Year 6 Maths reasoning (SATs): Missing numbers, equations and pairs

Method. Subtract the known number from the total.

1. Write the number sentence. 37 + b = 100.
   37 + b = 100
2. Find the missing number. Take 37 from 100.
   b = 100 - 37
3. Write the answer.
   63

Check. 37 + 63 = 100. ✓

Method. Subtract the known number from the total.

1. Write the number sentence. 19 + b = 56.
   19 + b = 56
2. Find the missing number. Take 19 from 56.
   b = 56 - 19
3. Write the answer.
   37

Check. 19 + 37 = 56. ✓

Method. Write an equation with n, then solve it by undoing the operations.

1. Write the equation. Let the number be n. Multiply by 2, add 9, and get 33.
   2n + 9 = 33
2. Subtract the added number. Take 9 from 33.
   2n = 24
3. Divide by the multiplier. Divide 24 by 2.
   n = 12
4. Write the answer.
   12

Check. 2 x 12 + 9 = 33. ✓

Watch out. Undo the operations in reverse order.

Method. Write an equation with n, then solve it by undoing the operations.

1. Write the equation. Let the number be n. Multiply by 5, add 4, and get 39.
   5n + 4 = 39
2. Subtract the added number. Take 4 from 39.
   5n = 35
3. Divide by the multiplier. Divide 35 by 5.
   n = 7
4. Write the answer.
   7

Check. 5 x 7 + 4 = 39. ✓

Watch out. Undo the operations in reverse order.

Method. Use inverse operations: subtract, then divide.

1. Undo the addition. Take 7 from both sides.
   3x = 31 - 7 = 24
2. Undo the multiplication. Divide both sides by 3.
   x = 24 / 3 = 8
3. Write the answer.
   8

Check. 3 x 8 + 7 = 31. ✓

Watch out. Undo the addition or subtraction first, then the multiplication.

Method. Use inverse operations: subtract, then divide.

1. Undo the addition. Take -6 from both sides.
   6x = 18 - -6 = 24
2. Undo the multiplication. Divide both sides by 6.
   x = 24 / 6 = 4
3. Write the answer.
   4

Check. 6 x 4 - 6 = 18. ✓

Watch out. Undo the addition or subtraction first, then the multiplication.

Method. Use inverse operations: subtract, then divide.

1. Undo the addition. Take 1 from both sides.
   2x = 23 - 1 = 22
2. Undo the multiplication. Divide both sides by 2.
   x = 22 / 2 = 11
3. Write the answer.
   11

Check. 2 x 11 + 1 = 23. ✓

Watch out. Undo the addition or subtraction first, then the multiplication.

Method. List the pairs systematically, starting with the smallest value of a.

1. List the pairs with a smaller than b. Start with a = 1 and count up, so a is always less than b.
   1 + 11, 2 + 10, 3 + 9, 4 + 8, 5 + 7
2. Count the pairs. Each pair is one answer.
   5 pairs
3. Write the answer.
   5

Check. Each pair adds to 12. ✓

Watch out. Do not count the pair where a = b, and do not count a pair twice.

Method. List the pairs systematically, starting with the smallest value of a.

1. List the pairs with a smaller than b. Start with a = 1 and count up, so a is always less than b.
   1 + 14, 2 + 13, 3 + 12, 4 + 11, 5 + 10, 6 + 9, 7 + 8
2. Count the pairs. Each pair is one answer.
   7 pairs
3. Write the answer.
   7

Check. Each pair adds to 15. ✓

Watch out. Do not count the pair where a = b, and do not count a pair twice.

Method. Test each choice against the question.

1. Read what the question asks. Decide what the answer must do or show.
2. Test the choice. 6 + 9 = 15 and 9 - 6 = 3.
   6 and 9 fits
3. Reject the other choices. 5 + 10 = 15 but the difference is 5; 7 + 9 = 16, so it is not 15.
   5 and 10 and 7 and 9 do not fit
4. Write the answer.
   6 and 9

Check. 6 and 9 is the one that fits. ✓

Method. Test each option.

1. Check each option. Test each one against the rule or the calculation.
2. Tick the true ones. In each ticked pair, the two numbers add to 12.
   (3, 9), (4, 8)
3. Leave the others unticked. These do not match.
   (5, 6), (10, 1) are not ticked
4. Write the answer.
   (3, 9), (4, 8)

Check. Each ticked option is true. ✓

Watch out. (5, 6) adds to 11 and (10, 1) adds to 11, so they are not ticked.

Method. Start with the smallest value and count up.

1. List in order. 0 + 10, 1 + 9, 2 + 8, and so on.
   0 + 10
2. Check none are missing. Each pair appears once, so the list is complete.
   complete
3. Write the answer.
   It lists the pairs in order, starting with 0 and 10, so that every pair appears once and none are missed.

Check. Every pair adds to 10. ✓

Method. Write the equation, then undo the operations.

1. Equation. 2(n + 7) = 34, or 2n + 14 = 34.
   2n + 14 = 34
2. Undo the addition. 2n = 34 - 14 = 20.
   2n = 20
3. Undo the multiplication. n = 20 / 2 = 10.
   10
4. Write the answer.
   10

Check. 2 x (10 + 7) = 34. ✓

Method. Add 4 to both sides, then divide by 5.

1. Add 4. 5x = 26 + 4 = 30.
   30
2. Divide by 5. x = 30 / 5 = 6.
   6
3. Write the answer.
   6

Check. 5 x 6 - 4 = 26. ✓

Method. Subtract the known number from the total.

1. Write the number sentence. 45 + b = 81.
   45 + b = 81
2. Find the missing number. Take 45 from 81.
   b = 81 - 45
3. Write the answer.
   36

Check. 45 + 36 = 81. ✓