Year 6 Arithmetic (SATs) Mental arithmetic: check-up and practice test questions

Method. Add the thousands, then the rest.

1. Split each number into thousands and the rest. 6,300 is 6,000 and 300; 2,850 is 2,000 and 850.
   6,000 + 300 and 2,000 + 850
2. Add the thousands. The thousands add first.
   6,000 + 2,000 = 8,000
3. Add the rest. Add the smaller parts.
   300 + 850 = 1150
4. Put the parts together. Add the two totals.
   8,000 + 1150 = 9,150
5. Write the answer.
   9,150

Check. About 6,000 + 3,000 = 9,000, close to 9,150. ✓

Method. Subtract a friendly number, then correct.

1. Round the number taken away to the nearest thousand. 3,400 is close to 3,000.
   3,400 ≈ 3,000
2. Subtract the rounded number. This is easier to work out.
   8,000 - 3,000 = 5,000
3. Correct the answer. 3,000 is 400 less than 3,400, so take 400 away.
   5,000 - 400 = 4,600
4. Write the answer.
   4,600

Check. 4,600 + 3,400 = 8,000. ✓

Method. Split 12 into 10 and 2.

1. Split the bigger number into 10 and the rest. 12 is 10 + 2.
   12 = 10 + 2
2. Multiply each part. 10 × 7 = 70 and 2 × 7 = 14.
   70 + 14
3. Add the parts. Add the two products.
   70 + 14 = 84
4. Write the answer.
   84

Check. 7 × 12 = 84. ✓

Method. Use the 9 times table.

1. Recall. 9 × 9 = 81.
   9
2. Write the answer.
   9

Check. 9 × 9 = 81. ✓

Method. Double each part.

1. Split and double. 4,000 + 600 + 50 doubled is 8,000 + 1,200 + 100.
   9,300
2. Write the answer.
   9,300

Check. 9,300 ÷ 2 = 4,650. ✓

Method. Think of 0.7 × 4 as seven tenths times 4.

1. Multiply. 7 × 4 = 28, so 0.7 × 4 = 2.8.
   2.8
2. Write the answer.
   2.8

Check. 2.8 ÷ 4 = 0.7. ✓

Method. Find one fifth, then take three.

1. Divide the amount by the bottom number. 60 ÷ 5 = 12.
   60 ÷ 5 = 12
2. Multiply by the top number. Take 3 of those parts.
   12 × 3 = 36
3. Write the answer.
   36

Check. 12 × 5 = 60. ✓

Method. Add the two numbers.

1. Add. 480 + 250 = 730.
   730
2. Write the answer.
   730

Check. 730 - 250 = 480. ✓

Method. Round 39 to 40, then take away 5 from 200.

1. Estimate. 40 × 5 = 200.
   200
2. Correct. 200 - 5 = 195, because 39 is 1 less than 40.
   195
3. Write the answer.
   195

Check. 195 is close to 200. ✓

Method. Split one of the numbers into parts you know.

1. Split 18. 18 = 10 + 8.
   10 + 8
2. Multiply each part. 5 × 10 = 50 and 5 × 8 = 40.
   50 + 40
3. Add. 50 + 40 = 90.
   90
4. Write the answer.
   Split 18 into 10 and 8, then 5 × 10 = 50 and 5 × 8 = 40, so the total is 90.

Check. 5 × 18 = 90, and 90 ÷ 5 = 18. ✓

Method. Add the thousands, then the rest.

1. Add. 5,000 + 1,000 = 6,000 and 400 + 800 = 1,200.
   7,200
2. Write the answer.
   7,200

Check. About 5,000 + 2,000 = 7,000, close to 7,200. ✓

Method. Round 2,600 to 3,000, subtract, then correct.

1. Round the number taken away to the nearest thousand. 2,600 is close to 3,000.
   2,600 ≈ 3,000
2. Subtract the rounded number. This is easier to work out.
   7,000 - 3,000 = 4,000
3. Correct the answer. 3,000 is 400 more than 2,600, so add 400 back.
   4,000 + 400 = 4,400
4. Write the answer.
   4,400

Check. 4,400 + 2,600 = 7,000. ✓

Method. Use the times table fact.

1. Split the bigger number into 10 and the rest. 11 is 10 + 1.
   11 = 10 + 1
2. Multiply each part. 10 × 8 = 80 and 1 × 8 = 8.
   80 + 8
3. Add the parts. Add the two products.
   80 + 8 = 88
4. Write the answer.
   88

Check. 8 × 11 = 88. ✓

Method. Split 1.5 into 1 and 0.5.

1. Split. 1 × 6 = 6 and 0.5 × 6 = 3.
   6 + 3
2. Add. 6 + 3 = 9.
   9
3. Write the answer.
   9

Check. 9 ÷ 6 = 1.5. ✓

Method. Find one eighth of 40, then take three eighths.

1. Divide the amount by the bottom number. 40 ÷ 8 = 5.
   40 ÷ 8 = 5
2. Multiply by the top number. Take 3 of those parts.
   5 × 3 = 15
3. Write the answer.
   15

Check. 15 × 8 = 120 and 40 ÷ 8 = 5, so 3 × 5 = 15. ✓

Method. Subtract the number in Key Stage 2 from the total.

1. Subtract. 2,450 - 1,380. Round 1,380 to 1,400, then take away 1,400 to get 1,050, and add 20 back.
   1,070
2. Write the answer.
   1,070

Check. 1,070 + 1,380 = 2,450. ✓

Method. Double first, then subtract.

1. Double. 3,000 × 2 = 6,000.
   6,000
2. Subtract. 6,000 - 1,500 = 4,500.
   4,500
3. Write the answer.
   4,500

Check. 4,500 + 1,500 = 6,000. ✓

Method. Split 10.5 into 10 and 0.5.

1. Split. 10 × 4 = 40 and 0.5 × 4 = 2.
   40 + 2
2. Add. 40 + 2 = 42.
   42
3. Write the answer.
   42

Check. 42 ÷ 4 = 10.5. ✓

Method. Add 1,000, then take away 100.

1. Add 1,000. 9,350 + 1,000 = 10,350.
   10,350
2. Take away 100. 10,350 - 100 = 10,250.
   10,250
3. Write the answer.
   10,250

Check. 10,250 + 100 - 1,000 = 9,350. ✓

Method. Split 20 into 2 and 10.

1. Split. 20 = 2 × 10.
   2 × 10
2. Multiply. 25 × 10 = 250, then × 2 = 500.
   500
3. Write the answer.
   Yes, because 25 × 20 = 500, found by doubling 250.

Check. 500 ÷ 25 = 20. ✓