Strand: GEOMETRY (7.G)

Draw, construct, and describe geometrical figures, and describe the relationships between them (Standards 7.G.1-3). Solve real-life and mathematical problems involving angle measure, area, surface area, and volume (Standards 7.G.4-6).

Standard 7.G.4

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

• Angles
Students are introduced to all kinds of angles in this lesson plan, including acute, obtuse, right, vertical, adjacent, and corresponding among others.
• Applying Angle Theorems
This lesson unit is intended to help educators assess how well students are able to use geometric properties to solve problems.
• Approximating the area of a circle
The goal of this task is twofold: Use the idea of scaling to show that the ratio Area of Circle: (Radius of Circle)2 does not depend on the radius. Use formulas for the area of squares and triangles to estimate the value a real number.
• Area
This lesson is designed to help students be able to calculate the area of a random shape on a grid, explain the correlation between the size of the perimeter and the number of different possible areas that can be contained within that perimeter.
• Area Explorations
In this lesson, students will explore the area of irregular shapes to find multiple different methods for calculating area
• Chapter 5 - Mathematical Foundation (UMSMP)
This is Chapter 5 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Geometry I - Scale Drawings, Geometric Figures.
• Chapter 5 - Student Workbook (UMSMP)
This is Chapter 5 of the Utah Middle School Math: Grade 7 student workbook. It focuses on these topics: Geometry I - Scale Drawings and Geometric Figures.
• Chapter 8 - Mathematical Foundation (UMSMP)
This is Chapter 8 of the Utah Middle School Math Grade 7 textbook. It provides a Mathematical Foundation for Measurement in 2-3 Dimensions and Cross-Sections of Solids.
• Chapter 8 - Student Workbook (UMSMP)
This is Chapter 8 of the Utah Middle School Math Grade 7 student workbook. It focuses on Measurement in 2-3 Dimensions and Cross-Sections of Solids.
• Circumference of a Circle
The goal of this task is to study the circumferences of different sized circles, both using manipulatives and from the point of view of scaling.
• Estimating: Counting Trees
This lesson unit is intended to help educators assess how well students are able to solve simple problems involving ratio and direct proportion, choose an appropriate sampling method, and collect discrete data and record them using a frequency table.
• Estimations and Approximations: The Money Munchers
This lesson unit is intended to help educators assess how well students are able to model a situation, make sensible, realistic assumptions and estimates, and use assumptions and estimates to create a chain of reasoning, in order to solve a practical problem.
• Formulas for Circle Area and Circumference: Simple as Pie
A video from Cyberchase shows Bianca undertaking the selling of pies. She has to understand the relationship between the diameter and the circumference of pie pans. In the classroom activity you will learn how to calculate the circumference of wheels. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Grade 7 Math Module 3: Expressions and Equations (EngageNY)
This module consolidates and expands upon students understanding of equivalent expressions as they apply the properties of operations to write expressions in both standard form and in factored form. They use linear equations to solve unknown angle problems and other problems presented within context to understand that solving algebraic equations is all about the numbers. Students use the number line to understand the properties of inequality and recognize when to preserve the inequality and when to reverse the inequality when solving problems leading to inequalities. They interpret solutions within the context of problems. Students extend their sixth-grade study of geometric figures and the relationships between them as they apply their work with expressions and equations to solve problems involving area of a circle and composite area in the plane, as well as volume and surface area of right prisms.
• Grade 7 Unit 4: Geometry (Georgia Standards)
The units in this instructional framework emphasize key standards that assist students to develop a deeper understanding of numbers. In this unit they will be engaged in using what they have previously learned about drawing geometric figures using rulers and protractor with an emphasis on triangles, students will also write and solve equations involving angle relationships, area, volume, and surface area of fundamental solid figures.
• Holes
After watching a clip of the movie Holes from Walt Disney Pictures students will answer a series of questions, such as "If Stanley and X-Ray both dig one hole per day for a year, how much extra dirt will Stanley have dug than X-Ray?" and "How many times could that extra dirt fill one of the holes X-Ray digs?"
• Maximizing Area: Gold Rush
This lesson unit is intended to help educators assess how well students are able to interpret a situation and represent the variables mathematically, select appropriate mathematical methods to use, explore the effects on the area of a rectangle of systematically varying the dimensions whilst keeping the perimeter constant, as well as interpret and evaluate the data generated and identify the optimum case.
• Solving Linear Inequalities with Negative Numbers
Students will learn how to solve linear equations that have a negative number solution. They then solve a series of equations with both positive and negative coefficients and solutions in the classroom activity. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
In this task, students have to decide how you would describe the design of a mosaic pattern over the telephone.
In this task, the student will look at a pattern of black and white circles and describe, mathematically, what is happening to the areas of black and white as the pattern develops.
In this task, students will figure out some problems about a strange old bicycle.
In this task, students will explore the geometry of a pattern made by arranging squares within an octagon.
• Surface Area of a Rectangular Prisms
This lesson will help students understand surface area and solve problems using the surface area of a rectangular prism.
• Surface Area of Prisms
In this lesson students will understand surface area and how solve for the surface area of triangular prisms.
• Volume of Prisms
This is a lesson designed to help students understand how to solve problems for the volume of triangular prisms.
• Volume of Rectangular Prisms
This lesson is designed to help students understand how to solve for the volume of rectangular prisms.

http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey  Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.