By Yusupha Auber from East Cary Magnet Middle School: Center for Global Studies & World Languages

**OVERVIEW OF LESSON: **The mathematical goal of this lesson is to reinforce the concept of proportional relationships. It is assumed that students have completed Unit 1: Scale Drawings and Unit 2: Introducing Proportional Relationships. In this lesson, students will review concepts from Units 1 and 2 while continuing their study of proportionality, which is the theme running through 7^{th} grade mathematics. The lesson should take two days to complete. In terms of the connection to the UN Sustainable Development Goals (SDGs), the lesson relates to the following: SDG 8: Decent Work and Economic Growth, and SDG 9: Industry, Innovation, and Infrastructure.

In Activity 1, students will collaborate and perform several tasks in pairs: they will use scaled copies of squares to investigate the relationship of perimeter and area to side length. They will gather data in tables, graph the data and then perform analyses to determine whether proportional relationships exist between perimeter or area and side length. In Activity 2, they will collect data of the square footage of tiny homes. Students will access the Lowes’ website, choose a tile, and determine the cost of renovating the floor space of the tiny homes based on their size. In Activity 3, the learning extension, they will independently investigate the relationship of circumference and area to the diameter of various circles.

To act, students will write a letter to city hall advocating for more affordable housing targeting teachers so that it is possible for teachers to live in the districts where they work. Due to the inflation in housing prices and rent, teachers, for example, are often unable to buy homes or rent in the cities they work. School districts are struggling with staffing, and the lack of housing also contributes to the teacher shortage which is a crisis in the state of North Carolina. Some homeowners are building tiny homes on their lots as rental properties to take advantage of the opportunity; however, tiny homes are not necessarily the solution. In Cary, the town has partnered with a construction company to build apartments with affordable housing to ease the cost of living for low-income families, including for teachers and firefighters, which will likely make it more appealing for teachers to work in the town.

**SUGGESTED GRADE LEVEL: **Grade 7

**SUBJECT: **Mathematics

**CORRESPONDING NATIONAL AND/OR STATE OF NORTH CAROLINA STANDARDS**:

Analyze proportional relationships and use them to solve real-world and mathematical problems.

**NC.7.RP.2: **Recognize and represent proportional relationships between quantities.

a. Understand that a proportion is a relationship of equality between ratios.

- Represent proportional relationships using tables and graphs.
- Recognize whether ratios are in a proportional relationship using tables and graphs.
- Compare two different proportional relationships using tables, graphs, equations, and verbal descriptions.

b. Identify the unit rate (constant of proportionality) within two quantities in a proportional relationship using tables, graphs, equations, and verbal descriptions.

c. Create equations and graphs to represent proportional relationships.

d. Use a graphical representation of a proportional relationship in context to:

- Explain the meaning of any point (x, y).
- Explain the meaning of (0, 0) and why it is included.
- Understand that the y-coordinate of the ordered pair (1, r) corresponds to the unit rate and explain its meaning.

**ESSENTIAL QUESTIONS: **

- Is the perimeter or area of a square proportional to its side length?
- Is the perimeter or area of a circle proportional to its side length?
- How can we tell, using tables and graphs, whether scaled copies are proportional?
- Is it possible to see a constant of proportionality in a table, graph, or equation?

**LESSON OBJECTIVES: **

- By the end of this lesson, students will be able to analyze tables and graphs to determine whether the perimeters and areas of squares and circles are proportional to their side lengths.
- By the end of the lesson, students will be able to research the impact of inflation on housing affordability and take action by writing a letter to their local government advocating for the building of affordable housing for teachers.

**BACKGROUND INFORMATION FOR THE EDUCATOR or RESOURCES TO EXPLORE FURTHER:
**

- Squares: Proportionality between side length and perimeter | 7th grade | Khan Academy – YouTube
- Circles: Area of a circle | Perimeter, area, and volume | Geometry | Khan Academy – YouTube

**SPECIFIC STUDENT STRATEGIES & ACTIVITIES: **

**Launch**: The teacher will introduce the lesson by showing students a video about the lack of affordable housing for teachers: Affordable Teacher Housing – NC IMPACT Initiative (unc.edu)**Do Now:**The students will complete the Do Now Handout: Area and Perimeter. (3mins)**Activity 1: Collecting and Graphing Data for Squares**.- The teacher will pair students up and give a squares worksheet & squares handout to each one. (5mins)
- Differentiation: Measurement and Graphing Requirement will be Adjusted.
- All students will measure and graph side length and perimeter with respect to radius (r,p) to the nearest tenth of a cm.
- In-class resource dependent and less confident students will measure and graph the same to the nearest natural number.

- Differentiation: Measurement and Graphing Requirement will be Adjusted.
- The teacher will instruct students to collaborate and complete the table. (3 mins)
- The students will measure the side lengths and calculate the perimeter, and area of all the squares. (15 mins)
- The students will record the data in the table and then graph it in the coordinate plane. (10 mins)
- Students will analyze the tables and graphs to determine if proportional relationships exist. (5 mins)

- The teacher will walk around, listen to student conversations, ask essential questions and provide help as needed.

- The teacher will pair students up and give a squares worksheet & squares handout to each one. (5mins)
**Activity 2: Collecting Data and Graphing Dimensions of Tiny Homes****.**- Students will visit this website: Designs — Tiny Homes Raleigh and record the square footage of all the tiny houses on the website. Students will complete the worksheet, Tiny Houses: Modeling Proportional Relationships.
- Students will visit the Lowes company website and choose a square tile design.
- Students will calculate the cost of tiling each tiny house and create coordinate pairs showing cost with respect to area for each tiny house.
- Students will create a graph showing the cost of tiling all the featured tiny houses.
- Students will determine whether the graph is proportional.

**Taking****Action:**Affordable Housing for Teachers- Students will read the following articles and watch the video:
- Read the story “Elementary teacher seeks flexibility and financial independence”
- Watch this video: Teacher launches tiny house company(spectrumlocalnews.com)
- Read the article: Town of Cary, NC works with developer to build affordable housing – Axios Raleigh

- Read the story “Elementary teacher seeks flexibility and financial independence”
- Students will write a letter to their city government advocating for the building of more affordable housing, specifically targeting teachers, to address the teacher shortage in their school district.

- Students will read the following articles and watch the video:

**ASSESSMENT: **Student will complete the cool-down activity Cool-down 10.5:** **“Measuring a Circular Lawn” available here: Illustrative Mathematics Grade 7, Unit 3.10 – Teachers | Kendall Hunt

**LEARNING EXTENSION: **

**Activity 3: Collecting and Gathering Data for Circles **

- The teacher will give a circles worksheet & circles handout to each student. (5 mins)
- The teacher will instruct students to measure the diameter of all the circles and complete tables. (3 mins)
- Students will follow the instructions and collect and graph the data. (15 mins)
- Students will analyze the tables and graphs to determine if proportional relationships exist

**MATERIALS: **

**Supplies: **pencils, rulers, and calculators.

**Handouts: **Do Now Handout: Area and Perimeter

**Activity 1:****Activity 2**:**Activity 3 (Learning Extension)**:

**REFERENCES: **

Illustrative Mathematics. (n.d.). Unit 2: Introducing Proportional Relationships. Retrieved from: https://curriculum.illustrativemathematics.org/MS/teachers/2/2/index.html