Standard 1: Solve problems involving two-dimensional figures, including circles.

General Information
Number: MA.7.GR.1
Title: Solve problems involving two-dimensional figures, including circles.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 7
Strand: Geometric Reasoning

Related Benchmarks

This cluster includes the following benchmarks.

Related Access Points

This cluster includes the following access points.

Access Points

MA.7.GR.1.AP.1
Given the formulas, find the area of parallelograms and rhombi.
MA.7.GR.1.AP.2
Decompose complex shapes (polygon, trapezoid, and pentagon) into simple shapes (rectangles, squares, triangles) to measure area.
MA.7.GR.1.AP.3
Apply a given formula for the circumference of a circle to solve mathematical problems.
MA.7.GR.1.AP.4
Apply a given formula to find the area of a circle to solve mathematical problems.
MA.7.GR.1.AP.5
Use a scale factor to draw a scale drawing of a real-world two-dimensional polygon on graph paper.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this topic.

3D Modeling

Wind Farm Design Challenge:

In this engineering design challenge, students are asked to create the most efficient wind turbine while balancing cost constraints. Students will apply their knowledge of surface area and graphing while testing 3D-printed wind farm blades. In the end, students are challenged to design and test their own wind farm blades, using Tinkercad to model a 3D-printable blade.

Type: 3D Modeling

Formative Assessments

The Meaning of Pi:

Students are asked to explain the relationship between the circumference and diameter of a circle in terms of pi.

Type: Formative Assessment

Eye on Circumference:

Students are asked to solve a problem involving the circumference of a circle.

Type: Formative Assessment

Circumference Formula:

Students are asked to write the formula for the circumference of a circle, explain what each symbol represents, and label the variables on a diagram.

Type: Formative Assessment

Circle Area Formula:

Students are asked to write the formula for the area of a circle, explain what each symbol represents, and label the radius on a diagram.

Type: Formative Assessment

Center Circle Area:

Students are asked to solve a problem involving the area of a circle.

Type: Formative Assessment

Broken Circles:

Students are asked to complete and explain an informal derivation of the relationship between the circumference and area of a circle.

Type: Formative Assessment

Space Station Scale:

Students are asked to find the ratio of the area of an object in a scale drawing to its actual area and then relate this ratio to the scale factor in the drawing.

Type: Formative Assessment

Flying Scale:

Students are asked to find the length and area of an object when given a scale drawing of the object.

Type: Formative Assessment

Octagon Area:

Students are asked to find the area of a composite figure.

Type: Formative Assessment

Composite Polygon Area:

Students are asked to find the area of a composite figure.

Type: Formative Assessment

Image/Photograph

Clipart: Geometric Shapes:

In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes.

Type: Image/Photograph

Lesson Plans

Clean It Up:

Students will help a volunteer coordinator choose cleanup projects that will have the greatest positive impact on the environment and the community.  They will apply their knowledge of how litter can impact ecosystems along with some math skills to make recommendations for cleanup zones to prioritize.  Students will explore the responsibilities of citizens to maintain a clean environment and the impact that litter can have on society in this integrated Model Eliciting Activity.  

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations.  Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Guiding Grids: Math inspired self-portraits:

Students will create a proportional self portrait from a photo using a gridded drawing method and learn how a grid system can help accurately enlarge an image in a work of art. Students will use the mathematical concepts of scale, proportion and ratio, to complete their artwork.

Type: Lesson Plan

Breaking Up is Hard to Do:

Student will use geoboards to decompose composite figures and polygons into squares, rectangles, and triangles in order to find the total area.

Type: Lesson Plan

Fish Kribs:

In this lesson, students create a fish tank for a fish supply company for a future sales campaign. They will use scale drawings and proportions to design the perfect fish tank.

  • First, students have to complete a ranking activity of items that will be included in their scale drawing along with three types of fish.
  • Next, students will conduct a pH lab activity to gain knowledge about how pH levels will affect population and the ecosystem within the tank.
  • Finally, students will adjust their item selection and re-engineer their tank drawing to support their findings and additional information provided by the client. Students must determine what objects would be beneficial to the living things that the students chose in relation to available space and pH balance.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

How Fast Can One Travel on a Bicycle?:

Students investigate how the pedal and rear wheel gears affect the speed of a bicycle. A GeoGebra sketch is included that allows a simulation of the turning of the pedal and the rear wheel. A key goal is to provide an experience for the students to apply and integrate the key concepts in seventh-grade mathematics in a familiar context.

Type: Lesson Plan

Discovering Dilations:

This resource is designed to allow students to discover the effects of dilations on geometric objects using the free online tools in GeoGebra.

Type: Lesson Plan

Circumference/Rotation Relationship in LEGO/NXT Robots or Do I Wheely need to learn this?:

7th grade math/science lesson plan that focuses on the concept of circumference and rotation relationship. Culminates in a problem-solving exercise where students apply their knowledge to the "rotations" field in programming a LEGO/NXT robot to traverse a set distance.

Type: Lesson Plan

Building Graduation Caps:

Students will apply skills from the Geometry Domain to build graduation caps for themselves using heavyweight poster paper. They will also apply some basic mathematical skills to determine dimensions and to determine minimum cost. Some of the Geometric skills reinforced in Building Graduation Caps: Cooperative Assignment are finding area, applying the concept of similarity, and the application of the properties of parallelograms. Other skills also involved in this application are measuring, and statistical calculations, such as finding the mean and the range. In addition to the hands-on group project that takes place during the lesson, there is the Prerequisite Skills Assessment: Area that should be administered before the group activity and a home-learning activity. Building Graduation Caps: Individual Assignment is the home-learning assignment; it is designed to reinforce the skills learned in the group activity.

Type: Lesson Plan

My Favorite Slice:

The lesson introduces students to sectors of circles and illustrates ways to calculate their areas. The lesson uses pizzas to incorporate a real-world application for the of area of a sector. Students should already know the parts of a circle, how to find the circumference and area of a circle, how to find an arc length, and be familiar with ratios and percentages.

Type: Lesson Plan

Finding Area with Hands-On Measurement:

This lesson allows students to apply the area of triangles, quadrilaterals, and trapezoids to composite figures, and gives students a chance to work with classmates to find the area by taking measurements and making the necessary calculations. Students will also see the relationship between the area formulas for rectangles, triangles, trapezoids, and polygons. 

Type: Lesson Plan

Raising Your Garden MEA:

Raising Your Garden MEA provides students with a real world engineering problem in which they must work as a team to design a procedure to select the best material for building raised garden beds. The main focus of this MEA is to recognize the importance of choosing the correct material for building a raised garden bed, what information is needed before starting a gardening project, and to consider the environmental and economic impact the garden will have on the school. Students will conduct individual and team investigations in order to arrive at a scientifically sound solution to the problem.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. 

Type: Lesson Plan

How does scale factor affect the areas and perimeters of similar figures?:

In this lesson plan, students will observe and record the linear dimensions of similar figures, and then discover how the values of area and perimeter are related to the ratio of the linear dimensions of the figures.

Type: Lesson Plan

Original Student Tutorials

Pizza Pi: Circumference:

Explore the origins of Pi as the ratio of Circumference to diameter of a circle. In this interactive tutorial you'll work with the circumference formula to determine the circumference of a circle and work backwards to determine the diameter and radius of a circle.

Type: Original Student Tutorial

Pizza Pi: Area:

Explore how to calculate the area of circles in terms of pi and with pi approximations in this interactive tutorial. You will also experience irregular area situations that require the use of the area of a circle formula.

Type: Original Student Tutorial

Swimming in Circles:

Learn to solve problems involving the circumference and area of circle-shaped pools in this interactive tutorial.

Type: Original Student Tutorial

Scale Round Up:

Learn to use architectural scale drawings to build a new horse arena and solve problems involving scale drawings in this interactive tutorial. By the end, you should be able to calculate actual lengths using a scale and proportions.

Type: Original Student Tutorial

Perspectives Video: Experts

B.E.S.T. Journey:

What roles do exploration, procedural reliability, automaticity, and procedural fluency play in a student's journey through the B.E.S.T. benchmarks? Dr. Lawrence Gray explains the path through the B.E.S.T. maththematics benchmarks in this Expert Perspectives video.

Type: Perspectives Video: Expert

Practical Use of Area and Circumference:

A math teacher describes the relationship between area and circumference and gives examples in nature.

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiasts

Pizza Pi: Area, Circumference & Unit Rate:

How many times larger is the area of a large pizza compared to a small pizza?  Which pizza is the better deal? Michael McKinnon of Gaines Street Pies talks about how the area, circumference and price per square inch is different depending on the size of the pizza.  

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Modeling with Polygons for 3D Printers:

Understand 3D modeling from a new angle when you learn about surface geometry and 3D printing.

Type: Perspectives Video: Professional/Enthusiast

Using Geometry for Interior Design and Architecture:

An architect discusses how he uses circumference and area calculations to accurately create designs and plans.

Type: Perspectives Video: Professional/Enthusiast

Geometry for Dance Costume Designs:

A dance costume designer describes how she uses circumference and area calculations to make clothing for the stage.

Type: Perspectives Video: Professional/Enthusiast

Perspectives Video: Teaching Ideas

Surface Area Misconception:

Unlock an effective teaching strategy for identifying the base and height of figures in this Teacher Perspectives video for educators.

Type: Perspectives Video: Teaching Idea

Cookies and Pi:

A math teacher presents an idea for a classroom activity to engage students in measuring diameter and circumference to calculate pi.

Type: Perspectives Video: Teaching Idea

KROS Pacific Ocean Kayak Journey: Kites, Geometry, and Vectors:

Set sail with this math teacher as he explains how kites were used for lessons in the classroom.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set [.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth [.KML]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

Bicycle Mathematics: Speed and Distance Calculations:

Cycling involves a lot of real-time math when you use an on-board computer. Learn about lesson ideas and how computers help with understanding performance.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

Robot Mathematics: Gearing Ratio Calculations for Performance:

A science teacher demonstrates stepwise calculations involving multiple variables for designing robots with desired characteristics.

Type: Perspectives Video: Teaching Idea

Problem-Solving Task

Surface Area and Volume:

In this activity, students adjust the dimensions of either a rectangular or triangular prism and the surface area and volume are calculated for those dimensions. Students can also switch into compute mode where they are given a prism with certain dimensions and they must compute the surface area and volume. The application keeps score so students can track their progress. This application allows students to explore the surface area and volume of rectangular and triangular prisms and how changing dimensions affect these measurements. This activity also includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Problem-Solving Task

Tutorials

Impact of a Radius Change on the Area of a Circle:

This video shows how the area and circumference relate to each other and how changing the radius of a circle affects the area and circumference.

 

Type: Tutorial

Circles: Radius, Diameter, Circumference, and Pi:

In this video, students are shown the parts of a circle and how the radius, diameter, circumference and Pi relate to each other.

Type: Tutorial

Circumference of a Circle:

This video shows how to find the circumference, the distance around a circle, given the area.

Type: Tutorial

Area of a Circle:

In this video, watch as we find the area of a circle when given the diameter.

Type: Tutorial

Area of a Parallelogram:

This video portrays a proof of the formula for area of a parallelogram.  

Type: Tutorial

Area of a Trapezoid:

A trapezoid is a type of quadrilateral with one set of parallel sides. Here we explain how to find its area.

Type: Tutorial

Perimeter and Area:

Students will learn the basics of finding the perimeter and area of squares and rectangles.  

Type: Tutorial

Student Resources

Vetted resources students can use to learn the concepts and skills in this topic.

Original Student Tutorials

Pizza Pi: Circumference:

Explore the origins of Pi as the ratio of Circumference to diameter of a circle. In this interactive tutorial you'll work with the circumference formula to determine the circumference of a circle and work backwards to determine the diameter and radius of a circle.

Type: Original Student Tutorial

Pizza Pi: Area:

Explore how to calculate the area of circles in terms of pi and with pi approximations in this interactive tutorial. You will also experience irregular area situations that require the use of the area of a circle formula.

Type: Original Student Tutorial

Swimming in Circles:

Learn to solve problems involving the circumference and area of circle-shaped pools in this interactive tutorial.

Type: Original Student Tutorial

Scale Round Up:

Learn to use architectural scale drawings to build a new horse arena and solve problems involving scale drawings in this interactive tutorial. By the end, you should be able to calculate actual lengths using a scale and proportions.

Type: Original Student Tutorial

Perspectives Video: Expert

Practical Use of Area and Circumference:

A math teacher describes the relationship between area and circumference and gives examples in nature.

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiast

Modeling with Polygons for 3D Printers:

Understand 3D modeling from a new angle when you learn about surface geometry and 3D printing.

Type: Perspectives Video: Professional/Enthusiast

Tutorials

Impact of a Radius Change on the Area of a Circle:

This video shows how the area and circumference relate to each other and how changing the radius of a circle affects the area and circumference.

 

Type: Tutorial

Circles: Radius, Diameter, Circumference, and Pi:

In this video, students are shown the parts of a circle and how the radius, diameter, circumference and Pi relate to each other.

Type: Tutorial

Circumference of a Circle:

This video shows how to find the circumference, the distance around a circle, given the area.

Type: Tutorial

Area of a Circle:

In this video, watch as we find the area of a circle when given the diameter.

Type: Tutorial

Area of a Parallelogram:

This video portrays a proof of the formula for area of a parallelogram.  

Type: Tutorial

Area of a Trapezoid:

A trapezoid is a type of quadrilateral with one set of parallel sides. Here we explain how to find its area.

Type: Tutorial

Perimeter and Area:

Students will learn the basics of finding the perimeter and area of squares and rectangles.  

Type: Tutorial

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this topic.

Image/Photograph

Clipart: Geometric Shapes:

In this lesson, you will find clip art and various illustrations of polygons, circles, ellipses, star polygons, and inscribed shapes.

Type: Image/Photograph

Perspectives Video: Expert

Practical Use of Area and Circumference:

A math teacher describes the relationship between area and circumference and gives examples in nature.

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiast

Modeling with Polygons for 3D Printers:

Understand 3D modeling from a new angle when you learn about surface geometry and 3D printing.

Type: Perspectives Video: Professional/Enthusiast