Year 4: Comparing, ordering and estimating measures
Part of the Year 4 perimeter, area and measures chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Comparing, ordering and estimating measures
Comparing measures. Which is longer: 3 km or 2,500 m? The numbers 3 and 2,500 look different, but the units are different too. We can only compare measures when they are in the same unit. Change both to the smaller unit: 3 km = 3,000 m. Now compare 3,000 m and 2,500 m. So 3 km is longer.
Ordering measures. Change every measure to the same unit. Put the numbers in order. Then write the original measures in that order. Ascending order is smallest first. Descending order is biggest first.
Choosing a sensible unit. Picture the thing and compare it with a size you know.
| Unit | About the size of… |
|---|---|
| 1 mm | the thickness of a coin |
| 1 cm | the width of your little fingernail |
| 1 m | one big step |
| 1 km | a 12-minute walk |
| 1 g | a paper clip |
| 1 kg | a bag of sugar |
| 5 ml | a teaspoon |
| 1 l | a big carton of juice |
Estimating. An estimate is a sensible guess. Use these sizes to help. A pencil is about 15 cm (about the length of your hand). A door is about 2 m tall. An apple is about 150 g. A cup of tea is about 250 ml.
Rounding measures. We can round a measure just like any number. 2,450 g to the nearest 100 g: the digit to the right of the hundreds is 5, so round up to 2,500 g. We use ≈ to mean “is about”.
Key words. To compare is to say which is bigger. To order is to put in a list. To estimate is to make a sensible guess. To round is to change to a nearby number.
Key ideas
- Change measures to the same unit (the smaller one) before comparing or ordering.
- 3 km > 2,500 m because 3,000 > 2,500.
- Order: smallest first (ascending) or biggest first (descending).
- Know some sizes: 1 cm is a fingernail, 1 m is a big step, 1 kg is a bag of sugar, 1 l is a big carton.
- A sensible estimate has the right size and the right unit.
- To round to the nearest 100, look at the tens digit: 5 or more rounds up.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change both measures to the same unit (the smaller one). Then compare the numbers.
- Look at the units. We can only compare measures that are in the same unit.3 km and 2,500 m: the units are different.
- Change both to the smaller unit, metres. Changing to the smaller unit gives whole numbers that are easy to compare.3 km = 3 × 1,000 = 3,000 m
2,500 m - Compare the numbers. Compare the digits from the left, starting with the biggest place value.3,000 > 2,500
- Write the answer. Put the sign between the two original measures.3 km > 2,500 m
Check. 3,000 m and 2,500 m: the bigger number is the bigger measure. ✓
Watch out. Do not compare the numbers in the question as they are. 3 km is more than 2,500 m even though 2,500 is more than 3.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change both measures to the same unit (the smaller one). Then compare the numbers.
- Look at the units. We can only compare measures that are in the same unit.1.5 kg and 1,450 g: the units are different.
- Change both to the smaller unit, grams. Changing to the smaller unit gives whole numbers that are easy to compare.1.5 kg = 1.5 × 1,000 = 1,500 g
1,450 g - Compare the numbers. Compare the digits from the left, starting with the biggest place value.1,500 > 1,450
- Write the answer. Pick the measure with the bigger number.1.5 kg is the bigger measure.
Check. 1,500 g and 1,450 g: the bigger number is the bigger measure. ✓
Watch out. Do not compare the numbers in the question as they are. 3 km is more than 2,500 m even though 2,500 is more than 3.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change everything to the same unit, put the numbers in order, then write the original measures in that order.
- Change every measure to centimetres. Measures in different units cannot be ordered until they are in the same unit. Use the smaller unit so we have whole numbers.2.5 m = 2.5 × 100 = 250 cm
240 cm
2 m = 2 × 100 = 200 cm
260 cm - Put the whole numbers in order. Compare the digits from the left. Order them smallest first.200, 240, 250, 260
- Write the original measures in that order. Match each number back to its measure.2 m, 240 cm, 2.5 m, 260 cm
Check. Read the ordered list again in centimetres: 200, 240, 250, 260. Each one is bigger than the one before. ✓
Watch out. Keep the original units in your final answer. Do not write the changed numbers.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change everything to the same unit, put the numbers in order, then write the original measures in that order.
- Change every measure to millilitres. Measures in different units cannot be ordered until they are in the same unit. Use the smaller unit so we have whole numbers.1.5 l = 1.5 × 1,000 = 1,500 ml
1,200 ml
0.75 l = 0.75 × 1,000 = 750 ml
1,050 ml - Put the whole numbers in order. Compare the digits from the left. Order them biggest first.1,500, 1,200, 1,050, 750
- Write the original measures in that order. Match each number back to its measure.1.5 l, 1,200 ml, 1,050 ml, 0.75 l
Check. Read the ordered list again in millilitres: 1,500, 1,200, 1,050, 750. Each one is smaller than the one before. ✓
Watch out. Keep the original units in your final answer. Do not write the changed numbers.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Picture how big the thing is. Compare it with a size you know, then pick the unit that gives a sensible number.
- Think about the size. Picture the thing. How big, heavy or full is it?The length of a pencil.
- Compare with something you know. These are good sizes to remember.Sizes to know:
1 mm is about the thickness of a coin
1 cm is about the width of your little fingernail
1 m is about one big step, or the height of a door handle
1 km is about a 12-minute walk - Choose the unit. A pencil is about as long as your hand.The best unit is cm (centimetres).
Check. A measure like 5 cm makes sense for this. Another unit would give a number that is far too big or too small. ✓
Watch out. A silly number means the unit is wrong, like a pencil that is 15 km long.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Picture how big the thing is. Compare it with a size you know, then pick the unit that gives a sensible number.
- Think about the size. Picture the thing. How big, heavy or full is it?The mass of a bag of sugar.
- Compare with something you know. These are good sizes to remember.Sizes to know:
1 g is about a paper clip
1 kg is about a bag of sugar - Choose the unit. A bag of sugar is the example of 1 kg.The best unit is kg (kilograms).
Check. A measure like 5 kg makes sense for this. Another unit would give a number that is far too big or too small. ✓
Watch out. A silly number means the unit is wrong, like a pencil that is 15 km long.
A 15 g B 150 g C 1.5 kg
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Picture the thing and compare it with a size you know. Pick the estimate that is sensible.
- Picture the thing. Use something you know to help you.An apple is a bit lighter than a bag of sugar (1 kg). 150 g is sensible.
- Test each answer. Ask whether the number and unit are sensible.A: 15 g is too small.
B: 150 g is sensible.
C: 1.5 kg is too big. - Choose the sensible estimate. 150 g
Check. 150 g is about the right size, while the other two are far too big or far too small. ✓
Watch out. An estimate does not need to be exact, but it must be sensible.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Use the 1 cm block as a ruler. Count how many blocks fit along the line.
- Look at the block. The block shows 1 cm. It has the same size as one centimetre on this picture.One block = 1 cm
- Compare the line with the block. Picture the block placed end to end along the line. Count how many blocks it takes.About 8 blocks fit along the line.
- Write the estimate. Each block is 1 cm, so the number of blocks is the number of centimetres.The line is about 8 cm long.
Check. 8 × 1 cm = 8 cm. ✓
Watch out. An estimate needs the unit as well as the number.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Round to the nearest 100 g: look at the digit in the next place to the right.
- Find the hundreds digit and the digit to its right. We round to the nearest 100, so we look at the digit one place to the right of the hundreds.2,450 g: the digit to look at is 5
- Decide whether to round up or down. 5 or more rounds up. 4 or less rounds down.5 is 5 or more, so round UP
- Write the rounded measure. The numbers between are 2,400 and 2,500.2,450 g ≈ 2,500 g
Check. 2,450 is between 2,400 and 2,500. It is closer to 2,500. ✓
Watch out. Keep the unit. A rounded measure is only an estimate, so use ≈ (about).
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Round to the nearest 1,000 ml: look at the digit in the next place to the right.
- Find the thousands digit and the digit to its right. We round to the nearest 1,000, so we look at the digit one place to the right of the thousands.3,260 ml: the digit to look at is 2
- Decide whether to round up or down. 5 or more rounds up. 4 or less rounds down.2 is less than 5, so round DOWN
- Write the rounded measure. The numbers between are 3,000 and 4,000.3,260 ml ≈ 3,000 ml
Check. 3,260 is between 3,000 and 4,000. It is closer to 3,000. ✓
Watch out. Keep the unit. A rounded measure is only an estimate, so use ≈ (about).
Watch out
Do not compare the numbers as they are. 2,500 g is less than 3 kg, even though 2,500 is bigger than 3. Always change to the same unit first. And when you choose a unit, check that the number makes sense: a pencil that is “15 m long” is silly.Exercise 7E Comparing, ordering and estimating
Non-calculatorKey words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change both measures to the same unit (the smaller one). Then compare the numbers.
- Look at the units. We can only compare measures that are in the same unit.2 m and 150 cm: the units are different.
- Change both to the smaller unit, centimetres. Changing to the smaller unit gives whole numbers that are easy to compare.2 m = 2 × 100 = 200 cm
150 cm - Compare the numbers. Compare the digits from the left, starting with the biggest place value.200 > 150
- Write the answer. Put the sign between the two original measures.2 m > 150 cm
Check. 200 cm and 150 cm: the bigger number is the bigger measure. ✓
Watch out. Do not compare the numbers in the question as they are. 3 km is more than 2,500 m even though 2,500 is more than 3.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change both measures to the same unit (the smaller one). Then compare the numbers.
- Look at the units. We can only compare measures that are in the same unit.3 kg and 3,500 g: the units are different.
- Change both to the smaller unit, grams. Changing to the smaller unit gives whole numbers that are easy to compare.3 kg = 3 × 1,000 = 3,000 g
3,500 g - Compare the numbers. Compare the digits from the left, starting with the biggest place value.3,000 < 3,500
- Write the answer. Put the sign between the two original measures.3 kg < 3,500 g
Check. 3,000 g and 3,500 g: the bigger number is the bigger measure. ✓
Watch out. Do not compare the numbers in the question as they are. 3 km is more than 2,500 m even though 2,500 is more than 3.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change both measures to the same unit (the smaller one). Then compare the numbers.
- Look at the units. We can only compare measures that are in the same unit.2,000 ml and 2 l: the units are different.
- Change both to the smaller unit, millilitres. Changing to the smaller unit gives whole numbers that are easy to compare.2,000 ml
2 l = 2 × 1,000 = 2,000 ml - Compare the numbers. Compare the digits from the left, starting with the biggest place value.2,000 = 2,000
- Write the answer. Put the sign between the two original measures.2,000 ml = 2 l
Check. 2,000 ml and 2,000 ml: the bigger number is the bigger measure. ✓
Watch out. Do not compare the numbers in the question as they are. 3 km is more than 2,500 m even though 2,500 is more than 3.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change both measures to the same unit (the smaller one). Then compare the numbers.
- Look at the units. We can only compare measures that are in the same unit.4 km and 3,900 m: the units are different.
- Change both to the smaller unit, metres. Changing to the smaller unit gives whole numbers that are easy to compare.4 km = 4 × 1,000 = 4,000 m
3,900 m - Compare the numbers. Compare the digits from the left, starting with the biggest place value.4,000 > 3,900
- Write the answer. Put the sign between the two original measures.4 km > 3,900 m
Check. 4,000 m and 3,900 m: the bigger number is the bigger measure. ✓
Watch out. Do not compare the numbers in the question as they are. 3 km is more than 2,500 m even though 2,500 is more than 3.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change both measures to the same unit (the smaller one). Then compare the numbers.
- Look at the units. We can only compare measures that are in the same unit.50 mm and 5 cm: the units are different.
- Change both to the smaller unit, millimetres. Changing to the smaller unit gives whole numbers that are easy to compare.50 mm
5 cm = 5 × 10 = 50 mm - Compare the numbers. Compare the digits from the left, starting with the biggest place value.50 = 50
- Write the answer. Put the sign between the two original measures.50 mm = 5 cm
Check. 50 mm and 50 mm: the bigger number is the bigger measure. ✓
Watch out. Do not compare the numbers in the question as they are. 3 km is more than 2,500 m even though 2,500 is more than 3.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change both measures to the same unit (the smaller one). Then compare the numbers.
- Look at the units. We can only compare measures that are in the same unit.2.5 kg and 2,450 g: the units are different.
- Change both to the smaller unit, grams. Changing to the smaller unit gives whole numbers that are easy to compare.2.5 kg = 2.5 × 1,000 = 2,500 g
2,450 g - Compare the numbers. Compare the digits from the left, starting with the biggest place value.2,500 > 2,450
- Write the answer. Pick the measure with the bigger number.2.5 kg is the bigger measure.
Check. 2,500 g and 2,450 g: the bigger number is the bigger measure. ✓
Watch out. Do not compare the numbers in the question as they are. 3 km is more than 2,500 m even though 2,500 is more than 3.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change both measures to the same unit (the smaller one). Then compare the numbers.
- Look at the units. We can only compare measures that are in the same unit.1.2 l and 1,250 ml: the units are different.
- Change both to the smaller unit, millilitres. Changing to the smaller unit gives whole numbers that are easy to compare.1.2 l = 1.2 × 1,000 = 1,200 ml
1,250 ml - Compare the numbers. Compare the digits from the left, starting with the biggest place value.1,200 < 1,250
- Write the answer. Pick the measure with the bigger number.1,250 ml is the bigger measure.
Check. 1,200 ml and 1,250 ml: the bigger number is the bigger measure. ✓
Watch out. Do not compare the numbers in the question as they are. 3 km is more than 2,500 m even though 2,500 is more than 3.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change both measures to the same unit (the smaller one). Then compare the numbers.
- Look at the units. We can only compare measures that are in the same unit.0.5 m and 45 cm: the units are different.
- Change both to the smaller unit, centimetres. Changing to the smaller unit gives whole numbers that are easy to compare.0.5 m = 0.5 × 100 = 50 cm
45 cm - Compare the numbers. Compare the digits from the left, starting with the biggest place value.50 > 45
- Write the answer. Pick the measure with the bigger number.0.5 m is the bigger measure.
Check. 50 cm and 45 cm: the bigger number is the bigger measure. ✓
Watch out. Do not compare the numbers in the question as they are. 3 km is more than 2,500 m even though 2,500 is more than 3.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change everything to the same unit, put the numbers in order, then write the original measures in that order.
- Change every measure to centimetres. Measures in different units cannot be ordered until they are in the same unit. Use the smaller unit so we have whole numbers.3 m = 3 × 100 = 300 cm
295 cm
3.5 m = 3.5 × 100 = 350 cm
310 cm - Put the whole numbers in order. Compare the digits from the left. Order them smallest first.295, 300, 310, 350
- Write the original measures in that order. Match each number back to its measure.295 cm, 3 m, 310 cm, 3.5 m
Check. Read the ordered list again in centimetres: 295, 300, 310, 350. Each one is bigger than the one before. ✓
Watch out. Keep the original units in your final answer. Do not write the changed numbers.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change everything to the same unit, put the numbers in order, then write the original measures in that order.
- Change every measure to grams. Measures in different units cannot be ordered until they are in the same unit. Use the smaller unit so we have whole numbers.1.2 kg = 1.2 × 1,000 = 1,200 g
1,150 g
1 kg = 1 × 1,000 = 1,000 g
1,300 g - Put the whole numbers in order. Compare the digits from the left. Order them smallest first.1,000, 1,150, 1,200, 1,300
- Write the original measures in that order. Match each number back to its measure.1 kg, 1,150 g, 1.2 kg, 1,300 g
Check. Read the ordered list again in grams: 1,000, 1,150, 1,200, 1,300. Each one is bigger than the one before. ✓
Watch out. Keep the original units in your final answer. Do not write the changed numbers.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change everything to the same unit, put the numbers in order, then write the original measures in that order.
- Change every measure to metres. Measures in different units cannot be ordered until they are in the same unit. Use the smaller unit so we have whole numbers.2 km = 2 × 1,000 = 2,000 m
1,900 m
2.5 km = 2.5 × 1,000 = 2,500 m
2,050 m - Put the whole numbers in order. Compare the digits from the left. Order them biggest first.2,500, 2,050, 2,000, 1,900
- Write the original measures in that order. Match each number back to its measure.2.5 km, 2,050 m, 2 km, 1,900 m
Check. Read the ordered list again in metres: 2,500, 2,050, 2,000, 1,900. Each one is smaller than the one before. ✓
Watch out. Keep the original units in your final answer. Do not write the changed numbers.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change everything to the same unit, put the numbers in order, then write the original measures in that order.
- Change every measure to millilitres. Measures in different units cannot be ordered until they are in the same unit. Use the smaller unit so we have whole numbers.0.5 l = 0.5 × 1,000 = 500 ml
450 ml
600 ml
0.25 l = 0.25 × 1,000 = 250 ml - Put the whole numbers in order. Compare the digits from the left. Order them biggest first.600, 500, 450, 250
- Write the original measures in that order. Match each number back to its measure.600 ml, 0.5 l, 450 ml, 0.25 l
Check. Read the ordered list again in millilitres: 600, 500, 450, 250. Each one is smaller than the one before. ✓
Watch out. Keep the original units in your final answer. Do not write the changed numbers.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Picture how big the thing is. Compare it with a size you know, then pick the unit that gives a sensible number.
- Think about the size. Picture the thing. How big, heavy or full is it?The height of a classroom door.
- Compare with something you know. These are good sizes to remember.Sizes to know:
1 mm is about the thickness of a coin
1 cm is about the width of your little fingernail
1 m is about one big step, or the height of a door handle
1 km is about a 12-minute walk - Choose the unit. A door is about 2 big steps tall.The best unit is m (metres).
Check. A measure like 5 m makes sense for this. Another unit would give a number that is far too big or too small. ✓
Watch out. A silly number means the unit is wrong, like a pencil that is 15 km long.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Picture how big the thing is. Compare it with a size you know, then pick the unit that gives a sensible number.
- Think about the size. Picture the thing. How big, heavy or full is it?The length of an ant.
- Compare with something you know. These are good sizes to remember.Sizes to know:
1 mm is about the thickness of a coin
1 cm is about the width of your little fingernail
1 m is about one big step, or the height of a door handle
1 km is about a 12-minute walk - Choose the unit. An ant is smaller than a fingernail.The best unit is mm (millimetres).
Check. A measure like 5 mm makes sense for this. Another unit would give a number that is far too big or too small. ✓
Watch out. A silly number means the unit is wrong, like a pencil that is 15 km long.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Picture how big the thing is. Compare it with a size you know, then pick the unit that gives a sensible number.
- Think about the size. Picture the thing. How big, heavy or full is it?The mass of a grape.
- Compare with something you know. These are good sizes to remember.Sizes to know:
1 g is about a paper clip
1 kg is about a bag of sugar - Choose the unit. A grape is much lighter than a bag of sugar.The best unit is g (grams).
Check. A measure like 5 g makes sense for this. Another unit would give a number that is far too big or too small. ✓
Watch out. A silly number means the unit is wrong, like a pencil that is 15 km long.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Picture how big the thing is. Compare it with a size you know, then pick the unit that gives a sensible number.
- Think about the size. Picture the thing. How big, heavy or full is it?The mass of a watermelon.
- Compare with something you know. These are good sizes to remember.Sizes to know:
1 g is about a paper clip
1 kg is about a bag of sugar - Choose the unit. A watermelon is a few bags of sugar heavy.The best unit is kg (kilograms).
Check. A measure like 5 kg makes sense for this. Another unit would give a number that is far too big or too small. ✓
Watch out. A silly number means the unit is wrong, like a pencil that is 15 km long.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Picture how big the thing is. Compare it with a size you know, then pick the unit that gives a sensible number.
- Think about the size. Picture the thing. How big, heavy or full is it?The amount of medicine on a spoon.
- Compare with something you know. These are good sizes to remember.Sizes to know:
1 ml is about a few drops, or 5 ml is a teaspoon
1 l is about a big carton of juice - Choose the unit. A spoonful is only a few millilitres.The best unit is ml (millilitres).
Check. A measure like 5 ml makes sense for this. Another unit would give a number that is far too big or too small. ✓
Watch out. A silly number means the unit is wrong, like a pencil that is 15 km long.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Picture how big the thing is. Compare it with a size you know, then pick the unit that gives a sensible number.
- Think about the size. Picture the thing. How big, heavy or full is it?The amount of water in a bath.
- Compare with something you know. These are good sizes to remember.Sizes to know:
1 ml is about a few drops, or 5 ml is a teaspoon
1 l is about a big carton of juice - Choose the unit. A bath holds many big cartons of juice.The best unit is l (litres).
Check. A measure like 5 l makes sense for this. Another unit would give a number that is far too big or too small. ✓
Watch out. A silly number means the unit is wrong, like a pencil that is 15 km long.
A 2 cm B 2 m C 2 km
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Picture the thing and compare it with a size you know. Pick the estimate that is sensible.
- Picture the thing. Use something you know to help you.A door is about 2 big steps high, so 2 m.
- Test each answer. Ask whether the number and unit are sensible.A: 2 cm is too small.
B: 2 m is sensible.
C: 2 km is too big. - Choose the sensible estimate. 2 m
Check. 2 m is about the right size, while the other two are far too big or far too small. ✓
Watch out. An estimate does not need to be exact, but it must be sensible.
A 25 ml B 250 ml C 2.5 l
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Picture the thing and compare it with a size you know. Pick the estimate that is sensible.
- Picture the thing. Use something you know to help you.A cup holds a quarter of a big carton of juice. 250 ml is sensible.
- Test each answer. Ask whether the number and unit are sensible.A: 25 ml is too small.
B: 250 ml is sensible.
C: 2.5 l is too big. - Choose the sensible estimate. 250 ml
Check. 250 ml is about the right size, while the other two are far too big or far too small. ✓
Watch out. An estimate does not need to be exact, but it must be sensible.
A 3 kg B 30 kg C 300 kg
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Picture the thing and compare it with a size you know. Pick the estimate that is sensible.
- Picture the thing. Use something you know to help you.A child is about 30 bags of sugar. 3 kg is a tiny baby and 300 kg is far too heavy.
- Test each answer. Ask whether the number and unit are sensible.A: 3 kg is too small.
B: 30 kg is sensible.
C: 300 kg is too big. - Choose the sensible estimate. 30 kg
Check. 30 kg is about the right size, while the other two are far too big or far too small. ✓
Watch out. An estimate does not need to be exact, but it must be sensible.
A 5 mm B 50 cm C 50 m
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Picture the thing and compare it with a size you know. Pick the estimate that is sensible.
- Picture the thing. Use something you know to help you.It is about 50 big steps, so 50 m.
- Test each answer. Ask whether the number and unit are sensible.A: 5 mm is too small.
B: 50 cm is too small.
C: 50 m is sensible. - Choose the sensible estimate. 50 m
Check. 50 m is about the right size, while the other two are far too big or far too small. ✓
Watch out. An estimate does not need to be exact, but it must be sensible.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Round to the nearest 100 g: look at the digit in the next place to the right.
- Find the hundreds digit and the digit to its right. We round to the nearest 100, so we look at the digit one place to the right of the hundreds.3,460 g: the digit to look at is 6
- Decide whether to round up or down. 5 or more rounds up. 4 or less rounds down.6 is 5 or more, so round UP
- Write the rounded measure. The numbers between are 3,400 and 3,500.3,460 g ≈ 3,500 g
Check. 3,460 is between 3,400 and 3,500. It is closer to 3,500. ✓
Watch out. Keep the unit. A rounded measure is only an estimate, so use ≈ (about).
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Round to the nearest 100 ml: look at the digit in the next place to the right.
- Find the hundreds digit and the digit to its right. We round to the nearest 100, so we look at the digit one place to the right of the hundreds.2,340 ml: the digit to look at is 4
- Decide whether to round up or down. 5 or more rounds up. 4 or less rounds down.4 is less than 5, so round DOWN
- Write the rounded measure. The numbers between are 2,300 and 2,400.2,340 ml ≈ 2,300 ml
Check. 2,340 is between 2,300 and 2,400. It is closer to 2,300. ✓
Watch out. Keep the unit. A rounded measure is only an estimate, so use ≈ (about).
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Round to the nearest 1,000 m: look at the digit in the next place to the right.
- Find the thousands digit and the digit to its right. We round to the nearest 1,000, so we look at the digit one place to the right of the thousands.4,820 m: the digit to look at is 8
- Decide whether to round up or down. 5 or more rounds up. 4 or less rounds down.8 is 5 or more, so round UP
- Write the rounded measure. The numbers between are 4,000 and 5,000.4,820 m ≈ 5,000 m
Check. 4,820 is between 4,000 and 5,000. It is closer to 5,000. ✓
Watch out. Keep the unit. A rounded measure is only an estimate, so use ≈ (about).
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Round to the nearest 10 cm: look at the digit in the next place to the right.
- Find the tens digit and the digit to its right. We round to the nearest 10, so we look at the digit one place to the right of the tens.685 cm: the digit to look at is 5
- Decide whether to round up or down. 5 or more rounds up. 4 or less rounds down.5 is 5 or more, so round UP
- Write the rounded measure. The numbers between are 680 and 690.685 cm ≈ 690 cm
Check. 685 is between 680 and 690. It is closer to 690. ✓
Watch out. Keep the unit. A rounded measure is only an estimate, so use ≈ (about).
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change everything to the same unit, put the numbers in order, then write the original measures in that order.
- Change every measure to centimetres. Measures in different units cannot be ordered until they are in the same unit. Use the smaller unit so we have whole numbers.3 m = 3 × 100 = 300 cm
280 cm
3.2 m = 3.2 × 100 = 320 cm
310 cm - Put the whole numbers in order. Compare the digits from the left. Order them smallest first.280, 300, 310, 320
- Write the original measures in that order. Match each number back to its measure.280 cm, 3 m, 310 cm, 3.2 m
Check. Read the ordered list again in centimetres: 280, 300, 310, 320. Each one is bigger than the one before. ✓
Watch out. Keep the original units in your final answer. Do not write the changed numbers.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Use the ordered list. The shortest rope is the first one in the list.
- Change the lengths to centimetres. We need the same unit to compare.Red: 3 m = 300 cm
Blue: 280 cm = 280 cm
Green: 3.2 m = 320 cm
Yellow: 310 cm = 310 cm - Find the smallest number. The smallest number of centimetres is the shortest rope.The smallest is 280 cm.
- Write the colour. The shortest rope is the blue rope.
Check. The other ropes are all longer than 280 cm. ✓
Watch out. Change the units first.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change everything to the same unit, put the numbers in order, then write the original measures in that order.
- Change every measure to centimetres. Measures in different units cannot be ordered until they are in the same unit. Use the smaller unit so we have whole numbers.2.1 m = 2.1 × 100 = 210 cm
215 cm
2.05 m = 2.05 × 100 = 205 cm - Put the whole numbers in order. Compare the digits from the left. Order them biggest first.215, 210, 205
- Write the original measures in that order. Match each number back to its measure.215 cm, 2.1 m, 2.05 m
Check. Read the ordered list again in centimetres: 215, 210, 205. Each one is smaller than the one before. ✓
Watch out. Keep the original units in your final answer. Do not write the changed numbers.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change 1.5 litres to millilitres. Then find the smallest container that holds at least that amount.
- Change 1.5 l to millilitres. 1 l = 1,000 ml. Half a litre is 500 ml.1.5 l = 1,000 + 500 = 1,500 ml
- Compare each container with 1,500 ml. The container must hold 1,500 ml or more.A: 1,000 ml is less than 1,500 ml. It is too small.
B: 1,400 ml is less than 1,500 ml. It is too small.
C: 1,600 ml is more than 1,500 ml. It is big enough.
D: 2,000 ml is big enough, but it is bigger than C. - Choose the smallest container that is big enough. Container C
Check. 1,600 ml is 100 ml more than 1,500 ml, and the next smaller one holds less than 1,500 ml. ✓
Watch out. Change to the same unit first.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change 3 kg to grams so both are in the same unit.
- Look at what Aisha did. She compared the numbers 2,500 and 3 without looking at the units.2,500 is bigger than 3
- Find the mistake. The units are different (g and kg). We cannot compare 2,500 g and 3 kg until they are in the same unit.1 kg = 1,000 g
- Change 3 kg to grams. Multiply by 1,000.3 × 1,000 = 3,000 g
- Compare again. 2,500 g is less than 3,000 g. So 2,500 g is less than 3 kg. Aisha is wrong.
Check. 2,500 g = 2.5 kg, and 2.5 is less than 3. ✓
Watch out. Never compare numbers when the units are different.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change 1.5 kg to grams first. Then think of other ways to write the same mass.
- Change 1.5 kg to grams. 1 kg = 1,000 g and half a kilogram is 500 g.1.5 kg = 1,000 + 500 = 1,500 g
- Write it in kilograms and grams. 1,500 g is 1 kg and 500 g.1 kg 500 g
- Write it with a fraction. The 0.5 is a half.1
1 2
Check. 1,500 g ÷ 1,000 = 1.5. ✓
Watch out. There are many correct answers. Check that each one equals 1.5 kg.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Try some pairs of measures and see if the longer number always means the bigger measure.
- Try 500 m and 4 m. Both are in metres. 500 has 3 digits and 4 has 1 digit.500 m is bigger. The number with more digits is bigger.
- Try 12 cm and 2 m. 2 m = 200 cm. 12 cm has 2 digits and 2 has 1 digit, but 2 m is bigger.2 m is bigger than 12 cm, but 12 has more digits than 2.
- Decide. It works for some pairs but not for others.Sometimes.
Check. We found an example that works and one that does not. ✓
Watch out. Change to the same unit before you look at the digits.
Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.
Method. Change 2.4 m and 2.5 m to centimetres. Then pick a number between them.
- Change 2.4 m to centimetres. 2 m = 200 cm and 0.4 m = 40 cm.2.4 m = 240 cm
- Change 2.5 m to centimetres. 2 m = 200 cm and 0.5 m = 50 cm.2.5 m = 250 cm
- Choose a number between 240 and 250. The number must be more than 240 and less than 250.For example 245 cm. Any whole number from 241 to 249 works.
Check. 240 cm < 245 cm < 250 cm, so 2.4 m < 245 cm < 2.5 m. ✓
Watch out. Change everything to the same unit.