Unit Plan 23 (Grade 5 Math): Patterns & Relationships on the Grid
5th graders analyze numerical patterns, generate ordered pairs, and graph them on the coordinate plane—explaining each rule clearly in words and with matching numerical expressions.
Focus: Analyze numerical patterns, generate ordered pairs, and graph relationships on the coordinate plane; explain rules clearly in words and with numerical expressions.
Grade Level: 5
Subject Area: Mathematics (Operations & Algebraic Thinking; Geometry)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students explore how a rule can generate a numeric pattern, fill an input–output table, and become points in the first quadrant. They practice writing and interpreting numerical expressions that describe the rule (without needing to fully evaluate every expression), then graph and explain what the coordinates mean in context.
Essential Questions
- How do I describe a pattern rule precisely so others can reproduce it?
- How do ordered pairs (x, y) show the relationship between an input and an output?
- What does a graphed pattern reveal about how two quantities change together?
II. Objectives and Standards
Learning Objectives — Students will be able to:
- Describe pattern rules in clear language and record them with numerical expressions (e.g., “triple then add 2”).
- Generate ordered pairs from a rule and organize them in an input–output list.
- Plot points in the first quadrant, label axes with meaningful titles and scales, and interpret what the coordinates mean.
- Compare two patterns by analyzing outputs, differences, and graphs.
- Explain reasoning using precise vocabulary, units, and labeled graphs.
Standards Alignment — CCSS Grade 5
- 5.OA.2: Write simple numerical expressions that record calculations described in words and interpret numerical expressions without evaluating them (e.g., “double a number, then add 5”).
- 5.G.1: Use a coordinate system with perpendicular number lines and the origin to locate points by their ordered pairs in the first quadrant.
- 5.G.2: Represent real-world and mathematical problems by graphing points in the first quadrant and interpret coordinate values.
Success Criteria — Student Language
- I can state the rule in words and as a numerical expression.
- I can make ordered pairs that follow the rule.
- I can plot and label points correctly and explain what they mean.
- I can compare two patterns and tell how their outputs and graphs differ.