MA.7.GR.1.5

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Solve mathematical and real-world problems involving dimensions and areas of geometric figures, including scale drawings and scale factors.

Clarifications

Clarification 1: Instruction focuses on seeing the scale factor as a constant of proportionality between corresponding lengths in the scale drawing and the original object.

Clarification 2: Instruction includes the understanding that if the scaling factor is k, then the constant of proportionality between corresponding areas is k² .

Clarification 3: Problem types include finding the scale factor given a set of dimensions as well as finding dimensions when given a scale factor.

General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 7
Strand: Geometric Reasoning
Standard: Solve problems involving two-dimensional figures, including circles.
Date Adopted or Revised: 08/20
Status: State Board Approved

Related Courses

This benchmark is part of these courses.
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.7.GR.1.AP.5: Use a scale factor to 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.

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

Lesson Plans

Fish Kribs:

In this lesson, students create a fish tank for a fish supply company for a future sales campaign. They will use scale drawings 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.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Type: Lesson Plan

Raising Your Garden MEA:

Raising Your Garden MEA provides students with a real world engineering problem in which they must work as a team to design a procedure to select the best material for building raised garden beds. The main focus of this MEA is to recognize the importance of choosing the correct material for building a raised garden bed, what information is needed before starting a gardening project, and to consider the environmental and economic impact the garden will have on the school. Students will conduct individual and team investigations in order to arrive at a scientifically sound solution to the problem.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. 

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

Original Student Tutorial

Scale Round Up:

Learn to use architectural scale drawings to build a new horse arena and solve problems involving scale drawings in this interactive tutorial. By the end, you should be able 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

STEM Lessons - Model Eliciting Activity

Fish Kribs:

In this lesson, students create a fish tank for a fish supply company for a future sales campaign. They will use scale drawings 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.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Raising Your Garden MEA:

Raising Your Garden MEA provides students with a real world engineering problem in which they must work as a team to design a procedure to select the best material for building raised garden beds. The main focus of this MEA is to recognize the importance of choosing the correct material for building a raised garden bed, what information is needed before starting a gardening project, and to consider the environmental and economic impact the garden will have on the school. Students will conduct individual and team investigations in order to arrive at a scientifically sound solution to the problem.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. 

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.

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:

Learn to use architectural scale drawings to build a new horse arena and solve problems involving scale drawings in this interactive tutorial. By the end, you should be able 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:

Learn to use architectural scale drawings to build a new horse arena and solve problems involving scale drawings in this interactive tutorial. By the end, you should be able to calculate actual lengths using a scale and proportions.

Type: Original Student Tutorial

Parent Resources

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