Calculat
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’; rightangled triangles; calculating areas of rectangles and rightangled 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 reentering 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
 Rightangled 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 rightangled 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 constructionrelated 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 selfemployed, 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
 Rightangled 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 12 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 (Leanto)
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/grade6mathematicsmodule5topiclesson5
Mathworksheets4kids
http://www.mathworksheets4kids.com/area.php
Polygons/Quadrilaterals
https://www.youtube.com/watch?v=_wfTsmmteVE
Attribution Statements
This work, Calculating Areas of Rectangles (remix), is a derivative of ‘Calculating Areas of Rectangles' by Winston Lawrence, used under a Creative Commons Attribution CCBY4.0 International license. Calculating Areas of Rectangles (remix) is licensed under a Creative Commons Attribution CCBY4.0 International by David Cowell.