Common Core math homework worksheet focusing on addition and number sentence sorting.

Let's solve and sort the number sentences from your homework step by step.

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Step 1: Solve Each Number Sentence

We'll compute each expression:

1. 5 + 1 = 6
2. 6 + 2 = 8
3. 2 + 3 = 5
4. 3 + 3 = 6
5. 7 + 1 = 8
6. 2 + 2 = 4
7. ____ = 4 + 4 → 8 = 4 + 4
8. 8 + 2 = 10
9. 3 + 4 = 7
10. ____ = 5 + 4 → 9 = 5 + 4
11. 10 = 1 + ____ → 10 = 1 + 9
12. ____ = 5 + 2 → 7 = 5 + 2

So now, we have:

- 5 + 1 = 6
- 6 + 2 = 8
- 2 + 3 = 5
- 3 + 3 = 6
- 7 + 1 = 8
- 2 + 2 = 4
- 8 = 4 + 4
- 8 + 2 = 10
- 3 + 4 = 7
- 9 = 5 + 4
- 10 = 1 + 9
- 7 = 5 + 2

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Step 2: Categorize into the Chart

The categories are:

- Doubles: Both numbers are the same (e.g., 3 + 3)
- Doubles +1: One number is one more than the other (e.g., 3 + 4)
- +1: Adding 1 to a number (e.g., 5 + 1)
- +2: Adding 2 to a number (e.g., 6 + 2)
- Mentally visualized 5-groups: Numbers that relate to 5 (like 5 + 1, or combinations that use knowledge of 5s)

Let’s go through each sentence and sort it.

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#### ✔ Doubles
These are when both addends are equal:
- 3 + 3 = 6
- 2 + 2 = 4
- 4 + 4 = 8 (from "____ = 4 + 4")

> So:
> - 3 + 3 = 6
> - 2 + 2 = 4
> - 8 = 4 + 4

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#### ✔ Doubles +1
These are like 3 + 4, 5 + 6 — consecutive numbers.
- 2 + 3 = 5
- 3 + 4 = 7
- 5 + 2 = 7 → This is 5 + 2, which is not consecutive, but 2 + 3 is, so maybe better in +1?
Wait — let’s clarify.

Actually, "Doubles +1" means adding two numbers that differ by 1, e.g., 3 + 4, 2 + 3, etc.

So:
- 2 + 3 = 5 → yes
- 3 + 4 = 7 → yes
- 5 + 2 = 7 → 5 and 2 differ by 3 → no
- But 5 + 2 = 7 → not a double +1
- 4 + 4 = 8 → double
- 5 + 1 = 6 → differs by 4 → not double +1
- 6 + 2 = 8 → differs by 4 → not

So only:
- 2 + 3 = 5
- 3 + 4 = 7

But wait: 5 + 2 = 7 → 5 and 2 are not consecutive → not doubles +1

So Doubles +1:
- 2 + 3 = 5
- 3 + 4 = 7

Also, note: 7 = 5 + 2 → this is just 5 + 2 = 7, which is not a double +1 because 5 and 2 aren't consecutive.

So only those two.

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#### ✔ +1
Adding 1 to a number:
- 5 + 1 = 6
- 7 + 1 = 8
- 10 = 1 + 9 → this is 1 + 9 = 10 → adding 9 to 1 → not +1
- But 10 = 1 + 9 → this is +9, not +1

So only:
- 5 + 1 = 6
- 7 + 1 = 8

Also, 1 + 9 = 10 → could be seen as 1 + 9 → not +1
But 9 = 5 + 4 → not +1

So +1:
- 5 + 1 = 6
- 7 + 1 = 8

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#### ✔ +2
Adding 2 to a number:
- 6 + 2 = 8
- 8 + 2 = 10

Also, 2 + 3 = 5 → 2 + 3 = 5 → not +2
But 6 + 2 = 8 → yes
8 + 2 = 10 → yes

Also, 2 + 3 = 5 → 2 + 3 is not adding 2 to a number unless you think of it as 2 + 3, but that's not a standard "+2" pattern.

So +2:
- 6 + 2 = 8
- 8 + 2 = 10

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#### ✔ Mentally visualized 5-groups
This refers to facts where students use knowledge of 5 (like 5 + 1, 5 + 2, etc.) or thinking about 5 as a benchmark.

Examples:
- 5 + 1 = 6 → uses 5
- 5 + 2 = 7 → uses 5
- 5 + 4 = 9 → uses 5
- 4 + 4 = 8 → doesn’t involve 5 directly
- 3 + 3 = 6 → no 5
- 2 + 2 = 4 → no 5

So any fact involving 5:
- 5 + 1 = 6
- 5 + 2 = 7 → from "___ = 5 + 2"
- 5 + 4 = 9 → from "___ = 5 + 4"

Also, 10 = 1 + 9 → not related to 5
But 10 = 5 + 5 → not here

So:
- 5 + 1 = 6
- 5 + 2 = 7
- 5 + 4 = 9

Note: The equation "___ = 5 + 2" → 7 = 5 + 2 → so write 7 = 5 + 2 or 5 + 2 = 7

Similarly, "___ = 5 + 4" → 9 = 5 + 4

So these three are 5-groups.

Also, 3 + 4 = 7 → could be thought of as 3 + 4 = 7, but not necessarily using 5-group

But 5 + 1 = 6 → yes, clearly a 5-group

So Mentally visualized 5-groups:
- 5 + 1 = 6
- 5 + 2 = 7
- 5 + 4 = 9

Also, 4 + 4 = 8 → not 5-group
But 8 = 4 + 4 → no 5

So only those three.

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Now let’s compile the chart.

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✔ Final Chart

| Doubles | Doubles +1 | +1 | +2 | Mentally visualized 5-groups |
|--------|------------|-----|-----|-------------------------------|
| 3 + 3 = 6 | 2 + 3 = 5 | 5 + 1 = 6 | 6 + 2 = 8 | 5 + 1 = 6 |
| 2 + 2 = 4 | 3 + 4 = 7 | 7 + 1 = 8 | 8 + 2 = 10 | 5 + 2 = 7 |
| 8 = 4 + 4 | | | | 5 + 4 = 9 |

> Note: Some equations can go in more than one place.

Let’s check:

- 5 + 1 = 6 → appears in +1 and 5-groups
- 7 + 1 = 8 → +1
- 6 + 2 = 8 → +2
- 8 + 2 = 10 → +2
- 2 + 3 = 5 → doubles +1
- 3 + 4 = 7 → doubles +1
- 3 + 3 = 6 → doubles
- 2 + 2 = 4 → doubles
- 8 = 4 + 4 → doubles
- 9 = 5 + 4 → 5-groups
- 10 = 1 + 9 → not in any category? Let's see.

Wait: 10 = 1 + 9 → this is 1 + 9 = 10 → this is not a double, not +1, not +2, not a 5-group?

But 10 = 1 + 9 → could be considered +9, but not listed.

Alternatively, perhaps it's meant to be 9 + 1 = 10, which is +1.

So 10 = 1 + 9 → same as 1 + 9 = 10 → +9, not in categories.

But 10 = 5 + 5 → not here.

So maybe it’s not categorized? Or perhaps it’s under +1 if we think of it as 9 + 1 = 10?

But the equation is written as 10 = 1 + ___, so it’s 1 + 9 = 10, which is +9.

So it doesn't fit any of the given categories.

But perhaps the intention is for students to recognize 1 + 9 = 10 as part of +1? But 9 is not 1 more than 10 — no.

Actually, +1 means adding 1 to something: like 5 + 1 = 6, 7 + 1 = 8.

So 1 + 9 = 10 is not a "+1" fact.

Similarly, +2 would be like 6 + 2 = 8.

So 1 + 9 = 10 does not fit any category.

But maybe we can interpret it as 9 + 1 = 10, which is +1.

So perhaps the equation 10 = 1 + 9 is equivalent to 9 + 1 = 10, so it belongs in +1.

Similarly, 5 + 4 = 9 → could also be 4 + 5 = 9, which is +5, but not listed.

So likely, the categories are based on the structure of the problem.

Let’s assume:

- +1: Any addition where one number is increased by 1 → e.g., 5 + 1 = 6, 7 + 1 = 8
- +2: 6 + 2 = 8, 8 + 2 = 10
- Doubles: 2 + 2 = 4, 3 + 3 = 6, 4 + 4 = 8
- Doubles +1: 2 + 3 = 5, 3 + 4 = 7
- 5-groups: Facts that use 5 as a base: 5 + 1 = 6, 5 + 2 = 7, 5 + 4 = 9

And 10 = 1 + 9 → 1 + 9 = 10 → this is not a +1 fact (because 1 is not being added to 9; rather, 9 is being added to 1), but it's 9 + 1 = 10, which is a +1 fact.

So we can write it as 9 + 1 = 10, and put it in +1.

Similarly, 5 + 4 = 9 → could be 4 + 5 = 9, which is +5, but not listed.

So best to keep as is.

But since the original says 10 = 1 + 9, it’s not in the form of "a + b", but still, it represents 1 + 9 = 10, which is not a +1 fact unless we reframe.

Wait — +1 means adding 1 to a number. So 9 + 1 = 10 is +1.

But here it’s 1 + 9 = 10, which is +9, not +1.

So unless the student thinks of it as 9 + 1 = 10, it’s not a +1 fact.

So perhaps it should go in none of the categories?

But the instruction says “One number sentence can go in more than one place.”

So let’s list all solved equations and assign them:

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Final Assignments

1. 5 + 1 = 6 → +1, 5-groups
2. 6 + 2 = 8 → +2
3. 2 + 3 = 5 → Doubles +1
4. 3 + 3 = 6 → Doubles
5. 7 + 1 = 8 → +1
6. 2 + 2 = 4 → Doubles
7. 8 = 4 + 4 → Doubles
8. 8 + 2 = 10 → +2
9. 3 + 4 = 7 → Doubles +1
10. 9 = 5 + 4 → 5-groups
11. 10 = 1 + 9 → 1 + 9 = 10 → +9 → not in categories → maybe +1 if flipped? No. Not really.
12. 7 = 5 + 2 → 5-groups

So 10 = 1 + 9 doesn’t fit any category.

But perhaps it’s intended to be recognized as 9 + 1 = 10, so it belongs in +1.

Similarly, 5 + 4 = 9 → 4 + 5 = 9 → +5 → not listed.

So maybe the +1 column includes 9 + 1 = 10, even though written as 10 = 1 + 9.

So we can include it as 1 + 9 = 10 → +9, but not +1.

Alternatively, perhaps it’s 10 = 9 + 1, so +1.

But the equation is written as 10 = 1 + 9, so it’s 1 + 9 = 10, which is +9.

So probably, it doesn’t belong in any category.

But since the directions say “one number sentence can go in more than one place,” and there are 12 sentences, and 5 columns, maybe some are left out.

But let’s try to fill the chart with what fits.

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Final Chart Filled In

| Doubles | Doubles +1 | +1 | +2 | Mentally visualized 5-groups |
|--------|------------|-----|-----|-------------------------------|
| 3 + 3 = 6 | 2 + 3 = 5 | 5 + 1 = 6 | 6 + 2 = 8 | 5 + 1 = 6 |
| 2 + 2 = 4 | 3 + 4 = 7 | 7 + 1 = 8 | 8 + 2 = 10 | 5 + 2 = 7 |
| 8 = 4 + 4 | | | | 5 + 4 = 9 |

Now, 10 = 1 + 9 → not placed

But maybe we can write it as 1 + 9 = 10, and put it in +1? Only if we accept that +1 means adding 1, regardless of order.

But 1 + 9 = 10 is adding 9 to 1, not adding 1 to 9.

So it's not +1.

But 9 + 1 = 10 is +1.

So perhaps the student should rewrite it.

But since it’s given as 10 = 1 + 9, it’s fine to leave it unplaced.

Alternatively, maybe it’s meant to be 10 = 9 + 1, so +1.

But it’s written as 1 + 9.

So best to not include it in any category.

But let’s check: 10 = 1 + 9 → this is a true statement, but not a fact that fits the patterns.

So perhaps it's extra.

Now, Write your own number sentences:

You can add:
- 4 + 4 = 8 → already in doubles
- 6 + 3 = 9 → could be +3 or doubles +1? 6 + 3 → not consecutive
- 5 + 5 = 10 → doubles, 5-groups
- 4 + 5 = 9 → 5-groups, +5

So you can write:
- 5 + 5 = 10 → doubles, 5-groups
- 4 + 5 = 9 → 5-groups
- 6 + 1 = 7 → +1

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✔ Final Answer

Here is the completed chart:

| Doubles | Doubles +1 | +1 | +2 | Mentally visualized 5-groups |
|--------|------------|-----|-----|-------------------------------|
| 3 + 3 = 6 | 2 + 3 = 5 | 5 + 1 = 6 | 6 + 2 = 8 | 5 + 1 = 6 |
| 2 + 2 = 4 | 3 + 4 = 7 | 7 + 1 = 8 | 8 + 2 = 10 | 5 + 2 = 7 |
| 8 = 4 + 4 | | | | 5 + 4 = 9 |

Notes:
- 10 = 1 + 9 does not fit any category and can be omitted or noted as an exception.
- Some equations appear in multiple categories (e.g., 5 + 1 = 6 is in both +1 and 5-groups).

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✔ Write Your Own Number Sentences

Add:
- 5 + 5 = 10 → doubles, 5-groups
- 4 + 5 = 9 → 5-groups
- 6 + 1 = 7 → +1

Place them appropriately.

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✔ Summary of Solutions:

- 5 + 1 = 6
- 6 + 2 = 8
- 2 + 3 = 5
- 3 + 3 = 6
- 7 + 1 = 8
- 2 + 2 = 4
- 8 = 4 + 4
- 8 + 2 = 10
- 3 + 4 = 7
- 9 = 5 + 4
- 10 = 1 + 9
- 7 = 5 + 2

All solved correctly.

Let me know if you'd like this printed in a table format!