Year 6 Maths reasoning (SATs): Explaining patterns and checking terms

Method. Find the difference.

1. Difference. 12 - 15 = -3.
   -3
2. Rule. Each term is 3 less, so subtract 3.
   subtract 3
3. Write the answer.
   subtract 3

Check. 6 + 3 = 9. ✓

Method. Check whether the difference from the first term is a multiple of the difference.

1. Find the difference from the first term. 50 - 5 = 45.
   45
2. Divide by the difference. 45 / 3 = 15, a whole number.
   15
3. Decide. So 50 is term number 16.
   term 16
4. Write the answer.
   yes

Check. The terms are 5 + 3 x (whole number). ✓

Watch out. A number is in the sequence only if it can be reached by adding the difference repeatedly.

Method. Check whether the difference from the first term is a multiple of the difference.

1. Find the difference from the first term. 100 - 7 = 93.
   93
2. Check the division by the difference. 93 / 6 is not a whole number.
   not whole
3. Decide. The terms never land on 100.
   no
4. Write the answer.
   no

Check. The terms are 7 + 6 x (whole number). ✓

Watch out. A number is in the sequence only if it can be reached by adding the difference repeatedly.

Method. Check the difference from the first term.

1. Difference. 10 - 3 = 7.
   7
2. Divide. 7 / 4 is not a whole number, so 10 is not a term.
   not whole
3. Write the answer.
   no

Check. The terms go up by 4. ✓

Method. Test each option.

1. Check each option. Test each one against the rule or the calculation.
2. Tick the true ones. The difference is 3, so the 4th term is 11 and the 5th term is 14.
   It goes up by 3 each time, The 5th term is 14
3. Leave the others unticked. These do not match.
   The 4th term is 12, The difference is 4 are not ticked
4. Write the answer.
   It goes up by 3 each time, The 5th term is 14

Check. Each ticked option is true. ✓

Watch out. The 4th term is 11, not 12, and the difference is 3, not 4.

Method. Use first term + (n - 1) x difference.

1. Steps. The 10th term is 9 steps after 2.
   9 steps
2. Work out. 2 + 9 x 2 = 20, not 10.
   20
3. Write the answer.
   no

Check. 2 + 18 = 20. ✓

Method. Find the difference between each pair of neighbours.

1. Differences. 4 - 1 = 3, 9 - 4 = 5, 16 - 9 = 7.
   3, 5, 7
2. Decide. The differences are not the same, so it is not linear.
   not linear
3. Write the answer.
   Because the differences are 3, 5, 7, which are not equal.

Check. 3, 5 and 7 are not equal. ✓

Method. Check whether 50 is a multiple of 5 as the sequence goes down.

1. Difference from the first term. 58 - 8 = 50.
   50
2. Divide. 50 / -5 = -10 steps, which means 58 is before the first term, so it is not a term.
   no
3. Write the answer.
   no

Check. The sequence goes down from 8, so 58 is not reached. ✓

Method. Look at the first term.

1. First term. The sequence starts at 1.
   1
2. Conclude. So 1 is always a term.
   yes
3. Write the answer.
   Yes, because the first term is 1 and it is always the first term.

Check. 1 is the first term. ✓

Method. Start at the first term and add the difference for each step after it.

1. Find the first term and the difference. The first term is 1, and the difference is 2.
   1 and 2
2. Count the steps to the nth term. The 100th term is 99 steps from the first term.
   100 - 1 = 99 steps
3. Work out the term. Start at 1 and add 2 for each step.
   1 + 198 = 199
4. Write the answer.
   199

Check. 1 + (100 - 1) x 2 = 199. ✓

Watch out. The 1st term has 0 steps added, so the 10th term has 9 steps.