Lesson 1: Systems of Measurement and Personal Referents

Most people have a favourite place. That spot might be your bedroom at home, a cabin at the lake, or a beach in a tropical location. Perhaps your favourite place only exists in your imagination; a place where you can go to create, meditate, or take refuge. How would you describe your favourite place to someone who has never been there? One way you would likely describe your place is to explain how big it is—in other words, you could describe its dimensions.

In Canada, two measurement systems are commonly used—the SI (International System of Units) or metric system, and the imperial system. The SI is the measurement system officially adopted by Canada, but the imperial system is used frequently in the trades and in day-to-day conversations. For example, many people only know their height and weight in imperial units of measure—feet and inches and pounds, for example. In this lesson you will take a look at both systems of measurement.

Since most people don’t usually carry tape measures around with them, you will also relate these measures to common objects, which will allow you to quickly estimate a measurement. Such objects are called referents.

Outcomes

At the end of this lesson, you will be able to

• provide referents for linear measure including millimetre, centimetre, metre, kilometre, inch, foot, yard, and mile and explain the choices
• compare SI and imperial units, using referents
• estimate a linear measure using a referent, and explain the process used

Lesson Questions

• How can referents be used to estimate measurements?
• Why are there two systems of measurement?

Lesson Completion and Assessment

As you work through each lesson, complete all the questions and learning activities in your binder using paper and pencil, clearly labeling your work (they refer to this as your course folder). These include the Are you Ready, Try This, Share and Self Check questions. Check your work if answers are provided. Remember that these questions provide you with the practice and feedback that you need to successfully complete this course.
Once you have completed all of the learning activities, take the Lesson Quiz. This is the assessment for each lesson and is located under the Assess tab or by using the Quizzes link under the Activities block.

** Note – Share questions may have to be done on your own depending on your learning situation**

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Are You Ready?

Complete these questions in your course folder (binder). If you are experiencing difficulty, you may want to use the information and the multimedia in the Refresher section to clarify concepts before completing these exercises.

1. What is a system of measurement?

2. Name three common units used for measuring length in the metric system.

3. Name three common units used for measuring length in the imperial system.

4. Perform the following fraction operations. Reduce to lowest terms, where possible. 

Once you have completed these exercises to the best of your ability, use the answer link provided to check your work.

Answers

If you feel comfortable with the concepts covered in the questions, move forward to Discover. If you experienced difficulties, use the resources in Refresher to review these important concepts before continuing through the lesson or contact your teacher.

Refresher

The formal system of measurement used in Canada is the SI, but imperial units are still used in ordinary conversation. Imperial unit usage is found, for example, in recipes, construction, house renovation, and gardening. The imperial system of measurement actually has a longer history than the SI. Imperial units of length were initially based on human dimensions. In this lesson you will create a body ruler to help you understand these units.

As you start making measurements in the imperial system, you will need to be familiar with fractions. Use the multimedia piece titled “Exploring Fractions” to practise basic fraction operations. (Make sure you maximize the screen by clicking on the button in the top-right corner of the video.) ( You may need to log in using username LA53 and password 4487)

This page includes both a video and an interactive component. Go to the left side of the web page, and choose “Exploring Fractions (Object Interactive).”

Materials

• rulers and measuring tapes marked in both SI and imperial units

Mathematics 10C Learn EveryWare © 2010 Alberta Education

Go through the Referents Table, which introduces the idea of using referents. For example, you may discover that the thickness of 10 sheets of paper is a good approximation of 1 mm.

REFERENTS TABLE

Referent	Description	Example
Millimetre	The millimetre is 1/1000th of a metre. The millimetre is roughly the thickness of a dime. You can also think of 1 mm as the thickness of 10 sheets of paper.
Centimetre	The centimetre is 1/100th of a metre. The centimetre is approximately the thickness of 10 dimes. The centimetre can also be thought of as the width of the fingernail on your smallest finger.
Metre	One metre is the same as the height of a small child. One metre could also be the length of a running stride.	PhotoObjects.net/Thinkstock
Kilometre	One kilometre is equal to 1000 m. You can think of 1 km as the length of 7 football fields. Another way to think about 1 km is the distance you can walk in 10 minutes.
Inch	One inch is an imperial unit. It can be approximated by the width of your thumbnail.	Mark Poprocki/iStockphoto/Thinkstock
Foot	A foot is equal to 12 inches. There’s no better referent for a foot than your own foot! The foot can also be approximated by the length from your wrist to your elbow. Another convenient referent for 1 ft is the length of a 30-cm ruler. This is one of the most accurate estimations of 1 ft.
Yard	One yard is equal to 3 ft or 36 in. One referent for 1 yd is the width of a doorway. You can also think of 1 yd as the length of a normal walking stride.	© Zdenek Krchak /shutterstock
Mile	One mile is equal to 1760 yards or 5280 feet. One mile is the distance of 15 to 20 city blocks. Another way to think of 1 mile is the distance the average person can jog in 10 minutes.	© Laurens Parsons Photography/shutterstock

Every person’s body is different. The length of your foot is most likely different from that of a classmate. In this lab you will determine the measurements of your body parts described in a chart in order to use the body parts as referents for measurement.

The multimedia piece “Body Parts as Referents” demonstrates the way body parts can be used as referents.

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Math Lab: Body Referents

Complete Math Lab: Body Referents activity below.

Complete the table below by measuring each body part described in the chart. Record your measurements in both centimetres (SI units) and inches (imperial units).You may want to work with a classmate or a family member.

Procedure

You are now going to use the information gathered in the videos and the Math Lab to complete the following steps.

Step 1: Estimate the length of your desk or your kitchen table using one of the referents discussed in the videos and the Math Lab. Record the referent you used (e.g., thumbnail, foot, cubit) and your estimates, both in SI units and imperial units, in the following table.

Step 2: Repeat Step 1 for each of the following lengths or heights and distances:

• height of a wall
• length of an object that you can hold in your hand, such as your calculator
• distance from one corner of the room to the opposite corner
• perimeter of the classroom or other room

Step 3: Now measure each of the lengths, heights, and distances using a tape measure or ruler so that you can compare the results to your estimated values.

Analysis

Answer the following the questions in your course folder ( binder).

  1.   How close were your estimated values to the measured values?

  2.   What strategy could you use to make your estimation better?

  3.   What benefits are there when you measure using referents?

  4.   What drawbacks are there when you measure using referents?

Share

You now have an opportunity to share, with other students ( if possible), the answers to Math Lab: Body Referents questions you have just completed.

To make the most of this sharing opportunity you need to do the following:

• Ensure you have completed all the questions to the best of your ability and place them in a form that is convenient for sharing.
• Share your solutions with a classmate or other appropriate partner ( if possible).
• Review the results you recorded for steps 1 to 3. Are the results of other students similar to yours? Can you explain reasons for any differences?
• Review the answers provided to questions 1 and 2. If possible, discuss the answers to these questions with your partner. Your discussion might focus on clarifying meaning, or developing a clearer understanding of other students’ strategies and ideas.
• Finally, if necessary, revise your answers for questions 3 and 4 to incorporate what you have learned from the sharing you have done. Save a copy of your revised work in your course folder ( binder), along with a record of your discussion.

Mathematics 10C Learn EveryWare © 2010 Alberta Education

Glossary Terms

In this course you will often come across math-related words that may be unfamiliar to you. These words will likely be used over and over again, so it is important that you understand the meaning of these words. You will also need to record the words and their meanings so that you can refer to them when necessary.

In this course you will create your own glossary. Use the document titled Glossary Terms as a guide for how to design your own Glossary terms to keep a record of the math terms that you come across in Mathematics 10C.

In this lesson the suggested glossary terms you should add to Glossary Terms include the following:

• imperial measurement
• referent
• SI measurement

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Read

A non-standard measurement unit is a unit that you would not normally use to report a measurement. Non-standard units are not found on measuring devices. For example, at one time the height of a horse was measured in hands. Personal referents, such as the ones you developed in the Math Lab, are examples of non-standard measurement units. Referents help you to estimate lengths in standard units. For example, you may know that the length of your foot is 25 cm. If you determine that the width of the hallway is as long as eight of your feet, then you can estimate that the hallway is 8 × 25 cm = 200 cm, or 2-m wide.

Try This

Please complete the following exercises in your course folder ( binder).

TT 1.(Try This 1) Complete “Exercises” questions 3, 4, 5, and 6 on page 11 of your textbook.

TT 2. (Try This 2) Complete “Assess Your Understanding” questions 4, 5, and 6 on page 15 of your textbook.

Use the link below to check your work.

Possible TT1 and TT2 Solutions.

Self-Check

So far, you have learned about referents and the two systems of measurement. Test yourself using the link below,=.

Mathematics 10C Learn EveryWare © 2010 Alberta Education

Complete the lesson quiz posted under under the Assess tab or using the Quizzes link under the Activities block. Also ensure all of and your work in your binder (course folder) is complete.

Project Connection (NOT ASSIGNED)

Think some more about the special place that will be the basis of your Unit 1 Project. Do you see places where you will use metric measures and other places where you will use imperial measures? How will you decide?

Go to the navigation tree and view the Unit 1 Project to review the initial requirements of the project. Please make a few notes and store them in your course folder.

In Lesson 2 you will be ready to represent your place visually using simple shapes such as cylinders, cones, rectangular solids, and spheres. You will also calculate the volumes and surface areas of these solids using both imperial and metric units.

Going Beyond

There are other units of measure based on referents. Such units have their origins in agriculture and navigation, for example. Use your favourite Internet search engine to extend your learning by researching the origins of such units of measure as bolt, furlong, league, milestone, and chain. In your search, identify the imperial and metric equivalents of these measures, as well as the referents that are associated with these measures, and explain why these particular referents were chosen.

Mathematics 10C Learn EveryWare © 2010 Alberta Education

• How can referents be used to estimate measurements?
• Why are there two systems of measurement?

In this lesson you used referents to approximate both SI units and imperial units. You examined referents for linear measure including millimetre, centimetre, metre, kilometre, inch, foot, yard, and mile. You used referents to estimate linear measurements, and then you compared those estimates to the actual measurements. You also learned about the origins of the SI and imperial systems of measurement. In your discussions with your peers and with tradespeople in your community, you learned that some trades have adopted the SI, whereas others continue to use the imperial system.

In the next lesson you will use your knowledge of referents to choose appropriate units for measuring, and you will also learn strategies for solving measurement problems.

Mathematics 10C Learn EveryWare © 2010 Alberta Education