Montague Township School District
Math Curriculum Guide
Grade 7
2025-2026
Carl Ferriere
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Description
This seventh-grade pre-algebra mathematics curriculum spans five units across 225 days of instruction, integrating major content standards from both seventh and eighth grade. The first unit covers operations on rational numbers and algebraic expressions, establishing foundational skills in arithmetic with integers, fractions, and decimals, along with work on exponents and properties of operations. The second unit addresses equations, inequalities, and proportional relationships, guiding students through multi-step problem solving, ratio and proportion, and scale drawings. Unit 3 advances to linear equations and explores exponents, roots, and scientific notation, providing a bridge to more sophisticated algebraic thinking. Unit 4 focuses on statistics and probability, including sampling, inference, and probability models for both simple and compound events. The final unit applies geometric reasoning and algebraic skills to solve problems involving area, volume, surface area, transformations, and similarity. Throughout, students engage with multiple representations and tools, including coordinate planes, tables, graphs, and technology, while connecting mathematical concepts to real-world contexts.
Big Ideas
- Operations on rational numbers and properties of operations form the foundation for algebraic manipulation and equation solving.
- Proportional relationships can be represented in multiple forms (tables, graphs, equations, verbal descriptions) and used to model and solve real-world problems.
- Exponents, roots, and scientific notation provide efficient ways to represent and compute with very large and very small quantities.
- Random sampling and probability models enable us to draw valid inferences about populations and predict outcomes of uncertain events.
- Geometric transformations preserve or modify properties of figures in predictable ways, and similarity and congruence can be established through sequences of transformations.
Essential Questions
- How do properties of operations extend from whole numbers to rational numbers and algebraic expressions?
- How can equations, inequalities, and proportional relationships model real-world situations and facilitate problem solving?
- What patterns and relationships exist among exponents, roots, and different representations of numbers?
- How do we use samples and probability to draw inferences and make predictions about populations and events?
- How do geometric transformations, measurements, and algebraic reasoning work together to solve spatial and real-world problems?
Core Textbook
CPM Mathematics
Expressions and Equations
Geometry
The Number System
Ratios and Proportional Relationships
Statistics and Probability
Students write in science notebooks, construct viable arguments, and critique reasoning of others using mathematical evidence and precise language to communicate mathematical thinking.
Students apply mathematical reasoning to analyze scientific data, represent relationships using equations and graphs, and solve real-world problems involving physical phenomena such as temperature, distance, and population dynamics.
Students use proportional reasoning and quantitative analysis to examine historical economic data, evaluate policy decisions, and assess demographic information across different time periods and societies.
Assessment is ongoing and multifaceted throughout the year, using a balance of formative and summative measures. Formative assessments include daily exit and entrance tickets, observational notes, pair-and-share discussions, quizzes, and CPM checkups that provide real-time feedback on student understanding. Study Island by Edmentum and math fluency assessments track computational skills and conceptual grasp. Formal summative assessments include unit tests, performance assessments tied to real-world scenarios, and benchmark assessments that measure progress toward grade-level standards. Post-assessments on CPM units and bridges allow students to demonstrate mastery after instruction. Self-evaluations encourage metacognition. All assessments are adapted for students with special needs, English language learners, gifted learners, and those with 504 plans, ensuring equitable access to assessment and opportunities to show what they know.
| Unit | Formative | Summative | Benchmark | Alternative |
|---|---|---|---|---|
| 01Operations on Rational Numbers & Expressions | ✓ | ✓ | — | ✓ |
| 02Equations and Ratio & Proportion | ✓ | ✓ | — | ✓ |
| 03Linear Equations, and Solutions | ✓ | ✓ | ✓ | ✓ |
| 04Drawing Inferences about Populations & Probability Models | ✓ | ✓ | — | ✓ |
| 05Problem Solving with Geometry | ✓ | ✓ | ✓ | ✓ |
| Coverage | 5/5 | 5/5 | 2/2 | 5/5 |
| Unit | IEP | 504 | MLL | At-Risk | Gifted |
|---|---|---|---|---|---|
| 01Operations on Rational Numbers & Expressions | ✓ | ✓ | ✓ | ✓ | ✓ |
| 02Equations and Ratio & Proportion | ✓ | ✓ | ✓ | ✓ | ✓ |
| 03Linear Equations, and Solutions | ✓ | ✓ | ✓ | ✓ | ✓ |
| 04Drawing Inferences about Populations & Probability Models | ✓ | ✓ | ✓ | ✓ | ✓ |
| 05Problem Solving with Geometry | ✓ | ✓ | ✓ | ✓ | ✓ |
| Coverage | 5/5 | 5/5 | 5/5 | 5/5 | 5/5 |