The plus sign and triangle

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In this lesson, students use a plus sign to explore the concepts of identity, inverse, commutativity, and associativity.

Students will:

Illuminations provides handouts for completing the activity.

This lesson follows NCTM Standards and Expectations that teach students how to:

Relate and compare different forms of representation for a relationship.
Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.
Use geometric models to represent and explain numerical and algebraic relationships.

Goal 3: Geometry -The learner will understand and use properties and relationships of geometric figures in the coordinate plane.
- Objective 3.01: Identify and describe the intersection of figures in a plane.
- Objective 3.03: Transform figures in the coordinate plane and describe the transformation.
- Objective 3.04: Solve problems involving geometric figures in the coordinate plane.
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.

Goal 3: Geometry - The learner will understand and use properties and relationships in geometry.
- Objective 3.01: Using three-dimensional figures:
  - Identify, describe, and draw from various views (top, side, front, corner).
  - Build from various views.
  - Describe cross-sectional views.
Goal 5: Algebra - The learner will demonstrate an understanding of linear relations and fundamental algebraic concepts.
- Objective 5.03: Use and evaluate algebraic expressions, linear equations or inequalities to solve problems.
- Objective 5.04: Develop fluency in the use of formulas to solve problems.

Goal 3: Geometry - The learner will understand and use properties and relationships in geometry.
- Objective 3.01: Represent problem situations with geometric models.
Goal 5: Algebra - The learner will understand and use linear relations and functions.
- Objective 5.04: Solve equations using the inverse relationships of addition and subtraction, multiplication and division, squares and square roots, and cubes and cube roots.