check: 9000 is 9 thousands written as a number.
Watch out. Do not give just the digit. Say what it is worth, such as 300 not 3.
Method. Read the number from the right, column by column.
- Count from the right to the thousands column. Ones are on the right, then tens, hundreds and thousands.7505: thousands, hundreds, tens, ones
- Read the digit in that column. It is the digit that stands in that place.the thousands digit is 7
- Write the digit. Write only the digit.7
Check. Check: the picture shows 7 squares in the thousands column.
Watch out. Count the place columns from the right, not from the left.
Method. The value of a digit depends on its place. Multiply the digit by the place value.
- Find the digit in the tens place. Read the digit in that column.5 is in the tens place
- Multiply the digit by its place value. Each ten is worth 10.5 × 10 = 50
- Write the value. This is what the digit is worth in this number.50
Check. Check: 50 is 5 tens written as a number.
Watch out. Do not give just the digit. Say what it is worth, such as 300 not 3.
Method. The value of a digit depends on its place. Multiply the digit by the place value.
- Find the digit in the ones place. Read the digit in that column.1 is in the ones place
- Multiply the digit by its place value. Each one is worth 1.1 × 1 = 1
- Write the value. This is what the digit is worth in this number.1
Check. Check: 1 is 1 ones written as a number.
Watch out. Do not give just the digit. Say what it is worth, such as 300 not 3.
Method. The value of a digit depends on its place. Multiply the digit by the place value.
- Find the digit in the thousands place. Read the digit in that column.5 is in the thousands place
- Multiply the digit by its place value. Each thousand is worth 1000.5 × 1000 = 5000
- Write the value. This is what the digit is worth in this number.5000
Check. Check: 5000 is 5 thousands written as a number.
Watch out. Do not give just the digit. Say what it is worth, such as 300 not 3.
Partitioning, reading and writing numbers
Partitioning means splitting a number into its parts: 4826 = 4000 + 800 + 20 + 6.
In words, the thousands come first, then the hundreds, then the tens and ones. Use and before the tens and ones.
Keep a zero in any empty column: 4006 has no hundreds and no tens.
Key ideas
- Partition: split the number into thousands, hundreds, tens and ones.
- Use and before the last two digits in words.
- Empty columns need a zero in figures.
Method. Find the parts we know, then subtract them from the whole.
- Add the parts we know. These are the parts in the sum.4000 + 800 + 6 = 4806
- Take this from the number to find the missing part. 4826 minus 4806 is the gap.4826 - 4806 = 20
- Write the missing part. It is the value of the tens column.20
Check. Check: 4000 + 800 + 20 + 6 = 4826.
Watch out. The gap is a value, not a digit: it is 20, not 2.
Method. Read the number in parts: thousands, hundreds, then the last two digits.
- Say the thousands. Read the thousands digit first.three thousand
- Say the hundreds. Then read the hundreds.six hundred
- Say the tens and ones. Use and before the last two digits.and four
- Write the answer in words. Join the parts together.three thousand six hundred and four
Check. Check: 3000 + 600 + 4 = 3604.
Watch out. The zero tens digit still needs a place in the words: and four.
Method. Put each part of the words into its place in the number.
- Find the thousands. Six thousand is the first part.6000
- Find the hundreds, tens and ones. There are no hundreds or tens, and nine ones.0 hundreds, 0 tens, 9 ones
- Add the parts together. Each part goes in its own column.6000 + 0 + 9 = 6009
- Write the number in figures. Keep a zero in the empty columns.6009
Check. Check: read 6009 back as six thousand and nine.
Watch out. Keep a zero in the hundreds and tens columns when they are empty.
Watch out
Watch out. Six thousand and nine is 6009, not 6090 or 609. Keep the zero in the hundreds and tens places.
Exam tip
Grown-up tip. Let the child write each number in words, then check it back by reading the words aloud from the figures.
Exercise 1E Practice: partitioning, words and figures
Non-calculatorMethod. Find the parts we know, then subtract them from the whole.
- Add the parts we know. These are the parts written in the sum.435
- Take this from the number to find the missing part. 3435 minus the known parts is the gap.3435 - 435 = 3000
- Write the missing part. It is the value of that column.3000
Check. Check: 3000 + 400 + 30 + 5 = 3435.
Watch out. The parts are the thousands, hundreds, tens and ones values, not the digits on their own.
Method. Put each part of the words into its place in the number.
- Find the thousands. Thousands come first.3 thousand = 3000
- Find the hundreds and the tens and ones. Hundreds are the next part; the last two digits follow.200 and 62
- Add the parts together. Each part goes in its own column.3000 + 200 + 62 = 3262
- Write the number in figures. Keep a zero in any empty place.3262
Check. Read 3262 back in words: three thousand two hundred and sixty-two.
Watch out. A zero is needed for any place with nothing in it, such as four thousand and six is 4006.
Method. Find the parts we know, then subtract them from the whole.
- Add the parts we know. These are the parts written in the sum.2000
- Take this from the number to find the missing part. 2700 minus the known parts is the gap.2700 - 2000 = 700
- Write the missing part. It is the value of that column.700
Check. Check: 2000 + 700 + 0 + 0 = 2700.
Watch out. The parts are the thousands, hundreds, tens and ones values, not the digits on their own.
Method. Find the parts we know, then subtract them from the whole.
- Add the parts we know. These are the parts written in the sum.2308
- Take this from the number to find the missing part. 2398 minus the known parts is the gap.2398 - 2308 = 90
- Write the missing part. It is the value of that column.90
Check. Check: 2000 + 300 + 90 + 8 = 2398.
Watch out. The parts are the thousands, hundreds, tens and ones values, not the digits on their own.
Method. Find the parts we know, then subtract them from the whole.
- Add the parts we know. These are the parts written in the sum.1009
- Take this from the number to find the missing part. 1089 minus the known parts is the gap.1089 - 1009 = 80
- Write the missing part. It is the value of that column.80
Check. Check: 1000 + 0 + 80 + 9 = 1089.
Watch out. The parts are the thousands, hundreds, tens and ones values, not the digits on their own.
Method. Put each part of the words into its place in the number.
- Find the thousands. Thousands come first.2 thousand = 2000
- Find the hundreds and the tens and ones. Hundreds are the next part; the last two digits follow.700 and 5
- Add the parts together. Each part goes in its own column.2000 + 700 + 5 = 2705
- Write the number in figures. Keep a zero in any empty place.2705
Check. Read 2705 back in words: two thousand seven hundred and five.
Watch out. A zero is needed for any place with nothing in it, such as four thousand and six is 4006.
Method. Find the parts we know, then subtract them from the whole.
- Add the parts we know. These are the parts written in the sum.2208
- Take this from the number to find the missing part. 2278 minus the known parts is the gap.2278 - 2208 = 70
- Write the missing part. It is the value of that column.70
Check. Check: 2000 + 200 + 70 + 8 = 2278.
Watch out. The parts are the thousands, hundreds, tens and ones values, not the digits on their own.
Method. Put each part of the words into its place in the number.
- Find the thousands. Thousands come first.1 thousand = 1000
- Find the hundreds and the tens and ones. Hundreds are the next part; the last two digits follow.600 and 93
- Add the parts together. Each part goes in its own column.1000 + 600 + 93 = 1693
- Write the number in figures. Keep a zero in any empty place.1693
Check. Read 1693 back in words: one thousand six hundred and ninety-three.
Watch out. A zero is needed for any place with nothing in it, such as four thousand and six is 4006.
Method. Read the number in parts: thousands, hundreds, then the last two digits.
- Say the thousands. Read the thousands digit first.one thousand
- Say the hundreds. Then read the hundreds.three hundred
- Say the tens and ones. Put the last two digits together. Use and before them.thirty-six
- Write the answer in words. Join the parts together.one thousand three hundred and thirty-six
Check. Check: 1000 + 300 + 36 = 1336.
Watch out. Put and before the tens and ones when there are hundreds, as in four hundred and six.
Method. Find the parts we know, then subtract them from the whole.
- Add the parts we know. These are the parts written in the sum.470
- Take this from the number to find the missing part. 5470 minus the known parts is the gap.5470 - 470 = 5000
- Write the missing part. It is the value of that column.5000
Check. Check: 5000 + 400 + 70 + 0 = 5470.
Watch out. The parts are the thousands, hundreds, tens and ones values, not the digits on their own.
Method. Find the parts we know, then subtract them from the whole.
- Add the parts we know. These are the parts written in the sum.1003
- Take this from the number to find the missing part. 1083 minus the known parts is the gap.1083 - 1003 = 80
- Write the missing part. It is the value of that column.80
Check. Check: 1000 + 0 + 80 + 3 = 1083.
Watch out. The parts are the thousands, hundreds, tens and ones values, not the digits on their own.
Method. Find the parts we know, then subtract them from the whole.
- Add the parts we know. These are the parts written in the sum.6090
- Take this from the number to find the missing part. 6490 minus the known parts is the gap.6490 - 6090 = 400
- Write the missing part. It is the value of that column.400
Check. Check: 6000 + 400 + 90 + 0 = 6490.
Watch out. The parts are the thousands, hundreds, tens and ones values, not the digits on their own.
Method. Read the number in parts: thousands, hundreds, then the last two digits.
- Say the thousands. Read the thousands digit first.five thousand
- Say the hundreds. Then read the hundreds.four hundred
- Say the tens and ones. Put the last two digits together. Use and before them.eighty-four
- Write the answer in words. Join the parts together.five thousand four hundred and eighty-four
Check. Check: 5000 + 400 + 84 = 5484.
Watch out. Put and before the tens and ones when there are hundreds, as in four hundred and six.
Method. Find the parts we know, then subtract them from the whole.
- Add the parts we know. These are the parts written in the sum.8703
- Take this from the number to find the missing part. 8753 minus the known parts is the gap.8753 - 8703 = 50
- Write the missing part. It is the value of that column.50
Check. Check: 8000 + 700 + 50 + 3 = 8753.
Watch out. The parts are the thousands, hundreds, tens and ones values, not the digits on their own.
Method. Read the number in parts: thousands, hundreds, then the last two digits.
- Say the thousands. Read the thousands digit first.four thousand
- Say the hundreds. Then read the hundreds.eight hundred
- Say the tens and ones. Put the last two digits together. Use and before them.thirty
- Write the answer in words. Join the parts together.four thousand eight hundred and thirty
Check. Check: 4000 + 800 + 30 = 4830.
Watch out. Put and before the tens and ones when there are hundreds, as in four hundred and six.
Method. Read the number in parts: thousands, hundreds, then the last two digits.
- Say the thousands. Read the thousands digit first.two thousand
- Say the hundreds. Then read the hundreds.seven hundred
- Say the tens and ones. Put the last two digits together. Use and before them.seven
- Write the answer in words. Join the parts together.two thousand seven hundred and seven
Check. Check: 2000 + 700 + 7 = 2707.
Watch out. Put and before the tens and ones when there are hundreds, as in four hundred and six.
Chapter summary
| Skill | Method |
|---|---|
| Counting in hundreds | Add or take away 100 each time; the thousands digit changes when the hundreds pass 9 |
| Counting in thousands | 1000 more or less changes only the thousands digit |
| Counting in fifties | Fifties end in 00 or 50; count in steps of 50 |
| Place value | Value = digit × place value (1000, 100, 10 or 1) |
| Partitioning and words | Split into thousands, hundreds, tens and ones; use and before the tens and ones |
Can you…?
- I can count on and back in hundreds from any number to 10000
- I can say 1000 more and 1000 less than any number
- I can count in fifties from a multiple of 50
- I can say the value of each digit in a four-digit number
- I can partition a four-digit number in more than one way
- I can read and write four-digit numbers in figures and in words
Key terms
- thousands
- the first column on the left of a four-digit number
- place value
- what a digit is worth because of its column
- partition
- split a number into parts, such as 4000 + 800 + 20 + 6
- digit
- one of the symbols 0 to 9 that make a number
Exercise 1Z Check-up
Non-calculatorMethod. Find the step between the numbers, then count on to fill the gap.
- Find the step size from two numbers that are next to each other. The step is the same all the way along.7722 - 7622 = 100
- Count from the number before the gap. Add the step to get the missing number.7522 + 100 = 7622
- Write the missing number. It fits the pattern.7622
Check. Check: 7622 + 100 is the next number, 7722.
Watch out. Look at the numbers either side of the gap. The step is the same each time.
Method. Find the parts we know, then subtract them from the whole.
- Add the parts we know. These are the parts written in the sum.595
- Take this from the number to find the missing part. 1595 minus the known parts is the gap.1595 - 595 = 1000
- Write the missing part. It is the value of that column.1000
Check. Check: 1000 + 500 + 90 + 5 = 1595.
Watch out. The parts are the thousands, hundreds, tens and ones values, not the digits on their own.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.5951
- Take 1000 each time. Each count moves by the same step.5951 - 1000 = 4951
- Take 1000 each time. Each count moves by the same step.4951 - 1000 = 3951
- Take 1000 each time. Each count moves by the same step.3951 - 1000 = 2951
- Take 1000 each time. Each count moves by the same step.2951 - 1000 = 1951
- Write the answer. This is the last number we reached.1951
Check. Count the steps back: 1951 + 4000 = 5951.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Find the parts we know, then subtract them from the whole.
- Add the parts we know. These are the parts written in the sum.3505
- Take this from the number to find the missing part. 3595 minus the known parts is the gap.3595 - 3505 = 90
- Write the missing part. It is the value of that column.90
Check. Check: 3000 + 500 + 90 + 5 = 3595.
Watch out. The parts are the thousands, hundreds, tens and ones values, not the digits on their own.
Method. Read the number from the right, column by column.
- Count from the right to the thousands column. Ones are on the right, then tens, hundreds and thousands.4882: thousands, hundreds, tens, ones
- Read the digit in that column. It is the digit that stands in that place.the thousands digit is 4
- Write the digit. Write only the digit.4
Check. Check: the picture shows 4 squares in the thousands column.
Watch out. Count the place columns from the right, not from the left.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.7100
- Add 50 each time. Each count moves by the same step.7100 + 50 = 7150
- Add 50 each time. Each count moves by the same step.7150 + 50 = 7200
- Add 50 each time. Each count moves by the same step.7200 + 50 = 7250
- Write the answer. This is the last number we reached.7250
Check. Count the steps back: 7250 - 150 = 7100.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.4531
- Take 100 each time. Each count moves by the same step.4531 - 100 = 4431
- Take 100 each time. Each count moves by the same step.4431 - 100 = 4331
- Take 100 each time. Each count moves by the same step.4331 - 100 = 4231
- Write the answer. This is the last number we reached.4231
Check. Count the steps back: 4231 + 300 = 4531.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Find the parts we know, then subtract them from the whole.
- Add the parts we know. These are the parts written in the sum.2340
- Take this from the number to find the missing part. 2341 minus the known parts is the gap.2341 - 2340 = 1
- Write the missing part. It is the value of that column.1
Check. Check: 2000 + 300 + 40 + 1 = 2341.
Watch out. The parts are the thousands, hundreds, tens and ones values, not the digits on their own.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.5054
- Add 1000 each time. Each count moves by the same step.5054 + 1000 = 6054
- Add 1000 each time. Each count moves by the same step.6054 + 1000 = 7054
- Add 1000 each time. Each count moves by the same step.7054 + 1000 = 8054
- Add 1000 each time. Each count moves by the same step.8054 + 1000 = 9054
- Write the answer. This is the last number we reached.9054
Check. Count the steps back: 9054 - 4000 = 5054.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.5549
- Add 100 each time. Each count moves by the same step.5549 + 100 = 5649
- Add 100 each time. Each count moves by the same step.5649 + 100 = 5749
- Add 100 each time. Each count moves by the same step.5749 + 100 = 5849
- Add 100 each time. Each count moves by the same step.5849 + 100 = 5949
- Add 100 each time. Each count moves by the same step.5949 + 100 = 6049
- Write the answer. This is the last number we reached.6049
Check. Count the steps back: 6049 - 500 = 5549.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Total 19 marks. Allow about 19 minutes.
Exercise 1X Practice test questions
Non-calculatorMethod. Change the thousands digit by one; the other digits stay the same.
- Look at the thousands digit. Only the thousands digit changes when we add or take away 1000.6518 has 6 thousands
- Take away one thousand. The thousands digit goes up or down by 1.6 - 1 = 5 thousands
- Write the answer. The hundreds, tens and ones stay the same.5518
Check. Check: 5518 and 6518 differ by exactly 1000.
Watch out. Do not change the hundreds, tens or ones when you add or take away 1000.
Method. Read the number from the right, column by column.
- Count from the right to the hundreds column. Ones are on the right, then tens, hundreds and thousands.6891: thousands, hundreds, tens, ones
- Read the digit in that column. It is the digit that stands in that place.the hundreds digit is 8
- Write the digit. Write only the digit.8
Check. Check: the picture shows 8 squares in the hundreds column.
Watch out. Count the place columns from the right, not from the left.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.8350
- Take 50 each time. Each count moves by the same step.8350 - 50 = 8300
- Take 50 each time. Each count moves by the same step.8300 - 50 = 8250
- Write the answer. This is the last number we reached.8250
Check. Count the steps back: 8250 + 100 = 8350.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.6900
- Add 50 each time. Each count moves by the same step.6900 + 50 = 6950
- Add 50 each time. Each count moves by the same step.6950 + 50 = 7000
- Add 50 each time. Each count moves by the same step.7000 + 50 = 7050
- Write the answer. This is the last number we reached.7050
Check. Count the steps back: 7050 - 150 = 6900.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.7000
- Take 50 each time. Each count moves by the same step.7000 - 50 = 6950
- Take 50 each time. Each count moves by the same step.6950 - 50 = 6900
- Take 50 each time. Each count moves by the same step.6900 - 50 = 6850
- Take 50 each time. Each count moves by the same step.6850 - 50 = 6800
- Write the answer. This is the last number we reached.6800
Check. Count the steps back: 6800 + 200 = 7000.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.2214
- Take 100 each time. Each count moves by the same step.2214 - 100 = 2114
- Take 100 each time. Each count moves by the same step.2114 - 100 = 2014
- Take 100 each time. Each count moves by the same step.2014 - 100 = 1914
- Write the answer. This is the last number we reached.1914
Check. Count the steps back: 1914 + 300 = 2214.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Find the parts we know, then subtract them from the whole.
- Add the parts we know. These are the parts written in the sum.6000
- Take this from the number to find the missing part. 6060 minus the known parts is the gap.6060 - 6000 = 60
- Write the missing part. It is the value of that column.60
Check. Check: 6000 + 0 + 60 + 0 = 6060.
Watch out. The parts are the thousands, hundreds, tens and ones values, not the digits on their own.
Method. Put each part of the words into its place in the number.
- Find the thousands. Thousands come first.9 thousand = 9000
- Find the hundreds and the tens and ones. Hundreds are the next part; the last two digits follow.300 and 39
- Add the parts together. Each part goes in its own column.9000 + 300 + 39 = 9339
- Write the number in figures. Keep a zero in any empty place.9339
Check. Read 9339 back in words: nine thousand three hundred and thirty-nine.
Watch out. A zero is needed for any place with nothing in it, such as four thousand and six is 4006.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.4836
- Take 100 each time. Each count moves by the same step.4836 - 100 = 4736
- Take 100 each time. Each count moves by the same step.4736 - 100 = 4636
- Write the answer. This is the last number we reached.4636
Check. Count the steps back: 4636 + 200 = 4836.
Watch out. Each step adds or takes away the same amount. Do not start counting again from the beginning.
Method. Put each part of the words into its place in the number.
- Find the thousands. Thousands come first.6 thousand = 6000
- Find the hundreds and the tens and ones. Hundreds are the next part; the last two digits follow.200 and 55
- Add the parts together. Each part goes in its own column.6000 + 200 + 55 = 6255
- Write the number in figures. Keep a zero in any empty place.6255
Check. Read 6255 back in words: six thousand two hundred and fifty-five.
Watch out. A zero is needed for any place with nothing in it, such as four thousand and six is 4006.