Place Value with Base Ten Blocks (MAB / Dienes Blocks) - Maths ... - Free Printable

Problem Description:

The task involves interpreting numbers represented by Base 10 blocks. Base 10 blocks are a visual and tactile tool used to teach place value, where:
- Ones blocks represent single units.
- Tens rods represent groups of 10 units.
- Hundreds flats represent groups of 100 units.

We need to determine the numbers represented in the two parts of the image:
1. Part (a): Involves Tens and Ones.
2. Part (b): Involves Hundreds, Tens, and Ones.

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Solution:

#### Part (a): Tens and Ones
- Tens: There are 4 rods, each representing 10 units. Therefore, the total value from the Tens is:
\[
4 \times 10 = 40
\]
- Ones: There are 6 individual blocks, each representing 1 unit. Therefore, the total value from the Ones is:
\[
6 \times 1 = 6
\]
- Total Number: Adding the values from Tens and Ones:
\[
40 + 6 = 46
\]

Thus, the number represented in Part (a) is:
\[
\boxed{46}
\]

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#### Part (b): Hundreds, Tens, and Ones
- Hundreds: There are 3 red flats, each representing 100 units. Therefore, the total value from the Hundreds is:
\[
3 \times 100 = 300
\]
- Tens: There are 5 rods, each representing 10 units. Therefore, the total value from the Tens is:
\[
5 \times 10 = 50
\]
- Ones: There are no individual blocks in this part, so the value from the Ones is:
\[
0 \times 1 = 0
\]
- Total Number: Adding the values from Hundreds, Tens, and Ones:
\[
300 + 50 + 0 = 350
\]

Thus, the number represented in Part (b) is:
\[
\boxed{350}
\]

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Final Answers:

- Part (a): \(\boxed{46}\)
- Part (b): \(\boxed{350}\)

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Explanation:

Base 10 blocks help visualize place value by breaking down numbers into their component parts (Hundreds, Tens, and Ones). By counting the number of blocks in each category and multiplying by their respective place values, we can accurately determine the total number represented. This method reinforces the concept of place value and makes abstract numerical concepts more concrete for learners.