Ratios and Proportional Reasoning
Mathematics • 360 • 25 students • Created with AI following Aligned with Common Core State Standards
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Teaching Instructions
Create a substitute teacher package for 7th and 8th grade students aligned with TEKS standards. Include Math with 'I can' statements, success criteria, differentiation strategies, extension activities, and dyslexia-friendly options for Friday, December 12, 2025.
Overview
This substitute teacher package is designed for 7th & 8th grade students and spans 360 minutes (~6 hours) of instructional time. It is aligned with the Common Core State Standards (CCSS) for Mathematics, specifically focusing on Ratios and Proportional Relationships. This package includes detailed student-friendly "I can" statements, success criteria, differentiation strategies, extension activities, and dyslexia-friendly options tailored to support an inclusive classroom environment.
Standards Alignment
CCSS.MATH.CONTENT.7.RP.A.1
- Understand and compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units.
CCSS.MATH.CONTENT.7.RP.A.2
- Recognize and represent proportional relationships between quantities.
CCSS.MATH.CONTENT.7.RP.A.3
- Use proportional relationships to solve multistep ratio and percent problems.
CCSS.MATH.PRACTICE.MP1
- Make sense of problems and persevere in solving them.
CCSS.MATH.PRACTICE.MP4
- Model with mathematics.
Learning Objectives
I can...
- Understand the concept of ratios and identify ratios in real-world contexts.
- Calculate unit rates, including those involving fractions and different units.
- Recognize and represent proportional relationships with tables, graphs, equations, and verbal descriptions.
- Solve real-world problems involving proportional relationships and percentages.
Success Criteria
By the end of this day, students will be able to:
- Correctly write and simplify ratios.
- Calculate unit rates involving whole numbers and fractions with accuracy.
- Create tables and graphs to model proportional relationships.
- Solve word problems involving proportional reasoning with correct computations.
- Explain their mathematical reasoning clearly, orally or in writing.
Class Schedule & Activities
Welcome & Introduction (10 minutes)
- Quick icebreaker: Students share one example of ratios in everyday life (e.g., recipes, speed).
- Preview learning objectives using "I can..." statements on the board.
Activity 1: Exploring Ratios (40 minutes)
- Instruction (15 min): Define ratios and show examples with pictures and numbers. Emphasize unit rates.
- Guided Practice (20 min): Students work on ratio problems from worksheet (writing ratios, identifying unit rates in context).
- Wrap-up (5 min): Discuss answers as a class; clarify misconceptions.
Activity 2: Proportional Relationships with Tables & Graphs (60 minutes)
- Instruction (20 min): Teach how to identify proportional relationships, and represent them in tables and graphs.
- Hands-On Group Work (30 min): Using graph paper, students create tables and graphs from story problems.
- Class Discussion (10 min): Groups share their graphs; teacher highlights proportional relationships.
Break (15 minutes)
Activity 3: Solving Multi-step Ratio & Percent Problems (60 minutes)
- Mini-Lesson (20 min): Review percent calculations, connect to unit rates and ratios.
- Problem-Solving (40 min): Students work individually on a multi-step problem set involving percents and ratios (e.g., discounts, tax, mixture problems). Teacher circulates and supports.
Lunch Break (30 minutes)
Activity 4: Real World Application Project (45 minutes)
- Students work in pairs to create a brochure or presentation about using ratios and proportional reasoning to solve a real-world problem (recipes, travel, shopping, sports stats).
Activity 5: Reflection and Exit Ticket (10 minutes)
- Students write a short response to:
- "How can understanding ratios and proportional reasoning help me outside of school?"
- Exit ticket quiz on key concepts (5 questions).
Differentiation Strategies
| Learner Type | Strategy |
|---|---|
| Struggling learners | Use graphic organizers, step-by-step scaffolds, and visuals, pair with peer buddy. |
| English Language Learners | Provide bilingual glossary of math terms; use gestures and visuals; allow sentence frames for explanations. |
| Advanced learners | Offer complex multi-step problems, explore non-proportional relationships for contrast, and encourage use of algebraic formulas. |
| Students with Dyslexia | Dyslexia-friendly font handouts (e.g., OpenDyslexic), highlight key vocabulary, allow oral responses, and provide audio instructions. |
Extension Activities
- Investigate proportional relationships using different units (e.g., miles to kilometers).
- Introduce scale drawings and maps showing proportional reasoning in a real-world context.
- Create their own ratio word problems and swap with classmates for solving.
Materials Needed
- Whiteboard & markers
- Graph paper
- Calculators
- Worksheets for ratios, unit rates, and percent problems
- Dyslexia-friendly reading materials with large font, colored overlays when possible
- Computers/tablets optional for presentation creation
Substitute Teacher Tips
- Keep the pace steady but check for understanding frequently by asking students to restate concepts in their own words.
- Use clear, concise instructions and visual steps to reduce confusion.
- Encourage collaboration but monitor small groups for focus.
- Use the "I can" statements at the start of each activity to frame objectives.
- Be patient and positive to build student confidence—these topics can be challenging but very rewarding.
Thank you for using this package!
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