Let’s work through each line step by step.
We’re using the
Associative Property of Addition, which means:
> You can group numbers in different ways when adding, and the sum stays the same.
Example: (2 + 3) + 4 = 2 + (3 + 4) → both equal 9.
Also, remember: addition is commutative too — you can switch order: 2+3 = 3+2. But here we focus on grouping.
---
Line 1:
`2 + (3 + 1) = ___ = 3 + (2 + 1)`
First, calculate inside parentheses:
3 + 1 = 4 → so 2 + 4 =
6
Check right side: 2 + 1 = 3 → 3 + 3 =
6 ✔
So blank =
6
---
Line 2:
`3 + (__ + 1) = ___ = 4 + (3 + 1)`
Right side first: 3 + 1 = 4 → 4 + 4 =
8
So left side must also be 8.
We have: 3 + (__ + 1) = 8
→ __ + 1 = 5 → so __ =
4
Then middle box =
8
---
Line 3:
`4 + (2 + __) = 9 = 3 + (2 + __)`
Middle is given as 9.
Left: 4 + (2 + __) = 9 → 2 + __ = 5 → __ =
3
Right: 3 + (2 + __) = 9 → 2 + __ = 6 → __ =
4
So blanks: left inner =
3, right inner =
4
---
Line 4:
`5 + (3 + __) = 10 = 2 + (3 + __)`
Middle = 10
Left: 5 + (3 + __) = 10 → 3 + __ = 5 → __ =
2
Right: 2 + (3 + __) = 10 → 3 + __ = 8 → __ =
5
Blanks: left inner =
2, right inner =
5
---
Line 5:
`6 + (4 + 1) = ___ = 1 + (__ + 4)`
Left: 4 + 1 = 5 → 6 + 5 =
11
Right: must also be 11 → 1 + (__ + 4) = 11 → __ + 4 = 10 → __ =
6
So middle =
11, blank =
6
---
Line 6:
`7 + (3 + 2) = ___ = 2 + (__ + __)`
Left: 3 + 2 = 5 → 7 + 5 =
12
Right: 2 + (__ + __) = 12 → __ + __ = 10
We need two numbers that add to 10. Since original was 7 + 3 + 2, and now it's 2 + ? + ?, likely 7 and 3 → so blanks =
7 and
3 (order doesn’t matter for sum, but let’s match pattern: probably 7 then 3)
Actually, looking at structure: “2 + (__ + __)” — since total is 12, and 2 is already there, the other two must add to 10. Original numbers were 7, 3, 2 — so yes, 7 and 3. So blanks =
7 and
3
---
Line 7:
`8 + (5 + 3) = ___ = 5 + (__ + __)`
Left: 5 + 3 = 8 → 8 + 8 =
16
Right: 5 + (__ + __) = 16 → __ + __ = 11
Original numbers: 8, 5, 3 → so remaining are 8 and 3 → 8 + 3 = 11
So blanks =
8 and
3
---
Now let’s write all answers clearly:
Line 1: 6
Line 2: 4, 8
Line 3: 3, 4
Line 4: 2, 5
Line 5: 11, 6
Line 6: 12, 7, 3
Line 7: 16, 8, 3
Final Answer:
6; 4, 8; 3, 4; 2, 5; 11, 6; 12, 7, 3; 16, 8, 3
Parent Tip: Review the logic above to help your child master the concept of properties of addition worksheet for grade 1.
