Similarity and Scale

Grade: 7

Duration: 60 minutes
Class size: 25 students
School: Crockett Middle School, Odessa, TX
Subject: Mathematics
Curriculum: International Baccalaureate (IB) Middle Years Programme (MYP) Mathematics
Standards:

Texas TEKS 7.5.A: Apply mathematics to solve problems connected to everyday experiences and activities.
Texas TEKS 7.5.C: Solve problems involving similar figures using scale factors, ratios, and proportions.

IB MYP Alignment & Key Concepts:

IB MYP Framework	Details
Criterion C: Communicating	Students represent mathematical ideas in multiple forms: equations, scale drawings, and verbal explanations.
Criterion D: Applying Mathematics in Real-life Contexts	Students solve complex problems involving similarity and use appropriate technology and mathematical reasoning.
Approaches to Learning (ATL) Focus	Critical thinking, collaboration, communication, and self-management through blended learning.
Key Concept	Relationships — understanding how ratios and proportions relate within and between similar figures.

Learning Objectives

By the end of this lesson, students will be able to:

Define and identify similar shapes by recognizing angle and side relationships (IB MYP Criterion B).
Explain the properties of similarity through ratios within and between similar figures.
Solve real-world and mathematical problems involving scale drawings and similarity using scale factors and ratios (TEKS 7.5.C and 7.5.A).
Create scale drawings using hands-on activities and digital tools demonstrating understanding of ratios and scale factors.
Justify reasoning and communicate results effectively during problem-solving tasks (MYP Criterion C).

Materials & Resources

Graph paper and rulers for hands-on drawing
Pre-prepared scale drawing worksheet (real-world objects like playground equipment or rooms)
Calculators for ratio and proportion calculations
Tablets or laptops with GeoGebra (or any dynamic geometry software)
Whiteboard and markers
Mini whiteboards for student responses
Scale factor ratio flashcards for hands-on matching activity
Projector for displaying examples and student work
Timer/chime for activity transitions

Lesson Procedure

Time	Activity	Details & Strategies
0-10 min	Introduction & Activate Prior Knowledge	- Begin with a stimulating question: “Have you ever used a map or blueprint? How do these help us in real life?” - Show images of a map and two similar triangles with sides labeled. - Use a Think-Pair-Share to have students discuss what they notice about the shapes and ratios. - Directly connect to IB key concepts of relationships and real-world context.
10-20 min	Mini-Lecture & Demonstration	- Define similarity: Same shape, corresponding angles equal, sides proportional. - Show examples of similar and non-similar shapes. - Demonstrate how to identify scale factors and ratios within and between shapes. - Use GeoGebra on projector to scale a figure dynamically. - Explicitly link to TEKS 7.5.C and IB criterion D by showing real-world applications (e.g., designing models).
20-25 min	Hands-on Scale Drawing Exercise	- Students work in pairs to create a scale drawing of a simple object (e.g., a rectangle or triangle room plan) using rulers and graph paper. - Provide scale (e.g., 1 inch = 2 feet) and have them calculate and draw based on this scale. - Honors students can be challenged to create scale drawings with fractional scale factors. - Circulate for formative assessment and targeted support.
25-35 min	Interactive Ratio Matching Game (Blended & Hands-on)	- Flashcard activity where one half of the class matches ratio cards of sides with corresponding scale factors. - The other half uses tablets to solve quick ratio and proportion problems in GeoGebra or a math app. - Switch roles after 5 minutes. - Encourage students to explain their reasoning out loud or write brief justifications on mini whiteboards. - Honors students attempt challenge problems involving irrational ratios.
35-50 min	Real-World Problem Solving - Collaborative Activity	- Present a multi-step problem involving a blueprint or model (e.g., playground design) where students calculate missing lengths and verify similarity. - Groups of 4 collaborate to calculate, draw, explain solutions. - Incorporate IB Criterion C by having students prepare a brief oral or written presentation of their solution. - Use whiteboard space or digital doc for visualization. - Honors students may explore the impact of scale factor changes.
50-60 min	Exit Ticket & Reflection	- Individual quick-write: "Explain in your own words why similar shapes have proportional sides and equal angles." - Include a ratio problem they solve independently on mini whiteboards. - Collect these for formative assessment. - End class with a brief reflection prompt on what was challenging and what they enjoyed (can be verbal or written). - Discuss how scale and similarity relate to their daily lives (architecture, art, maps).

Differentiation & Inclusion

Gifted/enrichment (honors) students work with fractional and irrational scale factors and create more complex scale drawings.
Visual & tactile learners benefit from hands-on drawing and physical matching activities.
Use scaffolded discussion prompts and sentence starters for ELL and SPED students to support communication.
Group work promotes peer support, collaboration, and social learning.

Assessment

Formative	Summative
- Observation during hands-on drawing and interactive games. - Mini whiteboard ratio solutions. - Exit ticket problem solving and explanation.	- Group presentation of real-world problem solution demonstrating understanding of similarity. - Honors students submit an extended scale drawing incorporating feedback and justifications.

Reflection and Follow-up

Reflect with students on the real-world applications of similarity and scale drawings in engineering, architecture, and design.
Follow-up lesson: Introduce dilations and non-rigid transformations linked with similarity in coordinate planes (TEKS 7.6.C).
Share student work on classroom bulletin or digital portfolio to celebrate creativity and understanding.

Teacher Notes

Prioritize clear explanations of ratio language and scale factor relationships, as confusion often arises around these terms.
Use the projector demo as an anchor for abstract to concrete understanding.
Encourage students to verbalize their mathematical thinking as per IB communication skills goals.
Maintain a lively pace but provide enough time for hands-on work to prevent cognitive overload.

Teaching Instructions