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).
• 2D Nets and 3D Decorative Boxes
Calculating the surface area of cardboard boxes is the focus of this interactive activity. The classroom activity takes this knowledge and asks the students for figure out how many square inches of wrapping paper is needed to wrap a gift. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• A task related to standard 7.G.A.2
When students successfully complete this task, they will have shown that there is more than one triangle with a 30-degree angle adjacent to a side of length 4 units and opposite to a side of length 3 units. This task can be part of a more general study directed at "noticing when" "three measures of angles or sides" "determine a unique triangle, more than one triangle, or no triangle."
• AAS Triangle construction exploration
If you know two angles of a triangle and a side not between those two angles, will you create a unique triangle? This activity will help you to explore the answer to that question.
• 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
• ASA Exploration
If you know two angles of a triangle and a side between those two angles, will you create a unique triangle? This activity will help you to explore the answer to that question.
• Boxed In and Wrapped Up
This lesson asks students to find the volume and surface area of a rectangular box and then convert it into a cubical box with the same volume.
• 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.
• 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.
• Chris McCloud's Lesson: Expert Analysis
This Teaching Channel video highlights and critiques the techniques used in a lesson on cylinders. (14 min.)
• 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.
• Comparing Volumes of Cylinders, Spheres, and Cones
This interactive explains how to calculate the volumes of cylinders, cones and spheres. Students then apply this understanding to an activity where cylinders, cones and spheres are filled with water so that their volumes can be compared. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
The Annenberg interactive in this lesson gives the students a chance to manipulate linkage strips to form quadrilaterals. In the activity students are given side lengths and then must build different types of quadrilaterals. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Constructing Triangles
In this interactive students manipulate line segments on a grid to see if they can make a triangle. Students then work with straw segments to discover which side length combinations are able to make a triangle. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Cross Sections of a Cube
In this interactive cubes are sliced in different ways in order to explore cross sections. Students then create cubes out of play dough and slice them with dental floss to create cross-sections of specific shapes. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Cube Ninjas!
The purpose of this task is to have students explore various cross sections of a cube and use precise language to describe the shape of the resulting faces.
• Designs
The purpose of this task is for students to find the area and perimeter of figures composed of squares and fractions of circles.
• Drinking the Lake
The purpose of this task is for students to solve a volume problem in a modeling context (MP.4). It requires multiple conversions using units of time and volume. It also requires thinking about some reasonable hypotheses for how much an individual drinks each day and also how many days there are in that individual's lifetime.
• Eight Circles
The purpose of this task is to strengthen students' understanding of area. It could be assigned in class to individuals or small groups or given as a homework exercise to generate interesting discussions the following day. The relatively high levels of complexity and technical demand enhance its instructional value. Seventh grade student may require some teacher guidance to be successful with this task.
• Escaramuza: 2D Drawing
The real-life equestrian event known as Escaramuza is used to help student make 2D drawings to make triangles. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Escaramuza: Coordinates, Reflection, Rotation
A real-life equestrian event known as Escaramuza is used to demonstrate how to draw a two-dimensional diagram and then represent it on a coordinate plane. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• 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.
This task has students design a fence that meets the city ordinances and the client's specifications.
• 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.
• 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.
• Formulas for a Circle
The 3 videos in this lesson teach students about the parts of a circle, how to label a circle, and define pi. Students must then test the theories presented in the videos 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.
• 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.
• Framing a House - student task
This task has students recreate house plans on graph paper and then determine how many linear feet of wall plate material will be needed.
• Geometry (7.G) - 7th Grade Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 7 - Geometry.
• Grade 7 Math Module 1:Ratios and Proportional Relationship (EngageNY)
In this 30-day Grade 7 module, students build upon sixth grade reasoning of ratios and rates to formally define proportional relationships and the constant of proportionality. Students explore multiple representations of proportional relationships by looking at tables, graphs, equations, and verbal descriptions. Students extend their understanding about ratios and proportional relationships to compute unit rates for ratios and rates specified by rational numbers. The module concludes with students applying proportional reasoning to identify scale factor and create a scale drawing.
• 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 4: Percent and Proportional Relationships (EngageNY)
In Module 4, students deepen their understanding of ratios and proportional relationships from Module 1 by solving a variety of percent problems. They convert between fractions, decimals, and percents to further develop a conceptual understanding of percent and use algebraic expressions and equations to solve multi-step percent problems. An initial focus on relating 100% to the whole serves as a foundation for students. Students begin the module by solving problems without using a calculator to develop an understanding of the reasoning underlying the calculations.
• 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.
In order to assist educators with the implementation of the Common Core, the New York State Education Department provides curricular modules in Pre-K-Grade 12 English Language Arts and Mathematics that schools and districts can adopt or adapt for local purposes.
• Grade 7 Unit 3: Ratio and Proportional Relationships (Georgia Standards)
The units in this instructional framework emphasize key standards that assist students to develop a deeper understanding of numbers. They learn to express different representations of rational numbers (e.g., fractions, decimals, and percents), discover how to identify and explain the constant of proportionality, and represent proportional relationships and scale drawings within real-world contexts. The Big Ideas that are expressed in this unit are integrated with such routine topics as estimation, mental and basic computation. All of these concepts need to be reviewed throughout the year.
• 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.
• Great Modeling Tasks in Three Acts - File Cabinet
This surface area activity has students answer the question: How many stickies cover the cabinet?
• 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?"
• Map Distance
The purpose of this task is for students to translate between information provided on a map that is drawn to scale and the distance between two cities represented on the map.
• 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.
• Measuring Henry's cabin
In this lesson and activity students will determine the surface area and volume of a house and also reconstruct it on a smaller scale.
• Measuring the area of a circle
This goal of this task is to give students familiarity using the formula for the area of a circle while also addressing measurement error and addresses both 7.G.4 and 7.RP.3.
• Miniature Golf - student task
This task requires students to redesign a miniature golf course to make it more challenging.
• Mr. McCloud: Discovering Surface Area of a Cylinder
This Teaching Channel video and lesson plan will help students discover and apply the formula for the surface area of a cylinder. (27 minutes)
• Rescaling Washington Park
The goal of this task is to get students to think critically about the effect that changing from one scaling to another has on an image, and then to physically produce the desired image.
• Sand Under the Swing Set
The purpose of this task is for students to solve a contextual problem where there are multiple entry points to this geometry based concept. The student can choose to solve the problem using a scale factor or a unit rate, but must first must analyze the context of the problem to understand the situation and choose their approach. This task provides opportunities for students to reason about their computations to see if they make sense. This task could be used as an assessment question or for guided instruction on scale factoring and/or unit rate.
• SAS Exploration
If you know two sides of a triangle and the angle between those two sides, will you create a unique triangle? This activity will help you to explore the answer to that question.
• Scale Models in the Real World
This video show scale models of railroads, dollhouses, and architecture to explain what the ratios represent. The hands-on classroom activity then has students create their own models. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Scaling
An interactive from Annenberg asks students to scale a picture by using the math strategies of multiplicative and additive relationships. Students then use those strategies to compare photocopies and rectangles in different scales. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Scaling angles and polygons
The goal of this task is to gather together knowledge and skills from the seventh grade in a context which prepares students for the important eighth grade notion of similarity.
• Scaling Up Rectangles in the Real World
By looking at murals in this video students see how artists use proportion and measurement to create them. The class then does an activity where they enlarge a drawing by using scale and then create a classroom mural. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Scaling Up Rectangles Using Simulations
This interactive allows students to create murals in different sizes by understanding two-dimensional scaling. The activity for the classroom has students use graph paper to draw and compare squares with different proportional dimensions and record the data as they change. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Slicing Three Dimensional Figures
In this video students are shown how 2 dimensional figures are created by slicing 3 dimensional ones. Play dough is used in the classroom activity with students slicing figures and then describing the shape that results. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• 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.
• SSA Exploration
If you know two sides of a triangle and an angle not between those two sides, will you create a unique triangle? This activity will help you to explore the answer to that question.
• Stained Glass
The purpose of this task is for students to find the area and perimeter of geometric figures whose boundaries are segments and fractions of circles and to combine that information to calculate the cost of a project. The shape of the regions in the stained glass window are left purposefully unspecified, as one component skill of modeling with mathematics (MP4) is for students to make simplifying assumptions themselves.
This task students to design a stairway for a custom home. They will need to gather information regarding design, safety, and the utility of staircases.
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.
In this task, students need to figure out how to fit three different-sized photographs on a single sheet.
A set of short tasks for grades 7 & 8 dealing with geometry.
In this task, students must figure out how to cut out the material to make a cylindrical sports bag.
In this task students determine how many different triangles can be made that follow a set of rules.
• 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.
• The Circumference of a Circle and the Area of the Region it Encloses
The purpose of this task is to help students differentiate between a circle and the region inside of the circle so that they understand what is being measured when the circumference and area are being found. This task is best used as a lead-in to the formulas for circumference and area of a circle.
• The Largest Container: Problems Using Volume and Shape
By using a single sheet of paper this interactive leads students to construct shapes, calculate volume, and think about the relationships between different shapes. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Three-Dimensional Printing
Via this video students will obtain an understanding of how 3-D printing works and is used in manufacturing. These printers use the basic shape of the triangle to build complex polygon shapes. Students will then create two-dimensional drawings to represent 3-D figures. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Triangle construction exploration: Version 1
Triangle construction exploration: If you know three sides of a triangle, will you create a unique triangle? This activity will help you to explore the answer to that question.
• Triangle construction exploration: Version 2
Triangle construction exploration: If you know three sides of a triangle, will you create a unique triangle? This activity will help you to explore the answer to that question.
• Triangle Explorer
The applet in this lesson allows students to draw triangles and calculate their area.
• Using Dimensions: Designing a Sports Bag
This lesson unit is intended to help educators assess how well students are able to recognize and use common 2D representations of 3D objects, as well as identify and use the appropriate formula for finding the circumference of a circle.
• 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.
• Wedges of a Circle
The purpose of this task is to help students visualize one way to derive the formula for the area of a circle, which uses the formulas for the circumference of a circle and the area of a parallelogram.

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.