CPALMS Logo Generated on 9/18/2025 at 2:44 PM
The webpage this document was printed/exported from can be found at the following URL:
https://www.cpalms.org/PreviewIdea/Preview/3516
Standard 1 : Solve problems involving two-dimensional figures, including circles.
Cluster Standards

This cluster includes the following benchmarks.

Visit the specific benchmark webpage to find related instructional resources.

  • MA.7.GR.1.1 : Apply formulas to find the areas of trapezoids, parallelograms and rhombi.
  • MA.7.GR.1.2 : Solve mathematical or real-world problems involving the area of polygons or composite figures by decomposing them into triangles or quadrilaterals.
  • MA.7.GR.1.3 : Explore the proportional relationship between circumferences and diameters of circles. Apply a formula for the circumference of a circle to solve mathematical and real-world problems.
  • MA.7.GR.1.4 : Explore and apply a formula to find the area of a circle to solve mathematical and real-world problems.
  • MA.7.GR.1.5 : Solve mathematical and real-world problems involving dimensions and areas of geometric figures, including scale drawings and scale factors.
Cluster 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
Cluster Access Points

This cluster includes the following 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.
Cluster Resources

Vetted resources educators can use to teach 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.

  • 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.

  • Swimming in Circles: Learn to solve problems involving the circumference and area of circle-shaped pools in this interactive 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.

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.

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.

  • Eye on Circumference: Students are asked to solve a problem involving the circumference of a circle.

  • 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.

  • 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.

  • Center Circle Area: Students are asked to solve a problem involving the area of a circle.

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

  • 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.

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

  • Octagon Area: Students are asked to find the area of a composite figure.

  • Composite Polygon Area: Students are asked to find the area of a composite figure.

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.

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.

  • 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.

  • 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.

  • 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.

  • 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.

  • 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.

  • Bubble Burst Corporation's Chewing Gum Prototypes: In this Model Eliciting Activities, MEA, students will calculate unit rate & circumference, compare & order decimals, convert metric units, and round decimals. Bubble Burst Corporation has developed some chewing gum prototypes and has requested the students to assist in the selection of which gum prototypes will be mass produced by using both quantitative and qualitative data to rank the prototypes for Bubble Burst Corporation.

    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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

  • 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.

  • 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.

  • 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.

  • Sir Cumference introduces Radius and Diameter: This lesson is designed to be a fun and creative way to introduce math vocabulary (radius, diameter, and circumference) related to circles. Students will create a story board (comic strip) to retell or create a story using targeted vocabulary, and then demonstrate understanding of the relationships among radii, diameter, and circumference by completing the worksheet.

  • Installing Tile Floor: In this Model Eliciting Activity (MEA), students will analyze data related to tiling rooms in a house. Students will calculate the square footage of various rooms, convert measurements to determine the amount of tile needed, and compute both the cost of the tiles and the cost of installation. They will evaluate and compare different flooring options based on cost, quality, and installation factors, and develop a procedure to recommend the best choices.

    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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

  • Makeover, Home Edition Part III: This is the third part of the lesson, "Makeover, Home Edition". This lesson is designed to teach students how to put ideas into reality by creating and using scale drawings in the real world. In Part I (#48705) students determined backyard dimensions for fence installation. Part II (#48967) concentrated on inserting a pool and patio into the backyard. In Part III (#49025) students will create a scale drawing of the backyard. Part IV (#49090) will focus on inserting a window and painting walls inside the house.

  • The Ins and Outs of Polygons: In this lesson, students will explore how to find the sum of the measures of the angles of a triangle, then use this knowledge to find the sum of the measures of angles of other polygons. They will also be able to find the sum of the exterior angles of triangles and other polygons. Using both concepts, students will be able to find missing measurements.

  • 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. 

  • Survival Journal Part Two: Outdoor Gardening: In this lesson, students will design two outdoor gardens, 1) a raised garden bed and 2) a ground level garden (traditional). Students will, with help of the teacher, till the ground with removal of ground cover, build border for garden, add soil, attach poles with string to create a life size graph all so they can grow tomatoes and plot the data easily in their survival journals.This is Part 2 of a 4-Part Project on Survival.

  • How Many Degrees?: This lesson facilitates the discovery of a formula for the sum of the interior angles of a regular polygon. Students will draw all the diagonals from one vertex of various polygons to find how many triangles are formed. They will use this and their prior knowledge of triangles to figure out the sum of the interior angles. This will lead to the development of a formula for finding the sum of interior angles and the measure of one interior angle.

  • Boxing Candles: In this MEA, students select jars for candles based on a variety of factors and then design boxes to contain the jars.

    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.

  • Fastest Route: In this Model Eliciting Activity, MEA, students will interpret and analyze a scale drawing to provide possible routes from a teacher’s home to the school. Students will consider factors including traffic patterns, construction zones, and wait times to recommend the best route including the total distance, in miles, and estimated delay times.

    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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

  • 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.

  • It's All About the Scale!: Students will apply their knowledeg of scale drawings, scale models, scale factors, and scale to create their own enlargement of an image they choose.

Perspectives Video: Expert
  • 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. mathematics benchmarks in this Expert Perspectives video.

Perspectives Video: Professional/Enthusiasts
Perspectives Video: Teaching Ideas
Problem-Solving Tasks
  • Running around a track II: The goal of this task is to model a familiar object, an Olympic track, using geometric shapes. Calculations of perimeters of these shapes explain the staggered start of runners in a 400 meter race.

  • Running around a track I: In this problem, geometry is applied to a 400 meter track to find the perimeter of the track.

  • Paper Clip: In this task, a typographic grid system serves as the background for a standard paper clip. A metric measurement scale is drawn across the bottom of the grid and the paper clip extends in both directions slightly beyond the grid. Students are given the approximate length of the paper clip and determine the number of like paper clips made from a given length of wire.

  • Eight Circles: Students are asked to find the area of a shaded region using a diagram and the information provided. The purpose of this task is to strengthen student understanding of area.

  • Floor Plan: The purpose of this task is for students to translate between measurements given in a scale drawing and the corresponding measurements of the object represented by the scale drawing. If used in an instructional setting, it would be good for students to have an opportunity to see other solution methods, perhaps by having students with different approaches explain their strategies to the class. Students who can only solve this by first converting the linear measurements will have a hard time solving problems where only area measures are given.

  • 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.

Teaching Idea
  • Classroom Floor Plan: This resource guides the learner step-by-step in creating a scale floor plan of a classroom. The instructions include sample drawings of student work. The activity includes sketching a map of the classroom, measuring the room and calculating the area and perimeter, creating a scale drawing, and drafting a CAD (computer-aided design) floor plan through Google Slides or PPT. The lesson provides students with hands-on, real world practice solving problems of measurement, ratio, and scale.

Tutorials