Year 1: Zero and one-step problems
Part of the Year 1 adding and subtracting within 10 chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Zero and one-step problems
Zero means none. We write it as 0. It can be tricky when we add or take away.
Add zero: 5 + 0 = 5. Nothing is added, so 5 stays 5.
Take away zero: 5 − 0 = 5. Nothing is taken away, so 5 stays 5.
Take away all: 5 − 5 = 0. Nothing is left.
A one-step problem is a short story with one sum to work out. First, decide: are things joining together, or going away? Then write one number sentence.
Key ideas
- Zero means none.
- Adding zero does not change the number.
- Taking away zero does not change the number.
- Taking away all of them leaves zero.
- In a story, ask: are things joining together, or going away?
Key words. Zero means none at all. We write it as 0.
Method. Adding zero means adding nothing, so the number stays the same.
- Start with 5. This is the number we begin with.5
- Add zero. Nothing is added. Zero means none, so no new things are counted.5 + 0
- Write the answer. The total is the same as the start.5
Check. Count 5 things and add none. You still have 5. ✓
Watch out. Zero means none. Do not change the number when you add zero.
Key words. When nothing is left, the answer is zero, which we write as 0.
Method. Taking away all of the things leaves none.
- Start with 5. This is the number we begin with.5
- Take away all 5. Every thing goes.5 − 5
- Count what is left. Nothing is left.Nothing left
- Write the answer. Zero means none.0
Check. Add back 5 to zero: 0 + 5 = 5. ✓
Watch out. When you take away all of them, the answer is 0, not the number you started with.
Key words. Take away means some things go away. The − sign shows it.
Method. Read the story. Decide if we add or take away. Then write one number sentence.
- Find the two numbers in the story. Start with the number we had.7 and 3
- Decide: add or take away? Things going away means take away.Going away, so we take away
- Write the number sentence. The sentence shows the story.7 − 3 = 4
- Write the answer. Say what the number is for.4 children
Check. Add back the 3 that went: 4 + 3 = 7. ✓
Watch out. Start with the number you had at the beginning, not the number that went away.
Watch out
Watch out: when you take away all of them, the answer is 0, not the number you started with. 5 − 5 = 0.
Exam tip
Grown-up tip. Use a bag with 5 buttons. Take all 5 out and ask: “How many are left in the bag?” Then take none out and ask again. Zero is the answer when nothing is left.
Exercise 2F Zero and one-step problems
Non-calculatorKey words. Zero means none at all. We write it as 0.
Method. Adding zero means adding nothing, so the number stays the same.
- Start with 6. This is the number we begin with.6
- Add zero. Nothing is added. Zero means none, so no new things are counted.6 + 0
- Write the answer. The total is the same as the start.6
Check. Count 6 things and add none. You still have 6. ✓
Watch out. Zero means none. Do not change the number when you add zero.
Key words. Zero means none at all.
Method. Start with zero things. Then add the things.
- Start with zero. Zero means there are no things yet.0
- Add 8. Now there are 8 things.0 + 8
- Write the answer. The total is the number you added.8
Check. Count 8 things. ✓
Watch out. Zero on the left still means none. The answer is the other number.
Key words. Zero means none. The − sign means take away.
Method. Taking away zero means taking nothing away, so the number stays the same.
- Start with 4. This is the number we begin with.4
- Take away zero. Nothing is taken away. Zero means none, so nothing goes.4 − 0
- Write the answer. Everything is still there.4
Check. Count 4 things. None were taken away, so 4 are left. ✓
Watch out. Taking away zero does not change the number.
Key words. When nothing is left, the answer is zero, which we write as 0.
Method. Taking away all of the things leaves none.
- Start with 7. This is the number we begin with.7
- Take away all 7. Every thing goes.7 − 7
- Count what is left. Nothing is left.Nothing left
- Write the answer. Zero means none.0
Check. Add back 7 to zero: 0 + 7 = 7. ✓
Watch out. When you take away all of them, the answer is 0, not the number you started with.
Key words. Zero means none at all.
Method. Start with zero things. Then add the things.
- Start with zero. Zero means there are no things yet.0
- Add 6. Now there are 6 things.0 + 6
- Write the answer. The total is the number you added.6
Check. Count 6 things. ✓
Watch out. Zero on the left still means none. The answer is the other number.
Key words. Zero means none at all. We write it as 0.
Method. Adding zero means adding nothing, so the number stays the same.
- Start with 3. This is the number we begin with.3
- Add zero. Nothing is added. Zero means none, so no new things are counted.3 + 0
- Write the answer. The total is the same as the start.3
Check. Count 3 things and add none. You still have 3. ✓
Watch out. Zero means none. Do not change the number when you add zero.
Key words. Zero means none. The − sign means take away.
Method. Taking away zero means taking nothing away, so the number stays the same.
- Start with 8. This is the number we begin with.8
- Take away zero. Nothing is taken away. Zero means none, so nothing goes.8 − 0
- Write the answer. Everything is still there.8
Check. Count 8 things. None were taken away, so 8 are left. ✓
Watch out. Taking away zero does not change the number.
Key words. Zero means none at all. We write it as 0.
Method. Adding zero means adding nothing, so the number stays the same.
- Start with 4. This is the number we begin with.4
- Add zero. Nothing is added. Zero means none, so no new things are counted.4 + 0
- Write the answer. The total is the same as the start.4
Check. Count 4 things and add none. You still have 4. ✓
Watch out. Zero means none. Do not change the number when you add zero.
Key words. A story sum is a short problem told as a story.
Method. Read the story. Decide if we add or take away. Then write one number sentence.
- Find the two numbers in the story. The numbers tell us how many.0 and 4
- Decide: add or take away? Things joining together means add.Joining, so we add
- Write the number sentence. The sentence shows the story.0 + 4 = 4
- Write the answer. Say what the number is for.4 stickers
Check. Count 4 stickers in total. ✓
Watch out. Ask: are things joining together, or going away?
Key words. Take away means some things go away. The − sign shows it.
Method. Read the story. Decide if we add or take away. Then write one number sentence.
- Find the two numbers in the story. Start with the number we had.9 and 2
- Decide: add or take away? Things going away means take away.Going away, so we take away
- Write the number sentence. The sentence shows the story.9 − 2 = 7
- Write the answer. Say what the number is for.7 birds
Check. Add back the 2 that went: 7 + 2 = 9. ✓
Watch out. Start with the number you had at the beginning, not the number that went away.
Key words. A story sum is a short problem told as a story.
Method. Read the story. Decide if we add or take away. Then write one number sentence.
- Find the two numbers in the story. The numbers tell us how many.6 and 3
- Decide: add or take away? Things joining together means add.Joining, so we add
- Write the number sentence. The sentence shows the story.6 + 3 = 9
- Write the answer. Say what the number is for.9 beads
Check. Count 9 beads in total. ✓
Watch out. Ask: are things joining together, or going away?
Key words. Take away means some things go away. The − sign shows it.
Method. Read the story. Decide if we add or take away. Then write one number sentence.
- Find the two numbers in the story. Start with the number we had.10 and 4
- Decide: add or take away? Things going away means take away.Going away, so we take away
- Write the number sentence. The sentence shows the story.10 − 4 = 6
- Write the answer. Say what the number is for.6 children
Check. Add back the 4 that went: 6 + 4 = 10. ✓
Watch out. Start with the number you had at the beginning, not the number that went away.
Key words. The − sign means take away. The answer is after the = sign.
Method. Start with the whole. Take away the part that goes. Write the sentence.
- Start with the whole. Count everything at the start.Start: 5
- Take away the part that goes. The − sign means take away.5 − 5
- Count what is left and write the sentence. The answer goes after the = sign.5 − 5 = 0
- Write the answer. 5 − 5 = 0
Check. Add back to check: 0 + 5 = 5. ✓
Watch out. The sign is a minus, not a plus. Taking away makes the number smaller.