Number and place value | 2nd grade | Math | Pango - Free Printable

Problem Description:

The worksheet asks to represent numbers using different methods: base 10 blocks, counters, and number lines. The task is to determine the numbers represented by each visual representation.

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Solution:

#### Part 1: Representing Numbers with Base 10 Blocks
Base 10 blocks are used to represent numbers in a place value system. Each block type represents a specific value:
- A large square (green) represents 100.
- A long rectangle (purple) represents 10.
- A small square (yellow) represents 1.

We will count the blocks for each row:

1. First Row:
- 2 green squares: \( 2 \times 100 = 200 \)
- 3 purple rectangles: \( 3 \times 10 = 30 \)
- 4 yellow squares: \( 4 \times 1 = 4 \)
- Total: \( 200 + 30 + 4 = 234 \)

2. Second Row:
- 5 green squares: \( 5 \times 100 = 500 \)
- 6 purple rectangles: \( 6 \times 10 = 60 \)
- 7 yellow squares: \( 7 \times 1 = 7 \)
- Total: \( 500 + 60 + 7 = 567 \)

3. Third Row:
- 3 green squares: \( 3 \times 100 = 300 \)
- 2 purple rectangles: \( 2 \times 10 = 20 \)
- 5 yellow squares: \( 5 \times 1 = 5 \)
- Total: \( 300 + 20 + 5 = 325 \)

4. Fourth Row:
- 4 green squares: \( 4 \times 100 = 400 \)
- 1 purple rectangle: \( 1 \times 10 = 10 \)
- 8 yellow squares: \( 8 \times 1 = 8 \)
- Total: \( 400 + 10 + 8 = 418 \)

Answers for Part 1:
1. 234
2. 567
3. 325
4. 418

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#### Part 2: Representing Numbers with Counters
Counters are used to represent numbers based on their color-coded values:
- Purple counters represent 10.
- Green counters represent 1.
- Pink counters represent 1.

We will count the counters for each row:

1. First Row:
- 2 purple counters: \( 2 \times 10 = 20 \)
- 3 green counters: \( 3 \times 1 = 3 \)
- 1 pink counter: \( 1 \times 1 = 1 \)
- Total: \( 20 + 3 + 1 = 24 \)

2. Second Row:
- 3 purple counters: \( 3 \times 10 = 30 \)
- 4 green counters: \( 4 \times 1 = 4 \)
- 2 pink counters: \( 2 \times 1 = 2 \)
- Total: \( 30 + 4 + 2 = 36 \)

3. Third Row:
- 4 purple counters: \( 4 \times 10 = 40 \)
- 5 green counters: \( 5 \times 1 = 5 \)
- 3 pink counters: \( 3 \times 1 = 3 \)
- Total: \( 40 + 5 + 3 = 48 \)

4. Fourth Row:
- 5 purple counters: \( 5 \times 10 = 50 \)
- 6 green counters: \( 6 \times 1 = 6 \)
- 4 pink counters: \( 4 \times 1 = 4 \)
- Total: \( 50 + 6 + 4 = 60 \)

Answers for Part 2:
1. 24
2. 36
3. 48
4. 60

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#### Part 3: Representing Numbers with Number Lines
Number lines are marked with intervals, and arrows point to specific positions. We need to identify the number corresponding to the arrow's position.

1. First Number Line:
- The number line ranges from 0 to 500 in increments of 50.
- The arrow points to 350.

2. Second Number Line:
- The number line ranges from 100 to 600 in increments of 50.
- The arrow points to 400.

3. Third Number Line:
- The number line ranges from 100 to 500 in increments of 50.
- The arrow points to 300.

Answers for Part 3:
1. 350
2. 400
3. 300

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Final Answers:

1. Base 10 Blocks:
- 234
- 567
- 325
- 418

2. Counters:
- 24
- 36
- 48
- 60

3. Number Lines:
- 350
- 400
- 300

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
\text{Part 1: } 234, 567, 325, 418 \\
\text{Part 2: } 24, 36, 48, 60 \\
\text{Part 3: } 350, 400, 300
\end{array}
}
\]