Year 4 Perimeter, Area and Measures: check-up and SATs-style questions

Key words. A ruler measures length. Centimetres (cm) are the big numbered marks. Millimetres (mm) are the tiny marks: 10 mm make 1 cm. The scale is the line of numbers and marks.

Method. Read the ruler at the end of the object. The big marks are centimetres and the small marks are millimetres.

1. Find where the end of the ribbon is on the ruler. The left end of the ribbon is at 0, so the number at its right end is its length.
   the end of the ribbon is just after the 8 cm mark, with 6 small marks to go.
2. Count the small marks after the big mark. The tiny marks are millimetres. There are 10 of them in every centimetre. The long middle mark is 5 mm.
   6 small marks = 6 mm
3. Write the length. Say the centimetres, then the millimetres.
   8 cm and 6 mm = 8 cm 6 mm

Check. 8 cm = 80 mm and 80 mm + 6 mm = 86 mm. ✓

Watch out. Start counting from the 0 mark, not from the end of the ruler. Ten small marks make one centimetre, not five.

Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).

Method. Look at the scale. Find the numbered marks either side of the pointer, work out what each small mark is worth, then count on.

1. Find the unit on the scale. The unit tells us what the numbers mean.
   The unit is g (grams).
2. Find the two numbered marks either side of the pointer. We read the number below it first, then count on.
   The pointer is between 600 and 800.
3. Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.
   From 600 to 800 there are 4 gaps.
   800 − 600 = 200 g
   200 ÷ 4 = 50 g for each small mark
4. Count on from 600. Count how many small marks the pointer is past 600.
   1 small mark × 50 g = 50 g
   600 + 50 = 650 g
5. Write the reading with its unit. A measure always needs a unit.
   650 g

Check. Count back from 800: 3 small marks below it. 800 − 150 = 650. ✓

Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.

Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).

Method. Look at the scale. Find the numbered marks either side of the top of the liquid, work out what each small mark is worth, then count on.

1. Find the unit on the scale. The unit tells us what the numbers mean.
   The unit is ml (millilitres).
2. Find the two numbered marks either side of the top of the liquid. We read the number below it first, then count on.
   The top of the liquid is between 300 and 400.
3. Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.
   From 300 to 400 there are 5 gaps.
   400 − 300 = 100 ml
   100 ÷ 5 = 20 ml for each small mark
4. Count on from 300. Count how many small marks the top of the liquid is past 300.
   2 small marks × 20 ml = 40 ml
   300 + 40 = 340 ml
5. Write the reading with its unit. A measure always needs a unit.
   340 ml

Check. Count back from 400: 3 small marks below it. 400 − 60 = 340. ✓

Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. There are 1,000 grams in 1 kilogram, so multiply by 1,000 to change kilograms to grams.

1. Remember the fact. 1 kg is the same as 1,000 g. A gram is a much smaller unit, so we will have a bigger number.
   1 kg = 1,000 g
2. Split the number into whole kilograms and a part. It is easier to change the whole kilograms and the part separately.
   3.5 kg = 3 kg + 0.5 kg
3. Change the whole kilograms. Multiply by 1,000.
   3 × 1,000 = 3,000 g
4. Change the part. Think about what fraction of a kg it is.
   0.5 kg is half of 1 kg. Half of 1,000 = 500 g
5. Add the two answers together.
   3,000 + 500 = 3,500 g

Check. Go back: 3,500 ÷ 1,000 = 3.5. ✓

Watch out. Changing to a smaller unit gives a bigger number: 3.5 kg is 3,500 g, not 0.0035.

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. There are 1,000 metres in 1 kilometre, so divide by 1,000 to change metres to kilometres.

1. Remember the fact. 1 km is the same as 1,000 m. A kilometre is a much bigger unit, so we will have a smaller number.
   1,000 m = 1 km
2. Divide by 1,000 and keep the remainder. The whole kilometres come from the lots of 1,000 m. The remainder is the part left over.
   4,500 ÷ 1,000 = 4 remainder 500
3. Write the remainder as a part of 1 km. 500 m out of 1,000 m is 500/1,000 of a km.
   500 m is half of 1,000 m, so 500 m = 0.5 km
4. Put the whole kilometres and the part together. The whole number goes before the decimal point.
   4 + 0.5 = 4.5 km

Check. Go back: 4.5 × 1,000 = 4,500. ✓

Watch out. Changing to a bigger unit gives a smaller number. 4,500 m is 4.5 km, not 4,500,000.

Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.

Method. Change both measures to the same unit (the smaller one). Then compare the numbers.

1. Look at the units. We can only compare measures that are in the same unit.
   2.5 l and 2,400 ml: the units are different.
2. Change both to the smaller unit, millilitres. Changing to the smaller unit gives whole numbers that are easy to compare.
   2.5 l = 2.5 × 1,000 = 2,500 ml
   2,400 ml
3. Compare the numbers. Compare the digits from the left, starting with the biggest place value.
   2,500 > 2,400
4. Write the answer. Put the sign between the two original measures.
   2.5 l > 2,400 ml

Check. 2,500 ml and 2,400 ml: the bigger number is the bigger measure. ✓

Watch out. Do not compare the numbers in the question as they are. 3 km is more than 2,500 m even though 2,500 is more than 3.

Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.

Method. Change the measures to the same unit. Then add or subtract the numbers, and give the answer in the unit asked.

1. Change both measures to centimetres. We can only add or subtract measures that are in the same unit. Use the smaller unit so we have whole numbers.
   1 m 60 cm = 1 × 100 + 60 = 100 + 60 = 160 cm
   2 m 75 cm = 2 × 100 + 75 = 200 + 75 = 275 cm
2. Add the two measures. Add column by column, starting with the ones. Carry when a column makes 10 or more.
   160 cm + 275 cm = 435 cm
   

   	H	T	O
   	1	6	0
   +	2	7	5
   	4	3	5
   	1

3. Write the answer in metres and centimetres. 100 cm = 1 m, so divide by 100 and keep the remainder.
   435 ÷ 100 = 4 remainder 35
   435 cm = 4 m 35 cm

Check. Use the inverse: 435 − 275 = 160. ✓

Watch out. You can only add or subtract measures in the same unit. 1 m + 45 cm is not 46 of anything: change it to 145 cm first.

Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.

Method. The perimeter is the distance all the way round the shape. Add up the lengths of all the sides.

1. Write down all four sides. A rectangle has two long sides and two short sides. Opposite sides are equal.
   13 cm, 6 cm, 13 cm, 6 cm
2. Add the sides, one at a time. The perimeter is all the sides added together.
   13 + 6 = 19
   19 + 13 = 32
   32 + 6 = 38
3. Write the perimeter with its unit.
   Perimeter = 38 cm

Check. Another way: double the length and the width. 2 × (13 + 6) = 2 × 19 = 38. ✓

Watch out. Do not stop after two sides. A rectangle has FOUR sides. Do not multiply the length by the width: that is the area.

Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.

Method. Find the missing sides first. Then add up ALL the sides to get the perimeter.

1. Write down every side, going round the shape. The perimeter uses every side. Some sides have letters because their lengths are not given.
   6 cm, 2 cm, 3 cm, 3 cm, a, b
2. Find the missing side a. Imagine walking all the way round and back to the start. You must go right exactly as far as you go left.
   Going right: 6
   Going left: 3 + a
   These are equal, so: a = 6 − 3 = 3 cm
3. Find the missing side b. Imagine walking all the way round and back to the start. You must go down exactly as far as you go up.
   Going down: 2 + 3
   Going up: b
   These are equal, so: b = 5 cm
4. Add all the sides. Now every side has a length. Add them one at a time.
   6 + 2 = 8
   8 + 3 = 11
   11 + 3 = 14
   14 + 3 = 17
   17 + 5 = 22
5. Write the perimeter with its unit.
   Perimeter = 22 cm

Check. The shape fits inside a 6 cm by 5 cm rectangle. A shape like this one has the same perimeter as the rectangle round it. 2 × (6 + 5) = 22. ✓

Watch out. Do not forget the sides that have no number. A missing side is still part of the perimeter.

Key words. The area of a shape is the amount of flat space inside it. We count how many 1 cm squares cover it. The unit is the square centimetre, written cm². A row goes across and a column goes down.

Method. Area is the amount of flat space inside a shape. Count the squares that cover it, one row at a time.

1. Each square is 1 cm by 1 cm. The area is how many squares cover the shape. We count whole squares.
   Each square has an area of 1 cm² (one square centimetre).
2. Count the squares row by row. Counting one row at a time stops us missing or counting a square twice.
   Row 1: 1 square
   Row 2: 2 squares
   Row 3: 3 squares
   Row 4: 4 squares
   Row 5: 5 squares
3. Add the rows.
   1 + 2 = 3
   3 + 3 = 6
   6 + 4 = 10
   10 + 5 = 15
4. Write the area with its unit. Area is measured in square units.
   Area = 15 cm²

Check. Count in columns instead: 5 + 4 + 3 + 2 + 1 = 15. ✓

Watch out. Area is measured in square units (cm²), not in cm. Do not count the edges, count the squares.

Key words. A ruler measures length. Centimetres (cm) are the big numbered marks. Millimetres (mm) are the tiny marks: 10 mm make 1 cm. The scale is the line of numbers and marks.

Method. Read the ruler at the end of the object. The big marks are centimetres and the small marks are millimetres.

1. Find where the end of the pencil is on the ruler. The left end of the pencil is at 0, so the number at its right end is its length.
   the end of the pencil is just after the 6 cm mark, with 7 small marks to go.
2. Count the small marks after the big mark. The tiny marks are millimetres. There are 10 of them in every centimetre. The long middle mark is 5 mm.
   7 small marks = 7 mm
3. Look at the extra millimetres. To round to the nearest cm, look at the millimetres. 5 mm or more rounds UP.
   7 mm is 5 or more, so round up from 6 cm to 7 cm

Check. The length is 6 cm 7 mm. It is closer to 7 cm than to the other whole centimetre. ✓

Watch out. Start counting from the 0 mark, not from the end of the ruler. Ten small marks make one centimetre, not five.

Key words. A scale is a line of marks with numbers on it. The interval (step) is the amount between two small marks. Mass is how heavy something is (grams, kg). Capacity is how much a container holds (millilitres, litres).

Method. Look at the scale. Find the numbered marks either side of the top of the liquid, work out what each small mark is worth, then count on.

1. Find the unit on the scale. The unit tells us what the numbers mean.
   The unit is l (litres).
2. Find the two numbered marks either side of the top of the liquid. We read the number below it first, then count on.
   The top of the liquid is between 1 and 1.5.
3. Work out what each small mark is worth. Scales have different steps, so never guess. Count the gaps (not the marks) between two numbered marks, then divide.
   From 1 to 1.5 there are 5 gaps.
   1.5 − 1 = 0.5 l
   0.5 ÷ 5 = 0.1 l for each small mark
4. Count on from 1. Count how many small marks the top of the liquid is past 1.
   3 small marks × 0.1 l = 0.3 l
   1 + 0.3 = 1.3 l
5. Write the reading with its unit. A measure always needs a unit.
   1.3 l

Check. Count back from 1.5: 2 small marks below it. 1.5 − 0.2 = 1.3. ✓

Watch out. Different scales have different steps. Never assume each small mark is 1. Work out the step each time.

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. There are 1,000 grams in 1 kilogram, so multiply by 1,000 to change kilograms to grams.

1. Remember the fact. 1 kg is the same as 1,000 g. A gram is a much smaller unit, so we will have a bigger number.
   1 kg = 1,000 g
2. Multiply by 1,000. Each kg is 1,000 g. So 4 kg is 4 lots of 1,000 g. (Multiplying by 1,000 moves every digit 3 places to the left.)
   4 × 1,000 = 4,000
3. Write the answer with its unit. A measure always needs its unit.
   4 kg = 4,000 g

Check. Go back: 4,000 ÷ 1,000 = 4. ✓

Watch out. Changing to a smaller unit gives a bigger number: 4 kg is 4,000 g, not 0.004.

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. There are 100 centimetres in 1 metre, so divide by 100 to change centimetres to metres.

1. Remember the fact. 1 m is the same as 100 cm. A metre is a much bigger unit, so we will have a smaller number.
   100 cm = 1 m
2. Divide by 100 and keep the remainder. The whole metres come from the lots of 100 cm. The remainder is the part left over.
   650 ÷ 100 = 6 remainder 50
3. Write the remainder as a part of 1 m. 50 cm out of 100 cm is 50/100 of a m.
   50 cm is half of 100 cm, so 50 cm = 0.5 m
4. Put the whole metres and the part together. The whole number goes before the decimal point.
   6 + 0.5 = 6.5 m

Check. Go back: 6.5 × 100 = 650. ✓

Watch out. Changing to a bigger unit gives a smaller number. 650 cm is 6.5 m, not 65,000.

Key words. To convert is to change a measure from one unit to another unit. Kilo means 1000: 1 kilometre = 1000 m, 1 kilogram = 1000 g. Centi means a hundredth: 1 m = 100 cm. Milli means a thousandth.

Method. Change each measure to grams and compare it with 1.5 kg. 1.5 kg is 1,000 g and 500 g.

1. Change 1.5 kg to grams. 1 kg = 1,000 g and half a kilogram is 500 g.
   1.5 kg = 1,000 + 500 = 1,500 g
2. Check each option. We want the ones that are 1,500 g.
   A: 150 g is not 1,500 g
   B: 1,500 g ✓
   C: 1 kg 500 g = 1,000 + 500 = 1,500 g ✓
   D: 1.05 kg = 1,000 g + 50 g = 1,050 g, not 1,500 g
3. Choose the two.
   B and C

Check. Both B and C are 1,500 g. ✓

Watch out. 1.05 kg is not the same as 1.5 kg.

Key words. To compare measures is to say which is bigger. Change them to the same unit first. To estimate is to make a sensible guess. To order is to put them in a list.

Method. Change everything to the same unit, put the numbers in order, then write the original measures in that order.

1. Change every measure to grams. Measures in different units cannot be ordered until they are in the same unit. Use the smaller unit so we have whole numbers.
   0.5 kg = 0.5 × 1,000 = 500 g
   450 g
   550 g
2. Put the whole numbers in order. Compare the digits from the left. Order them smallest first.
   450, 500, 550
3. Write the original measures in that order. Match each number back to its measure.
   450 g,  0.5 kg,  550 g

Check. Read the ordered list again in grams: 450, 500, 550. Each one is bigger than the one before. ✓

Watch out. Keep the original units in your final answer. Do not write the changed numbers.

Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.

Method. A square has four equal sides, so the perimeter is 4 times the side length.

1. Remember: a square has 4 equal sides. We only need one side length.
   Each side is 9 cm.
2. Add the four sides, or multiply by 4. Adding the same number 4 times is the same as 4 times the number.
   9 + 9 + 9 + 9 = 4 × 9 = 36 cm
3. Write the perimeter with its unit.
   Perimeter = 36 cm

Check. Half way: 9 + 9 = 18 and 18 + 18 = 36. ✓

Watch out. Do not just give one side. The perimeter goes all the way round.

Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.

Method. A rectangle has 2 lengths and 2 widths. Take away the two sides you know, then halve what is left.

1. Take away the two sides we know. The perimeter is two lengths and two other sides. Take away the two lengths first.
   2 × 7 = 14 cm
   24 − 14 = 10 cm
2. Share what is left between the two other sides. The two other sides are equal, so halve the answer.
   10 ÷ 2 = 5 cm
3. Write the answer.
   The other side is 5 cm.

Check. Check by adding: 7 + 5 + 7 + 5 = 24. ✓

Watch out. Do not halve the perimeter and stop. Take away the known sides first.

Key words. The perimeter is the total distance all the way round the edge of a shape. A rectilinear shape has only straight sides and square corners (like a rectangle or an L-shape). A square has 4 equal sides.

Method. Find the missing sides first. Then add up ALL the sides to get the perimeter.

1. Write down every side, going round the shape. The perimeter uses every side. Some sides have letters because their lengths are not given.
   10 cm, 4 cm, 4 cm, 3 cm, a, b
2. Find the missing side a. Imagine walking all the way round and back to the start. You must go right exactly as far as you go left.
   Going right: 10
   Going left: 4 + a
   These are equal, so: a = 10 − 4 = 6 cm
3. Find the missing side b. Imagine walking all the way round and back to the start. You must go down exactly as far as you go up.
   Going down: 4 + 3
   Going up: b
   These are equal, so: b = 7 cm
4. Add all the sides. Now every side has a length. Add them one at a time.
   10 + 4 = 14
   14 + 4 = 18
   18 + 3 = 21
   21 + 6 = 27
   27 + 7 = 34
5. Write the perimeter with its unit.
   Perimeter = 34 cm

Check. The shape fits inside a 10 cm by 7 cm rectangle. A shape like this one has the same perimeter as the rectangle round it. 2 × (10 + 7) = 34. ✓

Watch out. Do not forget the sides that have no number. A missing side is still part of the perimeter.

Key words. To add or subtract measures, they must be in the same unit. The total is all the amounts added together. The difference is how much more one amount is than another.

Method. Find the total mass of the 3 bags in grams. Change 2.5 kg to grams. Then compare.

1. Find the mass of 3 bags. Each bag is 750 g. Multiply by 3.
   3 × 750 = 3 × 700 + 3 × 50 = 2,100 + 150 = 2,250 g
2. Change 2.5 kg to grams. 1 kg = 1,000 g and half a kilogram is 500 g.
   2.5 kg = 2,000 + 500 = 2,500 g
3. Compare and find the difference. 2,250 g is less than 2,500 g, so she does not have enough.
   2,500 − 2,250 = 250 g short. Zainab does not have enough.

Check. 2,250 + 250 = 2,500. ✓

Watch out. Change to the same unit before you compare.