### Topics

- Partial Products
- Factors
- 增殖
- Area Model

- Partial Products
- Factors
- 增殖
- Area Model

- Recognize that area represents the product of two numbers and is additive.
- Represent a multiplication problem as the area of a rectangle, proportionally or using generic area.
- Develop and justify a strategy to determine the product of two multi-digit numbers by representing the product as an area or the sum of areas.

7.NS.A.2c

Apply properties of operations as strategies to multiply and divide rational numbers.7.EE.A.1

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.6.NS.B.4

Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.*For example, express 36 + 8 as 4 (9 + 2).*.6.EE.A.4

Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).*For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.*.6.EE.A.3

Apply the properties of operations to generate equivalent expressions.*For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y*.4.NBT.B.5

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.3.MD.C.7d

Recognize area as additive. Find areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.3.MD.C.7c

Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths*a*and*b*+*c*is the sum of*a*×*b*and*a*×*c*. Use area models to represent the distributive property in mathematical reasoning.3.MD.C.7

Relate area to the operations of multiplication and addition.

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