# Calculating the Areas of Rectangles

## Lesson Title

Calculating the Area of Rectangles

## Abstract

This lesson focuses on calculating the areas of rectangles. It is designed to enable adult students to successfully master basic geometry knowledge in order to achieve their High School Equivalency (HSE). Areas to be covered include types of polygons, quadrilaterals, rectangles; calculating areas of rectangle and calculating costs. Students will apply this knowledge to practical areas of their lives such as calculating the costs of purchasing carpets or painting of walls.

## Learner Audience / Primary Users

This lesson is intended for individuals who have dropped out of school and are re-entering the education system at the adult education level (NRS level 3/4) in order to obtain their HSE and ultimately, secure a well-paying job or promotion in their current job.

## Educational Use

Curriculum and Instruction; Informal Education

## College & Career Readiness Standards (CCRS) Alignment

• Subject: Math

## Standard Description:

5G3. Classify 2 dimensional figures into categories based on their properties.

6G1 Solve real world and mathematical problems involving areas.

English

## Material Type

• Instructional Material,
• Homework and Assignment
• Interactives
• Lesson plans

## Learning Goals

The purpose of this lesson is for learners to be able to:

• Identify rectangular shapes within the framework of an understanding of polygons and quadrilaterals.
• Calculate the areas of rectangles and then determine the cost of purchasing carpet for rooms that are rectangular-shaped.

## Keywords

• Designers for Learning
• CCRS
• Polygons
• Areas
• Rectangles

30 minutes

## Prior Knowledge

Prior to this lesson, students would have discussed types of polygons including quadrilaterals.  They would have discussed also perimeter of triangles and other polygons and the notion of appropriate units of measurement. For example, if a person is measuring a room, he/she would use "inches" or “feet” or "meters" as a measuring unit. The total distance will be for example, 50 feet.

This lesson will be executed after the class had completed working on finding perimeters.

## Required Resources

• A Computer
• Worksheet #1 – Identifying polygons
• Worksheet #2 – Problem set
• Graph paper
• Ruler
• Pencil
• Eraser
• Student Journal

• Lesson Author: Winston Lawrence

## Learning Objectives

By the end of this lesson, the learner should be able to:

• Identify a rectangular polygon, when shown different quadrilaterals.
• Compute the areas of rectangular polygons with 80% accuracy, using length and width dimensions given by teacher or student generated.
• Calculate costs when purchasing rectangular pieces of carpets or services to paint a wall.

## Lesson Topics

Key topics covered in this lesson include:

• Review of types of polygons and quadrilaterals
• Characteristics of a rectangle
• How to calculate areas of rectangles
• How to calculate costs of buying goods and services based on the amount of area.

## Context Summary

The topic of rectangles was chosen because it falls within one of the areas of the math curriculum that students need to master for their High School Equivalency (HSE). In addition, most students who did not complete high school because of family circumstances and other reasons, tend to have poor skills in Geometry.

## Relevance to Practice

This activity will enable students to build their mathematical knowledge and skills to earn their High School Equivalency (HSE). They will engage in the practical task of using their math knowledge to calculate the area of floors in their living room or bedroom and the cost of carpeting them. In addition, they could even calculate the cost of painting any wall surface.

• Polygon
• Rectangle
• Area

## Instructional Activities and Strategies

### Warm Up

Time: 5 minutes

Ask students to indicate what are some things they remember about polygons. Take comments. Write students' responses on white board/ smart board or chart paper.

Tell students they will see a video on polygons.   Show the video.  After students have seen the video, ask them about the shapes they saw in the video,  drawing particular attention to the shape of the rectangles.

Ask class about their understanding of what a rectangle is, and how this could help them when purchasing carpet to cover the floor or painting a wall.  Write students responses.

### Introduction

Time: 5 minutes

Give students a sheet (Worksheet #1 ) showing different polygons, including quadrilaterals and rectangles. Ask them to circle the correct letters of shapes that are rectangles.

Pose questions about the characteristics of rectangles. (e.g. what do you know about the sides of rectangles? what makes a rectangle different from other polygons? what do you know about the angles?)

Answers may include: all angles are equal (90 degrees), opposite sides are equal; opposite sides are parallel, sum of angles is 360 degrees.

### Presentation / Modeling/Demonstration

Time: 10 minutes

Review:

Ask students to explain how to calculate perimeter of a rectangle.  Let students tell you what to do. Once you are satisfied with responses, tell students that they will now learn another skill - how to calculate the AREA of a rectangle.

Model:

Present the following problem set.

The problem - Jimmy has just gotten a room to rent. The room has a rectangular shape.  He needs to buy a piece of carpet for it. How is he going to calculate the amount of carpet to buy?

Step 1.  Drawing  rectangles

Distribute a graph paper to students.

Draw a rectangle on graph paper (or on a white board or chart paper) and place endpoints.

Ask questions about the dimensions. What is length? What is width?  Students could trace the width and length on graph paper by using colored markers  (or draw a double line along the width.)

Ask students to give the measurements based on the counting of the number of squares  (Formative assessment)

Expected answer could be : 8 cm long and 6 cm wide, when the number of squares between the end points are counted.

Emphasize that the measurement is 8cm by 6cm  = 48 sq cm. or 48 cm^2.

Point out that a Formula is usually used to give the answer: A = L x W

Show another simple figure with appropriate dimensions. Do the example so students could see what is done.

NOTE:  Advanced students may be able to work with a more complex shape such as the following example.

Show a polygon in which 2 or more rectangles have to be made in order to complete the problem. Example:

Show the students how the figure could be divided into two rectangles.  Show the two

(2 ) ways  1. By extending the short horizontal line upwards.  2. By extending upwards the short vertical line.

Calculate the area of each rectangle. Then add the two parts, to get the answer.

Step 2.   Calculate the cost of carpet

E.g.   If the length of one side of Jimmy’s room is 12 feet and the width is 8 feet, how much carpet should he buy? If the carpet costs $9.00 per square foot, how much would he pay? Show students step by step how to do this calculation, building on their new knowledge of how to calculate the area of a rectangle. Ask questions to clarify that students are understanding the method. (Formative) Demonstrate a second example. ### Guided Practice Time: 5 minutes Activity # 1 Students will work using graph paper to draw the total number of squares represented by multiplying the length by the width (Formula = L x W) to find the areas. Measurements will be given such as: L = 10" ; W = 9" Give students simple rectangles. Tell them to draw the rectangular area on the graph paper, and calculate the area in square units. Task : On graph paper, draw a rectangle with a length of 12 cm and a width of 8 cm. Tell students that the figures are not drawn to scale. Hence , they could represent each square as 1 unit. Let students calculate the area. of Problem #1 -- 12 squares x 8 squares = 96 squares = 96 sq cm/ 96cm^2 Tell students to try another example : #2. 14 cm by 11 cm Move around to see how students are performing the task. Give students feedback. Activity # 2 Calculate: If carpet is sold for$10.00 per square foot, how much will you pay for the carpet to cover a room that is 20’ x 25’ ?

More practice:  Find the cost if the area of the room is  12' x 18'

HOMEWORK ASSIGNMENT

Individual practice

Give students Worksheet # 2 with four to six problems to complete on their own. Give one or 2 shapes that contain at least 2 rectangles that could be identified out of the one polygon.

For added practice, complete the two exercises below from Engage NY -  Lesson 5

Exercise #1. Page #77 - Floor Plan

Exercise #2.  Page #78  - Wall

Review students' homework and provide feedback.

## Evaluation

Time: 5 minutes

Formative assessment is done while teacher is engaged in  demonstration and guided practice.

At end of class, pose the question:  What is the difference between finding perimeter and finding area?

Ask: How can you use this information at home or in the community.

Write a 1/2 page reflection in your journal of the process you used and what you learned from the lesson – challenges and success experienced.

Assessment of students' homework

### Application

Time: 5 minutes

Calculate the cost of painting a wall or of carpeting rooms of different measurements with different costs per square foot.

## Supplementary Resources

http://www.commoncoresheets.com/Math/Area/Finding%20Area%202/English/1.pdf

## References

EngageNY

Mathworksheets4kids

http://www.mathworksheets4kids.com/area.php