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Clarifications
Clarification 1: Instruction extends the development of algebraic thinking where the symbolic representation of the unknown uses a letter.Clarification 2: Problems involving multiplication are limited to products of up to 3 digits by 2 digits. Problems involving division are limited to up to 4 digits divided by 1 digit.
Clarification 3: Responses include the appropriate units in word form.
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Perimeter
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is for students to connect perimeter and area problems to algebraic concepts to find the measures of unknown side lengths. This new idea builds from solving area and perimeter problems with whole number side lengths when using models and formulas in grade 3 (MA.3.GR.2.3) and will form the foundation for problems involving fractional and decimal side lengths in grade 5 (MA.5.GR.2.1).- During instruction, students should use a letter (variable) to represent the missing side length and have experiences solving for unknowns in perimeter situations with a given area and vice-versa.
- Instruction includes having students use the fact that opposite sides in rectangles and squares are equal when solving problems involving area and perimeter.
Common Misconceptions or Errors
- Students frequently confuse area and perimeter. Instruction should provide lots of opportunity for students to work with both measures on the same object and have them explain which measure is area and which is perimeter and why? Instruction should also focus on naming the units properly.
Strategies to Support Tiered Instruction
- Instruction provides many opportunities for students to work with both measures on the same object and explain which measure is area and which is perimeter and why. Instruction should also focus on naming the units properly
- Instruction includes finding both the area and perimeter in real world examples and having students explain how they solved for both.
- For example, when provided with examples like the following, students use the measurements provided to create an equation to find area and perimeter and explain the difference. “A rectangular garden is being built at the school. The dimensions for the garden are 8 feet by 4 feet. Write and solve an equation to find the area of the garden and an equation to find the perimeter of the garden.”
- The teacher provides students with images created using square tiles. Student count and labels the side lengths based on the tiles, then write equations to show how they would find the area and how they would find the perimeter.
- For example: When provided with an image like the one shown below, students label each side length based on the number of tiles and write an equation for perimeter and then count the units around the outside of the figure to confirm their solution. Students multiply the length and width to find area and then count the number of squares that make up the figure to confirm their solution.
Instructional Tasks
Instructional Task 1 (MTR.7.1)
The perimeter of the patio below is 98 square feet.
Instructional Items
Instructional Item 1
A soccer field with its dimensions is shown.
Which equation can be used to find the area of the soccer field?
- a. 75 yards + 120 yards = A yards
- b. 75 yards + 75 yards + 120 yards + 120 yards = A yards
- c. 75 yards× 120 yards = A square yards
- d. 75 yards × 120 yards × 75 yards × 120 yards = A square yards
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorials
Perspectives Video: Teaching Idea
Problem-Solving Task
Tutorials
Video/Audio/Animations
STEM Lessons - Model Eliciting Activity
In this MEA, students will work in collaborative groups to solve real-world, multi-step problems with whole numbers and decimals by using different mathematical operations such as addition, subtraction, multiplication and/or division. The students will be asked to assist a business/property owner in purchasing holiday lights for his property. They will need to read several ads and decide which product would be the best for the property. They will be provided with an office plan to calculate the perimeter of the building to then calculate how many holiday lights will need to be purchased and its total cost for each. They also need to take into consideration the owner's primary concerns. In the twist, the owner finds different holiday lights made from another material.
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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
Students are asked to plan a playground for a new park within a given budget and area limit. They will analyze the best use of playground equipment using a data table of area requirements and cost. Students will convert units within a single measurement system, calculate the area of a rectangle, and perform addition/subtraction calculations involving money using decimal notation.
In this MEA, students decide which type of pioneer dwelling was the best to build if you were traveling west.
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.
In this Model Eliciting Activity (MEA), students are asked to help rank possible locations for a new park. They will need to perform certain calculations as part of the process, such as finding the unknown factor in a perimeter and area formula and multiply 2-digit by 1- and 2-digit numbers to calculate total costs.
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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem, while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought process. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
This video can be played with Data Set 1 for the Volunteer Trash Cleanup MEA (199167).
This video can be played with Data Set 2 for the Volunteer Trash Cleanup MEA (199167).
This video can be played with Reading Passage 1 for the Volunteer Trash Cleanup MEA (199167).
This video can be played with Reading Passage 2 for the Volunteer Trash Cleanup MEA (199167).
MFAS Formative Assessments
Students are asked to find the dimensions of rectangles by applying the formulas for area and perimeter.
Students are given the area and width of a rectangle in the context of a word problem and are asked to determine the perimeter.
Students are asked to find the perimeter of a hexagon in which the lengths of two sides are not given but can be found.
Students are asked to solve real world problems by applying the formulas for area and perimeter.
Students are asked to find the length of a missing side on two polygons given the perimeter of each and the lengths of the other sides.
Students are asked to use known lengths, areas, and perimeters to determine the perimeter of one section of a rectangle.
Original Student Tutorials Mathematics - Grades K-5
Help April calculate area and missing measurements for items in her perfect dream home in this interactive tutorial.
This is the first in a three-part series. Click below to open the other tutorials in this series
Learn how to calculate perimeter and find a missing side measurement for a shape given the perimeter in this interactive tutorial.
This is the third in a three-part series about designing a dream house. Click below to open the other tutorials in this series.
Learn to calculate the perimeter of rectangular and composite shapes to help April finish designing her dream home in this interactive tutorial.
This is the second in a three-part series. Click below to open the other tutorials in the series.
Student Resources
Original Student Tutorials
Learn to calculate the perimeter of rectangular and composite shapes to help April finish designing her dream home in this interactive tutorial.
This is the second in a three-part series. Click below to open the other tutorials in the series.
Type: Original Student Tutorial
Learn how to calculate perimeter and find a missing side measurement for a shape given the perimeter in this interactive tutorial.
This is the third in a three-part series about designing a dream house. Click below to open the other tutorials in this series.
Type: Original Student Tutorial
Help April calculate area and missing measurements for items in her perfect dream home in this interactive tutorial.
This is the first in a three-part series. Click below to open the other tutorials in this series
Type: Original Student Tutorial
Problem-Solving Task
The purpose of the task is for students to solve a multi-step multiplication problem in a context that involves area. In addition, the numbers were chosen to determine if students have a common misconception related to multiplication. Since addition is both commutative and associative, we can reorder or regroup addends any way we like. Students often believe the same is true for multiplication.
Type: Problem-Solving Task
Tutorials
This Khan Academy tutorial video presents a step-by-step solution for finding the length and width of a table when given its area and perimeter.
Type: Tutorial
Find area of two rectangles to solve a word problem.
Type: Tutorial
In this tutorial video from Khan Academy, explore the relationship between area and perimeter. For example, if you know the area and the length, can you find the perimeter?
Type: Tutorial
Parent Resources
Problem-Solving Task
The purpose of the task is for students to solve a multi-step multiplication problem in a context that involves area. In addition, the numbers were chosen to determine if students have a common misconception related to multiplication. Since addition is both commutative and associative, we can reorder or regroup addends any way we like. Students often believe the same is true for multiplication.
Type: Problem-Solving Task
Tutorial
In this tutorial video from Khan Academy, explore the relationship between area and perimeter. For example, if you know the area and the length, can you find the perimeter?
Type: Tutorial
