Units, perimeter, area, volume and time
By the end of this chapter you will be able to
- Convert between metric units of length, mass and capacity by multiplying or dividing, and move the decimal point correctly
- Use approximate imperial equivalents (inches, pounds and pints) and say when an answer is an estimate
- Find the perimeter of rectangles and composite rectilinear shapes, working out any missing sides
- Find the area of rectangles and squares in square centimetres and square metres, and estimate the area of an irregular shape
- Find the volume of a cuboid by counting 1 cm cubes in layers, and understand that 1 ml = 1 cm³
- Convert between hours, minutes, seconds, days and weeks, including decimal amounts of hours
- Solve problems with measures and money using all four operations, including scaling a recipe and sharing equally
You should already know
- Multiplying and dividing whole numbers and decimals by 10, 100 and 1,000 (Chapters 4 and 5)
- Place value and the decimal point, including tenths, hundredths and thousandths (Chapter 7)
- Multiplying and dividing by one- and two-digit numbers (Chapters 4 and 5)
- Measuring and comparing lengths, masses and capacities in Year 4
Where this leads
- Converting between metric and imperial units more precisely, and miles and kilometres (Year 6)
- Area of parallelograms and triangles, and volume of cuboids using formulae (Year 6)
- Using formulae and rates to solve problems with measures (Year 6)
National Curriculum for England, Key Stage 2 mathematics, Year 5. Content: Convert between different units of metric measure: km and m; cm and m; cm and mm; g and kg; litre and ml, Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints, Measure and calculate the perimeter of composite rectilinear shapes in cm and m, Calculate and compare the area of rectangles (including squares), using standard units cm² and m², and estimate the area of irregular shapes, Estimate volume (using 1 cm³ blocks to build cuboids and cubes) and capacity, Solve problems involving converting between units of time, Use all four operations to solve problems involving measure (length, mass, volume, money) using decimal notation, including scaling.
Exercise P Do you remember?
Non-calculatorKey words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Multiply or divide by 10, 100 or 1,000 by moving the digits. Do not add zeros in the middle.
- Write the number. We are going to move every digit.3.4
- Move the digits and the decimal point. Multiplying by 10 makes every digit 10 times as big, so the digits move 1 place to the left.3.4 × 10 = 34
- Write the answer. 34
Check. 34 ÷ 10 = 3.4. ✓
Watch out. Multiplying by 10 moves the digits to the LEFT, so the number gets bigger.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Multiply or divide by 10, 100 or 1,000 by moving the digits. Do not add zeros in the middle.
- Write the number. We are going to move every digit.2.75
- Move the digits and the decimal point. Multiplying by 100 makes every digit 100 times as big, so the digits move 2 places to the left.2.75 × 100 = 275
- Write the answer. 275
Check. 275 ÷ 100 = 2.75. ✓
Watch out. Multiplying by 100 moves the digits to the LEFT, so the number gets bigger.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Multiply or divide by 10, 100 or 1,000 by moving the digits. Do not add zeros in the middle.
- Write the number. We are going to move every digit.4,600
- Move the digits and the decimal point. Dividing by 100 makes every digit 100 times as small, so the digits move 2 places to the right.4,600 ÷ 100 = 46
- Write the answer. 46
Check. 46 × 100 = 4,600. ✓
Watch out. Dividing by 100 moves the digits to the RIGHT, so the number gets smaller.
Key words. To scale a quantity is to multiply or divide it by a number, for example to make a recipe for 6 people instead of 4.
Method. Multiply the top and the bottom by the same number.
- Compare the bottom numbers. What do we multiply 5 by to get 10? The answer is 2.5 × 2 = 10
- Do the same to the top number. Multiplying the top and the bottom by the same number keeps the fraction the same.4 × 2 = 8
- Write the answer. 8/10
Check. 8/10 and 4/5 both equal 0.8. ✓
Watch out. Multiply the top AND the bottom. Adding the same number to both changes the fraction.
Method. Multiply the number of bags by the number of sweets in each bag.
- Write what we know. Each bag has 6 sweets, and Sam has 8 bags.8 bags × 6 sweets
- Multiply the two numbers. Equal groups are found by multiplying.8 × 6 = 48
- Write the answer. 48 sweets
Check. 6 × 8 = 48 as well, so the order does not matter. ✓
Watch out. Multiply the bags by the sweets in each bag. Do not add them.
Converting metric units
A unit is the size we measure with. Metric units go up in tens, so each unit is a fixed number of the smaller unit below it:
| Measure | Units | Rule |
|---|---|---|
| Length | km and m | 1 km = 1,000 m |
| Length | m and cm | 1 m = 100 cm |
| Length | cm and mm | 1 cm = 10 mm |
| Mass | kg and g | 1 kg = 1,000 g |
| Capacity | litres and ml | 1 litre = 1,000 ml |
To change to a smaller unit, multiply. There are more small units, so the number gets bigger. To change to a bigger unit, divide. The number gets smaller. The decimal point moves in the same way: multiplying by 1,000 moves it three places to the right.
So 8.5 cm is the same as 85 mm. Five millimetres is half of one centimetre, so 0.5 cm = 5 mm.
Key ideas
- To change to a smaller unit, multiply. To change to a bigger unit, divide.
- Learn the rules: 1 km = 1,000 m, 1 m = 100 cm, 1 cm = 10 mm, 1 kg = 1,000 g, 1 litre = 1,000 ml.
- Check the size of your answer. 3.75 m must be less than 4 m, so 375 cm is the right size.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 km = 1,000 m
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2.35 × 1,000 = 2,350
- Write the answer with the new unit. 2,350 m
Check. 2,350 ÷ 1,000 = 2.35, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.100 cm = 1 m
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.375 ÷ 100 = 3.75
- Write the answer with the new unit. 3.75 m
Check. 3.75 × 100 = 375, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1,000 ml = 1 litre
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.6,040 ÷ 1,000 = 6.04
- Write the answer with the new unit. 6.04 litres
Check. 6.04 × 1,000 = 6,040, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Watch out
A common mistake is to think that 1 cm = 100 mm. It is 10 mm, so 4.7 cm is 47 mm, not 470 mm. Also, 1 km is 1,000 m, not 100 m.Exercise 8A Changing between metric units
Non-calculatorKey words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 km = 1,000 m
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2.4 × 1,000 = 2,400
- Write the answer with the new unit. 2,400 m
Check. 2,400 ÷ 1,000 = 2.4, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 km = 1,000 m
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.85 × 1,000 = 850
- Write the answer with the new unit. 850 m
Check. 850 ÷ 1,000 = 0.85, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 km = 1,000 m
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.1.06 × 1,000 = 1,060
- Write the answer with the new unit. 1,060 m
Check. 1,060 ÷ 1,000 = 1.06, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 km = 1,000 m
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.7.5 × 1,000 = 7,500
- Write the answer with the new unit. 7,500 m
Check. 7,500 ÷ 1,000 = 7.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 m = 100 cm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.3.6 × 100 = 360
- Write the answer with the new unit. 360 cm
Check. 360 ÷ 100 = 3.6, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 m = 100 cm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.45 × 100 = 45
- Write the answer with the new unit. 45 cm
Check. 45 ÷ 100 = 0.45, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 m = 100 cm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.12.8 × 100 = 1,280
- Write the answer with the new unit. 1,280 cm
Check. 1,280 ÷ 100 = 12.8, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 cm = 10 mm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.4.7 × 10 = 47
- Write the answer with the new unit. 47 mm
Check. 47 ÷ 10 = 4.7, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 cm = 10 mm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.9 × 10 = 9
- Write the answer with the new unit. 9 mm
Check. 9 ÷ 10 = 0.9, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 cm = 10 mm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.12.35 × 10 = 123.5
- Write the answer with the new unit. 123.5 mm
Check. 123.5 ÷ 10 = 12.35, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 kg = 1,000 g
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2.5 × 1,000 = 2,500
- Write the answer with the new unit. 2,500 g
Check. 2,500 ÷ 1,000 = 2.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 kg = 1,000 g
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.35 × 1,000 = 350
- Write the answer with the new unit. 350 g
Check. 350 ÷ 1,000 = 0.35, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 kg = 1,000 g
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.4.08 × 1,000 = 4,080
- Write the answer with the new unit. 4,080 g
Check. 4,080 ÷ 1,000 = 4.08, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1,000 g = 1 kg
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.4,500 ÷ 1,000 = 4.5
- Write the answer with the new unit. 4.5 kg
Check. 4.5 × 1,000 = 4,500, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1,000 g = 1 kg
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.750 ÷ 1,000 = 0.75
- Write the answer with the new unit. 0.75 kg
Check. 0.75 × 1,000 = 750, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1,000 g = 1 kg
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.2,080 ÷ 1,000 = 2.08
- Write the answer with the new unit. 2.08 kg
Check. 2.08 × 1,000 = 2,080, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1,000 ml = 1 litre
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.2,500 ÷ 1,000 = 2.5
- Write the answer with the new unit. 2.5 litres
Check. 2.5 × 1,000 = 2,500, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1,000 ml = 1 litre
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.450 ÷ 1,000 = 0.45
- Write the answer with the new unit. 0.45 litres
Check. 0.45 × 1,000 = 450, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1,000 ml = 1 litre
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.1,875 ÷ 1,000 = 1.875
- Write the answer with the new unit. 1.875 litres
Check. 1.875 × 1,000 = 1,875, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 litre = 1,000 ml
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.1.2 × 1,000 = 1,200
- Write the answer with the new unit. 1,200 ml
Check. 1,200 ÷ 1,000 = 1.2, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 litre = 1,000 ml
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.7 × 1,000 = 700
- Write the answer with the new unit. 700 ml
Check. 700 ÷ 1,000 = 0.7, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 litre = 1,000 ml
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.3.05 × 1,000 = 3,050
- Write the answer with the new unit. 3,050 ml
Check. 3,050 ÷ 1,000 = 3.05, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Change both lengths to metres, then compare them.
- Change 2.5 km to metres. There are 1,000 m in 1 km.2.5 km = 2.5 × 1,000 = 2,500 m
- Compare the two lengths in metres. Both lengths are now in the same unit.2,500 m > 2,400 m
- Write the answer. 2.5 km is longer.
Check. 2.5 km is 2,500 m, which is 100 m more than 2,400 m. ✓
Watch out. Compare in the same unit. 2.5 looks smaller than 2,400, but 2.5 is in kilometres.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Change every measure to the same unit first. Then the numbers can be compared.
- Change every length to mm. Then all the numbers use the same unit, so we can compare them.0.8 m = 800 mm
85 cm = 850 mm
0.9 m = 900 mm
790 mm = 790 mm - Put the numbers in order, smallest first. The smallest number is the shortest length.790 < 800 < 850 < 900
- Write the answer with the original units. Write each length as it was given in the question.790 mm, 0.8 m, 85 cm, 0.9 m
Check. Read the list back: each length is < the next one. ✓
Watch out. Do not compare 790 with 0.8 as if they were in the same unit. Change them first.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Change the rope to centimetres, then count how many 40 cm pieces fit.
- Change 3.6 m to centimetres. There are 100 cm in 1 m.3.6 m = 3.6 × 100 = 360 cm
- Share the rope into 40 cm pieces. Count how many 40s fit into 360. Divide.360 ÷ 40 = 9
- Write the answer. The rope is shared exactly, with nothing left over.9 pieces
Check. 9 pieces × 40 cm = 360 cm. ✓
Watch out. Change the units first. Dividing 3.6 by 40 gives a wrong answer.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Change the litres to millilitres, then divide by the size of one cup.
- Change 1.5 litres to millilitres. There are 1,000 ml in 1 litre.1.5 litres = 1.5 × 1,000 = 1,500 ml
- Count how many 250 ml cups fit. Divide the total by the amount in each cup.1,500 ÷ 250 = 6
- Write the answer. 6 cups
Check. 6 × 250 ml = 1,500 ml. ✓
Watch out. Make sure both amounts are in millilitres before you divide.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Change the metre length to centimetres, then compare.
- Change 0.6 m to centimetres. There are 100 cm in 1 m.0.6 m = 0.6 × 100 = 60 cm
- Compare with 65 cm. Both lengths are now in centimetres.60 cm < 65 cm
- Write the answer. No. 0.6 m is 60 cm, which is shorter than 65 cm.
Check. Jo compared the digits 6 and 5, but the place values are different. ✓
Watch out. Comparing 0.6 with 65 as if they were the same unit gives the wrong answer.
Approximate metric and imperial units
Some things are still measured in imperial units. You may see inches on a screen or a ruler, pounds on some food packets and pints of milk. An imperial unit does not fit exactly into a metric unit, so we use the word about.
| Measure | Imperial unit | Approximate metric equivalent |
|---|---|---|
| Length | 1 inch | ≈ 2.5 cm |
| Mass | 1 pound (lb) | ≈ 450 g |
| Mass | 2.2 pounds | ≈ 1 kg |
| Capacity | 1 pint | ≈ 0.57 litres |
| Capacity | 1.75 pints | ≈ 1 litre |
To change inches to centimetres, multiply by 2.5. To change kilograms to pounds, multiply by 2.2. To change litres to pints, multiply by 1.75. To change in the other direction, divide.
Key ideas
- Imperial units are only approximate in metric. Use the word about in your answer.
- Inches to centimetres: multiply by 2.5. Centimetres to inches: divide by 2.5.
- 1 kg ≈ 2.2 pounds, and 1 litre ≈ 1.75 pints.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 inch ≈ 2.5 cm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.10 × 2.5 = 25
- Write the answer with the new unit. about 25 cm
Check. 25 ÷ 2.5 = 10, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 kg ≈ 2.2 pounds
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.5 × 2.2 = 11
- Write the answer with the new unit. about 11 pounds
Check. 11 ÷ 2.2 = 5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 litre ≈ 1.75 pints
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2 × 1.75 = 3.5
- Write the answer with the new unit. about 3.5 pints
Check. 3.5 ÷ 1.75 = 2, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Watch out
Do not write exactly 25 cm for 10 inches or exactly 11 pounds for 5 kg. These are approximate conversions, so write about in your answer.Exercise 8B Inches, pounds and pints
Non-calculatorKey words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 inch ≈ 2.5 cm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.4 × 2.5 = 10
- Write the answer with the new unit. 10 cm
Check. 10 ÷ 2.5 = 4, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 inch ≈ 2.5 cm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.12 × 2.5 = 30
- Write the answer with the new unit. 30 cm
Check. 30 ÷ 2.5 = 12, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 inch ≈ 2.5 cm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.8 × 2.5 = 20
- Write the answer with the new unit. 20 cm
Check. 20 ÷ 2.5 = 8, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 inch ≈ 2.5 cm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.10 × 2.5 = 25
- Write the answer with the new unit. 25 cm
Check. 25 ÷ 2.5 = 10, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.2.5 cm ≈ 1 inch
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.15 ÷ 2.5 = 6
- Write the answer with the new unit. 6 inches
Check. 6 × 2.5 = 15, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.2.5 cm ≈ 1 inch
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.20 ÷ 2.5 = 8
- Write the answer with the new unit. 8 inches
Check. 8 × 2.5 = 20, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.2.5 cm ≈ 1 inch
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.5 ÷ 2.5 = 2
- Write the answer with the new unit. 2 inches
Check. 2 × 2.5 = 5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.2.5 cm ≈ 1 inch
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.10 ÷ 2.5 = 4
- Write the answer with the new unit. 4 inches
Check. 4 × 2.5 = 10, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 kg ≈ 2.2 pounds
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2 × 2.2 = 4.4
- Write the answer with the new unit. 4.4 pounds
Check. 4.4 ÷ 2.2 = 2, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 kg ≈ 2.2 pounds
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.5 × 2.2 = 11
- Write the answer with the new unit. 11 pounds
Check. 11 ÷ 2.2 = 5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 kg ≈ 2.2 pounds
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.10 × 2.2 = 22
- Write the answer with the new unit. 22 pounds
Check. 22 ÷ 2.2 = 10, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 kg ≈ 2.2 pounds
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.5 × 2.2 = 1.1
- Write the answer with the new unit. 1.1 pounds
Check. 1.1 ÷ 2.2 = 0.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.2.2 pounds ≈ 1 kg
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.11 ÷ 2.2 = 5
- Write the answer with the new unit. 5 kg
Check. 5 × 2.2 = 11, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.2.2 pounds ≈ 1 kg
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.22 ÷ 2.2 = 10
- Write the answer with the new unit. 10 kg
Check. 10 × 2.2 = 22, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.2.2 pounds ≈ 1 kg
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.4.4 ÷ 2.2 = 2
- Write the answer with the new unit. 2 kg
Check. 2 × 2.2 = 4.4, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.2.2 pounds ≈ 1 kg
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.2.2 ÷ 2.2 = 1
- Write the answer with the new unit. 1 kg
Check. 1 × 2.2 = 2.2, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 litre ≈ 1.75 pints
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.4 × 1.75 = 7
- Write the answer with the new unit. 7 pints
Check. 7 ÷ 1.75 = 4, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 litre ≈ 1.75 pints
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2 × 1.75 = 3.5
- Write the answer with the new unit. 3.5 pints
Check. 3.5 ÷ 1.75 = 2, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 litre ≈ 1.75 pints
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.8 × 1.75 = 14
- Write the answer with the new unit. 14 pints
Check. 14 ÷ 1.75 = 8, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1.75 pints ≈ 1 litre
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.7 ÷ 1.75 = 4
- Write the answer with the new unit. 4 litres
Check. 4 × 1.75 = 7, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1.75 pints ≈ 1 litre
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.3.5 ÷ 1.75 = 2
- Write the answer with the new unit. 2 litres
Check. 2 × 1.75 = 3.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1.75 pints ≈ 1 litre
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.14 ÷ 1.75 = 8
- Write the answer with the new unit. 8 litres
Check. 8 × 1.75 = 14, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 pint ≈ 0.57 litres
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2 × 0.57 = 1.14
- Write the answer with the new unit. about 1.14 litres
Check. 1.14 ÷ 0.57 = 2, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. Imperial units are older units, such as inches, pounds and pints. The symbol ≈ means “is about equal to”, so our answers are estimates.
Method. Change both weights to the same unit. Then compare.
- Write 1 kg in pounds. 1 kg is about 2.2 pounds.1 kg ≈ 2.2 pounds
- Compare with the 2 pound bag. Is 2.2 pounds more than 2 pounds?2.2 pounds > 2 pounds
- Write the answer. Yes. The 1 kg bag is heavier.
Check. 1 kg is about 0.2 pounds more than 2 pounds. ✓
Watch out. Two numbers of different units cannot be compared until they are changed to the same unit.
Key words. Imperial units are older units, such as inches, pounds and pints. The symbol ≈ means “is about equal to”, so our answers are estimates.
Method. Change 12 inches to centimetres, then compare with 30 cm.
- Change 12 inches to centimetres. Multiply the inches by 2.5.12 × 2.5 = 30 cm
- Compare the two rulers. Both rulers are about 30 cm long.30 cm ≈ 30 cm
- Write the answer. They are about the same length.
Check. 12 inches is about 30 cm, so the two rulers are about the same length. ✓
Watch out. The two lengths are approximately the same. Check the answer with the rule 1 inch ≈ 2.5 cm.
Key words. Imperial units are older units, such as inches, pounds and pints. The symbol ≈ means “is about equal to”, so our answers are estimates.
Method. Change 500 g to kilograms, then to pounds.
- Change 500 g to kilograms. There are 1,000 g in 1 kg, so 500 g is half a kilogram.500 g = 0.5 kg
- Change kilograms to pounds. Multiply the kilograms by 2.2, because 1 kg is about 2.2 pounds.0.5 × 2.2 = 1.1
- Write the answer. The answer is an estimate, so write about.about 1.1 pounds
Check. Half of 2.2 pounds is 1.1 pounds, so about 1.1 pounds is right. ✓
Watch out. Change grams to kilograms first. Do not multiply 500 by 2.2.
Perimeter of rectangles and composite shapes
The perimeter is the distance all the way round the outside of a shape. To find it, add the lengths of every outside side.
A rectilinear shape has only square corners. A composite shape is made from rectangles joined together, like the L-shape below. Some of its sides are not labelled. In a rectilinear shape, the sides can be found by subtracting: the top of the L-shape is the bottom length minus the width of the notch.
Key ideas
- The perimeter is the total length of the outside sides. Each outside side is counted once.
- Rectangle: perimeter = length + width + length + width, or 2 × (length + width).
- Missing side in a rectilinear shape: take away the known sides from a longer side.
- Check: an L-shape has the same perimeter as the rectangle that goes around it.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 7 cm, 4 cm, 7 cm, 4 cm
- Add the lengths of the sides. Add one side at a time and keep the unit.7 + 4 + 7 + 4 = 22 cm
- Write the answer. 22 cm
Check. The shortcut gives the same answer: 2 × (7 + 4) = 22 cm. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Find the hidden sides by subtracting, then add all the outside sides.
- Find the missing top side. The top is shorter than the bottom by the width of the notch (3 cm).8 − 3 = 5 cm
- Find the missing inside side. The left side is 6 cm tall. The lower right side is 3 cm, so the rest is the inside side.6 − 3 = 3 cm
- Add all six outside sides. Go all the way round the shape once and add each side.8 + 3 + 3 + 3 + 5 + 6 = 28 cm
- Write the answer. 28 cm
Check. Shortcut for an L-shape: 2 × (8 + 6) = 28 cm, which matches. ✓
Watch out. Count each outside side once. The two short sides inside the notch are outside sides too.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 2.5 m, 1.2 m, 2.5 m, 1.2 m
- Add the lengths of the sides. Add one side at a time and keep the unit.2.5 + 1.2 + 2.5 + 1.2 = 7.4 m
- Write the answer. 7.4 m
Check. The shortcut gives the same answer: 2 × (2.5 + 1.2) = 7.4 m. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Watch out
Do not add the lines inside a shape, and do not forget a side. Count every outside side once. For the L-shape, there are six outside sides, not four.Exercise 8C Perimeter of shapes
Non-calculatorKey words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 9 cm, 4 cm, 9 cm, 4 cm
- Add the lengths of the sides. Add one side at a time and keep the unit.9 + 4 + 9 + 4 = 26 cm
- Write the answer. 26 cm
Check. The shortcut gives the same answer: 2 × (9 + 4) = 26 cm. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 7 cm, 7 cm, 7 cm, 7 cm
- Add the lengths of the sides. Add one side at a time and keep the unit.7 + 7 + 7 + 7 = 28 cm
- Write the answer. 28 cm
Check. The shortcut gives the same answer: 2 × (7 + 7) = 28 cm. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 12 cm, 5 cm, 12 cm, 5 cm
- Add the lengths of the sides. Add one side at a time and keep the unit.12 + 5 + 12 + 5 = 34 cm
- Write the answer. 34 cm
Check. The shortcut gives the same answer: 2 × (12 + 5) = 34 cm. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 8.5 cm, 3 cm, 8.5 cm, 3 cm
- Add the lengths of the sides. Add one side at a time and keep the unit.8.5 + 3 + 8.5 + 3 = 23 cm
- Write the answer. 23 cm
Check. The shortcut gives the same answer: 2 × (8.5 + 3) = 23 cm. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 3.5 m, 2 m, 3.5 m, 2 m
- Add the lengths of the sides. Add one side at a time and keep the unit.3.5 + 2 + 3.5 + 2 = 11 m
- Write the answer. 11 m
Check. The shortcut gives the same answer: 2 × (3.5 + 2) = 11 m. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 4.2 m, 1.6 m, 4.2 m, 1.6 m
- Add the lengths of the sides. Add one side at a time and keep the unit.4.2 + 1.6 + 4.2 + 1.6 = 11.6 m
- Write the answer. 11.6 m
Check. The shortcut gives the same answer: 2 × (4.2 + 1.6) = 11.6 m. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 0.8 m, 0.8 m, 0.8 m, 0.8 m
- Add the lengths of the sides. Add one side at a time and keep the unit.0.8 + 0.8 + 0.8 + 0.8 = 3.2 m
- Write the answer. 3.2 m
Check. The shortcut gives the same answer: 2 × (0.8 + 0.8) = 3.2 m. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.6 sides: 7 cm, 3 cm, 2 cm, 2 cm, 5 cm, 5 cm
- Add the lengths of the sides. Add one side at a time and keep the unit.7 + 3 + 2 + 2 + 5 + 5 = 24 cm
- Write the answer. 24 cm
Check. The shortcut 2 × (7 + 5) = 24 cm agrees. ✓
Watch out. Do not add the lines inside a shape, and do not miss out a side.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Find the hidden sides by subtracting, then add all the outside sides.
- Find the missing top side. The top is shorter than the bottom by the width of the notch (4 cm).10 − 4 = 6 cm
- Find the missing inside side. The left side is 7 cm tall. The lower right side is 4 cm, so the rest is the inside side.7 − 4 = 3 cm
- Add all six outside sides. Go all the way round the shape once and add each side.10 + 4 + 4 + 3 + 6 + 7 = 34 cm
- Write the answer. 34 cm
Check. Shortcut for an L-shape: 2 × (10 + 7) = 34 cm, which matches. ✓
Watch out. Count each outside side once. The two short sides inside the notch are outside sides too.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Half the perimeter is one length plus one width.
- Find half the perimeter. A rectangle has two lengths and two widths, so half of the perimeter is one length plus one width.30 ÷ 2 = 15 cm
- Take away the known side. The other side is what is left of the 15 cm.15 − 9 = 6
- Write the answer. 6 cm
Check. 9 + 6 = 15, and 2 × 15 = 30. ✓
Watch out. Do not subtract 9 from 30 and stop. That gives the two sides together, not one side.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. A square has four equal sides, so divide the perimeter by 4.
- Share the perimeter between the four sides. All four sides of a square are the same length.36 ÷ 4 = 9
- Write the answer. 9 cm
Check. 9 + 9 + 9 + 9 = 36. ✓
Watch out. Divide by 4, not by 2. Two would be right for a rectangle, but not for a square.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Find the perimeter of each rectangle, then compare.
- Find the perimeter of the first rectangle. Add all four sides.6 + 2 + 6 + 2 = 16 cm
- Find the perimeter of the second rectangle. Add all four sides.5 + 3 + 5 + 3 = 16 cm
- Write the answer. The two perimeters are the same.Neither. Both have a perimeter of 16 cm.
Check. Both shapes add up to 16 cm. ✓
Watch out. Rectangles with different sides can have the same perimeter.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Find the perimeter of the field, then multiply by the number of laps.
- Find the perimeter of one lap. One lap goes all the way round the field.2 × (45 + 30) = 150 m
- Multiply by 3 laps. Three laps is three times the perimeter.150 × 3 = 450 m
- Write the answer. 450 m
Check. 150 m + 150 m + 150 m = 450 m. ✓
Watch out. Find the perimeter of one lap first. Then multiply by the number of laps.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Half the perimeter is one length plus one width. Then take away the length.
- Find half the perimeter. Half of the perimeter is one length plus one width.10.4 ÷ 2 = 5.2 m
- Take away the length. What is left is the width.5.2 − 3.2 = 2 m
- Write the answer. 2 m
Check. 3.2 + 2 = 5.2, and 2 × 5.2 = 10.4. ✓
Watch out. Halve the perimeter first. Do not subtract 3.2 from 10.4 and stop.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Find the hidden sides by subtracting, then add all the outside sides.
- Find the missing top side. The top is shorter than the bottom by the width of the notch (4 cm).9 − 4 = 5 cm
- Find the missing inside side. The left side is 5 cm tall. The lower right side is 3 cm, so the rest is the inside side.5 − 3 = 2 cm
- Add all six outside sides. Go all the way round the shape once and add each side.9 + 3 + 4 + 2 + 5 + 5 = 28 cm
- Write the answer. 28 cm
Check. Shortcut for an L-shape: 2 × (9 + 5) = 28 cm, which matches. ✓
Watch out. Count each outside side once. The two short sides inside the notch are outside sides too.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.6 sides: 4 cm, 2 cm, 2 cm, 2 cm, 2 cm, 4 cm
- Add the lengths of the sides. Add one side at a time and keep the unit.4 + 2 + 2 + 2 + 2 + 4 = 16 cm
- Write the answer. 16 cm
Check. Cutting the corner changes the shape, but not the total outside length. ✓
Watch out. When a corner square is cut out, the cut-out edges replace the edges that were removed. The total does not change.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Use the rectangle with length 3 times its width. Share the half-perimeter into four equal widths.
- Write the length in terms of the width. The length is three widths, so one length and one width make four widths.length + width = 4 widths
- Find half the perimeter. Half of the perimeter is one length plus one width.48 ÷ 2 = 24 cm
- Find the width. The 24 cm is 4 widths, so one width is 24 ÷ 4.24 ÷ 4 = 6 cm
- Find the length. The length is three times the width.3 × 6 = 18 cm
Check. 18 + 6 = 24, and 2 × 24 = 48. ✓
Watch out. Find the width first, then multiply it by 3 to find the length.
Area of rectangles, squares and irregular shapes
The area is the amount of surface inside a shape. We measure it by counting squares. A square with sides of 1 cm has an area of 1 square centimetre, written cm². A square with sides of 1 m has an area of 1 square metre, written m².
For a rectangle, we do not need to count every square. The picture below has 7 squares in each row and 5 rows. 5 rows of 7 squares is 35 squares, so the area is 35 cm². That is the same as length × width.
Key ideas
- Area of a rectangle or square = length × width.
- Area is measured in square units: cm² or m². Area is not measured in cm or m.
- For an irregular shape, count the whole squares. Two part squares together make one whole square.
- A square is a rectangle where all four sides are equal, so its area is side × side.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.7 × 5 = 35
- Write the answer with square units. We are counting squares, so the unit is squared.35 cm²
Check. 5 × 7 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.9 × 9 = 81
- Write the answer with square units. We are counting squares, so the unit is squared.81 cm²
Check. 9 × 9 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Count the whole squares, then count the part squares and make pairs. Each pair is one whole square.
- Count the whole squares inside the shape. A whole square is completely inside the outline.20 whole squares
- Count the part squares, then pair them up. Each part square is exactly half a square. Two of them make one whole square.4 part squares ÷ 2 = 2 whole squares
- Add the two counts. The total is the area of the shape in squares.20 + 2 = 22
- Write the answer with square units. This is an estimate, so we say about.about 22 cm²
Check. Count the shape again, row by row, to check you have not missed a square. ✓
Watch out. Do not count a part square as a whole square, and do not leave out the part squares.
Watch out
Area is not the same as perimeter. The perimeter is a length (cm) and the area is a number of squares (cm²). Also, 1 m² is not 100 cm². A square metre is 100 cm by 100 cm, which is 10 000 cm².Exercise 8D Area of rectangles and squares
Non-calculatorKey words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.5 × 4 = 20
- Write the answer with square units. We are counting squares, so the unit is squared.20 cm²
Check. 4 × 5 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.9 × 6 = 54
- Write the answer with square units. We are counting squares, so the unit is squared.54 cm²
Check. 6 × 9 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.12 × 3 = 36
- Write the answer with square units. We are counting squares, so the unit is squared.36 cm²
Check. 3 × 12 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.6 × 10 = 60
- Write the answer with square units. We are counting squares, so the unit is squared.60 cm²
Check. 10 × 6 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.6 × 6 = 36
- Write the answer with square units. We are counting squares, so the unit is squared.36 cm²
Check. 6 × 6 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.11 × 11 = 121
- Write the answer with square units. We are counting squares, so the unit is squared.121 cm²
Check. 11 × 11 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.12 × 12 = 144
- Write the answer with square units. We are counting squares, so the unit is squared.144 cm²
Check. 12 × 12 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.7 × 7 = 49
- Write the answer with square units. We are counting squares, so the unit is squared.49 cm²
Check. 7 × 7 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.2.5 × 4 = 10
- Write the answer with square units. We are counting squares, so the unit is squared.10 m²
Check. 4 × 2.5 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.1.5 × 2 = 3
- Write the answer with square units. We are counting squares, so the unit is squared.3 m²
Check. 2 × 1.5 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.3.2 × 2.5 = 8
- Write the answer with square units. We are counting squares, so the unit is squared.8 m²
Check. 2.5 × 3.2 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.0.5 × 6 = 3
- Write the answer with square units. We are counting squares, so the unit is squared.3 m²
Check. 6 × 0.5 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Find the area of each shape, then compare the two numbers.
- Find the area of the rectangle. Multiply the length by the width.3 × 8 = 24 cm²
- Find the area of the square. Multiply the side by itself.5 × 5 = 25 cm²
- Compare. The bigger number is the bigger area.25 > 24
- Write the answer. The square has the bigger area, 25 cm² compared with 24 cm².
Check. The square has area 25 cm², which is 1 square more. ✓
Watch out. The square looks like the rectangle in size, but its area is bigger.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Area = length × width. Use the area and one side to find the other side.
- Write the rule. The area is the length times the width.area = length × width
- Divide the area by the known width. The missing length is the area divided by the width.48 ÷ 6 = 8
- Write the answer. 8 cm
Check. 8 × 6 = 48 cm². ✓
Watch out. Divide the area by the side you know. Do not subtract the width from the area.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Count the whole squares, then count the part squares and make pairs. Each pair is one whole square.
- Count the whole squares inside the shape. A whole square is completely inside the outline.14 whole squares
- Count the part squares, then pair them up. Each part square is exactly half a square. Two of them make one whole square.4 part squares ÷ 2 = 2 whole squares
- Add the two counts. The total is the area of the shape in squares.14 + 2 = 16
- Write the answer with square units. This is an estimate, so we say about.about 16 cm²
Check. Count the shape again, row by row, to check you have not missed a square. ✓
Watch out. Do not count a part square as a whole square, and do not leave out the part squares.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Count the whole squares, then count the part squares and make pairs. Each pair is one whole square.
- Count the whole squares inside the shape. A whole square is completely inside the outline.21 whole squares
- Count the part squares, then pair them up. Each part square is exactly half a square. Two of them make one whole square.6 part squares ÷ 2 = 3 whole squares
- Add the two counts. The total is the area of the shape in squares.21 + 3 = 24
- Write the answer with square units. This is an estimate, so we say about.about 24 cm²
Check. Count the shape again, row by row, to check you have not missed a square. ✓
Watch out. Do not count a part square as a whole square, and do not leave out the part squares.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Count the squares in each row and the number of rows, then multiply.
- Count the squares in one row. Each row has the same number of squares.6 squares in each row
- Count the rows. Count the rows from top to bottom.3 rows
- Multiply. The total number of squares is the area.6 × 3 = 18
- Write the answer. 18 cm²
Check. Count every square one by one: 18 squares. ✓
Watch out. Write the unit as cm², because you are counting squares.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.4.5 × 3 = 13.5
- Write the answer with square units. We are counting squares, so the unit is squared.13.5 m²
Check. 3 × 4.5 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.40 × 30 = 1,200
- Write the answer with square units. We are counting squares, so the unit is squared.1,200 cm²
Check. 30 × 40 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Find the area of each rectangle, then the perimeter of each.
- Find the areas. Multiply the length by the width.10 × 2 = 20 cm², and 5 × 4 = 20 cm². The areas are the same.
- Find the perimeters. Add all four sides of each rectangle.10 + 2 + 10 + 2 = 24 cm, and 5 + 4 + 5 + 4 = 18 cm.
- Write the answer. The areas are the same, but the perimeters are not.Same area: yes. Same perimeter: no.
Check. Two shapes can have the same area and different perimeters. ✓
Watch out. Area and perimeter measure different things. Do not expect one to match the other.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. List the pairs of whole-number sides that multiply to make 36, then find the perimeter of each.
- List the pairs. Each pair of sides must multiply to make 36.1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6
- Find the perimeter of each pair. Perimeter = 2 × (length + width).2 × 37 = 74, 2 × 20 = 40, 2 × 15 = 30, 2 × 13 = 26, 2 × 12 = 24
- Find the smallest perimeter. The pair that is closest to a square has the smallest perimeter.24 is the smallest.
- Write the answer. 6 cm by 6 cm, with a perimeter of 24 cm.
Check. 6 × 6 = 36. A square has the smallest perimeter for a given area. ✓
Watch out. Check each pair. Do not stop at the first pair you find.
Volume and capacity
The volume of a solid is the amount of space it takes up. We can find the volume by building the solid from 1 cm cubes. Each cube is 1 cm long, 1 cm wide and 1 cm high, so its volume is 1 cubic centimetre, written cm³.
The cuboid below is built in three layers. Each layer has 4 cubes along and 2 cubes across, so it has 8 cubes. Three layers of 8 cubes is 24 cubes, so the volume is 24 cm³.
Capacity is how much a container can hold. Liquids are measured in litres and millilitres. A millilitre is the same as a cubic centimetre: 1 ml = 1 cm³. There are 1,000 ml in 1 litre, so 1 litre = 1,000 cm³.
Key ideas
- Volume of a cuboid of cubes = cubes in one layer × number of layers.
- Volume is measured in cubic centimetres (cm³). Area is measured in square centimetres (cm²).
- 1 ml = 1 cm³. 1 litre = 1,000 ml = 1,000 cm³.
- To change litres to millilitres, multiply by 1,000. To change millilitres to litres, divide by 1,000.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.4 × 2 = 8 cubes in one layer
- Count the layers. The layers are stacked on top of each other.3 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.8 × 3 = 24 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.24 cm³
Check. 4 × 3 × 2 = 24 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.5 × 4 = 20 cubes in one layer
- Count the layers. The layers are stacked on top of each other.3 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.20 × 3 = 60 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.60 cm³
Check. 5 × 3 × 4 = 60 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. One millilitre is the same as one cubic centimetre, so the number does not change.
- Write the rule. A millilitre and a cubic centimetre are the same amount.1 ml = 1 cm³
- Use the same number. 750 millilitres is 750 of these small cubes.750 ml = 750 cm³
- Write the answer. 750 cm³
Check. A cube with sides of 10 cm holds 1000 cm³, which is 1000 ml. ✓
Watch out. Do not multiply by 10 or 100. The number stays the same.
Watch out
Do not count the cubes on one face only. Count the layers and the cubes in each layer, or you will miss the cubes inside. Also do not use cm² for volume: a volume is always in cubic units.Exercise 8E Volume and capacity
Non-calculatorKey words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.5 × 2 = 10 cubes in one layer
- Count the layers. The layers are stacked on top of each other.3 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.10 × 3 = 30 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.30 cm³
Check. 5 × 3 × 2 = 30 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.2 × 3 = 6 cubes in one layer
- Count the layers. The layers are stacked on top of each other.4 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.6 × 4 = 24 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.24 cm³
Check. 2 × 4 × 3 = 24 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.5 × 2 = 10 cubes in one layer
- Count the layers. The layers are stacked on top of each other.2 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.10 × 2 = 20 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.20 cm³
Check. 5 × 2 × 2 = 20 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.3 × 3 = 9 cubes in one layer
- Count the layers. The layers are stacked on top of each other.3 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.9 × 3 = 27 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.27 cm³
Check. 3 × 3 × 3 = 27 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.6 × 2 = 12 cubes in one layer
- Count the layers. The layers are stacked on top of each other.1 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.12 × 1 = 12 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.12 cm³
Check. 6 × 1 × 2 = 12 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.4 × 4 = 16 cubes in one layer
- Count the layers. The layers are stacked on top of each other.4 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.16 × 4 = 64 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.64 cm³
Check. 4 × 4 × 4 = 64 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.10 × 5 = 50 cubes in one layer
- Count the layers. The layers are stacked on top of each other.2 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.50 × 2 = 100 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.100 cm³
Check. 10 × 2 × 5 = 100 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. A cube with sides of 10 cm is built from 1 cm cubes, so its volume is 1000 cm³.
- Find the volume of the cube. Each of the 10 layers has 10 × 10 cubes.10 × 10 × 10 = 1000 cm³
- Use the rule 1 ml = 1 cm³. A millilitre is the same as a cubic centimetre, so the number is the same.1000 cm³ = 1000 ml
- Write the answer. There are 1,000 ml in 1 litre, so this is exactly 1 litre.1000 ml (1 litre)
Check. 1000 ml ÷ 1000 = 1 litre. ✓
Watch out. The number does not change when you change cm³ to ml.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. One millilitre is the same as one cubic centimetre, so the number does not change.
- Write the rule. A millilitre and a cubic centimetre are the same amount.1 ml = 1 cm³
- Use the same number. 750 millilitres is 750 of these small cubes.750 ml = 750 cm³
- Write the answer. 750 cm³
Check. A cube with sides of 10 cm holds 1000 cm³, which is 1000 ml. ✓
Watch out. Do not multiply by 10 or 100. The number stays the same.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 litre = 1,000 ml
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2.5 × 1,000 = 2,500
- Write the answer with the new unit. 2,500 ml
Check. 2,500 ÷ 1,000 = 2.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. One litre is 1,000 ml, and each millilitre is 1 cm³.
- Write what one litre is in millilitres. There are 1,000 ml in 1 litre.1 litre = 1,000 ml
- Change the millilitres to cubic centimetres. One millilitre is 1 cm³, so the number is the same.1,000 ml = 1,000 cm³
- Write the answer. 1,000 cm³
Check. 1,000 cm³ is a cube with sides of 10 cm. ✓
Watch out. 1 litre is 1,000 cm³, not 100 cm³.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find out how much is missing from 1 litre. The jug has 600 ml, so take it away from 1000 ml.
- Read the amount in the jug. The jug has 600 ml of water.600 ml
- Take it away from 1 litre. One litre is 1,000 ml, so the jug needs 1,000 ml when it is full.1,000 − 600 = 400 ml
- Write the answer. 400 ml
Check. 600 ml + 400 ml = 1,000 ml, which is 1 litre. ✓
Watch out. Take the amount in the jug away from 1,000 ml, not from 600 ml.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the volume of each box, then compare.
- Find the volume of the first box. Multiply the three sides.4 × 3 × 2 = 24 cm³
- Find the volume of the second box. Multiply the three sides.6 × 4 × 1 = 24 cm³
- Write the answer. The volumes are equal.Yes. Both boxes have a volume of 24 cm³.
Check. Different shapes can have the same volume. ✓
Watch out. A box that looks bigger does not always hold more. Multiply the three sides.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. The base area is length × width. The volume divided by the base area is the height.
- Find the area of the base. Multiply the length by the width.6 × 2 = 12 cm²
- Find the height. The volume is the base multiplied by the height, so divide the volume by the base.24 ÷ 12 = 2
- Write the answer. 2 cm
Check. 12 × 2 = 24 cm³. ✓
Watch out. Divide the volume by the base, not by the length alone.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.4 × 3 = 12 cubes in one layer
- Count the layers. The layers are stacked on top of each other.5 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.12 × 5 = 60 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.60 cm³
Check. 4 × 5 × 3 = 60 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the volume in cm³, then change it to litres.
- Find the volume in cm³. Each layer of the base has 40 × 25 cubes, so the base area is 1,000 cm².40 × 25 = 1000 cm²
- Multiply by the height. The tank is 30 cm high, so there are 30 layers.1000 × 30 = 30,000 cm³
- Change cm³ to litres. 1 litre = 1,000 cm³, so divide by 1,000.30,000 ÷ 1,000 = 30 litres
- Write the answer. 30 litres
Check. 30 litres × 1000 = 30,000 cm³. ✓
Watch out. Check the unit: 1 litre is 1,000 cm³, not 100 cm³.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the side length of a cube with volume 27 cm³.
- Write the volume as a cube. A cube has the same length, width and height.side × side × side = 27
- Find the number that works. Try 1, 2, 3 ... until the product is 27. 1 × 1 × 1 = 1 and 2 × 2 × 2 = 8.3 × 3 × 3 = 27
- Write the answer. 3 cm
Check. 3 × 9 = 27 cm³. ✓
Watch out. A cube has the same length on all three sides. Multiply the side by itself three times.
Time and solving problems with measures
Units of time do not go up in tens. There are 60 seconds in 1 minute, 60 minutes in 1 hour, 24 hours in 1 day and 7 days in 1 week. To change to a smaller unit, multiply. To change to a bigger unit, divide.
A decimal number of hours can be split up. For example, 2.5 hours is 2 hours and half an hour, which is 2 hours 30 minutes.
Key ideas
- 1 hour = 60 minutes, 1 minute = 60 seconds, 1 day = 24 hours, 1 week = 7 days.
- Decimal hours: 0.5 hour = 30 minutes, 0.25 hour = 15 minutes, 0.1 hour = 6 minutes.
- Measures use all four operations: add lengths, take away to find the difference, multiply for equal amounts, and divide to share or to find how many.
- Scaling: find the amount for 1 first, then multiply to make a different amount. Use a bar model to show the steps.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 hour = 60 minutes
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2.5 × 60 = 150
- Write the answer with the new unit. 150 minutes
Check. 150 ÷ 60 = 2.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A duration is how long something lasts. There are 60 minutes in 1 hour, 60 seconds in 1 minute, 24 hours in 1 day and 7 days in 1 week.
Method. Change the hours to minutes, then add the extra minutes.
- Change the hours to minutes. Each hour is 60 minutes.3 × 60 = 180 minutes
- Add the extra minutes. The 20 minutes are added to the 180 minutes.180 + 20 = 200 minutes
- Write the answer. 200 minutes
Check. 200 minutes ÷ 60 = 3 remainder 20, which is 3 hours 20 minutes. ✓
Watch out. Do not write 3 hours 20 minutes as 3.20 hours. The 20 is minutes.
Key words. To scale a quantity is to multiply or divide it by a number, for example to make a recipe for 6 people instead of 4.
Method. Find the amount for 1 person, then multiply by the number of people.
- Find the amount for 1 person. Share the 250 g between the 4 people in the recipe.250 ÷ 4 = 62.5 g
- Multiply by 6 people. Each of the 6 people needs the same amount.62.5 × 6 = 375 g
- Write the answer. 375 g
Check. 375 ÷ 6 = 62.5 g, which matches the amount for 1 person. ✓
Watch out. Find the amount for 1 first. Multiplying 250 by 6 is wrong, because 250 g is for 4 people.
Watch out
When you change a unit of time, do not use the decimal point as a separator. 2.5 hours is 150 minutes, not 250 minutes. Check your answer by asking whether the bigger unit gives a smaller number.Exercise 8F Time and problems with measures
Non-calculatorKey words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 hour = 60 minutes
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.1.5 × 60 = 90
- Write the answer with the new unit. 90 minutes
Check. 90 ÷ 60 = 1.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 hour = 60 minutes
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.3.25 × 60 = 195
- Write the answer with the new unit. 195 minutes
Check. 195 ÷ 60 = 3.25, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 hour = 60 minutes
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.4 × 60 = 24
- Write the answer with the new unit. 24 minutes
Check. 24 ÷ 60 = 0.4, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 hour = 60 minutes
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.5 × 60 = 300
- Write the answer with the new unit. 300 minutes
Check. 300 ÷ 60 = 5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 minute = 60 seconds
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2.5 × 60 = 150
- Write the answer with the new unit. 150 seconds
Check. 150 ÷ 60 = 2.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 minute = 60 seconds
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.4.2 × 60 = 252
- Write the answer with the new unit. 252 seconds
Check. 252 ÷ 60 = 4.2, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 minute = 60 seconds
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.5 × 60 = 30
- Write the answer with the new unit. 30 seconds
Check. 30 ÷ 60 = 0.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 minute = 60 seconds
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.6 × 60 = 360
- Write the answer with the new unit. 360 seconds
Check. 360 ÷ 60 = 6, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 day = 24 hours
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2 × 24 = 48
- Write the answer with the new unit. 48 hours
Check. 48 ÷ 24 = 2, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 day = 24 hours
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.1.5 × 24 = 36
- Write the answer with the new unit. 36 hours
Check. 36 ÷ 24 = 1.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 day = 24 hours
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.25 × 24 = 6
- Write the answer with the new unit. 6 hours
Check. 6 ÷ 24 = 0.25, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 day = 24 hours
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.3 × 24 = 72
- Write the answer with the new unit. 72 hours
Check. 72 ÷ 24 = 3, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 week = 7 days
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.3 × 7 = 21
- Write the answer with the new unit. 21 days
Check. 21 ÷ 7 = 3, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 week = 7 days
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2.5 × 7 = 17.5
- Write the answer with the new unit. 17.5 days
Check. 17.5 ÷ 7 = 2.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 week = 7 days
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.6 × 7 = 42
- Write the answer with the new unit. 42 days
Check. 42 ÷ 7 = 6, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A duration is how long something lasts. There are 60 minutes in 1 hour, 60 seconds in 1 minute, 24 hours in 1 day and 7 days in 1 week.
Method. Change the hours to minutes, then add the extra minutes.
- Change 1 hour to minutes. One hour is 60 minutes.1 × 60 = 60 minutes
- Add the extra 35 minutes. Add the minutes to the 60 minutes.60 + 35 = 95 minutes
- Write the answer. 95 minutes
Check. 95 minutes is 1 hour 35 minutes. ✓
Watch out. Do not write 1 hour 35 minutes as 135 minutes. Change the hour to 60 first.
Key words. A duration is how long something lasts. There are 60 minutes in 1 hour, 60 seconds in 1 minute, 24 hours in 1 day and 7 days in 1 week.
Method. Change the minutes to seconds, then add the extra seconds.
- Change 2 minutes to seconds. One minute is 60 seconds.2 × 60 = 120 seconds
- Add the extra 45 seconds. Add the seconds to the 120 seconds.120 + 45 = 165 seconds
- Write the answer. 165 seconds
Check. 165 seconds ÷ 60 = 2 minutes 45 seconds. ✓
Watch out. Change the minutes to seconds before you add.
Key words. A duration is how long something lasts. There are 60 minutes in 1 hour, 60 seconds in 1 minute, 24 hours in 1 day and 7 days in 1 week.
Method. Find the total minutes, then change them to hours and minutes.
- Find the total minutes. Multiply the minutes for one day by the 7 days.25 × 7 = 175 minutes
- Change the minutes to hours. There are 60 minutes in 1 hour, so divide by 60.175 ÷ 60 = 2 remainder 55
- Write the answer. The remainder is the extra minutes.2 hours 55 minutes
Check. 2 hours is 120 minutes, and 120 + 55 = 175. ✓
Watch out. The remainder after dividing by 60 is the minutes, not hours.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Multiply the price of one notebook by the number of notebooks.
- Write the price of one notebook. Each notebook costs £1.85.£1.85
- Multiply by 3. Three notebooks cost three times as much. Multiply the decimal as if it were whole numbers, then put the point back.1.85 × 3 = 5.55
- Write the answer with £. £5.55
Check. £5.55 ÷ 3 = £1.85. ✓
Watch out. Keep two decimal places in money: £5.55, not £5.5.
Key words. To scale a quantity is to multiply or divide it by a number, for example to make a recipe for 6 people instead of 4.
Method. Multiply the weight of one bag by the number of bags.
- Write the weight of one bag. Each bag weighs 2.5 kg.2.5 kg
- Multiply by 4 bags. Four bags weigh four times as much.2.5 × 4 = 10 kg
- Write the answer. 10 kg
Check. 10 kg ÷ 4 = 2.5 kg. ✓
Watch out. A decimal number of kilograms can be multiplied in the same way as whole numbers.
Key words. To scale a quantity is to multiply or divide it by a number, for example to make a recipe for 6 people instead of 4.
Method. Find the amount for 1 person first, then scale up to 10 people.
- Find the amount for 1 person. The recipe serves 4 people, so share the 300 g between 4.300 ÷ 4 = 75 g
- Multiply by 10 people. Each of the 10 people needs 75 g.75 × 10 = 750 g
- Write the answer. 750 g
Check. 750 g ÷ 10 = 75 g, which matches the amount for 1 person. ✓
Watch out. Find the amount for 1 person first. Then multiply.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Change the litres to millilitres, then share the millilitres equally between the 5 cups.
- Change 2 litres to millilitres. There are 1,000 ml in 1 litre.2 × 1,000 = 2,000 ml
- Share the millilitres equally. Divide the total by the number of cups.2,000 ÷ 5 = 400
- Write the answer. 400 ml in each cup
Check. 5 × 400 ml = 2,000 ml. ✓
Watch out. Change to millilitres first, so that both amounts use the same unit.
Key words. A duration is how long something lasts. There are 60 minutes in 1 hour, 60 seconds in 1 minute, 24 hours in 1 day and 7 days in 1 week.
Method. Change 2.5 hours to minutes, then compare.
- Change 2.5 hours to minutes. Each hour is 60 minutes, so multiply 2.5 by 60.2.5 × 60 = 150 minutes
- Compare with 250 minutes. The two numbers must be in the same unit.150 minutes ≠ 250 minutes
- Write the answer. No. The journey is 150 minutes, not 250 minutes.
Check. 150 minutes is 2 hours 30 minutes, which is 2.5 hours. ✓
Watch out. Ali has multiplied by 100 instead of 60. There are 60 minutes in each hour, so 2.5 hours is 2 hours plus half an hour.
Chapter summary
| Skill | Method |
|---|---|
| Metric units | Smaller unit: multiply. Bigger unit: divide. 1 km = 1,000 m; 1 m = 100 cm; 1 cm = 10 mm; 1 kg = 1,000 g; 1 litre = 1,000 ml. |
| Imperial units (about) | These are approximate, so write about. 1 inch ≈ 2.5 cm; 1 kg ≈ 2.2 pounds; 1 litre ≈ 1.75 pints. |
| Perimeter | Add the lengths of all the outside sides. Find missing sides by subtracting a shorter side from a longer one. |
| Area of a rectangle or square | Length × width, in square units (cm² or m²). |
| Estimating area | Count the whole squares. Two part squares make one whole square. |
| Volume | Count the cubes in one layer, then multiply by the number of layers. The unit is cm³. |
| Capacity | 1 ml = 1 cm³, and 1 litre = 1,000 ml = 1,000 cm³. |
| Time | 1 hour = 60 minutes, 1 minute = 60 seconds, 1 day = 24 hours, 1 week = 7 days. |
| Problems with measures | Use the same unit, choose the operation, then check the size of the answer. To scale, find the amount for 1 first. |
Can you…?
- I can change between km and m, cm and m, cm and mm, g and kg, and litres and ml.
- I can use the words about and ≈ with inches, pounds and pints.
- I can find the perimeter of a rectangle and of an L-shape, including missing sides.
- I can find the area of a rectangle or square in cm² or m².
- I can estimate the area of an irregular shape by counting squares.
- I can find the volume of a cuboid by counting cubes in layers, and use 1 ml = 1 cm³.
- I can change between hours, minutes, seconds, days and weeks.
- I can solve problems with measures and money, including scaling a recipe.
Key terms
- Perimeter
- The distance all the way round the outside of a shape.
- Area
- The amount of surface inside a shape, measured in square units.
- Square centimetre (cm²)
- The area of a square with sides of 1 cm.
- Composite shape
- A shape made from two or more simple shapes, such as rectangles joined together.
- Rectilinear shape
- A shape whose sides meet at right angles, such as an L-shape.
- Volume
- The amount of space a solid takes up, measured in cubic units.
- Cubic centimetre (cm³)
- The volume of a cube with sides of 1 cm.
- Capacity
- How much a container can hold, often measured in litres or millilitres.
- Imperial unit
- An older unit, such as an inch, a pound or a pint. We use about when we change to metric units.
- Duration
- How long something lasts, such as 2 hours 30 minutes.
Exercise 8Z Check-up (non-calculator)
Non-calculatorKey words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 km = 1,000 m
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.4.2 × 1,000 = 4,200
- Write the answer with the new unit. 4,200 m
Check. 4,200 ÷ 1,000 = 4.2, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.100 cm = 1 m
- Divide, because the new unit is bigger. A bigger unit fits in fewer times, so the number gets smaller.625 ÷ 100 = 6.25
- Write the answer with the new unit. 6.25 m
Check. 6.25 × 100 = 625, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 inch ≈ 2.5 cm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.3 × 2.5 = 7.5
- Write the answer with the new unit. about 7.5 cm
Check. 7.5 ÷ 2.5 = 3, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 6.5 cm, 4 cm, 6.5 cm, 4 cm
- Add the lengths of the sides. Add one side at a time and keep the unit.6.5 + 4 + 6.5 + 4 = 21 cm
- Write the answer. 21 cm
Check. The shortcut gives the same answer: 2 × (6.5 + 4) = 21 cm. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.9 × 4 = 36
- Write the answer with square units. We are counting squares, so the unit is squared.36 m²
Check. 4 × 9 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.5 × 2 = 10 cubes in one layer
- Count the layers. The layers are stacked on top of each other.3 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.10 × 3 = 30 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.30 cm³
Check. 5 × 3 × 2 = 30 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 hour = 60 minutes
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.2.5 × 60 = 150
- Write the answer with the new unit. 150 minutes
Check. 150 ÷ 60 = 2.5, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 litre = 1,000 ml
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.1.75 × 1,000 = 1,750
- Write the answer with the new unit. 1,750 ml
Check. 1,750 ÷ 1,000 = 1.75, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Count the whole squares, then count the part squares and make pairs. Each pair is one whole square.
- Count the whole squares inside the shape. A whole square is completely inside the outline.10 whole squares
- Count the part squares, then pair them up. Each part square is exactly half a square. Two of them make one whole square.3 part squares ÷ 2 = 1.5 whole squares
- Add the two counts. The total is the area of the shape in squares.10 + 1.5 = 11.5
- Write the answer with square units. This is an estimate, so we say about.about 11.5 cm²
Check. Count the shape again, row by row, to check you have not missed a square. ✓
Watch out. Do not count a part square as a whole square, and do not leave out the part squares.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Find the hidden sides by subtracting, then add all the outside sides.
- Find the missing top side. The top is shorter than the bottom by the width of the notch (2 cm).6 − 2 = 4 cm
- Find the missing inside side. The left side is 4 cm tall. The lower right side is 3 cm, so the rest is the inside side.4 − 3 = 1 cm
- Add all six outside sides. Go all the way round the shape once and add each side.6 + 3 + 2 + 1 + 4 + 4 = 20 cm
- Write the answer. 20 cm
Check. Shortcut for an L-shape: 2 × (6 + 4) = 20 cm, which matches. ✓
Watch out. Count each outside side once. The two short sides inside the notch are outside sides too.
Total 23 marks. Allow about 23 minutes.
Exercise 8X SATs-style questions
Non-calculatorKey words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 kg = 1,000 g
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.3.2 × 1,000 = 3,200
- Write the answer with the new unit. 3,200 g
Check. 3,200 ÷ 1,000 = 3.2, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 litre = 1,000 ml
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.0.35 × 1,000 = 350
- Write the answer with the new unit. 350 ml
Check. 350 ÷ 1,000 = 0.35, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Add the lengths of all the sides on the outside.
- Find every side on the outside. The perimeter is the distance all the way round the outside, so each outside side counts once.4 sides: 12 cm, 7 cm, 12 cm, 7 cm
- Add the lengths of the sides. Add one side at a time and keep the unit.12 + 7 + 12 + 7 = 38 cm
- Write the answer. 38 cm
Check. The shortcut gives the same answer: 2 × (12 + 7) = 38 cm. ✓
Watch out. A rectangle has two lengths and two widths. Add all four sides once each.
Key words. The area is the amount of surface inside a shape. We measure area in square units, such as cm² (square centimetres) or m² (square metres).
Method. Multiply the length by the width. The answer is in square units.
- Write the rule. The area is the number of squares that cover the shape. For a rectangle we multiply the length by the width.Area = length × width
- Multiply the length by the width. Each row has as many squares as the length, and there is one row for each unit of width.12 × 7 = 84
- Write the answer with square units. We are counting squares, so the unit is squared.84 cm²
Check. 7 × 12 gives the same answer, because the order does not matter. ✓
Watch out. Area is in square units (cm²). Do not add the lengths: adding them gives the perimeter.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Use the rule to see how many of the new unit there are. Multiply for a smaller unit, and divide for a bigger unit.
- Write the rule. This rule links the two units, so we know how many of the smaller one make the bigger one.1 inch ≈ 2.5 cm
- Multiply, because the new unit is smaller. A smaller unit fits in more times, so the number gets bigger.6 × 2.5 = 15
- Write the answer with the new unit. about 15 cm
Check. 15 ÷ 2.5 = 6, which is the number we started with. ✓
Watch out. Check the size: a smaller unit must give a bigger number, and a bigger unit must give a smaller number.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Find the hidden sides by subtracting, then add all the outside sides.
- Find the missing top side. The top is shorter than the bottom by the width of the notch (3 cm).7 − 3 = 4 cm
- Find the missing inside side. The left side is 5 cm tall. The lower right side is 3 cm, so the rest is the inside side.5 − 3 = 2 cm
- Add all six outside sides. Go all the way round the shape once and add each side.7 + 3 + 3 + 2 + 4 + 5 = 24 cm
- Write the answer. 24 cm
Check. Shortcut for an L-shape: 2 × (7 + 5) = 24 cm, which matches. ✓
Watch out. Count each outside side once. The two short sides inside the notch are outside sides too.
Key words. The volume is the amount of space a solid takes up, measured in cubic units such as cm³. Capacity is how much a container can hold. 1 ml is the same as 1 cm³.
Method. Find the cubes in one layer, then multiply by the number of layers.
- Count the cubes in one layer. One layer is a rectangle of cubes, so multiply its length by its width.5 × 3 = 15 cubes in one layer
- Count the layers. The layers are stacked on top of each other.2 layers
- Multiply the cubes in one layer by the number of layers. Every layer has the same number of cubes.15 × 2 = 30 cubes
- Write the answer in cubic centimetres. Each cube is 1 cm long, 1 cm wide and 1 cm high, so the volume is in cm³.30 cm³
Check. 5 × 2 × 3 = 30 as well, so the answer does not depend on the order. ✓
Watch out. Volume is measured in cubic centimetres (cm³), not square centimetres.
Key words. A unit is the size we measure with. Metric units go up in tens, hundreds and thousands, so we convert between them by multiplying or dividing. A smaller unit gives a bigger number.
Method. Change the litres to millilitres, then divide by the size of one jug.
- Change 4.5 litres to millilitres. There are 1,000 ml in 1 litre.4.5 × 1,000 = 4,500 ml
- Divide by the size of one jug. Count how many 750 ml jugs fill 4,500 ml.4,500 ÷ 750 = 6
- Write the answer. The tank is filled exactly, with no part jug left over.6 jugs
Check. 6 × 750 ml = 4,500 ml. ✓
Watch out. Change the litres to millilitres first. Do not divide 4.5 by 750.
Key words. A duration is how long something lasts. There are 60 minutes in 1 hour, 60 seconds in 1 minute, 24 hours in 1 day and 7 days in 1 week.
Method. Change 1 hour 45 minutes to minutes, then to seconds.
- Change the hour and the minutes to minutes. One hour is 60 minutes. Add the 45 minutes.60 + 45 = 105 minutes
- Change minutes to seconds. One minute is 60 seconds.105 × 60 = 6,300 seconds
- Write the answer. 6,300 seconds
Check. 6,300 ÷ 60 = 105 minutes. ✓
Watch out. Change to minutes first, then to seconds. Check the number is bigger in seconds.
Key words. To scale a quantity is to multiply or divide it by a number, for example to make a recipe for 6 people instead of 4.
Method. Find the amount for 1 person first, then multiply by 5.
- Find the amount for 1 person. The recipe serves 3 people, so share 240 g between 3 people.240 ÷ 3 = 80 g
- Multiply by 5 people. Five people each need 80 g.80 × 5 = 400 g
- Write the answer. 400 g
Check. 400 g ÷ 5 = 80 g, the same as 1 person. ✓
Watch out. Scaling up: find 1 first, then multiply.
Key words. The perimeter is the distance all the way round the outside of a shape. A composite shape is made from two or more simple shapes, such as rectangles.
Method. Find the perimeter of the garden, then multiply by the cost per metre.
- Find the perimeter. The fence goes all the way round the garden.2 × (12.5 + 8) = 41 m
- Multiply by the cost of one metre. Each metre costs £4.50.41 × 4.50 = 184.50
- Check the size of the answer. About 40 m at about £4.50 a metre is about £180, which is close.£184.50 is about right.
- Write the answer with £. £184.50
Check. £184.50 ÷ 41 = £4.50. ✓
Watch out. Find the perimeter first. Multiplying by the length of only one side gives the wrong answer.