Year 6 SATs Maths Revision: check-up and SATs-style questions

Method. Use the column method, one digit at a time, and check with an estimate.

1. Multiply by the ones digit. Write 8 under the ones, and multiply the whole number by it.

       405
      × 28
   -------
     3,240
   + 8,100
   -------
    11,340

   405 × 8 = 3240
2. Multiply by the tens digit, using a 0 place holder. The tens digit is worth ten times more, so write a 0 first.
   405 × 2 = 810, then 810 × 10 = 8100
3. Add the two rows. Add the partial products to find the total.
   3240 + 8100 = 11,340
4. Write the answer. This is the product.
   11,340

Check. Estimate: 400 × 30 = 12,000. The exact answer 11,340 is close to the estimate. ✓

Watch out. Keep each column lined up. Multiply the tens row by 10 by writing a 0 first.

Key words. To round, look at the digit just after the place you are rounding to. If it is 5 or more, round up. If it is less than 5, round down.

Method. Look at the digit after the hundreds place, then keep the digits up to that place and make the rest zeros.

1. Look at the digit after the hundreds place. That digit decides whether to round up or down.
   the digit is 8
2. Decide whether to round up or down. 8 is 5 or more, so round up.
   round up
3. Write the answer. Keep the digits before the hundreds place and write 0 in the places after it.
   3,600

Check. 3,600 is a multiple of 100, and it is the closest one to 3,582. ✓

Watch out. Do not just cut the digits off. Look at the digit after the hundreds place first.

Key words. A factor divides exactly into a number. A multiple is in the times table of a number. A prime number has exactly two factors, 1 and itself. The highest common factor (HCF) is the biggest factor two numbers share, and the lowest common multiple (LCM) is the smallest multiple they share.

Method. List the multiples of each number, and find the smallest one that is on both lists.

1. List the multiples of 4. Multiply the number by 1, 2, 3 and so on.
   4, 8, 12, 16, 20, 24 ...
2. List the multiples of 6. Do the same for the other number.
   6, 12, 18, 24 ...
3. Find the smallest multiple on both lists. The first number that appears on both lists is the lowest common multiple.
   smallest common multiple = 12

Check. 12 ÷ 4 = 3 and 12 ÷ 6 = 2, so 12 is a multiple of both. ✓

Watch out. Do not stop at a number that is only on one list. Check both lists before you choose.

Key words. A simplified fraction is in its lowest terms. A mixed number has a whole part and a fraction part. An improper fraction has a top number that is bigger than its bottom number.

Method. Make the bottom numbers the same, then add or subtract the top numbers.

1. Find a common bottom number. The lowest common multiple of 3 and 5 is 15, so both fractions can use 15 as the bottom number.
   3 and 5: lowest common multiple = 15
2. Change both fractions to have the same bottom number. Multiply the top and bottom of each fraction by the same number.
   2/3 = 10/15, and 1/5 = 3/15
3. Subtract the top numbers. The bottom number stays the same.
   10 − 3 = 7, so 7/15
4. Simplify the answer. Divide the top and bottom by the same number to get the lowest terms.
   7/15 is already in its simplest form, so 7/15

Check. Both forms are the same amount: 7/15 is equal to 7/15. ✓

Watch out. Only add the top numbers. The bottom number stays the same when the fractions are added.

Key words. Per cent means out of 100. So 35 per cent means 35 out of 100, which is 0.35 as a decimal and 35/100 as a fraction.

Method. Find 1 per cent of the amount, then multiply it by the number of per cent.

1. Write the per cent and the amount. Per cent means out of 100.
   20 per cent of £65.00
2. Find 1 per cent. Per cent means out of 100, so divide the amount by 100.
   £65.00 ÷ 100 = £0.65
3. Multiply by 20. 20 per cent is 20 lots of 1 per cent.
   £0.65 × 20 = £13.00

Check. Check: £13.00 ÷ £65.00 = 0.2, which is 20 out of 100. ✓

Watch out. Divide by 100 first, then multiply. Do not multiply by 100.

Key words. A ratio compares two amounts, such as 2:3. A part is one of the equal shares in the ratio. A scale factor is the number you multiply by to make a shape bigger or smaller.

Method. Add the parts, share the total into one part, then multiply each share by its number of parts.

1. Add the parts of the ratio. The ratio 5:3 has 8 equal parts altogether.
   5 + 3 = 8
2. Find the value of one part. Share the total equally between all the parts.
   96 ÷ 8 = 12
3. Multiply each share by its number of parts. The first share has 5 parts and the second has 3 parts.
   5 × 12 = 60, and 3 × 12 = 36
4. Write the answer.
   60 and 36

Check. 60 + 36 = 96, so the shares add up to the total. ✓

Watch out. Share the total into all the parts, not just between two shares.

Key words. The perimeter is the distance round the outside of a shape. The area is the space inside it, in square units. The volume is the space inside a solid, in cubic units.

Method. Multiply the length, width and height together.

1. Write the formula. The volume of a cuboid is length times width times height.
   volume = length × width × height
2. Multiply the first two numbers. Find the area of the base first.
   7 × 2 = 14
3. Multiply by the height. Each layer has this many cubes, and there are this many layers.
   14 × 3 = 42

Check. Count the layers: there are 3 layers of 14 cubes, which is 42. ✓

Watch out. The answer is in cubic units, such as cm³, not in square units.

Key words. The perimeter is the distance round the outside of a shape. The area is the space inside it, in square units. The volume is the space inside a solid, in cubic units.

Method. Add the hours and the minutes separately, and carry any 60 minutes into an hour.

1. Write the start time and the length of time. Use the start time, then add the time that passes.
   14:50 + 2 h 40 min
2. Add the hours. Add the whole hours first.
   14 + 2 = 16 hours
3. Add the minutes. If the minutes are 60 or more, take 60 away and add 1 more hour.
   50 + 40 = 90 minutes, which is 1 hour and 30 minutes
4. Write the finishing time. Give the time on the 24-hour clock with two digits for the hours and minutes.
   17:30

Check. Count on: 2 hours and 40 minutes after 14:50 reaches 17:30. ✓

Watch out. There are 60 minutes in an hour, not 100. Do not add the hours and minutes as one number.

Key words. Angles on a straight line add up to 180 degrees. Angles at a point add up to 360 degrees. Angles in a triangle add up to 180 degrees, and in a quadrilateral they add up to 360 degrees.

Method. Find the total of the interior angles, then share it equally between the angles of the regular shape.

1. Write the number of sides. A regular shape has the same number of sides and angles.
   n = 10 sides
2. Find the total of the interior angles. A shape with 10 sides can be split into 8 triangles, and each triangle has 180 degrees.
   (10 − 2) × 180 = 1440°
3. Share the total equally. A regular shape has 10 angles that are all the same.
   1440 ÷ 10 = 144

Check. 144 × 10 = 1440, so the answer is right. ✓

Watch out. Use the number of sides minus 2, not the number of sides, when you find the total.

Key words. A pie chart shows a whole split into sectors. A sector is one slice of the pie. The whole pie is 360 degrees, and it is also 100 per cent.

Method. Write the sector as a fraction of the total, then multiply by 100.

1. Write the sector as a fraction of the total. Bus is 24 out of 60.
   24 ÷ 60 = 2/5
2. Change it to per cent. Per cent means out of 100.
   2/5 × 100 = 40

Check. 40 per cent of 60 is 24. ✓

Watch out. Per cent is out of 100.

Key words. The sum is the answer to an addition. A carry is the 1 ten (or 1 hundred) we move into the next column. The difference is the answer to a subtraction.

Method. Add the columns from the right, and carry any 1 ten into the next column.

1. Add the ones column. Add the two digits, and the carried number if there is one.
   7 + 5 = 12, so write 2 and carry 1
2. Add the tens column. Add the two digits, and the carried number if there is one.
   0 + 4 + 1 carried = 5, so write 5
3. Add the hundreds column. Add the two digits, and the carried number if there is one.
   1 + 8 = 9, so write 9
4. Add the thousands column. Add the two digits, and the carried number if there is one.
   5 + 2 = 7, so write 7
5. Write the answer. Read the column answers from left to right.
   7,952

Check. 7,952 − 2,845 = 5,107, so the sum is right. ✓

Watch out. Carry the 1 into the next column. Do not forget it, and do not write it in the same column.

Key words. Per cent means out of 100. So 35 per cent means 35 out of 100, which is 0.35 as a decimal and 35/100 as a fraction.

Method. Divide the top number by the bottom number.

1. Write the division. A fraction line means divide the top by the bottom.
   7 ÷ 20
2. Do the division. Add a decimal point and zeros until the division ends.
   7 ÷ 20 = 0.35

Check. 0.35 × 20 = 7, so the decimal is right. ✓

Watch out. Keep adding zeros after the decimal point until the division ends.

Key words. The value of a digit is the digit times its place value. In 4,250, the 2 is in the hundreds place, so its value is 200.

Method. Find the column of the digit, then multiply the digit by the value of that column.

1. Write the number in columns. Each digit sits in a column, with the ones on the right.
   1,070,482
2. Find the ten thousands column. Count from the right: ones, tens, hundreds, and so on.
   1,070,482: the ten thousands column has the digit 7
3. Multiply the digit by the place value. The value of a digit is the digit times the value of its column.
   7 × 10,000 = 70,000

Check. The other digits keep their own values, so this digit is worth 70,000 and no more. ✓

Watch out. The digit is worth its column value, not just the digit. A 6 in the thousands is worth 6,000.

Method. Use the column method, one digit at a time, and check with an estimate.

1. Multiply by the ones digit. Write 4 under the ones, and multiply the whole number by it.

      36
    × 24
   -----
     144
   + 720
   -----
     864

   36 × 4 = 144
2. Multiply by the tens digit, using a 0 place holder. The tens digit is worth ten times more, so write a 0 first.
   36 × 2 = 72, then 72 × 10 = 720
3. Add the two rows. Add the partial products to find the total.
   144 + 720 = 864
4. Write the answer. This is the product.
   864

Check. Estimate: 40 × 20 = 800. The exact answer 864 is close to the estimate. ✓

Watch out. Keep each column lined up. Multiply the tens row by 10 by writing a 0 first.

Key words. A ratio compares two amounts, such as 2:3. A part is one of the equal shares in the ratio. A scale factor is the number you multiply by to make a shape bigger or smaller.

Method. Divide the known amount by its parts to find one part, then multiply one part by the other number of parts.

1. Find the value of one part. The second amount is 5 parts, so divide it by 5.
   35 ÷ 5 = 7
2. Find the first amount. The first amount is 2 parts, so multiply the value of one part by 2.
   2 × 7 = 14

Check. The two amounts keep the ratio 2:5, because 14 : 35 = 2:5. ✓

Watch out. Find one part first. Do not just multiply the known amount by the ratio.

Key words. A pie chart shows a whole split into sectors. A sector is one slice of the pie. The whole pie is 360 degrees, and it is also 100 per cent.

Method. Find the fraction of the whole pie, then take that fraction of 360 degrees.

1. Write the sector and the total. The sector is one part of the whole pie.
   Dogs: 45 out of 60
2. Write the sector as a fraction of the total. Dogs is 45 out of 60.
   45 ÷ 60 = 3/4
3. Multiply by 360 degrees. The whole pie is 360 degrees.
   3/4 × 360 = 270

Check. All the sectors must add up to 360 degrees. ✓

Watch out. Use 360 degrees for the whole pie, not 100.