Year 6 Maths reasoning (SATs) Number reasoning: check-up and practice test questions

Method. Find the column, then multiply the digit by its column value.

1. Find the column of the digit. The digit 5 is in the thousands column.
   thousands
2. Work out the value. The value is the digit times the column value 1,000.
   5 x 1,000 = 5,000
3. Write the answer.
   5,000

Check. 5,000 = 5 x 1,000. ✓

Watch out. The value of a digit depends on its column, not just on the digit.

Method. Look at the digit next to the rounding column.

1. Find the rounding column and the digit next to it. Rounding to the nearest 100 looks at the tens digit.
   digit to check = 5
2. Decide up or down. A 5 or more rounds up; 4 or less rounds down.
   5 is 5 or more, so round up
3. Write the rounded number. Keep the digits to the left and make the rest zeros.
   8,400
4. Write the answer.
   8,400

Check. 8,400 is a multiple of 100 and is the closest one to 8,359. ✓

Watch out. Do not round a 5 down. A 5 always rounds up.

Method. Brackets, then multiply, then subtract.

1. Brackets. 6 + 4 = 10.
   10
2. Multiply. 9 x 10 = 90.
   90
3. Subtract. 90 - 15 = 75.
   75
4. Write the answer.
   75

Check. 90 - 15 = 75. ✓

Method. Count up 12 from -7.

1. Count to zero. From -7 to 0 is 7 steps.
   7 steps
2. Count on. 12 - 7 = 5.
   5
3. Write the answer.
   5

Check. -7 + 12 = 5. ✓

Method. Find the factors of 30, then keep the ones that are multiples of 5.

1. Factors of 30. 1, 2, 3, 5, 6, 10, 15, 30.
   1, 2, 3, 5, 6, 10, 15, 30
2. Keep the multiples of 5. Numbers in the 5 times table are 5, 10, 15 and 30.
   5, 10, 15, 30
3. Write the answer.
   5, 10, 15, 30

Check. Each of 5, 10, 15 and 30 divides 30. ✓

Method. Compare the digits, starting from the left.

1. Count the digits in each number. A number with more digits is larger.
   3,050 has 4 digits, 30,500 has 5 digits, 3,005 has 4 digits, 35,000 has 5 digits
2. Compare numbers with the same number of digits. Look at the leading digit, then the next one.
   compare from the left
3. Write them in order. Put them smallest to largest.
   3,005, 3,050, 30,500, 35,000
4. Write the answer.
   3,005, 3,050, 30,500, 35,000

Check. Each number is smaller than the one after it. ✓

Watch out. 4,500 has four digits and 45,000 has five, so 45,000 is larger.

Method. Divide and multiply first, then add.

1. Divide. 144 / 12 = 12.
   12
2. Multiply. 3 x 4 = 12.
   12
3. Add. 12 + 12 = 24.
   24
4. Write the answer.
   24

Check. 12 + 12 = 24. ✓

Method. Take away the Year 6 pupils.

1. Choose the operation. Other years = total minus Year 6.
   642 - 185
2. Work it out. 642 - 185 = 457.
   457
3. Write the answer.
   457

Check. 457 + 185 = 642. ✓

Method. Check the numbers 51 to 59 for factors other than 1 and themselves.

1. Test 51. 51 = 3 x 17, so it is not prime.
   no
2. Test 53. 53 is not in the 2, 3, 5 or 7 times tables.
   53 is prime
3. Write the answer.
   53

Check. 53 has only the factors 1 and 53. ✓

Method. Compare a number and its negative partner.

1. Pick a number. Use 4.
   4
2. Compare. 4 is above zero, -4 is below zero.
   4 > -4
3. Write the answer.
   Yes, because 4 is above zero and -4 is below zero, so 4 is bigger than -4.

Check. 4 > -4. ✓

Method. Add the two totals.

1. Add. 2,450 + 3,890.
   2,450 + 3,890
2. Write the total. Add the thousands, hundreds, tens and units.
   6,340
3. Write the answer.
   6340

Check. 6,340 - 3,890 = 2,450. ✓

Method. Find the column, then multiply the digit by its column value.

1. Find the column of the digit. The digit 5 is in the hundred thousands column.
   hundred thousands
2. Work out the value. The value is the digit times the column value 100,000.
   5 x 100,000 = 500,000
3. Write the answer.
   500,000

Check. 500,000 = 5 x 100,000. ✓

Watch out. The value of a digit depends on its column, not just on the digit.

Method. Look at the digit next to the rounding column.

1. Find the rounding column and the digit next to it. Rounding to the nearest 10,000 looks at the thousands digit.
   digit to check = 4
2. Decide up or down. A 5 or more rounds up; 4 or less rounds down.
   4 is 4 or less, so round down
3. Write the rounded number. Keep the digits to the left and make the rest zeros.
   260,000
4. Write the answer.
   260,000

Check. 260,000 is a multiple of 10,000 and is the closest one to 264,850. ✓

Watch out. Do not round a 5 down. A 5 always rounds up.

Method. Add two million.

1. Add. 4,375,210 + 2,000,000.
   6,375,210
2. Write the answer.
   6375210

Check. 6,375,210 - 2,000,000 = 4,375,210. ✓

Method. Count down 5 from -2.

1. Count down. -2 - 5 = -7.
   -7
2. Write the answer.
   -7

Check. -7 + 5 = -2. ✓

Method. Divide and multiply first, then add and subtract.

1. Divide. 20 / 4 = 5.
   5
2. Multiply. 5 x 3 = 15.
   15
3. Add and subtract. 5 + 15 - 1 = 19.
   19
4. Write the answer.
   19

Check. 5 + 15 - 1 = 19. ✓

Method. List multiples of 4 and 10 until one is in both lists.

1. Multiples of 4. 4, 8, 12, 16, 20.
   4, 8, 12, 16, 20
2. Multiples of 10. 10, 20.
   10, 20
3. Find the first shared one. 20 is in both lists.
   20
4. Write the answer.
   20

Check. 20 / 4 = 5 and 20 / 10 = 2. ✓

Method. Find the total seats first, then take away the seats sold.

1. Total seats. 24 x 36 = 864.
   864
2. Empty seats. 864 - 700 = 164.
   164
3. Write the answer.
   164

Check. 700 + 164 = 864. ✓

Method. Recall the rule for a prime.

1. Recall the rule. A prime has exactly two factors: 1 and itself.
   two factors
2. Test 1. 1 has only the factor 1, so it has one factor.
   one factor only
3. Write the answer.
   1 has only one factor, so it does not have exactly two factors.

Check. 1 has one factor, not two. ✓

Method. Test each option.

1. Check each option. Test each one against the rule or the calculation.
2. Tick the true ones. A number in both the 3 and the 4 times tables is a multiple of 12.
   12, 24
3. Leave the others unticked. These do not match.
   6, 18, 30 are not ticked
4. Write the answer.
   12, 24

Check. Each ticked option is true. ✓

Watch out. 6, 18 and 30 are not in the 4 times table, so they are not ticked.

Method. Look at the tens digit.

1. Look at the tens digit. The tens digit is 4, so round down.
   4 is 4 or less
2. Write the answer. 6,200 is the rounded number.
   6,200
3. Write the answer.
   6,200

Check. 6,200 is the nearest hundred to 6,249. ✓

Method. Smallest means the smallest digit first, but not zero first.

1. Choose the first digit. Zero cannot be first in a four-digit number, so use 3.
   3
2. Put the rest in order. Put 0, 5 and 7 in order.
   0, 5, 7
3. Write the number. The smallest is 3,057.
   3,057
4. Write the answer.
   3,057.

Check. 3,057 uses each digit once. ✓