Patterns in Numbers and Shapes: Using Algebraic Thinking

Students identify and describe number patterns as an introduction to algebraic thinking. Students first look for patterns in numbers, objects and a story and show the patterns in tables. They then learn to describe them using variables and expressions. Next, graphing on a coordinate grid is introduced as a tool for understanding patterns. Lastly, students explore some non-linear patterns, including doubling.

NCTM Standard: Geometry

• Specify locations and describe spatial relationships using coordinate geometry and other representational systems

NCTM Standard: Algebra

• Understand patterns, relations, and functions
• Represent and analyze mathematical situations and structures using algebraic symbols
• Use mathematical models to represent and understand quantitative relationships
• Analyze change in various contexts

NCTM Standard: Number and Operations

• Understand numbers, ways of representing numbers, relationships among numbers, and number systems
• Understand meanings of operations and how they relate to one another

Primary Mathematical Goals

• Describe patterns using words, tables, graphs, and algebraic expressions
• Use coordinate graphing to compare linear and nonlinear patterns
• Write algebraic expressions using variables
• Describe and extend numerical patterns
• Reason about multiples, factors, and arithmetic operations
• Describe and extending geometric patterns