Year 6 Maths reasoning (SATs) Measures in context: check-up and practice test questions

Method. Find the number of smaller units in one bigger unit, then multiply or divide.

1. Find how many g make one kg. There are 1000 g in 1 kg.
   1 kg = 1000 g
2. Multiply by 1000. Changing to a smaller unit needs more of them, so the number gets bigger: multiply.
   4.25 x 1000 = 4250
3. Write the answer with the new unit. Keep the same measure, in the new unit.
   4250 g
4. Write the answer.
   4250 g

Check. 4250 g is the same length, mass or volume as 4.25 kg. ✓

Watch out. Going from a bigger unit to a smaller one makes the number bigger.

Method. Find the number of smaller units in one bigger unit, then multiply or divide.

1. Find how many ml make one l. There are 1000 ml in 1 l.
   1 l = 1000 ml
2. Divide by 1000. Changing to a bigger unit needs fewer of them, so the number gets smaller: divide.
   3600 / 1000 = 3.6
3. Write the answer with the new unit. Keep the same measure, in the new unit.
   3.6 l
4. Write the answer.
   3.6 l

Check. 3.6 l is the same length, mass or volume as 3600 ml. ✓

Watch out. Going from a bigger unit to a smaller one makes the number bigger.

Method. Find the difference between the two times in minutes, then change to hours and minutes.

1. Change both times to minutes past midnight. 15:30 is 930 minutes and 17:05 is 1025 minutes.
   930 and 1025
2. Subtract the start from the end. 1025 - 930 = 95 minutes.
   95 minutes
3. Change back to hours and minutes. 95 minutes is 1 hour(s) and 35 minutes.
   1 h 35 min
4. Write the answer.
   1 h 35 min

Check. 15:30 + 1 h 35 min = 17:05. ✓

Watch out. Do not count 60 minutes as 100 when you change between hours and minutes.

Method. Multiply by the approximate conversion factor, then round.

1. Use the approximate rule: 1 mile is about 1.6 km. The rule is only an estimate, so the answer is about this amount.
   15 miles x 1.6 = 24.00
2. Round to the nearest whole number. Round to the nearest whole number for a sensible answer.
   about 24 km
3. Write the answer.
   about 24 km

Check. 15 x 1.6 is about 24. ✓

Watch out. Imperial and metric conversions are approximate. Write about in your answer.

Method. Multiply the length by the width.

1. Write the formula. Area of a rectangle = length x width.
   14 x 9
2. Multiply. Multiply the length by the width.
   14 x 9 = 126
3. Write the units as square units. The area is measured in square cm.
   126 cm²
4. Write the answer.
   126 cm²

Check. 126 / 14 = 9. ✓

Watch out. Area is measured in square units, so the answer ends with a small 2, such as cm².

Method. Multiply the base by the height, then halve.

1. Write the formula. Area of a triangle = base x height / 2.
   12 x 5 / 2
2. Multiply the base and the height. Multiply first.
   12 x 5 = 60
3. Halve the answer. A triangle is half of a rectangle with the same base and height.
   60 / 2 = 30
4. Write the answer. Square units for area.
   30 m²
5. Write the answer.
   30 m²

Check. A rectangle 12 by 5 has area 60, and half of it is 30. ✓

Watch out. Use the perpendicular height, not the slanted side.

Method. Multiply the base by the perpendicular height. No halving is needed.

1. Write the formula. Area of a parallelogram = base x perpendicular height.
   8 x 7
2. Multiply. Multiply the base by the perpendicular height.
   8 x 7 = 56
3. Write the answer. Square units for area.
   56 cm²
4. Write the answer.
   56 cm²

Check. A rectangle 8 by 7 has the same area. ✓

Watch out. A parallelogram is not halved, unlike a triangle with the same base and height.

Method. Split the shape into rectangles, find each area, then add.

1. Split the shape into two rectangles. Rectangle 1 is 7 cm by 3 cm; rectangle 2 is 5 cm by 2 cm.
   7 x 3 and 5 x 2
2. Find each area. Multiply the length and width of each rectangle.
   21 and 10
3. Add the areas. The total area is the sum of the two parts.
   21 + 10 = 31
4. Write the answer. Square units for area.
   31 cm²
5. Write the answer.
   31 cm²

Check. 21 + 10 = 31. ✓

Watch out. Check that the two rectangles do not overlap.

Method. Multiply the length, width and height.

1. Write the formula. Volume of a cuboid = length x width x height.
   5 x 4 x 3
2. Multiply. Multiply the three lengths.
   5 x 4 = 20, then 20 x 3 = 60
3. Write the units. Cubic units for volume.
   60 cm³
4. Write the answer.
   60 cm³

Check. 5 x 4 x 3 = 60. ✓

Watch out. Volume is measured in cubic units, so the answer ends with a small 3, such as cm³.

Method. List the pairs that multiply to the area, then find each perimeter.

1. List the whole-number pairs that multiply to the area. Each pair of sides gives area 18.
   1 x 18; 2 x 9; 3 x 6
2. Work out each perimeter. Perimeter = 2 x (length + width).
   1 by 18 gives 38; 2 by 9 gives 22; 3 by 6 gives 18
3. Choose the smallest perimeter. The smallest perimeter is the one with the sides closest in length.
   3 by 6 (perimeter 18)
4. Write the answer.
   3 by 6 (perimeter 18)

Check. The closest pair of sides gives the smallest perimeter. ✓

Watch out. The same area can have very different perimeters: a long thin rectangle has a bigger perimeter than a square.

Method. Find the number of smaller units in one bigger unit, then multiply or divide.

1. Find how many ml make one l. There are 1000 ml in 1 l.
   1 l = 1000 ml
2. Multiply by 1000. Changing to a smaller unit needs more of them, so the number gets bigger: multiply.
   0.3499999999999999777955395075 x 1000 = 349.9999999999999777955395075
3. Write the answer with the new unit. Keep the same measure, in the new unit.
   349.9999999999999777955395075 ml
4. Write the answer.
   349.9999999999999777955395075 ml

Check. 349.9999999999999777955395075 ml is the same length, mass or volume as 0.3499999999999999777955395075 l. ✓

Watch out. Going from a bigger unit to a smaller one makes the number bigger.

Method. Find the difference between the two times in minutes, then change to hours and minutes.

1. Change both times to minutes past midnight. 11:40 is 700 minutes and 13:15 is 795 minutes.
   700 and 795
2. Subtract the start from the end. 795 - 700 = 95 minutes.
   95 minutes
3. Change back to hours and minutes. 95 minutes is 1 hour(s) and 35 minutes.
   1 h 35 min
4. Write the answer.
   1 h 35 min

Check. 11:40 + 1 h 35 min = 13:15. ✓

Watch out. Do not count 60 minutes as 100 when you change between hours and minutes.

Method. Multiply by the approximate conversion factor, then round.

1. Use the approximate rule: 1 kg is about 2.2 pounds. The rule is only an estimate, so the answer is about this amount.
   12 kg x 2.2 = 26.40
2. Round to the nearest whole number. Round to the nearest whole number for a sensible answer.
   about 26 pounds
3. Write the answer.
   about 26 pounds

Check. 12 x 2.2 is about 26. ✓

Watch out. Imperial and metric conversions are approximate. Write about in your answer.

Method. Multiply the base by the height, then halve.

1. Write the formula. Area of a triangle = base x height / 2.
   14 x 9 / 2
2. Multiply the base and the height. Multiply first.
   14 x 9 = 126
3. Halve the answer. A triangle is half of a rectangle with the same base and height.
   126 / 2 = 63
4. Write the answer. Square units for area.
   63 cm²
5. Write the answer.
   63 cm²

Check. A rectangle 14 by 9 has area 126, and half of it is 63. ✓

Watch out. Use the perpendicular height, not the slanted side.

Method. Split the shape into rectangles, find each area, then add.

1. Split the shape into two rectangles. Rectangle 1 is 9 m by 4 m; rectangle 2 is 6 m by 2 m.
   9 x 4 and 6 x 2
2. Find each area. Multiply the length and width of each rectangle.
   36 and 12
3. Add the areas. The total area is the sum of the two parts.
   36 + 12 = 48
4. Write the answer. Square units for area.
   48 m²
5. Write the answer.
   48 m²

Check. 36 + 12 = 48. ✓

Watch out. Check that the two rectangles do not overlap.

Method. Multiply the length, width and height.

1. Write the formula. Volume of a cuboid = length x width x height.
   8 x 3 x 2
2. Multiply. Multiply the three lengths.
   8 x 3 = 24, then 24 x 2 = 48
3. Write the units. Cubic units for volume.
   48 cm³
4. Write the answer.
   48 cm³

Check. 8 x 3 x 2 = 48. ✓

Watch out. Volume is measured in cubic units, so the answer ends with a small 3, such as cm³.

Method. Add the journey time, then the break.

1. Add the journey. 08:20 + 1 h 50 min = 10:10.
   10:10
2. Add the break. 10:10 + 25 min = 10:35.
   10:35
3. Write the answer.
   10:35

Check. 10:35 - 08:20 = 2 h 15 min. ✓

Method. Change one length to the other unit.

1. Change metres to centimetres. 2 m = 2 x 100 cm = 200 cm.
   200 cm
2. Compare. The two lengths are the same.
   equal
3. Write the answer.
   Because 1 metre is 100 cm, so 2 metres is 2 x 100 = 200 cm.

Check. 2 x 100 = 200. ✓

Method. Divide the volume by the area of the base.

1. Use the volume formula. Volume = length x width x height, so length = volume / (width x height).
   length x 3 x 5 = 60
2. Find the length. 60 / (3 x 5) = 60 / 15 = 4 cm.
   4 cm
3. Write the answer.
   4

Check. 4 x 3 x 5 = 60. ✓

Method. List the pairs that multiply to 16.

1. List pairs. 1 x 16, 2 x 8 and 4 x 4 all make 16.
   16 square cm
2. Perimeters. 1 by 16 is 34 cm; 4 by 4 is 16 cm.
   34 cm and 16 cm
3. Write the answer.
   1 cm by 16 cm has a perimeter of 34 cm, and 4 cm by 4 cm has a perimeter of 16 cm.

Check. 2 x (1 + 16) = 34. ✓

Method. Multiply by the approximate conversion factor, then round.

1. Use the approximate rule: 1 mile is about 1.6 km. The rule is only an estimate, so the answer is about this amount.
   50 miles x 1.6 = 80.00
2. Round to the nearest whole number. Round to the nearest whole number for a sensible answer.
   about 80 km
3. Write the answer.
   about 80 km

Check. 50 x 1.6 is about 80. ✓

Watch out. Imperial and metric conversions are approximate. Write about in your answer.

Method. Change the height to centimetres, then divide.

1. Change to cm. 2 m = 200 cm.
   200 cm
2. Divide. 200 / 25 = 8 strips.
   8
3. Write the answer.
   8 strips

Check. 8 x 25 = 200. ✓