Year 6 Maths reasoning (SATs): Negative numbers and counting through zero

Method. Count up 6 from -4.

1. Count up to zero. From -4 to 0 is 4 steps.
   4 steps
2. Count on from zero. 6 - 4 = 2 steps more after zero.
   6 - 4 = 2
3. Write the answer.
   2

Check. -4 + 6 = 2. ✓

Method. Count down 8 from 3.

1. Count down to zero. From 3 to 0 is 3 steps.
   3 steps
2. Count on below zero. 8 - 3 = 5 steps below zero.
   8 - 3 = 5
3. Write the answer.
   -5

Check. 3 - 8 = -5. ✓

Method. Count left from -2.

1. Start at -2. The start is minus two.
   -2
2. Count 5 steps left. Each step left makes the number smaller.
   -2 -> -7
3. Write the answer.
   -7

Check. -7 + 5 = -2. ✓

Method. Count the steps from -6 up to 5.

1. Count to zero. From -6 to 0 is 6 steps.
   6 steps
2. Count from zero to 5. From 0 to 5 is 5 steps.
   6 + 5 = 11
3. Write the answer.
   11

Check. -6 + 11 = 5. ✓

Method. Count up from -8 until you reach 3.

1. Count to zero. From -8 to 0 is 8 steps.
   8 steps
2. Count to 3. From 0 to 3 is 3 more steps.
   8 + 3 = 11
3. Write the answer.
   11

Check. -8 + 11 = 3. ✓

Method. The coldest temperature is the smallest number.

1. Compare the negative numbers. -6 is further below zero than -1, so -6 is colder.
   -6 < -1
2. Place zero and the positive number. 0 is above all the negatives and 2 is above 0.
   0 < 2
3. Write them in order. From coldest to warmest.
   -6, -1, 0, 2
4. Write the answer.
   -6, -1, 0, 2

Check. -6 < -1 < 0 < 2. ✓

Method. Count up 25 from -18.

1. Count up to zero. From -18 to 0 is 18 steps.
   18 steps
2. Count on from zero. 25 - 18 = 7 steps after zero.
   25 - 18 = 7
3. Write the answer.
   7

Check. -18 + 25 = 7. ✓

Method. Test each option.

1. Check each option. Test each one against the rule or the calculation.
2. Tick the true ones. -9 and -6 are further left than -5 on the number line.
   -9, -6
3. Leave the others unticked. These do not match.
   -4, 0, -5 are not ticked
4. Write the answer.
   -9, -6

Check. Each ticked option is true. ✓

Watch out. -5 is not less than -5, so it is not ticked.

Method. The greater number is further to the right on the number line.

1. Place both numbers. -7 is 7 below zero and -15 is 15 below zero.
   -7 is nearer zero
2. Choose the greater. The one nearer zero is greater.
   -7 > -15
3. Write the answer.
   -7

Check. -7 > -15. ✓

Method. Work out each change in order.

1. Rise 45 metres. Rising adds to the number: -120 + 45.
   -120 + 45 = -75
2. Sink 70 metres. Sinking takes away from the number: -75 - 70.
   -75 - 70 = -145
3. Write the answer.
   -145

Check. -120 + 45 - 70 = -145. ✓

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. Subtracting -9 is the same as adding 9, so the answer is 5.
   positive fits
3. Reject the other choices. 5 is positive, so negative and zero are wrong.
   negative and zero do not fit
4. Write the answer.
   positive

Check. positive is the one that fits. ✓

Method. Count 10 steps on a number line from the negative number.

1. Pick a negative number. Choose -4.
   -4
2. Count 10 steps up. From -4 to 0 is 4 steps; 6 more steps reach 6.
   -4 + 10 = 6
3. Write the answer.
   -4 and 6.

Check. 6 - (-4) = 10. ✓

Method. Place both numbers on a number line.

1. Place -5 and 5. -5 is 5 steps left of zero and 5 is 5 steps right of zero.
   -5 < 0 < 5
2. Write the reason. A negative number is always below zero.
   -5 < 5
3. Write the answer.
   Yes, because -5 is below zero and 5 is above zero, so -5 is smaller.

Check. -5 is further left than 5. ✓