Step-by-step Maths Level 3 Length and mass: check-up and practice test questions

Method. Change every measurement to the same unit, then order the numbers.

1. Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.
   3 kg 500 g = 3500 g, 2 kg 500 g = 2500 g, 2 kg = 2000 g
2. Put the numbers in order. Compare the numbers, then write the measurements in that order.
   2000, 2500, 3500
3. Write the order. Write the original measurements in order.
   2 kg, 2 kg 500 g, 3 kg 500 g

Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.

Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.

Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.

1. Find the number of whole kilograms. 1000 g make 1 kg.
   8250 ÷ 1000 = 8 rem 250
2. Write the grams that are left. The rest are grams.
   8 kg and 250 g
3. Write the answer. Use kilograms and grams.
   8 kg 250 g

Check. Add back: 8 kg + 250 g = 8250 g.

Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.

Method. Use the ruler: find the start and the end of the line, then the difference.

1. Put the 0 at the start of the line. Line up the ruler so the line begins at 0.
   0 cm
2. Read where the line ends. The end of the line is on this number.
   The end is at 4
3. Write the length. The length is the end number, because we started at 0.
   4 cm

Check. Count the centimetres from 0 to 4: 4 cm.

Watch out. Put the 0 of the ruler at the start of the line, then read the end.

Method. Change every measurement to the same unit, then order the numbers.

1. Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.
   2 kg 800 g = 2800 g, 1 kg 500 g = 1500 g, 800 g = 800 g
2. Put the numbers in order. Compare the numbers, then write the measurements in that order.
   2800, 1500, 800
3. Write the order. Write the original measurements in order.
   2 kg 800 g, 1 kg 500 g, 800 g

Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.

Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.

Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.

1. Find the number of whole metres. 100 cm make 1 m.
   450 ÷ 100 = 4 rem 50
2. Write the centimetres that are left. The rest are centimetres.
   4 m and 50 cm
3. Write the answer. Use metres and centimetres.
   4 m 50 cm

Check. Add back: 4 m + 50 cm = 450 cm.

Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.

Method. Use the ruler: find the start and the end of the line, then the difference.

1. Put the 0 at the start of the line. Line up the ruler so the line begins at 0.
   0 cm
2. Read where the line ends. The end of the line is on this number.
   The end is at 13
3. Write the length. The length is the end number, because we started at 0.
   13 cm

Check. Count the centimetres from 0 to 13: 13 cm.

Watch out. Put the 0 of the ruler at the start of the line, then read the end.

Method. Use the ruler: find the start and the end of the line, then the difference.

1. Find where the line starts. The line starts at this mark.
   start = 2 cm
2. Find where the line ends. The line ends at this mark.
   end = 9 cm
3. Subtract the start from the end. The length is the distance between the two marks.
   9 - 2 = 7
4. Write the length. This is how long the line is.
   7 cm

Check. Add the length to the start: 2 + 7 = 9 cm.

Watch out. Put the 0 of the ruler at the start of the line, then read the end.

Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.

1. Find the number of whole kilograms. 1000 g make 1 kg.
   2250 ÷ 1000 = 2 rem 250
2. Write the grams that are left. The rest are grams.
   2 kg and 250 g
3. Write the answer. Use kilograms and grams.
   2 kg 250 g

Check. Add back: 2 kg + 250 g = 2250 g.

Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.

Method. Change every measurement to the same unit, then order the numbers.

1. Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.
   3 m 50 cm = 350 cm, 1 m 20 cm = 120 cm, 3 m 75 cm = 375 cm
2. Put the numbers in order. Compare the numbers, then write the measurements in that order.
   375, 350, 120
3. Write the order. Write the original measurements in order.
   3 m 75 cm, 3 m 50 cm, 1 m 20 cm

Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.

Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.

Method. Change every measurement to the same unit, then order the numbers.

1. Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.
   1 kg = 1000 g, 3 kg 800 g = 3800 g, 250 g = 250 g
2. Put the numbers in order. Compare the numbers, then write the measurements in that order.
   3800, 1000, 250
3. Write the order. Write the original measurements in order.
   3 kg 800 g, 1 kg, 250 g

Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.

Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.

Method. Change to g, work it out, then change back.

1. Change both to the smaller unit. 1000 g make one bigger unit.
   4 kg 750 g = 4750 g, 2 kg 150 g = 2150 g
2. Add the g. Work with the numbers in g.
   4750 + 2150 = 6900
3. Change back to the bigger units. 6900 g is written with 1000 g as one bigger unit.
   6900 g = 6 kg 900 g
4. Write the answer. This is the answer.
   6 kg 900 g

Check. Check: 6 kg 900 g - 2 kg 150 g = 4 kg 750 g.

Watch out. Work in g to avoid mistakes. Change back at the end.

Method. Use the rule: 100 cm make 1 m, and 1000 g make 1 kg.

1. Remember the rule. 1 m is 100 cm.
   1 m = 100 cm
2. Multiply the metres by 100. There are 2 metres, so 2 lots of 100.
   2 × 100 = 200
3. Write the answer in centimetres. This is the length in centimetres.
   200 cm

Check. Divide 200 cm by 100 to get 2 m.

Watch out. The number of metres is the number of hundreds of centimetres. Check the rule before you change.

Method. Find the operation, then work out what is left.

1. Find the operation. Words like cut off and used mean take away.
   4500 - 3250
2. Work out what is left. Change to the smaller unit, then take away.
   4500 - 3250 = 1250
3. Write the answer. Change back to the bigger units.
   1 kg 250 g

Check. Check: 1 kg 250 g plus 3 kg 250 g is 4 kg 500 g.

Watch out. Use the same unit for both amounts before you take away.

Method. Change every measurement to the same unit, then order the numbers.

1. Change them all to the same unit. Use the smallest unit so the numbers are easy to compare.
   3 kg 800 g = 3800 g, 2 kg 500 g = 2500 g, 3 kg 250 g = 3250 g
2. Put the numbers in order. Compare the numbers, then write the measurements in that order.
   3800, 3250, 2500
3. Write the order. Write the original measurements in order.
   3 kg 800 g, 3 kg 250 g, 2 kg 500 g

Check. Read the list again: each one is bigger or smaller than the one before, as the question asks.

Watch out. Change to the same unit before you order. 2 m is bigger than 150 cm.

Method. Put both measurements in the same unit, then compare them.

1. Change both to the same unit. 1000 g = 1 kg, so change both to the smaller unit.
   4 kg 500 g = 4500 g, 2 kg 500 g = 2500 g
2. Compare the numbers. Compare the bigger numbers.
   4500 g and 2500 g
3. Write the sign. 4 kg 500 g is more than 2 kg 500 g.
   >

Check. 4 kg 500 g > 2 kg 500 g is true.

Watch out. Change to the smaller unit first. Then compare the numbers.

Method. Put both measurements in the same unit, then compare them.

1. Change both to the same unit. 100 cm = 1 m, so change both to the smaller unit.
   2 m = 200 cm, 3 m 50 cm = 350 cm
2. Compare the numbers. Compare the bigger numbers.
   200 cm and 350 cm
3. Write the sign. 2 m is less than 3 m 50 cm.
   <

Check. 2 m < 3 m 50 cm is true.

Watch out. Change to the smaller unit first. Then compare the numbers.

Method. Change to cm, work it out, then change back.

1. Change both to the smaller unit. 100 cm make one bigger unit.
   4 m 30 cm = 430 cm, 55 cm = 55 cm
2. Take away the cm. Work with the numbers in cm.
   430 - 55 = 375
3. Change back to the bigger units. 375 cm is written with 100 cm as one bigger unit.
   375 cm = 3 m 75 cm
4. Write the answer. This is the answer.
   3 m 75 cm

Check. Check: 3 m 75 cm + 55 cm = 4 m 30 cm.

Watch out. Work in cm to avoid mistakes. Change back at the end.

Method. Find the operation, then work out what is left.

1. Find the operation. Words like cut off and used mean take away.
   4200 - 800
2. Work out what is left. Change to the smaller unit, then take away.
   4200 - 800 = 3400
3. Write the answer. Change back to the bigger units.
   3 kg 400 g

Check. Check: 3 kg 400 g plus 800 g is 4 kg 200 g.

Watch out. Use the same unit for both amounts before you take away.

Method. Put both measurements in the same unit, then compare them.

1. Change both to the same unit. 1000 g = 1 kg, so change both to the smaller unit.
   3 kg = 3000 g, 3 kg 100 g = 3100 g
2. Compare the numbers. Compare the bigger numbers.
   3000 g and 3100 g
3. Write the sign. 3 kg is less than 3 kg 100 g.
   <

Check. 3 kg < 3 kg 100 g is true.

Watch out. Change to the smaller unit first. Then compare the numbers.

Method. Change to g, work it out, then change back.

1. Change both to the smaller unit. 1000 g make one bigger unit.
   4 kg 750 g = 4750 g, 2 kg 450 g = 2450 g
2. Add the g. Work with the numbers in g.
   4750 + 2450 = 7200
3. Change back to the bigger units. 7200 g is written with 1000 g as one bigger unit.
   7200 g = 7 kg 200 g
4. Write the answer. This is the answer.
   7 kg 200 g

Check. Check: 7 kg 200 g - 2 kg 450 g = 4 kg 750 g.

Watch out. Work in g to avoid mistakes. Change back at the end.