Unit Plan 7 (Grade 7 Math): Integer Operations—Adding and Subtracting Rational Numbers
7th graders build fluency with adding and subtracting signed numbers using number lines, additive inverse rules, and real-world contexts like elevation and money changes. They connect direction, distance, and sign to explain and justify results with clarity and precision.
Focus: Use number line and rules for adding/subtracting signed numbers; interpret contexts (gains/losses, elevation).
Grade Level: 7
Subject Area: Mathematics (The Number System • Problem Solving)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
This unit builds deep understanding of addition and subtraction with signed rational numbers (integers, fractions, and decimals). Students connect number line models (direction and distance) to operation rules, view subtraction as adding the additive inverse, and explain results in real contexts (temperature, money, elevation, game scores). Emphasis: clear representations, units, and reasonableness checks per context.
Essential Questions
- How do direction (sign) and distance (absolute value) on a number line model addition and subtraction with negatives?
- Why is subtraction the same as adding the opposite?
- How can I explain signed-number results clearly in real situations?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Represent signed numbers on the number line and interpret absolute value as distance from zero.
- Model addition of rational numbers using directed segments/arrows; apply commutative/associative properties to regroup.
- Interpret subtraction as adding the additive inverse and justify with number line and algebraic reasoning.
- Add and subtract rational numbers (integers, fractions, decimals) accurately, showing conversions and common denominators when needed.
- Solve and explain real-world problems (7.NS.3 connection) involving gains/losses, temperature changes, and elevation differences, including reasonableness checks.
Standards Alignment — CCSS Grade 7
- 7.NS.1a–d: a) Describe addition and subtraction of rational numbers as combining and removing directed quantities; represent on a number line. b) Understand p + q as moving q units from p; show p − q as the number that makes p = q + ?; represent subtraction on a number line. c) Show subtraction as adding the additive inverse (p − q = p + (−q)); apply properties of operations. d) Apply properties of operations to add and subtract rational numbers; use equivalent forms.
- 7.NS.3: Solve real-world and mathematical problems involving the four operations with rational numbers (emphasis here on add/subtract; others spiral in later units).
- Mathematical Practices highlighted: MP.1 (make sense), MP.3 (construct arguments), MP.4 (model), MP.6 (precision), MP.7 (structure).
Success Criteria — Student Language
- I can place signed numbers on a number line and use absolute value to describe distance.
- I can add signed numbers by thinking about direction and distance and by using rules.
- I can subtract by adding the opposite and show it on a number line.
- I can add/subtract fractions and decimals with negatives and explain each step.
- I can explain my answers in context and check if they are reasonable.