Step-by-step Maths Level 4: Number lines to 10000
Part of the Step-by-step Maths Level 4 comparing, ordering and rounding chapter. Chapter overview · whole chapter on one page
Number lines to 10000
On a number line from 0 to 10000, the labels show the thousands. A number is between the two thousands on either side of it.
Halfway between two numbers is halfway along the line. Add the two numbers, then halve the total.
Key ideas
- Find the labels on either side of the number.
- Halfway = (the total of the two numbers) ÷ 2.
Method. Find the two labelled thousands on either side of the dot.
- Find the thousand just below the dot. Look for the labelled number on the left.6000 is just below 6420
- Find the thousand just above the dot. Look for the labelled number on the right.7000 is just above 6420
- Write the two numbers. The dot is between them.Between 6000 and 7000
Check. Check: 6000 < 6420 < 7000.
Watch out. The dot is between two labels, not on one of them.
Method. Halfway between two numbers is half of their total.
- Add the two numbers. Find the total of the two ends.2000 + 4000 = 6000
- Halve the total. Halfway is half of the total.6000 ÷ 2 = 3000
- Write the answer. This number is the same distance from both ends.3000
Check. Check: 3000 - 2000 = 4000 - 3000 = 1000.
Watch out. Halfway is not the same as adding a fixed amount.
Method. Halfway between two numbers is half of their total.
- Add the two numbers. Find the total of the two ends.1600 + 2400 = 4000
- Halve the total. Halfway is half of the total.4000 ÷ 2 = 2000
- Write the answer. This number is the same distance from both ends.2000
Check. Check: 2000 - 1600 = 400 and 2400 - 2000 = 400.
Watch out. Check the two distances are the same.
Watch out
Watch out. Halfway between 2000 and 4000 is 3000, not 2000 + 1000 + 1000. Find the total, then halve it.
Exam tip
Grown-up tip. Draw a line from 0 to 10000 on paper and mark 0, 5000 and 10000. Ask where 2500 and 7500 go.
Exercise 2C Practice: number lines and halfway
Non-calculatorMethod. Find the two labelled thousands on either side of the dot.
- Find the thousand just below the dot. Look for the labelled number on the left.5000 is just below 5752
- Find the thousand just above the dot. Look for the labelled number on the right.6000 is just above 5752
- Write the two numbers. The dot is between them.Between 5000 and 6000
Check. Check: 5000 < 5752 < 6000.
Watch out. The dot is between two labels, not on one of them.
Method. Halfway between two numbers is half of their total.
- Add the two numbers. The total of the two ends is shared equally in the middle.6600 + 7600 = 14200
- Halve the total. Halfway is half of the sum of the two numbers.14200 ÷ 2 = 7100
- Write the answer. This number is the same distance from both ends.7100
Check. Check: 7100 - 6600 = 7600 - 7100, the same distance each way.
Watch out. Halfway is not the same as adding a fixed amount. Find the total, then halve it.
Method. Halfway between two numbers is half of their total.
- Add the two numbers. The total of the two ends is shared equally in the middle.600 + 2800 = 3400
- Halve the total. Halfway is half of the sum of the two numbers.3400 ÷ 2 = 1700
- Write the answer. This number is the same distance from both ends.1700
Check. Check: 1700 - 600 = 2800 - 1700, the same distance each way.
Watch out. Halfway is not the same as adding a fixed amount. Find the total, then halve it.
Method. Find the two labelled thousands on either side of the dot.
- Find the thousand just below the dot. Look for the labelled number on the left.2000 is just below 2124
- Find the thousand just above the dot. Look for the labelled number on the right.3000 is just above 2124
- Write the two numbers. The dot is between them.Between 2000 and 3000
Check. Check: 2000 < 2124 < 3000.
Watch out. The dot is between two labels, not on one of them.
Method. Find the two labelled thousands on either side of the dot.
- Find the thousand just below the dot. Look for the labelled number on the left.9000 is just below 9055
- Find the thousand just above the dot. Look for the labelled number on the right.10000 is just above 9055
- Write the two numbers. The dot is between them.Between 9000 and 10000
Check. Check: 9000 < 9055 < 10000.
Watch out. The dot is between two labels, not on one of them.
Method. Find the two labelled thousands on either side of the dot.
- Find the thousand just below the dot. Look for the labelled number on the left.5000 is just below 5185
- Find the thousand just above the dot. Look for the labelled number on the right.6000 is just above 5185
- Write the two numbers. The dot is between them.Between 5000 and 6000
Check. Check: 5000 < 5185 < 6000.
Watch out. The dot is between two labels, not on one of them.
Method. Halfway between two numbers is half of their total.
- Add the two numbers. The total of the two ends is shared equally in the middle.5500 + 8300 = 13800
- Halve the total. Halfway is half of the sum of the two numbers.13800 ÷ 2 = 6900
- Write the answer. This number is the same distance from both ends.6900
Check. Check: 6900 - 5500 = 8300 - 6900, the same distance each way.
Watch out. Halfway is not the same as adding a fixed amount. Find the total, then halve it.
Method. Halfway between two numbers is half of their total.
- Add the two numbers. The total of the two ends is shared equally in the middle.3200 + 4200 = 7400
- Halve the total. Halfway is half of the sum of the two numbers.7400 ÷ 2 = 3700
- Write the answer. This number is the same distance from both ends.3700
Check. Check: 3700 - 3200 = 4200 - 3700, the same distance each way.
Watch out. Halfway is not the same as adding a fixed amount. Find the total, then halve it.
Method. Halfway between two numbers is half of their total.
- Add the two numbers. The total of the two ends is shared equally in the middle.1900 + 2300 = 4200
- Halve the total. Halfway is half of the sum of the two numbers.4200 ÷ 2 = 2100
- Write the answer. This number is the same distance from both ends.2100
Check. Check: 2100 - 1900 = 2300 - 2100, the same distance each way.
Watch out. Halfway is not the same as adding a fixed amount. Find the total, then halve it.
Method. Find the two labelled thousands on either side of the dot.
- Find the thousand just below the dot. Look for the labelled number on the left.9000 is just below 9069
- Find the thousand just above the dot. Look for the labelled number on the right.10000 is just above 9069
- Write the two numbers. The dot is between them.Between 9000 and 10000
Check. Check: 9000 < 9069 < 10000.
Watch out. The dot is between two labels, not on one of them.
Method. Halfway between two numbers is half of their total.
- Add the two numbers. The total of the two ends is shared equally in the middle.5200 + 6800 = 12000
- Halve the total. Halfway is half of the sum of the two numbers.12000 ÷ 2 = 6000
- Write the answer. This number is the same distance from both ends.6000
Check. Check: 6000 - 5200 = 6800 - 6000, the same distance each way.
Watch out. Halfway is not the same as adding a fixed amount. Find the total, then halve it.
Method. Find the two labelled thousands on either side of the dot.
- Find the thousand just below the dot. Look for the labelled number on the left.3000 is just below 3355
- Find the thousand just above the dot. Look for the labelled number on the right.4000 is just above 3355
- Write the two numbers. The dot is between them.Between 3000 and 4000
Check. Check: 3000 < 3355 < 4000.
Watch out. The dot is between two labels, not on one of them.
Method. Find the two labelled thousands on either side of the dot.
- Find the thousand just below the dot. Look for the labelled number on the left.3000 is just below 3143
- Find the thousand just above the dot. Look for the labelled number on the right.4000 is just above 3143
- Write the two numbers. The dot is between them.Between 3000 and 4000
Check. Check: 3000 < 3143 < 4000.
Watch out. The dot is between two labels, not on one of them.
Method. Find the two labelled thousands on either side of the dot.
- Find the thousand just below the dot. Look for the labelled number on the left.5000 is just below 5438
- Find the thousand just above the dot. Look for the labelled number on the right.6000 is just above 5438
- Write the two numbers. The dot is between them.Between 5000 and 6000
Check. Check: 5000 < 5438 < 6000.
Watch out. The dot is between two labels, not on one of them.
Method. Find the two labelled thousands on either side of the dot.
- Find the thousand just below the dot. Look for the labelled number on the left.2000 is just below 2928
- Find the thousand just above the dot. Look for the labelled number on the right.3000 is just above 2928
- Write the two numbers. The dot is between them.Between 2000 and 3000
Check. Check: 2000 < 2928 < 3000.
Watch out. The dot is between two labels, not on one of them.
Method. Halfway between two numbers is half of their total.
- Add the two numbers. The total of the two ends is shared equally in the middle.800 + 1400 = 2200
- Halve the total. Halfway is half of the sum of the two numbers.2200 ÷ 2 = 1100
- Write the answer. This number is the same distance from both ends.1100
Check. Check: 1100 - 800 = 1400 - 1100, the same distance each way.
Watch out. Halfway is not the same as adding a fixed amount. Find the total, then halve it.