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Mathematics - Secondary Curriculum Mathematics Grade 7
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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.1

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

  • Access Ramp - Student Task
    This task has students design an access ramp, which complies with the Americans with Disabilities Act (ADA) requirements and include pricing based on local costs.
  • 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.
  • 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.
  • 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.
  • Fences - student task
    This task has students design a fence that meets the city ordinances and the client's specifications.
  • 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 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 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.
  • 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.
  • Miniature Golf - student task
    This task requires students to redesign a miniature golf course to make it more challenging.
  • 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.
  • 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.
  • Stairway - Student Task
    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.
  • Student Task: Photographs
    In this task, students need to figure out how to fit three different-sized photographs on a single sheet.
  • Student Task: Sports Bag
    In this task, students must figure out how to cut out the material to make a cylindrical sports bag.
  • Student Task: Triangular Frameworks
    In this task students determine how many different triangles can be made that follow a set of rules.
  • Triangle Explorer
    The applet in this lesson allows students to draw triangles and calculate their area.

UEN logo - 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.