Year 5 | Counting Backwards Through Zero Worksheets | KS2 Number ... - Free Printable

Here are the solutions to the problems on the worksheet.

1. Use the number line to help you work out these calculations.

To solve these, imagine starting at the first number and moving left for subtraction (or adding a negative) and right for addition (or subtracting a negative).

* a) $5 - 11$
* Start at 5. Move 11 steps to the left. You pass 0 and go into the negatives.
* Calculation: $5 - 11 = -6$

* b) $3 - 10$
* Start at 3. Move 10 steps to the left.
* Calculation: $3 - 10 = -7$

* c) $8 - 14$
* Start at 8. Move 14 steps to the left.
* Calculation: $8 - 14 = -6$

* d) $-2 + 5$
* Start at -2. Move 5 steps to the right (positive direction).
* Calculation: $-2 + 5 = 3$

* e) $-6 + 10$
* Start at -6. Move 10 steps to the right.
* Calculation: $-6 + 10 = 4$

* f) $-8 + 13$
* Start at -8. Move 13 steps to the right.
* Calculation: $-8 + 13 = 5$

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2. Moving in a positive direction, complete these number sequences.

"Positive direction" means the numbers are getting bigger (adding). We need to find the pattern (how much we add each time) and continue it.

* a) $-6, -4, -2, \dots$
* Pattern: Add 2 each time ($-6 + 2 = -4$, $-4 + 2 = -2$).
* Next numbers:
* $-2 + 2 = 0$
* $0 + 2 = 2$
* $2 + 2 = 4$
* $4 + 2 = 6$
* $6 + 2 = 8$
* Sequence: $0, 2, 4, 6, 8$

* b) $-11, -8, -5, \dots$
* Pattern: Add 3 each time ($-11 + 3 = -8$, $-8 + 3 = -5$).
* Next numbers:
* $-5 + 3 = -2$
* $-2 + 3 = 1$
* $1 + 3 = 4$
* $4 + 3 = 7$
* $7 + 3 = 10$
* Sequence: $-2, 1, 4, 7, 10$

* c) $-22, -15, -8, \dots$
* Pattern: Add 7 each time ($-22 + 7 = -15$, $-15 + 7 = -8$).
* Next numbers:
* $-8 + 7 = -1$
* $-1 + 7 = 6$
* $6 + 7 = 13$
* $13 + 7 = 20$
* $20 + 7 = 27$
* Sequence: $-1, 6, 13, 20, 27$

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3. Moving in a negative direction, complete these number sequences.

"Negative direction" means the numbers are getting smaller (subtracting).

* a) $12, 8, 4, \dots$
* Pattern: Subtract 4 each time ($12 - 4 = 8$, $8 - 4 = 4$).
* Next numbers:
* $4 - 4 = 0$
* $0 - 4 = -4$
* $-4 - 4 = -8$
* $-8 - 4 = -12$
* $-12 - 4 = -16$
* Sequence: $0, -4, -8, -12, -16$

* b) $15, 9, 3, \dots$
* Pattern: Subtract 6 each time ($15 - 6 = 9$, $9 - 6 = 3$).
* Next numbers:
* $3 - 6 = -3$
* $-3 - 6 = -9$
* $-9 - 6 = -15$
* $-15 - 6 = -21$
* $-21 - 6 = -27$
* Sequence: $-3, -9, -15, -21, -27$

* c) $20, 12, 4, \dots$
* Pattern: Subtract 8 each time ($20 - 8 = 12$, $12 - 8 = 4$).
* Next numbers:
* $4 - 8 = -4$
* $-4 - 8 = -12$
* $-12 - 8 = -20$
* $-20 - 8 = -28$
* $-28 - 8 = -36$
* Sequence: $-4, -12, -20, -28, -36$

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Final Answer:

1. Calculations:
a) -6
b) -7
c) -6
d) 3
e) 4
f) 5

2. Positive Direction Sequences:
a) 0, 2, 4, 6, 8
b) -2, 1, 4, 7, 10
c) -1, 6, 13, 20, 27

3. Negative Direction Sequences:
a) 0, -4, -8, -12, -16
b) -3, -9, -15, -21, -27
c) -4, -12, -20, -28, -36