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Illustrative Mathematics

Representing Half of a Circle

For Teachers 2nd - 4th Standards
Geometric shapes make great visual models for introducing young mathematicians to the concept of fractions. Looking at a series of four circles, students are asked to determine whether or not one half of each circle is shaded. To support...
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Lesson Plan
Curated OER

Area and Perimeter

For Teachers 10th
Learners find the area and perimeter of regular polygons and composite figures and examine the effect on the area and perimeter of a figure if the dimensions are multiplied by a constant. The nine page worksheet contains thirty-seven...
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Worksheet
Curated OER

Comparing Areas

For Teachers 2nd - 3rd Standards
Before your scholars know how to multiply side lengths to find an area, give them some practice in simply counting units. They examine shapes that have already been segmented into units, counting them to get the area. There are three...
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Lesson Plan
EngageNY

What Is Area?

For Teachers 9th - 10th Standards
What if I can no longer justify area by counting squares? Lead a class discussion to find the area of a rectangular region with irrational side lengths. The class continues on with the idea of lower approximations and...
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Lesson Plan
Curated OER

Surface Area, Who Needs it?

For Teachers 6th - 10th
For this geometry lesson on cylinders, geometers explore how to find the smallest surface area for a given volume.  They use their knowledge to relate it to the real world by making a model of a livestock tank.
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Lesson Plan
Mathematics Assessment Project

Calculating Arcs and Areas of Sectors of Circles

For Teachers 9th - 12th Standards
Going around in circles trying to find a resource on sectors of circles? Here is an activity where pupils first complete an assessment task to determine the areas and perimeters of sectors of circles. They then participate in an...
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Assessment
Concord Consortium

Strings and Areas

For Students 9th - 11th Standards
You'd be surprised what you can do with a string! The constraint is the length of string, and the task is to maximize area. Given a series of composite shapes, learners must create a formula for the maximum area for a specified...
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Unit Plan
Mathematics Vision Project

Module 5: Circles A Geometric Perspective

For Teachers 9th - 12th Standards
Circles, circles, everywhere! Pupils learn all about circles, central angles, inscribed angles, circle theorems, arc length, area of sectors, and radian measure using a set of 12 lessons. They then discover volume formulas through...
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Lesson Plan
Illustrative Mathematics

Stained Glass

For Teachers 7th - 9th Standards
A complex question looking for the total cost of a stained glass window by calculating area and circumference of a circle. With detailed components, this activity will challenge your designers to figure out if they have enough money to...
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Lesson Plan
Mascil Project

Circular Pave-Stones Backyard

For Teachers 6th - 12th Standards
Pack the lesson into your plans. Young mathematicians learn about packing and optimization with the context of circular paving stones. They use coins to model the paving stones, and then apply knowledge of circles and polygons to...
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Assessment
Mathematics Assessment Project

Circles and Squares

For Students 9th - 12th Standards
Squares, and circles ... and squares, and more circles. In this high school assessment task, pupils investigate the ratio of areas of two squares that are circumscribed and inscribed in a circle. They then determine the ratio of the area...
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Lesson Plan
EngageNY

Properties of Area

For Teachers 9th - 10th Standards
What properties does area possess? Solidify the area properties that pupils learned in previous years. Groups investigate the five properties using four problems, which then provide the basis for a class discussion.
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Lesson Plan
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Curated OER

The Geometry Of An Ox Skin

For Teachers 9th - 12th
High schoolers investigate the concepts of area and perimeter. The lesson uses a legend to create a context for the proposed word problem. They use the skill of estimation in order to create an ox skin that is found in the story. 
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Lesson Plan
Alabama Learning Exchange

How Big Can a Bee Be?

For Teachers 7th - 10th Standards
Mathematicians analyze the relationships between surface area and volume. They conduct Internet research, conduct various experiments, record the data in a spreadsheet, and graph the results and compare the rate of increase of surface...
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Worksheet
Curated OER

Finding The Area

For Students 9th - 11th
In this geometry worksheet, students calculate the area of a given shape. They use the formulas for squares and circles to help them find the area. There are 2 questions with an answer key.
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Lesson Plan
Curated OER

Perpendicular Segments in a Circle

For Teachers 9th - 12th Standards
High schoolers explore the concept of circles as they construct a circle using a program such as Cabri Jr. Learners construct a chord and a diameter that are perpendicular, then measure the bisected chord and notice that both sides of...
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Lesson Plan
Curated OER

Circumscribing a Circle About a Triangle

For Teachers 9th - 12th Standards
Pupils circumscribe a circle about a triangle. They construct a triangle using Cabri Jr and then circumscribe it. They then use knowledge of perpendicular bisectors and circumcenters to locate the center of the circle and then...
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Lesson Plan
Curated OER

Construction Circles

For Teachers 9th - 12th Standards
Pupils investigate the number of points needed to determine a unique circle in a plane. Using Cabri Jr., they apply construction techniques to generate a circle that passes through a given number of points.
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Worksheet
Curated OER

Quiz: Area of Sector and Segment

For Students 10th - 12th
In this area of sector and segment instructional activity, students find the area of a shaded sector. Given the central angle of a segment and the radius, students identify the area of a sector. This one-page instructional activity...
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Worksheet
Curated OER

Chapter 8 Worksheet 3 Circumference & Area

For Students 8th - 12th
For this circumference and area worksheet, students determine the circumference and area of given circles. They find the area of shaded regions of circles and areas around circles. This two-page worksheet contains 18 multi-step problems.
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Interactive
Curated OER

Area of Figures That Include Circles

For Students 10th - 12th
In this area worksheet, learners calculate the perimeter and area of given complex figures.  They determine the area of shaded regions, and find the distance between straight lines.  This one-page worksheet contains 4...
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Interactive
Curated OER

Find the Area of Four Shaded Figures that Include Circles

For Students 9th - Higher Ed
In this area worksheet, students calculate the area of four figures that each include circles.  Students can check their answers and get hint by clicking on the "Check" or "Hint" button at the bottom of the page.
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Interactive
Curated OER

Online Math Learning: Surface Area of Spheres

For Students 9th - 12th
In this surface area of spheres worksheet, students solve 4 short answer problems. Students find the surface area of spheres, hemispheres, and cones given a radius or a radius and height.
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Lesson Plan
Virginia Department of Education

Going the Distance

For Teachers 6th Standards
Estimate the value of one of the most famous irrational numbers. The hands-on lesson instructs classmates to measure the circumference and diameters of circles using yarn. The ratio of these quantities defines pi.

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