Commutative rectangle
http://illuminations.nctm.org/LessonDetail.aspx?ID=L566
A lesson plan for grade 6 Mathematics
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Students typically learn about the concepts of identity, inverse, commutativity, and associativity by exploring the four basic operations (+, –, ×, and ÷) with integers. In this lesson, students investigate these concepts using a geometric model. Moves are performed with a rectangle, and the results of an operation that combines two moves are analyzed. Students determine if the operation is commutative or associative; if an identity element exists; or if there are inverses for any of the moves. Illuminations provides an activity sheet and detailed instructions for completing the lesson.
Students will:
- Determine the identity element.
- Decide if there is an inverse for each element.
- Determine if an operation is commutative or associative.
North Carolina Curriculum Alignment
Mathematics (2004)
Grade 6
- Goal 1: Number and Operations - The learner will understand and compute with rational numbers.
- Objective 1.04: Develop fluency in addition, subtraction, multiplication, and division of non-negative rational numbers.
- Analyze computational strategies.
- Describe the effect of operations on size.
- Estimate the results of computations.
- Judge the reasonableness of solutions.
- Objective 1.07: Develop flexibility in solving problems by selecting strategies and using mental computation, estimation, calculators or computers, and paper and pencil.
- Objective 1.04: Develop fluency in addition, subtraction, multiplication, and division of non-negative rational numbers.
- Goal 5: Algebra - The learner will demonstrate an understanding of simple algebraic expressions.
- Objective 5.01: Simplify algebraic expressions and verify the results using the basic properties of rational numbers.
- Identity.
- Commutative.
- Associative.
- Distributive.
- Order of operations.
- Objective 5.02: Use and evaluate algebraic expressions.
- Objective 5.04: Use graphs, tables, and symbols to model and solve problems involving rates of change and ratios.
- Objective 5.01: Simplify algebraic expressions and verify the results using the basic properties of rational numbers.
