Calculating the Areas of Rectangles - Remix


Lesson Title

Calculating the Area of Rectangles                

Abstract

This lesson focuses on calculating the areas of rectangles. It is designed to enable adult students in mastering basic geometry knowledge in order to achieve their High School Equivalency Diploma (HSED). Areas to be covered include polygons, quadrilaterals, and rectangles; calculating areas of rectangles and costs. Students can apply this knowledge to practical areas of their lives such as calculating the costs of purchasing carpet or painting 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 HSED and ultimately, secure a well-paying job or a promotion in their current job.

Educational Use

Curriculum / Instruction; Informal Education

College & Career Readiness Standards (CCRS) Alignment

  • Level: Adult Education
  • Grade Level: Level C
  • Subject: Mathematics
  • Domain: Geometry

Standard Description:

5GB3 Classify two dimensional figures into categories based on their properties.

6GA1 Solve real world and mathematical problems involving area, surface area, and volume.

Language

English


Material Type


  • Instructional Material
  • Games
  • Video lectures
  • 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.
  • Determine the cost of purchasing carpet for rooms that are rectangular-shaped.

Keywords

  • Designers for Learning
  • Adult Education
  • College and Career Readiness Standards (CCRS)
  • Polygons
  • Areas
  • Quadrilaterals
  • Rectangles

Time Required for Lesson

30 minutes

Prior Knowledge

Students should know how to measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, and measuring tapes; relate addition and subtraction to length; work with time and money; represent and interpret data.

Required Resources

  • Access to the internet
  • A computer
  • A mobile device
  • Worksheet #2 – Problem set
  • Graph paper
  • Ruler
  • Pencil
  • Eraser
  • Student Journal

Lesson Author & License

  • Lesson Author: Sandra James

Part 2: Lesson

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. 
  • Calculate costs of purchasing rectangular pieces of carpet.

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 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 Diploma (HSED). 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 Diploma (HSED). They will engage in the practical task of using their math knowledge to calculate the area of floors in their living space and buying carpet to fit the space/s. 

Key Terms and Concepts

  • Polygon
  • Quadrilateral
  • Rectangle
  • Area


Instructional Activities and Strategies

Warm-up

Time: 10:00 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. 

VIDEO : What is a Quadrilateral? - Socratica 

What is a Quadrilateral?

   

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. 

Direct students to website on their mobile device where they can play a quadrilateral identification game.  Give students 5 minutes to play the game. Recommend that the students bookmark the game in order to practice after class if desired.

Quadrilateral Shape Game

Demonstration: 

Time: 2:00 minutes

Tell students they will see a video on how to calculate square footage of a rectangle.   Show the video.

VIDEO: How to Calculate Square Footage - Mahalodotcom

How to Calculate Square Footage


Guided Practice:

Time: 3:00 minutes

 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.

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

https://www.engageny.org/resource/grade-6-mathematics-module-5-topic-lesson-5

Exercise #1. Page #77 - Floor Plan

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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.

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 carpeting rooms of different measurements with different costs per square foot.


Part 3: Supplementary Resources & References

Supplementary Resources

Area of Rectangles Review

References

EngageNY

https://www.engageny.org/resource/grade-6-mathematics-module-5-topic-lesson-5

Mathworksheets4kids

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

 Polygons/Quadrilaterals

https://www.youtube.com/watch?v=_wfTsmmteVE

Attribution Statements

This work, Calculating Areas of Rectangles, is a derivative of ‘The Area of Polygons Through Composition and Decomposition’ by Engage NY, used under a CC BY-NC-SA.  Creative Commons Attribution Non-Commercial Share-Alike. Calculating Areas of Rectangles  is licensed under a  Creative Commons Attribution CC-BY-4.0 International by Winston Lawrence.


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