 Mathematics Grade 7

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.5

Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

• 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.
• 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 6 - Mathematical Foundation (UMSMP)
This is Chapter 6 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Expressions and Equations II - Real-world equations, Inequalities.
• Chapter 6 - Student Workbook (UMSMP)
This is Chapter 6 of the Utah Middle School Math: Grade 7 textbook. It focuses on these topics: Real-world equations and Inequalities.
• 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.
• Finding Unknown Angles
In this Math Shorts video from the Utah Education Network students learn to find unknown supplementary, complementary, vertical and adjacent angles. 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 Math Module 6: Geometry (EngageNY)
In Module 6, students delve further into several geometry topics they have been developing over the years. Grade 7 presents some of these topics, (e.g., angles, area, surface area, and volume) in the most challenging form students have experienced yet. Module 6 assumes students understand the basics. The goal is to build a fluency in these difficult problems. The remaining topics, (i.e., working on constructing triangles and taking slices (or cross-sections) of three-dimensional figures) are new to students.
• 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.
• 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.
• Miniature Golf - student task
This task requires students to redesign a miniature golf course to make it more challenging.
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.