Step-by-step Maths Level 4: Numbers to 10000: counting, place value, comparing and rounding
Part of the Step-by-step Maths Level 4 level 4 check chapter. Chapter overview · whole chapter on one page
Numbers to 10000: counting, place value, comparing and rounding
This section mixes the skills from chapters 1 and 2. Read each question, then write the answer.
Count in steps when the question gives you a pattern. Compare the thousands first, and round by looking at the digits on the right.
Key ideas
- Count in steps of the same size.
- Compare the thousands first, then the hundreds.
- Round by looking at the digits on the right.
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. Compare the thousands first, then the hundreds, then the tens, then the ones.
- Compare the thousands and the hundreds. They are the same: 3 thousands and 0 hundreds.3 and 3, then 0 and 0
- Compare the tens. The first column that is different decides the order.6 and 9: 6 is less
- Write the sign between the numbers. The smaller number is on the left, so the sign is <.<
Check. Check: 3069 is less than 3096.
Watch out. The arrow always points to the smaller number.
Method. Round to the nearest 10: look at the ones digit.
- Look at the ones digit. The ones digit tells us which ten it is nearer to.the ones digit is 6
- Decide: five or more. Six is five or more, so round up.6 is at least 5
- Round up to the next ten. Keep the same tens and add one more ten.4830 + 10 = 4840
- Write the answer. This is the nearest multiple of 10.4840
Check. Check: 4840 is a multiple of 10 and is 4 away from 4836.
Watch out. Exactly 5 rounds up.
Watch out
Watch out. Check the step first. Do not count in ones when the pattern goes up in hundreds.
Exam tip
Grown-up tip. Ask the child to explain how they found the answer, not only to say it.
Exercise 10A Mixed practice: numbers to 10000
Non-calculatorMethod. The first column that is different decides which number is greater.
- Compare the thousands. Look at the first digit on the left.8 and 5
- Compare the thousands. This is the first column that is different.8 and 5
- Write the greater number. The larger digit makes the larger number.8475
Check. Check: 8475 > 5663.
Watch out. Do not compare the last digits first.
Method. Round to the nearest 10: look at the digits to the right of the ten place.
- Look at the ones digit. The digits on the right tell us which way to go.the ones digit is 1
- Decide: less than 5. Half of 10 is 5. 5 or more rounds up; less than 5 rounds down.1 is less than 5
- Round down. Keep the same tens, and the digits to the right become 0.6601 rounds down to 6600
- Write the answer. This is the nearest multiple.6600
Check. Check: 6600 is a multiple of 10, and it is the closest one to 6601.
Watch out. Exactly 5 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.
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.seven 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.four thousand seven hundred and thirty-six
Check. Check: 4000 + 700 + 36 = 4736.
Watch out. Put and before the tens and ones when there are hundreds, as in four hundred and six.
Method. Round to the nearest 10: look at the digits to the right of the ten place.
- Look at the ones digit. The digits on the right tell us which way to go.the ones digit is 8
- Decide: 5 or more. Half of 10 is 5. 5 or more rounds up; less than 5 rounds down.8 is at least 5
- Round up. Add one more ten, and the digits to the right become 0.5318 rounds up to 5320
- Write the answer. This is the nearest multiple.5320
Check. Check: 5320 is a multiple of 10, and it is the closest one to 5318.
Watch out. Exactly 5 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.
Method. Count in steps of the same size, one step at a time.
- Start at the first number. It is where we begin.8656
- Add 100 each time. Each count moves by the same step.8656 + 100 = 8756
- Add 100 each time. Each count moves by the same step.8756 + 100 = 8856
- Add 100 each time. Each count moves by the same step.8856 + 100 = 8956
- Add 100 each time. Each count moves by the same step.8956 + 100 = 9056
- Add 100 each time. Each count moves by the same step.9056 + 100 = 9156
- Write the answer. This is the last number we reached.9156
Check. Count the steps back: 9156 - 500 = 8656.
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.9477
- Take 100 each time. Each count moves by the same step.9477 - 100 = 9377
- Take 100 each time. Each count moves by the same step.9377 - 100 = 9277
- Take 100 each time. Each count moves by the same step.9277 - 100 = 9177
- Write the answer. This is the last number we reached.9177
Check. Count the steps back: 9177 + 300 = 9477.
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.1792
- Add 1000 each time. Each count moves by the same step.1792 + 1000 = 2792
- Add 1000 each time. Each count moves by the same step.2792 + 1000 = 3792
- Add 1000 each time. Each count moves by the same step.3792 + 1000 = 4792
- Add 1000 each time. Each count moves by the same step.4792 + 1000 = 5792
- Write the answer. This is the last number we reached.5792
Check. Count the steps back: 5792 - 4000 = 1792.
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.2890
- Take this from the number to find the missing part. 2895 minus the known parts is the gap.2895 - 2890 = 5
- Write the missing part. It is the value of that column.5
Check. Check: 2000 + 800 + 90 + 5 = 2895.
Watch out. The parts are the thousands, hundreds, tens and ones values, not the digits on their own.
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 1000.6210 has 6 thousands
- Add one thousand. The thousands digit goes up or down by 1.6 + 1 = 7 thousands
- Write the answer. The hundreds, tens and ones stay the same.7210
Check. Check: 7210 and 6210 differ by exactly 1000.
Watch out. Do not change the hundreds, tens or ones when you add or take away 1000.
Method. Round to the nearest 10: look at the digits to the right of the ten place.
- Look at the ones digit. The digits on the right tell us which way to go.the ones digit is 4
- Decide: less than 5. Half of 10 is 5. 5 or more rounds up; less than 5 rounds down.4 is less than 5
- Round down. Keep the same tens, and the digits to the right become 0.2224 rounds down to 2220
- Write the answer. This is the nearest multiple.2220
Check. Check: 2220 is a multiple of 10, and it is the closest one to 2224.
Watch out. Exactly 5 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.
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.724
- Take this from the number to find the missing part. 3724 minus the known parts is the gap.3724 - 724 = 3000
- Write the missing part. It is the value of that column.3000
Check. Check: 3000 + 700 + 20 + 4 = 3724.
Watch out. The parts are the thousands, hundreds, tens and ones values, not the digits on their own.
Method. Round to the nearest 1000: look at the digits to the right of the thousand place.
- Look at the hundreds, tens and ones together. The digits on the right tell us which way to go.the last three digits are 992
- Decide: 500 or more. Half of 1000 is 500. 500 or more rounds up; less than 500 rounds down.992 is at least 500
- Round up. Add one more thousand, and the digits to the right become 0.9992 rounds up to 10000
- Write the answer. This is the nearest multiple.10000
Check. Check: 10000 is a multiple of 1000, and it is the closest one to 9992.
Watch out. Exactly 500 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.
Method. Round to the nearest 10: look at the digits to the right of the ten place.
- Look at the ones digit. The digits on the right tell us which way to go.the ones digit is 3
- Decide: less than 5. Half of 10 is 5. 5 or more rounds up; less than 5 rounds down.3 is less than 5
- Round down. Keep the same tens, and the digits to the right become 0.4543 rounds down to 4540
- Write the answer. This is the nearest multiple.4540
Check. Check: 4540 is a multiple of 10, and it is the closest one to 4543.
Watch out. Exactly 5 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.
Method. Compare the thousands first, then the hundreds, then the tens, then the ones.
- Compare the thousands. The first column that is different decides the order.2 and 1: 2 is more
- Write the sign between the numbers. The sign points to the smaller number.>
Check. Check: read the sign as words. 2755 is greater than 1479.
Watch out. The arrow always points to the smaller number. Compare the thousands first, not the last digits.
Method. Round to the nearest 1000: look at the digits to the right of the thousand place.
- Look at the hundreds, tens and ones together. The digits on the right tell us which way to go.the last three digits are 205
- Decide: less than 500. Half of 1000 is 500. 500 or more rounds up; less than 500 rounds down.205 is less than 500
- Round down. Keep the same thousands, and the digits to the right become 0.6205 rounds down to 6000
- Write the answer. This is the nearest multiple.6000
Check. Check: 6000 is a multiple of 1000, and it is the closest one to 6205.
Watch out. Exactly 500 rounds up. Do not change the digits to the left of the place you round to, except when a carry is needed.
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.2600 - 2550 = 50
- Count from the number before the gap. Add the step to get the missing number.2550 + 50 = 2600
- Write the missing number. It fits the pattern.2600
Check. Check: 2600 + 50 is the next number, 2650.
Watch out. Look at the numbers either side of the gap. The step is the same each time.