Students must design a cylindrical drink can that uses the least aluminum for a given volume of drink. (This task is very similar to Funsize Cans, but with less step-by-step guidance.)

Students sketch a map of their classroom, make a scale drawing from the sketch, and draft a computer-aided design floor plan from the drawing.

In this task, you must design a cylindrical drink can that uses the least aluminum for a given volume of drink.

Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.

Proportional Relationships

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Understand what a rate and ratio are.
Make a ratio table.
Make a graph using values from a ratio table.

Lesson Flow

Students start the unit by predicting what will happen in certain situations. They intuitively discover they can predict the situations that are proportional and might have a hard time predicting the ones that are not. In Lessons 2–4, students use the same three situations to explore proportional relationships. Two of the relationships are proportional and one is not. They look at these situations in tables, equations, and graphs. After Lesson 4, students realize a proportional relationship is represented on a graph as a straight line that passes through the origin. In Lesson 5, they look at straight lines that do not represent a proportional relationship. Lesson 6 focuses on the idea of how a proportion that they solved in sixth grade relates to a proportional relationship. They follow that by looking at rates expressed as fractions, finding the unit rate (the constant of proportionality), and then using the constant of proportionality to solve a problem. In Lesson 8, students fine-tune their definition of proportional relationship by looking at situations and determining if they represent proportional relationships and justifying their reasoning. They then apply what they have learned to a situation about flags and stars and extend that thinking to comparing two prices—examining the equations and the graphs. The Putting It Together lesson has them solve two problems and then critique other student work.

Gallery 1 provides students with additional proportional relationship problems.

The second part of the unit works with percents. First, percents are tied to proportional relationships, and then students examine percent situations as formulas, graphs, and tables. They then move to a new context—salary increase—and see the similarities with sales taxes. Next, students explore percent decrease, and then they analyze inaccurate statements involving percents, explaining why the statements are incorrect. Students end this sequence of lessons with a formative assessment that focuses on percent increase and percent decrease and ties it to decimals.

Students have ample opportunities to check, deepen, and apply their understanding of proportional relationships, including percents, with the selection of problems in Gallery 2.

Students determine whether a relationship between two quantities that vary is a proportional relationship in three different situations: the relationship between the dimensions of the actual Empire State Building and a miniature model of the building; the relationship between the distance and time to travel to an amusement park; and the relationship between time and temperature at an amusement park.Key ConceptsWhen the ratio between two varying quantities remains constant, the relationship between the two quantities is called a proportional relationship. For a ratio A:B, the proportional relationship can be described as the collection of ratios equivalent to A:B, or cA:cB, where c is positive.Goals and Learning ObjectivesIdentify proportional relationships.Explain why a situation represents a proportional relationship or why it does not.Determine missing values in a table of quantities based on a proportional relationship.

Students must work out how much you need to change the radius of a propane gas tank in order to double its capacity.

Students investigate how changes in the scale factor influence the ratio of perimeters and the ratio of areas between two figures.

This task is from Tools for NC Teachers. Students explore the area and perimeter of rectangles using grid (graph) paper. This is remixable.

This task is from Tools for NC Teachers. Students explore and solve word problems related to area and perimeter. This is remixable.

In this lesson, students apply concepts of area and perimeter to solve multi-step problems involving real-world examples. This lesson will take 2-3 days.

This lesson is from Tools4NCTeachers. In this lesson, students will be creating monsters using a fixed area and fixed perimeter. This is remixable.

This task is from Tools 4 NC Teachers. Students explore the dimensions of a rectangular prism and its volume. This is remixable.

This task is from Tools 4 NC Teachers. Students consider ways to organize rectangular prisms into different sizes of moving trucks. This is remixable.

These two Tasks are from Tools for NC Teachers. Students consider a house and the volume of specific rooms. This is remixable.