Area Model Algebra_面積模型與代數

Area Model Algebra_面積模型與代數 螢幕截圖  下載  嵌入
  • Polynomials
  • Factors
  • Products

標題

  • Polynomials
  • Factors
  • Products

描述

Build rectangles of various sizes and relate multiplication to area. Discover new strategies for multiplying algebraic expressions. Use the game screen to test your multiplication and factoring skills!

學習目標

  • 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.

標準對齊

共用核心 - 數學

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.
版本 1.0.11

教學提示

下載教師教學提示 PDF 檔 模擬教學的控制概觀、模型簡化與引導學生思考 ( PDF ).

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老師提供的活動

Expanding and Factoring Algebraic Expressions A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. 此貢獻是由 PhET 所作之設計 Amanda McGarry 國中 指引 數學
Algebraic Expressions A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. 此貢獻是由 PhET 所作之設計 Amanda McGarry 國中 指引 數學
Exploring Factoring as Undoing the Distributive Property A gold star indicates high-quality, inquiry-based activities that follow the PhET design guidelines. Sarah Hampton 國中
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Middle School Math Sim Alignment 此貢獻是由 PhET 所作之設計 Amanda McGarry 國中 其它 數學
Using the area model with expressions 此貢獻是由 PhET 所作之設計 Jennifer Knudsen, Teresa Lara-Meloy, Amanda McGarry 國中 討論 數學
Would You Rather ... Karen Gann 高中 指引 數學
Area Model Algebra - Multiplying Polynomials Carolyn Felknor 國中 指引 數學
ARTICULANDO ÁLGEBRA E GEOMETRIA: O CASO DAS EQUAÇÕES ALGÉBRICAS NO ESTUDO DE ÁREAS Verusca Batista Alves; Ana Carolina Costa Pereira 國中 實驗室
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Distributive Property Review Tim Kissinger and Larry Peters 國中 討論
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