MAFS.7.G.1.1

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.
General Information
Subject Area: Mathematics
Grade: 7
Domain-Subdomain: Geometry
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them. (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
Test Item Specifications

  • Assessment Limits :
    Geometric figures must be two-dimensional polygons.
  • Calculator :

    yes

  • Context :

    allowable

Sample Test Items (4)

  • Test Item #: Sample Item 2
  • Question: Lisa drew a picture of a boat. She used the scale shown. 

    1 inch : 6 feet The boat in her picture is 7 inches long. 

    What is the length, in feet, of the actual boat?

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

  • Test Item #: Sample Item 3
  • Question: Lisa drew a picture of a boat. She used the scale shown. 

    1 inch : 6.5 feet The boat in her picture is 7.25 inches long. 

    What is the length, in feet, of the actual boat?

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

  • Test Item #: Sample Item 4
  • Question:

    Eric wants to create a scale drawing of a house.

    The scale drawing needs to fit on a piece of paper that is 6 inches wide. The drawing itself must be ate least 3 inches wide.

    A. Drag numbers into the box to show an appropriate scale for the drawing.

    B. Use the Connect Line tool to create a drawing based on the scale you chose in Part A.

  • Difficulty: N/A
  • Type: GRID: Graphic Response Item Display

Related Courses

This benchmark is part of these courses.
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1205050: M/J Grade 7 Accelerated Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022 (current), 2022 and beyond)
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101010: M/J Two-Dimensional Studio Art 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101020: M/J Two-Dimensional Studio Art 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101040: M/J Three-Dimensional Studio Art 1 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101050: M/J Three-Dimensional Studio Art 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond)
0101025: M/J Two-Dimensional Studio Art 2 & Career Planning (Specifically in versions: 2014 - 2015, 2015 - 2019, 2019 - 2022, 2022 and beyond)
0101005: M/J Exploring Two-Dimensional Art (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101026: M/J Two-Dimensional Studio Art 3 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101035: M/J Exploring Three-Dimensional Art (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
0101100: M/J Visual Art 1 (Specifically in versions: 2015 - 2022, 2022 and beyond)
0101110: M/J Visual Art 2 (Specifically in versions: 2015 - 2022, 2022 and beyond)
0101120: M/J Visual Art 3 (Specifically in versions: 2015 - 2022, 2022 and beyond)
0104100: M/J Drawing 1 (Specifically in versions: 2020 - 2022 (current), 2022 and beyond)
0104110: M/J Drawing 2 (Specifically in versions: 2020 - 2022 (current), 2022 and beyond)
0104200: M/J Painting (Specifically in versions: 2020 - 2022 (current), 2022 and beyond)
0110100: M/J Printmaking (Specifically in versions: 2020 - 2022 (current), 2022 and beyond)

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.7.G.1.AP.1a: Draw pairs of proportional polygons on graph paper.
MAFS.7.G.1.AP.1b: Draw a scale drawing of a real-world two-dimensional polygon on graph paper.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Assessments

Sample 4 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

Sample 1 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

Formative Assessments

Space Station Scale:

Students are asked to find the ratio of the area of an object in a scale drawing to its actual area and then relate this ratio to the scale factor in the drawing.

Type: Formative Assessment

Flying Scale:

Students are asked to find the length and area of an object when given a scale drawing of the object.

Type: Formative Assessment

Garden Design:

Students are asked to reproduce a scale drawing using a different scale.

Type: Formative Assessment

Lesson Plans

Guiding Grids: Math inspired self-portraits:

In this lesson students will create a proportional self portrait from a photo using a gridded drawing method and understand how a grid system can help accurately enlarge an image in a work of art.

Students will use mathematical concepts of scale, proportion and ratio, to complete their artwork and learn about the work of artist, Chuck Close.

Type: Lesson Plan

Coding Geometry Challenge 8, 9 & 17:

This set of geometry challenges focuses on using area/perimeter as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Type: Lesson Plan

Coding Geometry Challenge #10 & 11:

This set of geometry challenges focuses on scaled drawings and area as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Type: Lesson Plan

Coding Geometry Challenge # 16, 18 & 19:

This set of geometry challenges focuses on creating a variety of polygons using the coordinate plane as students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Type: Lesson Plan

Fish Kribs:

In this lesson, students create a fish tank for a fish supply company for a future sales campaign. They will use scale drawing and proportions to design the perfect fish tank.

  • First, students have to complete a ranking activity of items that will be included in their scale drawing along with three types of fish.
  • Next, students will conduct a pH lab activity to gain knowledge about how pH levels will affect population and the ecosystem within the tank.
  • Finally, students will adjust their item selection and re-engineer their tank drawing to support their findings and additional information provided by the client. Students must determine what objects would be beneficial to the living things that the students chose in relation to available space and pH balance.

Type: Lesson Plan

Designing an Ecofriendly City:

In this STEM design project, students will design and build a 3D model of an ecofriendly community in an existing ecosystem, taking into account the organisms that live there and applying their knowledge of the ecosystem and the needs of the organisms living in it to preserve the biodiversity there. Students will build a 3D model using their understanding of scale and size, create an electronic presentation, and write a summary of their findings.

Type: Lesson Plan

Making a Scale Drawing:

Objective: Students will create a detailed scale drawing. Context: Students have used tools to measure length, solve proportions, and interpret scale drawings. They will continue to use ratio and proportion in the study of similar figures, percent, and probability.

Type: Lesson Plan

Scale & Stage!:

This lesson provides students the opportunity of creating the floor plan of a stage for a future school play. The students will use scale ratio and proportions to find the size of scaled geometric shapes. Then, students will create a scale drawing of the objects required on the stage. Finally, students will reason and compute the size of the actual stage.

Type: Lesson Plan

Makeover, Home Edition Part III:

This is the third lesson of the Unit, "Makeover, Home Edition."This lesson is designed to teach students how to put ideas into reality by creating and using scale drawings in the real world. In Part I (#48705) students determine backyard dimensions for fence installation. Part II (#48967) concentrates on inserting a pool and patio into this backyard. In Part III (#49025) students create a scale drawing of this backyard. Part IV (#49090) focuses on inserting a window and painting walls inside the house.

Type: Lesson Plan

Survival Journal Part Two: Outdoor Gardening:

In this lesson, students will design two outdoor gardens, 1) a raised garden bed and 2) a ground level garden (traditional). Students will, with help of the teacher, till the ground with removal of ground cover, build border for garden, add soil, attach poles with string to create a life size graph all so they can grow tomatoes and plot the data easily in their survival journals.This is Part 2 of a 4-Part Project on Survival.

Type: Lesson Plan

Designing Geo-World: A Geometry based theme park:

In this lesson, students will investigate a contextual problem in which they will need to construct a 2-dimensional polygon, compute actual lengths and areas and then reproduce a scale drawing of the figure at a different scale. Students will also use the free application, GeoGebra (see download link under Suggested Technology) to help them design their parks.

Type: Lesson Plan

Fastest Route:

This MEA requires students to formulate a comparison-based solution to a problem involving finding the fastest driving routes from home to work 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.

Type: Lesson Plan

How does scale factor affect the areas and perimeters of similar figures?:

In this lesson plan, students will observe and record the linear dimensions of similar figures, and then discover how the values of area and perimeter are related to the ratio of the linear dimensions of the figures.

Type: Lesson Plan

It's All About the Scale!:

In this 2 part lesson, students will learn about scale drawings/models, scales, and scale factors culminating in an activity where they will produce an enlargement of an image they choose.

Type: Lesson Plan

Original Student Tutorial

Scale Round Up:

Howdy y’all! I’m Deputy Design, a cowboy architect. I am going to use my architectural scale drawings for a new horse arena to teach you how to solve problems involving scale drawings. In this tutorial, you will learn to calculate actual lengths using a scale and proportions.

Type: Original Student Tutorial

Perspectives Video: Teaching Idea

KROS Pacific Ocean Kayak Journey: Kites, Geometry, and Vectors:

Set sail with this math teacher as he explains how kites were used for lessons in the classroom.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set [.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth [.KML]

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

Problem-Solving Tasks

Maximizing Area: Gold Rush:

Before the lesson, students attempt the Gold Rush task individually. You then look at their responses and formulate questions for students to think about as they review their work. At the start of the lesson, students reflect on their individual responses and use the questions posed to think of ways to improve their work. Next, students work collaboratively in small groups to produce, in the form of a poster, a better solution to the Gold Rush task than they did individually. In a whole-class discussion students compare and evaluate the different methods they used. Working in small groups, students analyze sample responses to the Gold Rush task, then, in a whole-class discussion, review the methods they have seen. Finally, students reflect on their work.

Type: Problem-Solving Task

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. If used in an instructional setting, it would be good for students to have an opportunity to see other solution methods, perhaps by having students with different approaches explain their strategies to the class. Students who can only solve this by first converting the linear measurements will have a hard time solving problems where only area measures are given.

Type: Problem-Solving Task

Measuring Henry's Cabin:

This resource introduces students to the aspects a builder must think about before constructing a building. Students will study the cabin blueprint of Henry David Thoreau and then will find the surface area of the walls and how much paint would be needed. Then, students will find the volume of the cabin to determine the home heating needs. Third, students will study the blueprint and will create a 1/10 scale of it on graph paper and then will use art supplies to create a model of the cabin. Last, students will design and create models of furniture to scale for the cabin.

Type: Problem-Solving Task

Space Math: Lunar Cratering:

Students explore the formation of craters on the lunar surface using real world imaging data and mathematical reasoning. Students make observations and inferences about the time that impact craters were formed using probability and percentages.

Type: Problem-Solving Task

Teaching Ideas

Scaling the Pyramids:

This web page features activities that compare the Great Pyramid to such modern structures as the Statue of Liberty and the Eiffel Tower. In the first activity, students use a template to construct a scale model of the Great Pyramid. They must find the scale heights for the tallest building in their neighborhood or for their height. In the remaining activity, students are given the dimensions for two other pyramids and challenged to create models.

Type: Teaching Idea

Packing For A L-o-o-o-ng Trip To Mars:

In this engineering task, students will apply concepts of volume to decide what they will need to take on a 2-1/2 year journey to Mars. Then plan how to fit everything into a 1-cubic-meter box, using only a measuring tape, pencil and paper, and math.

Type: Teaching Idea

Tutorial

Converting Speed Units:

In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units.

Type: Tutorial

Unit/Lesson Sequence

Drawing to Scale: Designing a Garden:

In this lesson (or series of lessons), students interpret and use scale drawings to plan a garden layout. Students start by producing their own layout and then work together to refine their garden design. The activity requires that students use short rules (rulers), meter rules (meter sticks), string, protractors, scissors, glue, card, plain paper, graph paper, and colored pencils. Students work individually for 20 minutes, engage in a 100-minute lesson (or two 50-minute lessons), and complete a 10-minute follow up lesson or homework.

Type: Unit/Lesson Sequence

Virtual Manipulatives

Area Builder:

This manipulative allows you to create shapes using colorful blocks to explore the relationship between perimeter and area. The game screen challenges you to build shapes or find the area of figures.

Type: Virtual Manipulative

Transformations - Dilation:

Students use a slider to explore dilation and scale factor. Students can create and dilate their own figures. (source: NLVM grade 6-8 "Transformations - Dilation")

Type: Virtual Manipulative

Scale Factor:

Explore the effect on perimeter and area of two rectangular shapes as the scale factor changes.

Type: Virtual Manipulative

STEM Lessons - Model Eliciting Activity

Fastest Route:

This MEA requires students to formulate a comparison-based solution to a problem involving finding the fastest driving routes from home to work 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.

Fish Kribs:

In this lesson, students create a fish tank for a fish supply company for a future sales campaign. They will use scale drawing and proportions to design the perfect fish tank.

  • First, students have to complete a ranking activity of items that will be included in their scale drawing along with three types of fish.
  • Next, students will conduct a pH lab activity to gain knowledge about how pH levels will affect population and the ecosystem within the tank.
  • Finally, students will adjust their item selection and re-engineer their tank drawing to support their findings and additional information provided by the client. Students must determine what objects would be beneficial to the living things that the students chose in relation to available space and pH balance.

MFAS Formative Assessments

Flying Scale:

Students are asked to find the length and area of an object when given a scale drawing of the object.

Garden Design:

Students are asked to reproduce a scale drawing using a different scale.

Space Station Scale:

Students are asked to find the ratio of the area of an object in a scale drawing to its actual area and then relate this ratio to the scale factor in the drawing.

Original Student Tutorials Mathematics - Grades 6-8

Scale Round Up:

Howdy y’all! I’m Deputy Design, a cowboy architect. I am going to use my architectural scale drawings for a new horse arena to teach you how to solve problems involving scale drawings. In this tutorial, you will learn to calculate actual lengths using a scale and proportions.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorial

Scale Round Up:

Howdy y’all! I’m Deputy Design, a cowboy architect. I am going to use my architectural scale drawings for a new horse arena to teach you how to solve problems involving scale drawings. In this tutorial, you will learn to calculate actual lengths using a scale and proportions.

Type: Original Student Tutorial

Problem-Solving Tasks

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. If used in an instructional setting, it would be good for students to have an opportunity to see other solution methods, perhaps by having students with different approaches explain their strategies to the class. Students who can only solve this by first converting the linear measurements will have a hard time solving problems where only area measures are given.

Type: Problem-Solving Task

Measuring Henry's Cabin:

This resource introduces students to the aspects a builder must think about before constructing a building. Students will study the cabin blueprint of Henry David Thoreau and then will find the surface area of the walls and how much paint would be needed. Then, students will find the volume of the cabin to determine the home heating needs. Third, students will study the blueprint and will create a 1/10 scale of it on graph paper and then will use art supplies to create a model of the cabin. Last, students will design and create models of furniture to scale for the cabin.

Type: Problem-Solving Task

Tutorial

Converting Speed Units:

In this lesson, students will be viewing a Khan Academy video that will show how to convert ratios using speed units.

Type: Tutorial

Virtual Manipulatives

Transformations - Dilation:

Students use a slider to explore dilation and scale factor. Students can create and dilate their own figures. (source: NLVM grade 6-8 "Transformations - Dilation")

Type: Virtual Manipulative

Scale Factor:

Explore the effect on perimeter and area of two rectangular shapes as the scale factor changes.

Type: Virtual Manipulative

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Problem-Solving Task

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. If used in an instructional setting, it would be good for students to have an opportunity to see other solution methods, perhaps by having students with different approaches explain their strategies to the class. Students who can only solve this by first converting the linear measurements will have a hard time solving problems where only area measures are given.

Type: Problem-Solving Task

Virtual Manipulative

Transformations - Dilation:

Students use a slider to explore dilation and scale factor. Students can create and dilate their own figures. (source: NLVM grade 6-8 "Transformations - Dilation")

Type: Virtual Manipulative