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Understanding Multiplication: Base 4, Base 8, and Models

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This guide explores multiplication using various bases, including Base 4 and Base 8. Learn how to find products such as 214 × 334 and 258 × 578. Discover essential multiplication concepts such as terms, properties (identity, zero, commutative, associative, distributive), and models including repeated addition and area models. Understand how different strategies can be represented visually and how they apply to real-life scenarios like calculating distance. Engage with key multiplication principles to enhance your mathematical understanding.

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Understanding Multiplication: Base 4, Base 8, and Models

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  1. Understanding Multiplication Use the Base 4 blocks to find these products. 214 334 ×134×234

  2. Find the following products in Alphabitia: AB CD ×B0 ×DC

  3. Find the following products in Base 8: 258 578 ×138×648

  4. Multiplication terms multiplier: 4 multiplicand: 3 product: 12 factors: 4 and 3 are factors of 12 multiple: 12 is a multiple of 4 12 is a multiple of 3

  5. Multiplication Models • Repeated addition • Area • Cartesian product a1 a2 a3

  6. Figure 3.13

  7. Units • For addition and subtraction 3 hours plus 5 miles • For multiplication 8 miles per hour for 5 hours: how many miles? 8 mi • 5 hr = 40 mi hr

  8. Multiplication Properties • Identity • Zero • Commutative • Associative

  9. Multiplication Properties continued: Distributive property-- combines multiplication and addition or subtraction

  10. The area model and the standard multiplication algorithm

  11. Figure 3.20

  12. Figure 3.21

  13. Figure 3.22

  14. Expanded vs compacted Expanded Compacted

  15. Multiplication-the area model • How could Jemea’s strategy be represented using the rectangular area model?

  16. 10 + 10 + 10 + 2 10 + 4

  17. Understanding FOIL

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