**Subject Area:**Mathematics

**Grade:**7

**Domain-Subdomain:**Geometry

**Cluster:**Level 2: Basic Application of Skills & Concepts

**Cluster:**Solve real-life and mathematical problems involving angle measure, area, surface area, and volume. (Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

**Date Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved

**Assessed:**Yes

**Assessment Limits :**Circles are limited to whole circles and semicircles.

**Calculator :**Yes

**Context :**Allowable

**Test Item #:**Sample Item 1**Question:**A circle with its dimensions, in centimeters (cm), is shown.

What is the area, in square centimeters, of the circle?

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 2**Question:**A circle with its dimensions, in inches (in.), is shown.What is the area, in square inches, of half the circle?

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 3**Question:**Mark placed a pool in his backyard, which is enclosed by a triangular fence.The radius of the pool is 20.5 feet. How much of the backyard area is not covered by the pool?

**Difficulty:**N/A**Type:**EE: Equation Editor

**Test Item #:**Sample Item 4**Question:**The circumference of a circle is 53.38 centimeters.

What is the area in square centimeters? Use 3.14 for

**Difficulty:**N/A**Type:**EE: Equation Editor

## Related Courses

## Related Access Points

## Related Resources

## Assessment

## Formative Assessments

## Lesson Plans

## Original Student Tutorials

## Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiasts

## Perspectives Video: Teaching Ideas

## Problem-Solving Tasks

## Tutorials

## Video/Audio/Animation

## Virtual Manipulatives

## STEM Lessons - Model Eliciting Activity

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.

This MEA requires students to formulate a comparison-based solution to a problem involving finding the best plan for installing tile floor considering different aspects. Students are provided the context of the problem, a request letter from a client asking them to provide a recommendation, and data relevant to the situation. Students utilize the data to create a defensible model solution to present to the client.

## MFAS Formative Assessments

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

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.

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.

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

## Original Student Tutorials Mathematics - Grades 6-8

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.

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.

Learn to solve problems involving the circumference and area of a circle in this pool-themed, interactive tutorial.

## Student Resources

## Original Student Tutorials

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

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

Learn to solve problems involving the circumference and area of a circle in this pool-themed, interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Expert

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

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

## Problem-Solving Task

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.

Type: Problem-Solving Task

## Tutorials

This tutorial shows how the area and circumference relate to each other. Students will investigate how changing the radius of a circle affects the area and circumference.

Type: Tutorial

A circle is at the foundation of geometry. In this tutorial, students are shown the parts of a circle and how the radiius, diameter, circumference and Pi relate to each other. Students will also learn how to find the area and circumference of a circle.

Type: Tutorial

This tutorial shows how to find the circumference, the distance around a circle, given the area. Students will build upon their knowledge of the parts of circle.

Type: Tutorial

In this example, students solve for the area of a circle when given the diameter. The diameter is the length of a line that runs across the circle and through the center.

Type: Tutorial

## Virtual Manipulative

This applet allows students to investigate the relationships between the area and circumference of a circle and its radius and diameter. There are three sections to the site: Intro, Investigation, and Problems.

- In the Intro section, students can manipulate the size of a circle and see how the radius, diameter, and circumference are affected. Students can also play movie clip to visually see how these measurements are related.
- The Investigation section allows students to collect data points by dragging the circle radius to various lengths, and record in a table the data for radius, diameter, circumference and area. Clicking on the x/y button allows students to examine the relationship between any two measures. Clicking on the graph button will take students to a graph of the data. They can plot any of the four measures on the x-axis against any of the four measures on the y-axis.
- The Problems section contains questions for students to solve and record their answers in the correct unit.

(NCTM's Illuminations)

Type: Virtual Manipulative

## Parent Resources

## Perspectives Video: Expert

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

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

## Problem-Solving Task

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.

Type: Problem-Solving Task

## Video/Audio/Animation

This video dynamically shows how Pi works, and how it is used.

Type: Video/Audio/Animation

## Virtual Manipulative

This interactive lesson introduces students to the circle, its attributes, and the formulas for finding its circumference and its area. Students then perform a few calculations to practice finding the area and circumference of circles, given the diameter.

Type: Virtual Manipulative