7th Grade Unit 3: Introduction to Proportional Relationships

Unit Driving Question 

What are proportional relationships? 

Essential Questions  

1. When is a proportional comparison useful?

2. Does comparing quantities describe the relationship between them?

3. Why are proportional relationships represented in multiple ways? 

Big Ideas 

1. A proportional relationship is when two quantities vary directly.
2. Proportionality is used in the real world
3. Proportional relationships can be represented in a variety of ways. Different representations are useful in different situations.  

   Technology Resources

• 7th Grade Technology Resources

Launch Task 

1 Lesson 

• Pre- Unit Diagnostic Assessment ( Open Up): In this initial task, students are asked to use their prior knowledge to assess their reasoning of proportional relationships. This initial task will give teachers insight into student understanding of proportional relationships.

Big Ideas for Development Lessons 

3-4 Weeks (approximately 1 week per big idea) 

Big Idea 1: A proportional relationship is when two quantities vary directly.

Key Resources  

1. Orangey- Pineapple Juice (Open Up) - This task is an informal introduction to proportionality. Students may have previous experience with equivalent ratios, this activity builds on previous experience with proportional relationships and moves students towards an algebraic representation of proportional relationships.

2. Introducing Proportional Relationships with Tables (Open Up) - The purpose of this task is to introduce students to the idea of proportional relationships using multiple representations. From previous work, students should be familiar with the idea of equivalent ratios, and they may very well recognize the table as a set of equivalent ratios.

3.  Pittsburgh to Phoenix (Open Up) - This task continues the work students did in the previous task on proportional relationships represented with tables. Encourage students to utilize the patterns in data to determine a unit rate. Students will use this unit rate to determine if a proportional relationship exists between the data.

Big Idea Probe

1.Proportions (Open Up) 

Evidence of Understanding 

Students can:

• Compare different values for proportionality.
• Identify the constant of proportionality from multiple representations.
• Explain how the slope, k, the constant of proportionality and the unit rate relate and why.
• Compare and analyze patterns in data to determine if a proportional relationship exists in the data.
• Describe and communicate what makes a relationship proportional.

Big Idea 2: Proportionality is used in the real world.

Key Resources 

1. Scaling the Mona Lisa (Open Up) - The purpose of this activity is to provide a context where a ratio of fractions arises in a real-world situation.

2. Denver to Chicago (Open Up) - This task is an introduction to proportionality in the real world. Students should have previous experience with proportionality. This task allows students to experience how proportionality is useful in a real-world situation.

3. Meters and Centimeters (Open Up 5.2) - This task allows students to experience proportionality in the real world while working with measurement.

 Big Idea Probe 

1.  Real World Proportionality (Open Up) 

Evidence of Understanding  

Students can:

• Check solutions for reasonableness.

• Analyze a real-world situation to determine if the mathematical reasoning is valid.

• Communicate mathematically if solutions are plausible based on mathematical reasoning.

• Explain how proportional reasoning is useful in a given real-world situation.  

Big Idea 3: Proportional relationships can be represented in a variety of ways. Different representations are useful in different situations.

Key Resources 

1. T-Shirts for Sale (Open Up) - This task introduces students to how proportionality can be expressed using a coordinate plane.
2. Matching Graphs of Proportional Relationships (Open Up) - The purpose of this task is to have students find the relationships between the different representations of proportional relationships. Sorting cards for Task 2
3. Andre’s Walk (Open Up) - This activity models proportional relationships as a table and graph. Students are asked to analyze each representation to determine if a proportional relationship exists. 

Big Idea Probe 

1. Representing Proportionality- Tables and Chairs (Open Up)

Evidence of Understanding 

Students can:

• Model proportional relationships as a table, verbal description, symbol or graph.

• Communicate how different types of representations can all represent the same proportional relationship.

• Use multiple representations of data to determine if a proportional relationship exists.

• Determine the unit rate from different mathematical representations of a proportional relationship.

• Identify the characteristics of a proportional relationship when graphed on the coordinate plane.

• Identify the slope from a proportional relationship graphed on the coordinate plane. Communicate how the slope relates to the constant of proportionality, k, and the unit rate.

Unit Closure

1 Week (includes time for probes, re-engagement, and assessment)  

• Unit 3 Assessment

• OK- Map Probe: To learn more about and access how to use the OKMAP common formative assessment probes, complete the NextThought Formative Assessment Probes training module.   

• Dia's Watch Performance Assessment (also covers 7.N.2.3): For access to scoring rubric and student samples, complete the NextThought PLC Common Assessment Discussion, Implementation, and Analysis training module.