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Comparing Base-10 Blocks and Diagonal Line Multiplication

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**1. **Comparing Base-10 Blocks and Diagonal Line Multiplication James Valles, Jr.
Department of Mathematics and Statistics
Texas Tech University

**2. **Multiplying using Base-10 Blocks One method to illustrate the procedures of multiplication is using the area of a rectangle interpretation of multiplication.
The factors are the length and width of the rectangle, and the product is the area of the rectangle.

**3. **Multiplying using Base-10 Blocks Note that this is not an algorithm for finding multiplication.
Rather, this is used
to help make sense of the
pencil-and-paper algorithm.

**4. **Multiplying using Base-10 Blocks To find the product, fill in the area using as few base-10 blocks as possible.
Start with blocks are area 100 units.

**5. **Multiplying using Base-10 Blocks Now find blocks that have area 10 units.

**6. **Multiplying using Base-10 Blocks Now find blocks that have area of 1 unit.

**7. **Multiplying using Base-10 Blocks Finally, count the blocks to find the area of the rectangle, i.e. the product.
2 hundreds
17 tens
21 ones

**8. **Multiplying using Base-10 Blocks By regrouping, we have
3 hundreds
7 tens
21 ones
Regrouping again, we have
3 hundreds
9 tens
1 one

**9. **Multiplying using Diagonal Lines Find the product of 17 and 23.

**10. **Multiplying using Diagonal Lines Find the product of 17 and 23.

**11. **Multiplying using Diagonal Lines Find the product of 17 and 23.

**12. **Multiplying using Diagonal Lines Find the product of 17 and 23.

**13. **Multiplying using Diagonal Lines Find the product of 17 and 23.

**14. **Multiplying using Diagonal Lines Find the product of 17 and 23.

**15. **Multiplying Fractions using Base-10 Blocks Find the product of and .

**16. **Multiplying Fractions using Diagonal Lines Find the product of and .

**17. **Benefits using Diagonal Lines

**18. **Drawbacks using Diagonal Lines

**19. **References

**20. **Acknowledgements