Year 6 Area, Volume and Measures: check-up and SATs-style questions

Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.

Method. Find how many m make one km, then multiply by that number.

1. Find how many m make one km. The table says 1 km = 1000 m.
   1 km = 1000 m
2. Multiply by 1000. The answer is in m, which is smaller than km, so there are more m. Multiplying makes the number bigger.
   4.6 × 1000 = 4600
3. Write the answer. Moving the decimal point 3 places to the right gives the answer in m.
   4600

Check. 4600 ÷ 1000 = 4.6, the number we started with. ✓

Watch out. A smaller unit gives a bigger number, so multiply. Move the decimal point to the right.

Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.

Method. Find how many ml make one l, then multiply by that number.

1. Find how many ml make one l. The table says 1 l = 1000 ml.
   1 l = 1000 ml
2. Multiply by 1000. The answer is in ml, which is smaller than l, so there are more ml. Multiplying makes the number bigger.
   0.35 × 1000 = 350
3. Write the answer. Moving the decimal point 3 places to the right gives the answer in ml.
   350

Check. 350 ÷ 1000 = 0.35, the number we started with. ✓

Watch out. A smaller unit gives a bigger number, so multiply. Move the decimal point to the right.

Key words. There are 60 minutes in 1 hour and 60 seconds in 1 minute. A decimal hour uses a decimal point: 30 minutes is 0.5 hours, because 30 is half of 60.

Method. Multiply the hours by 60 to get minutes.

1. Remember: 1 hour = 60 minutes. So each hour gives 60 minutes.
   1 h = 60 min
2. Multiply the hours by 60. This gives the number of minutes.
   2.5 × 60 = 150
3. Write the answer. The answer is in minutes.
   150

Check. 150 ÷ 60 = 2.5 hours. ✓

Watch out. Multiply by 60 to go from hours to minutes. Do not multiply by 100.

Key words. There are 60 minutes in 1 hour and 60 seconds in 1 minute. A decimal hour uses a decimal point: 30 minutes is 0.5 hours, because 30 is half of 60.

Method. Change the minutes to hours with a decimal, then add the whole hours.

1. Change the minutes to a fraction of an hour. Each minute is one sixtieth of an hour.
   15 ÷ 60 = 0.25
2. Add the whole hours. The whole hours stay the same.
   1 + 0.25 = 1.25
3. Write the answer. The answer is in hours, as a decimal.
   1.25

Check. 1.25 hours is 1 hours and 15 minutes: 15 ÷ 60 = 0.25. ✓

Watch out. Do not write 2 h 15 min as 2.15. The 15 minutes is a quarter of an hour, so it is 0.25.

Key words. 1 mile is about 1.6 kilometres (1 mile ≈ 1.6 km). The sign ≈ means "is about equal to".

Method. Divide the kilometres by 1.6, because 1 mile is about 1.6 km.

1. Use the rule: 1 mile is about 1.6 km. So we divide the kilometres by 1.6 to get miles.
   1 mile ≈ 1.6 km
2. Divide by 1.6. To avoid a decimal divisor, multiply the top and bottom by 10. Then 1.6 becomes 16.
   16 ÷ 1.6 = 160 ÷ 16
3. Work out the division. The answer may have a decimal part, which must end.
   160 ÷ 16 = 10
4. Write the answer. The answer is in miles.
   10

Check. 10 × 1.6 = 16 km. ✓

Watch out. Kilometres to miles: divide by 1.6. A mile is longer than a kilometre, so the number of miles is smaller.

Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.

Method. Multiply the base by the perpendicular height. Do not use the slanted side.

1. Find the base and the perpendicular height. The height goes straight up from the base. The slanted side is not the height.
   base = 11 cm, perpendicular height = 5 cm
2. Multiply the base by the perpendicular height. The area of a parallelogram is base times perpendicular height.
   11 × 5 = 55
3. Write the answer. The area is in square centimetres.
   55

Check. Cut the triangle off one end and move it to the other: a rectangle 11 cm by 5 cm has the same area, 55 cm². ✓

Watch out. Use the vertical height, not the slanted side. The slanted side is always longer than the height.

Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.

Method. Multiply the base by the height, then divide by 2.

1. Find the base and the perpendicular height. The height is the straight line from the top corner to the base, at a right angle.
   base = 12 cm, perpendicular height = 9 cm
2. Multiply the base by the height. Two copies of the triangle make a parallelogram with the same base and height.
   12 × 9 = 108
3. Halve the answer. One triangle is half of the parallelogram.
   108 ÷ 2 = 54
4. Write the answer. The area is in square centimetres.
   54

Check. Two of these triangles make a parallelogram with area 108 cm², so one triangle is 108 ÷ 2 = 54. ✓

Watch out. Do not forget the divide by 2. A triangle is half of a rectangle with the same base and height.

Key words. The perimeter is the total distance all the way round the outside of a shape. Add the lengths of all the outside sides.

Method. Add up the lengths of all the outside sides.

1. Name every outside side. Go all the way round the outside. Each side of the cut-out goes on the outside too.
   6, 2, 3, 5, 9, 7 cm
2. Add the six outside sides. This gives the total distance round the shape.
   6 + 2 + 3 + 5 + 9 + 7 = 32
3. Write the answer. The perimeter is in centimetres.
   32

Check. The same as the whole rectangle: 2 × (9 + 7) = 32 cm. ✓

Watch out. The cut moves some sides but keeps the total. Count the short sides of the cut as well.

Key words. The volume is the space inside a solid, in cubic units (cm³ or m³). A cuboid has six rectangular faces. A cube has six square faces, and all its edges are the same length.

Method. Multiply the length, the width and the height.

1. Write the formula. Volume = length times width times height.
   V = l × w × h
2. Multiply the length by the width. This gives the area of the base.
   7 × 3 = 21
3. Multiply by the height. This gives the number of cubes that fill the box.
   21 × 2 = 42
4. Write the answer. The volume is in cubic units.
   42

Check. Order does not matter: 2 × 3 × 7 = 42. ✓

Watch out. Volume is in cubic units, such as cm³. Multiply all three lengths in the same unit first.

Key words. The volume is the space inside a solid, in cubic units (cm³ or m³). A cuboid has six rectangular faces. A cube has six square faces, and all its edges are the same length.

Method. Find the volume in m³, then change it to cm³.

1. Multiply the three sides. A cube has three equal sides, so its volume is side times side times side.
   0.3 × 0.3 = 0.09, and 0.09 × 0.3 = 0.027 m³
2. Change m³ to cm³. 1 m³ = 1 000 000 cm³, so multiply by 1 000 000.
   0.027 × 1 000 000 = 27000
3. Write the answer. The volume is in cm³.
   27000

Check. 27000 ÷ 1000000 = 0.027 m³. ✓

Watch out. Change the volume to cm³ at the end. A cubic metre holds a million cubic centimetres.

Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.

Method. Find how many m make one km, then multiply by that number.

1. Find how many m make one km. The table says 1 km = 1000 m.
   1 km = 1000 m
2. Multiply by 1000. The answer is in m, which is smaller than km, so there are more m. Multiplying makes the number bigger.
   3.875 × 1000 = 3875
3. Write the answer. Moving the decimal point 3 places to the right gives the answer in m.
   3875

Check. 3875 ÷ 1000 = 3.875, the number we started with. ✓

Watch out. A smaller unit gives a bigger number, so multiply. Move the decimal point to the right.

Key words. There are 60 minutes in 1 hour and 60 seconds in 1 minute. A decimal hour uses a decimal point: 30 minutes is 0.5 hours, because 30 is half of 60.

Method. Multiply the hours by 60 to get minutes.

1. Remember: 1 hour = 60 minutes. So each hour gives 60 minutes.
   1 h = 60 min
2. Multiply the hours by 60. This gives the number of minutes.
   2.75 × 60 = 165
3. Write the answer. The answer is in minutes.
   165

Check. 165 ÷ 60 = 2.75 hours. ✓

Watch out. Multiply by 60 to go from hours to minutes. Do not multiply by 100.

Key words. To convert means to change a measure into another unit. Kilo means 1000, so 1 km = 1000 m. Centi means one hundredth, so 1 m = 100 cm. Milli means one thousandth, so 1 m = 1000 mm.

Method. Find how many mm make one m, then multiply by that number.

1. Find how many mm make one m. The table says 1 m = 1000 mm.
   1 m = 1000 mm
2. Multiply by 1000. The answer is in mm, which is smaller than m, so there are more mm. Multiplying makes the number bigger.
   2.4 × 1000 = 2400
3. Write the answer. Moving the decimal point 3 places to the right gives the answer in mm.
   2400

Check. 2400 ÷ 1000 = 2.4, the number we started with. ✓

Watch out. A smaller unit gives a bigger number, so multiply. Move the decimal point to the right.

Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.

Method. Multiply the base by the perpendicular height. Do not use the slanted side.

1. Find the base and the perpendicular height. The height goes straight up from the base. The slanted side is not the height.
   base = 14 cm, perpendicular height = 6 cm (the slanted side, 9 cm, is not used)
2. Multiply the base by the perpendicular height. The area of a parallelogram is base times perpendicular height.
   14 × 6 = 84
3. Write the answer. The area is in square centimetres.
   84

Check. Cut the triangle off one end and move it to the other: a rectangle 14 cm by 6 cm has the same area, 84 cm². ✓

Watch out. Use the vertical height, not the slanted side. The slanted side is always longer than the height.

Key words. The area is the space inside a flat shape, in square units (cm²). The perpendicular height is measured straight up from the base, at a right angle to it. It is not the slanted side.

Method. Multiply the base by the height, then divide by 2.

1. Find the base and the perpendicular height. The height is the straight line from the top corner to the base, at a right angle.
   base = 13 cm, perpendicular height = 8 cm
2. Multiply the base by the height. Two copies of the triangle make a parallelogram with the same base and height.
   13 × 8 = 104
3. Halve the answer. One triangle is half of the parallelogram.
   104 ÷ 2 = 52
4. Write the answer. The area is in square centimetres.
   52

Check. Two of these triangles make a parallelogram with area 104 cm², so one triangle is 104 ÷ 2 = 52. ✓

Watch out. Do not forget the divide by 2. A triangle is half of a rectangle with the same base and height.

Key words. 1 mile is about 1.6 kilometres (1 mile ≈ 1.6 km). The sign ≈ means "is about equal to".

Method. Multiply the miles by 1.6, because 1 mile is about 1.6 km.

1. Use the rule: 1 mile is about 1.6 km. So we multiply the miles by 1.6 to get kilometres.
   1 mile ≈ 1.6 km
2. Multiply the miles by 1.6. It is easier to multiply by 16 and then divide by 10.
   36 × 16 = 576, then 576 ÷ 10 = 57.6
3. Write the answer. The answer is in kilometres.
   57.6

Check. 57.6 ÷ 1.6 = 36 miles. ✓

Watch out. Miles to kilometres: multiply. Kilometres to miles: divide. Do not divide when you go from miles to kilometres.

Key words. The volume is the space inside a solid, in cubic units (cm³ or m³). A cuboid has six rectangular faces. A cube has six square faces, and all its edges are the same length.

Method. Divide the volume by the area of the base to find the height.

1. Write the formula with the missing height. Volume = length times width times height.
   200 = 8 × 5 × h
2. Multiply the length and the width. This is the area of the base.
   8 × 5 = 40
3. Divide the volume by the area of the base. This undoes the multiplication by the height.
   200 ÷ 40 = 5
4. Write the answer. The height is in the same unit as the other lengths.
   5

Check. 40 × 5 = 200. ✓

Watch out. Divide the volume by the base area. Do not divide by the length alone.

Key words. The perimeter is the total distance all the way round the outside of a shape. Add the lengths of all the outside sides.

Method. List the rectangles with this area, work out each perimeter, and choose the smallest.

1. Find every pair of whole-number sides that multiply to make the area. The sides must multiply to 48.
   1 × 48, 2 × 24, 3 × 16, 4 × 12, 6 × 8
2. Find the perimeter of each rectangle. Perimeter = 2 times (length + width).
   1 × 48: 2 × (1 + 48) = 98 ; 2 × 24: 2 × (2 + 24) = 52 ; 3 × 16: 2 × (3 + 16) = 38 ; 4 × 12: 2 × (4 + 12) = 32 ; 6 × 8: 2 × (6 + 8) = 28
3. Choose the smallest perimeter. The smallest number in the list is the answer.
   The smallest is 28
4. Write the answer. The perimeter is in centimetres.
   28

Check. Every pair was checked, so no rectangle is missed. ✓

Watch out. A square has the smallest perimeter for its area. Rectangles that are long and thin have big perimeters.

Key words. The volume is the space inside a solid, in cubic units (cm³ or m³). A cuboid has six rectangular faces. A cube has six square faces, and all its edges are the same length.

Method. Work out the volume in m³, then change it to cm³.

1. Multiply the three measurements. Multiply the decimals one pair at a time.
   1.2 × 0.5 = 0.6, and 0.6 × 0.8 = 0.48 m³
2. Change m³ to cm³. 1 m³ = 1 000 000 cm³.
   0.48 × 1 000 000 = 480000
3. Write the answer. The volume is in cm³.
   480000

Check. 480000 ÷ 1000000 = 0.48 m³. ✓

Watch out. Multiply the decimals carefully, then change the units. Count the decimal places.