Partitioning Numbers Worksheet | PDF printable Number Worksheets - Free Printable

Let's solve the worksheet "Partitioning Numbers to 1000" step by step and explain each part.

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✔ Section A: Partitioning using place value (Part-Whole Models)

We are given numbers in the top circle, and we need to split them into their place values (hundreds, tens, ones) or complete the missing parts.

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#### 1. 56
- Given: 6 (ones)
- So, the other part must be 50 (tens).
> ✔ 56 = 50 + 6

#### 2. 22
- Given: 20 (tens)
- So, the other part is 2 (ones).
> ✔ 22 = 20 + 2

#### 3. 85
- Given: 5 (ones)
- So, the other part is 80 (tens).
> ✔ 85 = 80 + 5

#### 4. 173
- Given: 70 (tens), 3 (ones)
- So, the remaining part is 100 (hundreds).
> ✔ 173 = 100 + 70 + 3

#### 5. 491
- Given: 400 (hundreds), 1 (one)
- So, the missing part is 90 (tens).
> ✔ 491 = 400 + 90 + 1

#### 6. 738
- Given: 700 (hundreds), 30 (tens)
- So, the missing part is 8 (ones).
> ✔ 738 = 700 + 30 + 8

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✔ Section B: Flexible Partitioning

We're now partitioning numbers in different ways, not just by place value.

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#### 1) Fill the gaps to complete the calculations

##### a)
64 = 50 + □
→ 64 - 50 = 14
✔ 64 = 50 + 14

##### b)
64 = □ + 34
→ 64 - 34 = 30
✔ 64 = 30 + 34

##### c)
97 = □ + 37
→ 97 - 37 = 60
✔ 97 = 60 + 37

##### d)
97 = 77 + □
→ 97 - 77 = 20
✔ 97 = 77 + 20

##### e)
285 = 180 + □ + 5
→ First, subtract 180 and 5 from 285:
285 - 180 - 5 = 100
✔ 285 = 180 + 100 + 5

##### f)
285 = 200 + 50 + □
→ 200 + 50 = 250; 285 - 250 = 35
✔ 285 = 200 + 50 + 35

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#### 2) Find three different ways of partitioning each number

We'll give three valid combinations for each number.

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##### 35

1. 30 + 5 → standard place value
2. 20 + 15 → flexible
3. 18 + 17 → any two numbers that add to 35

✔
- 35 = 30 + 5
- 35 = 20 + 15
- 35 = 18 + 17

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##### 73

1. 70 + 3 → place value
2. 50 + 23 → flexible
3. 40 + 33 → another way

✔
- 73 = 70 + 3
- 73 = 50 + 23
- 73 = 40 + 33

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##### 636

We need three different ways using three parts.

1. 600 + 30 + 6 → place value
2. 500 + 100 + 36 → flexible
3. 400 + 200 + 36 → another way

✔
- 636 = 600 + 30 + 6
- 636 = 500 + 100 + 36
- 636 = 400 + 200 + 36

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##### 818

Again, three ways with three parts.

1. 800 + 10 + 8 → place value
2. 700 + 100 + 18 → flexible
3. 600 + 200 + 18 → another combination

✔
- 818 = 800 + 10 + 8
- 818 = 700 + 100 + 18
- 818 = 600 + 200 + 18

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✔ Final Answer Summary:

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Section A – Part-Whole Models

| Number | Parts |
|--------|-------|
| 56 | 50, 6 |
| 22 | 20, 2 |
| 85 | 80, 5 |
| 173 | 100, 70, 3 |
| 491 | 400, 90, 1 |
| 738 | 700, 30, 8 |

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Section B – Flexible Partitioning

#### 1) Fill in the gaps:
- 64 = 50 + 14
- 64 = 30 + 34
- 97 = 60 + 37
- 97 = 77 + 20
- 285 = 180 + 100 + 5
- 285 = 200 + 50 + 35

#### 2) Three ways each:

35
- 30 + 5
- 20 + 15
- 18 + 17

73
- 70 + 3
- 50 + 23
- 40 + 33

636
- 600 + 30 + 6
- 500 + 100 + 36
- 400 + 200 + 36

818
- 800 + 10 + 8
- 700 + 100 + 18
- 600 + 200 + 18

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This worksheet helps students understand that numbers can be broken down in many ways, not just by place value — which supports mental math and number sense!

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