Lesson Title

Calculating the Area of Rectangles                

Abstract

This lesson focuses on using the properties of rectangles to calculate area. It is designed to aid adult students to successfully master and apply basic geometry knowledge in a professional setting (construction and related) and can also contribute to achieving High School Equivalency (HSE).

Areas to be covered include properties of rectangles and squares; definition of ‘square’; right-angled triangles; calculating areas of rectangles and right-angled triangles; decomposition of area into manageable units; and calculating costs. Students will apply this knowledge to calculating the costs of purchasing building materials.

Learner Audience / Primary Users

This lesson is intended for individuals who are re-entering the education system at the adult education level (NRS level 3/4) in order to upgrade professional skills or obtain their HSE and, ultimately, improve their employment prospects.

Educational Use

Curriculum and Instruction; Informal Education

College & Career Readiness Standards (CCRS) Alignment

• Level: Adult Education
• Grade Level: Level C
• Subject: Math

Standard Description:

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

6G1 Solve real world and mathematical problems involving areas.

Language

English

Material Type

• Instructional Material,
• Interactives
• Lesson plans

Learning Goals

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

• Calculate the areas of common geometric forms in building and then determine the cost of purchasing material to cover/construct the target form.

  Use geometric forms to identify practical means of calculating area.

Keywords

• Designers for Learning
• Adult Education
• CCRS
• Squares
• Areas
• Quadrilaterals  
• Rectangles
•  Right-angled Triangles
• Costing
•  

Time Required for Lesson

  90 minutes

Prior Knowledge

Prior to this lesson, students may have discussed building plans, common building materials, and the notion of appropriate units of measurement. For example, if a person is measuring a building feature, he/she would use "inches" or “feet” or "meters" as a measuring unit.

Learners should be able to complete multiplication involving dollars and cents; multiply by a half; and carry out addition and subtraction.

Required Resources

• Builder's square/ set square  
•  Tape measure/ ruler  
• Worksheet #1 – Rectangles ws1 
• Worksheet #2 – Rectangles ws2 
• Pencil
• Eraser
•  Paper  

Lesson Author & License

• Lesson Author: David Cowell
• License: This work is licensed under a Creative Commons Attribution 4.0 International License.

Part 2: Lesson

Learning Objectives

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

• Use geometric forms to identify practical means of calculating area.

• Calculate the areas of common geometric forms in building and then determine the cost of purchasing material to cover/construct the target form.

Lesson Topics

Key topics covered in this lesson include:

• Characteristics of a rectangle
• How to calculate areas of rectangles
•  How to calculate the area of squares
•  How to calculate the area of right-angled triangles
•  Decomposition
• How to calculate costs of buying goods and services based on the amount of area.

Context Summary

The topic of rectangles was chosen not only because it falls within one of the areas of the math curriculum that students need to master for their High School Equivalency (HSE), but also because rectangles are fundamental feature of many construction-related tasks.

Many students who did not complete high school because of family circumstances and other reasons, may lack the skills in Geometry which may help them advance from low skilled to higher skilled employment.  

Relevance to Practice

This activity will enable students to build their mathematical knowledge to upgrade their practical skills in a variety of trades, including self-employed, and , if relevant, to earn their High School Equivalency (HSE). They will engage in the practical tasks of using math knowledge to calculate the quantity and total cost of materials required for a specific job or project.

Key Terms and Concepts

• Square
• Right-angled triangle 
• Rectangle
• Area
• Costing

Instructional Activities and Strategies

Warm Up

Time: 3 minutes

Elicit examples of a rectangle in everyday life; classroom; house.

Write/illustrate students responses. (e.g. dollar bill, desk, door.)

Introduction

Time: 5 minutes

Ask class about their understanding of what a rectangle is, and what distinguishes a rectangle from other shapes/forms. List responses and refine under heading ‘Properties’.

Properties should include:

two pairs of equal length sides; opposite sides are parallel (distance between them maintained);diagonals equal length; all angles between sides are right angles (hence rectangle, ‘square’); consequently, Area = L x W

Explain that it is these properties that make the rectangle a useful tool and goal of lesson is to apply one of these properties to determine the quantity and cost of materials needed for a particular job.

First will examine properties, then use them – especially latter.

Presentation / Modeling/Demonstration

Time: 10 minutes

Demonstrate (rectangle properties)

List properties and demonstrate measurement of each property on board /table (large scale) and with piece of paper. ... use tape measure, set square. Distribute properties handout/worksheet and tools ( tape measure; builder's square; set square - you can make  different size set squares from the flaps of cardboard boxes if necessary.)

Guided Practice

Time: 15 minutes

(Single) Learners identify rectangle on worksheet.  Compare with partner. (Pairs) Carry out rectangle hunt.... Find 1-2 examples. Name object and record dimensions… (Instructor will monitor activity).

Demonstration (area)

Time: 10 minutes

Return to front of class.

Explain formula for area, A= L x W.

Demonstrate (large scale) use board as example. Use learners example rectangles...

Display object name, dimensions, and (elicit)area.

When learners comfortable/competent with A= L x W, hold up  paper. Give dimensions.

Elicit area.

Carefully fold paper in half. Tear paper. Hold up half. Elicit area.

Take another piece of paper and fold it half lengthways. Rip into two. Hold up one piece.

Elicit area.

Hold up whole piece paper with half piece. Elicit area. Form ‘T’, ‘L’ with paper samples and elicit area.

Model how irregular shapes can be divided into rectangles and area determined by addition.

On board.. include labelling, horizontal, vertical division, link method to properties (angle, parallel etc.)

Check for comprehension. Demonstrate costing.

Model Rectangle; then Composite (real world) examples (see worksheet2). Elicit answers for area. Demonstrate cost.

Finally, take A4 paper halves. Remind learners of area. (Half)

Fold another piece of paper diagonally – elicit area (= Half)

Area right -angle triangle = ½ Base x Height.

Model on board large example.

Model practical application (Lean-to)

Hand out worksheet 2   

Activation

Time: 25  minutes

Learners complete worksheet 2

Evaluation

  Time: 5 minutes

 The instructor can monitor learner progress through worksheet.

Toward end of lesson, elicit and work through answers to worksheet tasks/

Part 3: Supplementary Resources & References

Supplementary Resources

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

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 (re-mix), is a derivative of ‘Calculating Areas of Rectangles' by Winston Lawrence, used under a Creative Commons Attribution CC-BY-4.0 International license. Calculating Areas of Rectangles (re-mix)  is licensed under a  Creative Commons Attribution CC-BY-4.0 International by David Cowell.