Version 01 Area Apprenticeship and Workplace Mathematics (Grade 10/Literacy Foundations Level 7) © 2012 by Open School BC http://mirrors.org/presskit/buttons/88x31/eps/by-nc.eps This work is licensed under the Creative Commons Attribution-NonCommercial 4. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc/4.0/ Permissions beyond the scope of this license are identified in the materials by a copyright symbol and are outlined below. To request permission to use the exclusions to this Creative Commons license, contact the author/publisher of the third party materials: Third party copyright exclusions include: All photographs used under license from Shutterstock.com with exception of the following: • 7 photos "measuring circumference" copyright Alberta Education, Photos by Jennifer Southcombe • Photo "hopper" copyright Alberta Education, Photo by Dan Leskiew The Data Pages were reproduced with permission from the BC Ministry of Education. Course History New, March 2012 Project Partners This course was developed in partnership with the Distributed Learning Resources Branch of Alberta Education and the following organizations: • Black Gold Regional Schools • Calgary Board of Education • Edmonton Public Schools • Peace Wapiti School Division No.
76 • Pembina Hills Regional Division No. 7 • Rocky View School Division No. 41 Project Management: Jennifer Riddel Content Revisions: Jennifer Riddel Edit: Leanne Baugh Math Edit: Learning Centre of the Greater Victoria School District Continuing Education Program: Nigel Cocking, Keith Myles, Bill Scott, School District 47, Powell River: Tania Hobson Module Tests: Barb Lajeunesse, Michael Finnigan (SD 34) Copyright: Ilona Ugro Production Technicians: Sharon Barker, Beverly Carstensen, Brian Glover Art Coordination: Christine Ramkeesoon Media Coordination: Janet Bartz Art: Cal Jones Flash Programming: Sean Cunniam Narration Recording: MOH Productions and Neil Osborne Voice Talent: Felix LeBlanc, Kate Eldridge, Wendy Webb and MOH Productions Advisors: JD Caudle (Yukon Territory), Randy Decker (SD 40), Bev Fairful (Yukon Territory), Sonya Fern (SD 62), Sandra Garfinkel (SD 39), Richard Giroday (SD 58), Sharon Hann (SD 39), Tim Huttemann (SD 20), Dan Laidlaw (SD 73), Heather Lessard (SD 53), Gloria Lowe (SD 6), Jan Malcolm (SD 36), Christina Teskey (OSBC), Jennifer Waughtal (SD 57), Ray Wong (SD 91) Table of Contents Table of Contents Section Organization. 1 Lesson A: Estimating Area.
3 Lesson B: Area Formulas 1. 21 Lesson C: Area Formulas 2. 41 Lesson D: Surface Area—Prisms and Pyramids. 61 Lesson E: Surface Area—Cylinders and Cones.
83 Lesson F: Perimeter and Area. 181 Net for Activity 3. 183 Cone Net Template. 187 © OPEN SCHOOL BC APPRENTICESHIP AND WORKPLACE MATHEMATICS ETEXT | iii Viewing Your PDF Learning Package This PDF Learning Package is designed to be viewed in Acrobat.
If you are using the optional media resources, you should be able to link directly to the resource from the pdf viewed in Acrobat Reader. The links may not work as expected with other pdf viewers. Download Adobe Acrobat Reader: http://get.com/reader/ Section Organization Section Organization This section on Area is made up of several lessons. Lessons Lessons have a combination of reading and hands-on activities to give you a chance to process the material while being an active learner.
Each lesson is made up of the following parts: Essential Questions The essential questions included here are based on the main concepts in each lesson. These help you focus on what you will learn in the lesson. Focus This is a brief introduction to the lesson. Get Started This is a quick refresher of the key information and skills you will need to be successful in the lesson.
Activities Throughout the lesson you will see three types of activities: • Try This activities are hands-on, exploratory activities. • Self-Check activities provide practice with the skills and concepts recently taught. • Mastering Concepts activities extend and apply the skills you learned in the lesson. You will mark these activities using the solutions at the end of each section.
Explore Here you will explore new concepts, make predictions, and discover patterns. Bringing Ideas Together This is the main teaching part of the lesson. Here, you will build on the ideas from the Get Started and the Explore. You will expand your knowledge and practice your new skills.
Lesson Summary This is a brief summary of the lesson content as well as some instructions on what to do next. © OPEN SCHOOL BC APPRENTICESHIP AND WORKPLACE MATHEMATICS ETEXT | v Section Organization At the end of each section you will find: Solutions This contains all of the solutions to the Activities. Appendix Here you will find the Data Pages along with other extra resources that you need to complete the section. You will be directed to these as needed.
Glossary This is a list of key terms and their definitions. Throughout the section, you will see the following features: Icons Throughout the section you will see a few icons used on the left-hand side of the page. These icons are used to signal a change in activity or to bring your attention to important instructions. AWM online resource (optional) This indicates a resource available on the internet.
If you do not have access, you may skip these sections. Solutions vi | APPRENTICESHIP AND WORKPLACE MATHEMATICS ETEXT © OPEN SCHOOL BC Section Organization My Notes The column on the outside edge of most pages is called “My Notes”. You can use this space to: • write questions about things you don’t understand. • note things that you want to look at again.
• draw pictures that help you understand the math. • identify words that you don’t understand. • connect what you are learning to what you already know. • make your own notes or comments.
Materials and Resources There is no textbook required for this course. You will be expected to have certain tools and materials at your disposal while working on the lessons. When you begin a lesson, have a look at the list of items you will need. You can find this list on the first page of the lesson, right under the lesson title.
In general, you should have the following things handy while you work on your lessons: • a scientific calculator • a ruler • a geometry set • Data Pages (found in the appendix) © OPEN SCHOOL BC APPRENTICESHIP AND WORKPLACE MATHEMATICS ETEXT | vii Area Area Photo by Tischenko Irina © 2010 Honey bees are master designers. Mathematicians have proven that the hexagonal pattern on the comb is the best way of dividing up a region into cells of equal area. The amount of wax required, and the energy expended by the worker-bees, are kept to a minimum. The cells are all the exact same size.
There are approximately four cells per square centimetre or 25 per square inch. This section is all about the area measurements of shapes. You will estimate areas and use those estimates to ensure that your answers to area problems are reasonable. Some of the problem situations you will meet in this section involve areas of two-dimensional shapes such squares, rectangles, parallelograms, and circles.
As well, you will explore the surface area of prisms, pyramids, cylinders, and cones. You will also investigate how changing the dimensions of geometric shapes affects the perimeters and areas of those shapes. In this section you will: • solve problems that involve SI and imperial area measurements of a variety of 2-D and 3-D shapes, including decimal and fractional measurements. © OPEN SCHOOL BC APPRENTICESHIP AND WORKPLACE MATHEMATICS ETEXT | 1 Area—Lesson A: Estimating Area Lesson A Estimating Area To complete this lesson, you will need: In this lesson, you will complete: • a ruler or a tape measure that shows • 5 activities imperial and SI units Essential Questions • How are referents used to estimate area measurements using SI and imperial units? • In what situations are SI and/or imperial units for measurement used? • How can the area of a regular or irregular shape be estimated using a grid? © OPEN SCHOOL BC APPRENTICESHIP AND WORKPLACE MATHEMATICS ETEXT | 3 Area—Lesson A: Estimating Area My Notes Focus Photo by Dmitry Melnikov © 2010 Suppose you and your dad plan to renovate the family room in your home.
To estimate the cost of new laminate flooring, you need to prepare an estimate of: • the total coverage area of the floor • any possible waste (as a result of cuts) The flooring will have to be cut to fit: • along the walls • around a fireplace (if there is one) • on and/or around stairs • around furnace vents (if there are vents) • any smaller areas of the room, e., a closet Does your family room have any unusual features? How would you estimate the amount of flooring you should purchase? Get Started Try this next activity to refresh your memory about units of area in both the SI and imperial measurement systems. 4 | APPRENTICESHIP AND WORKPLACE MATHEMATICS ETEXT © OPEN SCHOOL BC Area—Lesson A: Estimating Area Activity 1 My Notes Self-Check Unit Name Symbol SI or Imperial? square foot ft2 imperial m2 square inch acre ha square centimetre yd2 square kilometre square mile Turn to the solutions at the end of the section and mark your work. Explore You may find it helpful to have reference objects for units of area measure. In the next activity, you’ll measure some common objects in order to establish your own area referents.
© OPEN SCHOOL BC APPRENTICESHIP AND WORKPLACE MATHEMATICS ETEXT | 5 Area—Lesson A: Estimating Area My Notes Choosing Units Before you estimate or measure an area, consider which units would be the best ones to use for a particular object. For example, the book cover in the picture has an area of 99 in2. This area is also equal to 0.076 yd2—not a whole number of square yards. It would be a bit strange to say that the area of the book cover is 0.000016 acres! Not only would it be strange, but it would also hard to visualize a small fraction of an acre.
So, why do you think a square inch is the best unit for measuring this area? Photo by AKaiser © 2010 _________________________________________________________________ _________________________________________________________________ A good choice of units allows for small, whole numbers to be used in the measurement. By choosing square inches, you can express the area measurement as 99 in2. Now think of your bedroom. Would it be appropriate to express the area of your bedroom in square inches? What would a more appropriate imperial unit be? _________________________________________________________________ You would likely use the square foot (ft2) or the square yard (yd2) to measure the area of your bedroom.
In SI units, you would probably use the square metre (m2). 6 | APPRENTICESHIP AND WORKPLACE MATHEMATICS ETEXT © OPEN SCHOOL BC Area—Lesson A: Estimating Area Activity 2 My Notes Self-Check Circle the appropriate unit of area measurement for each of the following objects. a TV screen in2 ft2 ac 2. the main floor of a home in2 ft2 ac 3.
a plot of land cm2 m2 km2 4. the screen on a digital camera cm2 m2 km2 Turn to the solutions at the end of the section and mark your work. Measurement Systems In your work in Module 1, you learned that in Canada many items are advertized in both imperial and SI units. The following is a partial guide for your reference.
See if you can think of one or two more items and add them to the table. Advertised In: Item ft2 yd2 m2 laminate flooring ✔ ✔ carpets ✔ ✔ house and floor area ✔ ✔ linoleum ✔ ✔ lawn area on bags of fertilizer ✔ ✔ © OPEN SCHOOL BC APPRENTICESHIP AND WORKPLACE MATHEMATICS ETEXT | 7 Area—Lesson A: Estimating Area My Notes Bringing Ideas Together Estimation can be a useful technique in many different applications. You may use a referent to estimate the area of an object when you don’t have a ruler or tape measure handy—or if you just want a quick estimate without having to perform any calculations.