Students explore methods employing simple machines likely used in ancient pyramid building, as well as common modern-day material transportation. They learn about the wheel and axle as a means to transport materials from rock quarry to construction site. They also learn about different types and uses of a lever for purposes of transport. In an open-ended design activity, students choose from everyday materials to engineer a small-scale cart and lever system to convey pyramid-building materials.

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 are asked whether they can determine the number of books in a stack by measuring the height of the stack, or the number of marbles in a collection of marbles by weighing the collection.Students are asked to identify for which situations they can determine the number of books in a stack of books by measuring the height of the stack or the number of marbles in a collection of marbles by weighing the collection.Key ConceptsAs students examine different numerical relationships, they come to understand that they can find the number of books or the number of marbles in situations in which the books are all the same thickness and the marbles are all the same weight. This “constant” is equal to the value BA for a ratio A : B; students begin to develop an intuitive understanding of proportional relationships.Goals and Learning ObjectivesExplore numerical relationshipsSWD: Some students with disabilities will benefit from a preview of the goals in each lesson. Have students highlight the critical features or concepts to help them pay close attention to salient information.

Students revisit Bernoulli's Principle (Lesson 1 of the Airplanes unit) and learn how engineers use this principle to design airplane wings. Airplane wings create lift by changing the pressure of the air around it. This is the first of four lessons exploring the four key forces in flight: lift, weight, thrust and drag.

The purpose of this lesson is to help students understand the relationship between the mass and the weight of an object. Students will study the properties of common materials and why airplanes use specific materials.

This short video and interactive assessment activity is designed to teach fourth graders about introduction to metric measures: how big is a meter?.

This short video and interactive assessment activity is designed to teach fourth graders about adding lengths in meters.

This short video and interactive assessment activity is designed to give fourth graders an overview of conversion of capacity units (metric units).

This short video and interactive assessment activity is designed to teach fourth graders about multiplication of lengths (metric units).

This short video and interactive assessment activity is designed to teach fourth graders about subtracting lengths in meters.

Students design, build and test model race cars made from simple materials (lifesaver-shaped candies, plastic drinking straws, Popsicle sticks, index cards, tape) as a way to explore independent, dependent and control variables. They measure the changes in distance travelled with the addition of mass to the vehicles. Students also practice the steps of the engineering design process by brainstorming, planning, building, testing, and improving their "mint-mobiles."

This short video and interactive assessment activity is designed to teach fourth graders about mixed adding and subtracting of capacities (english units).

This short video and interactive assessment activity is designed to give fourth graders an overview of capacity with compound units - word problems.

This short video and interactive assessment activity is designed to teach fourth graders about mixed operations with compound units using multiplication and division - word problems.

Student engineers learn to understand force and motion and how it is effected by slope, design and weight carried.

This short video and interactive assessment activity is designed to teach fourth graders about using scales and calculations to find weights (metric units).

This short video and interactive assessment activity is designed to teach fourth graders about multi-step compound unit addition (metric units) - word problems.

This short video and interactive assessment activity is designed to teach fourth graders about multi-step division problems with compound units.

This short video and interactive assessment activity is designed to teach fourth graders about multi-step problems using the four operations - word problems.