### 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.

**Subject Area:**Mathematics (B.E.S.T.)

**Grade:**4

**Strand:**Geometric Reasoning

**Date Adopted or Revised:**08/20

**Status:**State Board Approved

## 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)

What is the area of the patio?

### Instructional Items

*Instructional Item 1 *

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

## Problem-Solving Task

## Tutorials

## STEM Lessons - Model Eliciting Activity

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.

## 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