Adding integers using counters worksheet with visual aids for understanding positive and negative number operations.

Let's solve this step-by-step, explaining each section of the worksheet.

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Understanding the Counter System

- Yellow counters = +1
- Red counters = -1
- A pair of one yellow and one red counter = 0 (called a "zero pair")
- To find the total value: cancel out zero pairs first, then count the remaining counters.

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## ✔ Section A: What value does each set of counters have?

We'll count the +1s and -1s, cancel zero pairs, and find the net value.

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1)
- Yellow (+1): 5
- Red (-1): 3
- Zero pairs: 3 (3 yellows and 3 reds cancel)
- Remaining: 2 yellow (+1) → Answer: +2

2)
- Yellow: 4
- Red: 4
- Zero pairs: 4 → all cancel
- Remaining: 0 → Answer: 0

3)
- Yellow: 2
- Red: 4
- Zero pairs: 2 → 2 yellows and 2 reds cancel
- Remaining: 2 red (-1) → Answer: -2

4)
- Yellow: 0
- Red: 5
- No zero pairs
- Remaining: 5 red → Answer: -5

✔ Section A Answers:
1) +2
2) 0
3) -2
4) -5

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## ✔ Section B: Match each calculation to the correct collection of counters and answer

We’ll go through each expression and match it with the corresponding visual and final sum.

We’re given:
- Left column: expressions
- Middle: visuals of counters
- Right: possible answers

Let’s evaluate each:

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1) 3 + 4 = 7
→ This is already matched.
Visual: 3 yellow + 4 yellow = 7 yellow → +7
→ Correctly matched to 7

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2) -3 + 4
- -3 means 3 red counters
- +4 means 4 yellow counters
- 3 red + 4 yellow → 3 zero pairs, 1 yellow left → +1
→ Find the visual: 3 red + 4 yellow → matches the second row from top
→ Answer: 1

So connect -3 + 4 → 3 red + 4 yellow → 1

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3) 2 + (-7)
= 2 + (-7) = -5
- 2 yellow + 7 red
- 2 zero pairs cancel → 5 red left → -5
→ Visual: 2 yellow + 7 red → matches the third row from top
→ Answer: -5

So connect 2 + (-7) → 2 yellow + 7 red → -5

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4) 2 + 7 = 9
→ 2 yellow + 7 yellow = 9 yellow → +9
→ Visual: 2 yellow + 7 yellow → matches the fourth row from top
→ Answer: 9

Connect 2 + 7 → 2 yellow + 7 yellow → 9

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5) 3 + (-4)
= 3 - 4 = -1
- 3 yellow + 4 red → 3 zero pairs, 1 red left → -1
→ Visual: 3 yellow + 4 red → matches the fifth row from top
→ Answer: -1

Connect 3 + (-4) → 3 yellow + 4 red → -1

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6) -2 + (-7)
= -2 -7 = -9
- 2 red + 7 red = 9 red → -9
→ Visual: 2 red + 7 red → matches the sixth row from top
→ Answer: -9

Connect -2 + (-7) → 2 red + 7 red → -9

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7) -3 + (-4)
= -7
- 3 red + 4 red = 7 red → -7
→ Visual: 3 red + 4 red → matches the seventh row from top
→ Answer: -7

Connect -3 + (-4) → 3 red + 4 red → -7

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8) -2 + 7
= 5
- 2 red + 7 yellow → 2 zero pairs, 5 yellow left → +5
→ Visual: 2 red + 7 yellow → matches the eighth row from top
→ Answer: 5

Connect -2 + 7 → 2 red + 7 yellow → 5

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✔ Section B Final Matching:

| Expression | Visual | Answer |
|----------------|----------------------------|--------|
| 3 + 4 | 3 yellow + 4 yellow | 7 |
| -3 + 4 | 3 red + 4 yellow | 1 |
| 2 + (-7) | 2 yellow + 7 red | -5 |
| 2 + 7 | 2 yellow + 7 yellow | 9 |
| 3 + (-4) | 3 yellow + 4 red | -1 |
| -2 + (-7) | 2 red + 7 red | -9 |
| -3 + (-4) | 3 red + 4 red | -7 |
| -2 + 7 | 2 red + 7 yellow | 5 |

All matched correctly.

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## ✔ Section C: Find the sum using counters

Now compute these directly (we can use logic or counters):

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1) 1 + (-4)
= 1 - 4 = -3
(1 yellow + 4 red → 1 zero pair → 3 red left)

2) -3 + 9
= 6
(3 red + 9 yellow → 3 zero pairs → 6 yellow left) → +6

3) 6 + (-4)
= 6 - 4 = +2

4) 3 + 2
= 5

5) -7 + (-6)
= -13
(7 red + 6 red = 13 red → -13)

6) -4 + (-4)
= -8
(4 red + 4 red = 8 red → -8)

7) -33 + (-25)
= -58
(33 red + 25 red = 58 red → -58)

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❓ Why might drawing counters not be a good idea in #7?

Because -33 + (-25) involves large numbers, so drawing 33 red counters and 25 red counters would be:
- Time-consuming
- Cluttered
- Prone to error
- Not practical

👉 Better to use rules of adding integers instead:
When adding two negative numbers, add their absolute values and keep the negative sign.

So:
-33 + (-25) = -(33 + 25) = -58

✔ Answer: Drawing counters is impractical for large numbers because it's inefficient and hard to manage visually.

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## ✔ Final Answers Summary:

Section A:

1) +2
2) 0
3) -2
4) -5

Section B:

All matched as shown above.

Section C:

1) -3
2) 6
3) 2
4) 5
5) -13
6) -8
7) -58

> Why not draw counters in #7? Because the numbers are too large; it would take too long and be messy. Better to use arithmetic rules.

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