# 面积模型代数

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### 示范 学习目标

• Develop and justify a method to use the area model to determine the product of a monomial and a binomial or the product of two binomials.
• Factor an expression, including expressions containing a variable.
• 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.

### 标准对齐

#### Common Core - Math

3.MD.C.7
Relate area to the operations of multiplication and addition.
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.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.
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.
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.
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.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)..
7.EE.A.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
7.NS.A.2c
Apply properties of operations as strategies to multiply and divide rational numbers.
8.EE.C.7b
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

### 教师指南

 仿真程序控制概述,简化模型,学生视角的思考 ( PDF ).

### 教师提交的活动

Games Remote Lesson ideas Trish Loeblein 初中

K-5
Remote

Expanding and Factoring Algebraic Expressions Amanda McGarry 初中 指导 数学
Algebraic Expressions Amanda McGarry 初中 指导 数学
Exploring Factoring as Undoing the Distributive Property Sarah Hampton 高中

SECUNDARIA: Alineación PhET con programas de la SEP México (2011 y 2017) Diana López 初中

PREPARATORIA: Alineación de PhET con programas de la DGB México (2017) Diana López 本科生

Middle School Math Sim Alignment Amanda McGarry 初中 其它 数学
Using the area model with expressions Jennifer Knudsen, Teresa Lara-Meloy, Amanda McGarry 初中 讨论 数学
Modelo de Áreas, Cambio de Expresiones Andrés Gualberto Palomo Cuevas 高中 家庭作业
Remote

Would You Rather ... Karen Gann 高中 指导 数学
Area Model Algebra - Multiplying Polynomials Carolyn Felknor 初中 指导 数学
ARTICULANDO ÁLGEBRA E GEOMETRIA: O CASO DAS EQUAÇÕES ALGÉBRICAS NO ESTUDO DE ÁREAS Verusca Batista Alves; Ana Carolina Costa Pereira 初中 实验室

Distributive Property Review Tim Kissinger and Larry Peters 初中 指导

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