Measures - Community Literacy of · PDF file · 2015-05-12Tools Use Measures Community Literacy of Ontario Page | 4 Numeracy in Action Curriculum and Resources to Understand and Use

Community Literacy of Ontario

Use

Measures

Activ

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ist Use Measures

Community Literacy of Ontario Page | 2

Numeracy in Action Curriculum and Resources to Understand and Use Numbers

Use Measures:

Activities

USE MEASURES Activities List

Competency C: Understand and Use Numbers

Task Group 3: Use Measures

Level 1 Indicator: Measure and make simple comparisons and calculations

Level 2 Indicator: Use measures to make one-step calculations

Level 3 Indicator: Use measures to make multi-step calculations; use specialized measuring tools

* Level Indicators represent end of level

Page Activity Name Level Goal Paths Supported by this Activity

4

Activity 1. Using Parts of Your Body as Measuring Tools

Practitioner Notes

Learner Activity

C3.1

Apprenticeship

Employment

Independence

Post-Secondary

Secondary

12

Activity 2: Metric Games

Practitioner Notes

Learner Activity C3.1

Apprenticeship

Employment

Independence

Post-Secondary

Secondary

24

Activity 3: Redecorating Measures

Practitioner Notes


Employment

Independence

29

Activity 4: Weather Forecasts

Practitioner Notes


Employment

Independence

41

Activity 5: Comparing Weather Forecasts

Practitioner Notes


Employment

Independence

48

Activity 6: EnerGuide kWh Labels

Practitioner Notes


Apprenticeship

Employment

Independence

Activ

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57

Activity 7: Comparing Fuel Consumption

Practitioner Notes


Apprenticeship

Employment

Independence

Post-Secondary

Secondary

65

Activity 8: Measuring with an “App”

Practitioner Notes


Apprenticeship

Employment

Independence

Post-Secondary

Secondary

72

Activity 9: Increasing Gingerbread Measurements With Ratios

Practitioner Notes

Learner Activity

C3.3 Independence

Secondary

80

Activity 10: Volume of Prisms to Make a Concrete Pad

Practitioner Notes

Learner Activity

C3.3

Apprenticeship

Employment

Independence

Post-Secondary

Secondary

86

Activity 11: Planter Volumes

Practitioner Notes


Apprenticeship

Employment

Independence

Post-Secondary

Secondary

93

Activity 12: Shingling a Roof

Practitioner Notes


Apprenticeship

Employment

Independence

Post-Secondary

Secondary

Page Information Handouts

103 Information Handout: Understanding Weather Forecasts

106 Information Handout: Checking Your Calculations

108 Information Handout: kWh EnerGuide Ratings

110 Information Handout: Fuel Consumption

112 Information Handout: Multi Measures Application

113 Information Handout: Ratios and Rates

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Activity 1: Using Parts of Your Body as Measuring Tools

- Practitioner Notes

C3.1

Competency: Understand and Use Numbers

Task Group: Use Measures

Level 1: Measure and make simple comparisons and calculations

This activity will introduce learners to non-standard and standard units of measurement.

Learners will use different body parts as non-standard units of measurement to measure

different objects and distances. They will also be introduced to the centimetre and metre.

The learner will need to know how to:

Understand numerical order and ordering terms (e.g., larger, smaller, longer, shorter,

more, less, most, least)

Understand concepts of height, length, width, etc.

Count to 100 and/or add whole numbers

Background Information

For all goal paths, learners will need to learn that objects and spaces have measureable

properties. They will need to understand expressions that examine these properties (e.g., "How

long?" and "How heavy?") and terms that compare these properties (e.g., longer, heavier,

shorter, wider, deeper).

Teaching the concepts of measurement, measurement tools and standardized measurement

units without using some tangible applications can be difficult for both you and the learner.

Learners need many opportunities to explore measuring and to discuss their experiences with

others. After learners thoroughly understand concrete measurement experiences, they will be

ready for further investigations with the mathematical concepts. One useful way to help

learners explore measurement is by using parts of their own bodies as measuring tools.

Before standard units of measurement were established, people used body parts to measure.

(Some examples are provided in the instructions below.) Learning how to measure using body

parts is helpful because:

We always have the parts of our body with us. Learning to use body parts and the

“calibration” of certain parts, such as a baby fingertip being approximately 1 cm wide,

can be helpful.

By showing how these non-standard tools vary, we can open up discussions on the

importance of standardized tools and units.

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Materials Required

Flip chart or white board

Objects and space to measure

Metric rulers and metre sticks

Scissors

Learner Activity Handout

My Body Part to Metric Chart

Instructions

We have written the instructions for more than one learner, as this is a good group activity.

However, it can be used for one-to-one instruction with few adaptations.

The learner may have help in reading the task instructions and completing the chart;

however, this will affect the Competency A. Find and Use Information and Competency B.

Communicate Ideas and Information elements of the task.

The activity is broken into several different stages. You may deliver the stages all at one time or

over several days. You may also adapt it by removing stages.

1. Take time to discuss some of the historic information about people using parts of their

bodies for measuring before standardized tools came into effect. Some of the examples

that follow are still used for measuring; however, they have been standardized.

Inch – width of a thumb

Foot – length of foot from longest toe to the back of the heel

Yard – distance from tip of nose to end of thumb with arm outstretched

Hand – width of a hand including the thumb (still used to measure height of horses)

Hand-span – width of hand, from outspread thumb to little finger

Cubit – length of forearm from the point of the bent elbow to the tip of the middle

finger

Fathom – length from one hand to the other with arms outstretched to the sides

(from the Anglo-Saxon word for “embrace”)

Step – length of a single step

Mile – distance of 1,000 paces (from the Latin for 1,000, which is “mille”)

Pace – length of two steps

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2. Trace your foot on a piece of paper. (You do not need to take off your shoe to do this.)

Provide the learner(s) with paper and have them trace their foot on the paper. Each of

you should cut out the shape. Compare the sizes of the shapes to the other person’s(s’).

Discuss how each person’s body measurements will be slightly different sizes. Have a

short discussion about using real “feet” as measuring tools. Would they want to pay the

same amount for two different sizes? The discussion should help them understand the

need for measuring with standard units.

3. Provide the learners with blank pieces of paper. Ask the learner to move around the

room (or centre) and measure various objects and distances using parts of their bodies.

They should record the measurements on their paper. If there is hesitancy getting

started, you may provide examples such as: “Measure how wide the desk is.” “What

might be a good body part to use to measure the desk?“ “Use a body part to measure

the pencil.” or “Measure the length of the room.”

After about ten minutes, call the learners back together. Have a discussion about their

measurements.

If you have more than one learner doing the activity, chart the data on a flip chart or

white board to use as a visual reference. Ask questions that help the learners compare

their findings, for example:

Who measured the width of the desk? What body part did you use to measure the

desk? How wide did you find it to be?

Did anyone else measure the width of the desk? Was your measurement the same?

Was the desk really a different width?

Why do you think your measurement was different from ____'s?

4. Discuss how, in the past, standardized measurements were created. For example, a stick

the length of a king’s foot was used as a standard foot measure in one country. Since it

was the king’s or ruler’s foot, the stick became known as a ruler. This term is still used

today. (Show them a foot long ruler.) Another example is the cubit. In Egypt, a rod was

created to make a standard length for the cubit instead of each person using their

forearm.

Show the learner(s) a variety of rulers (wooden, plastic and metal). Further discuss why

we use these standard tools.

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5. To discuss appropriate units of measure, ask questions such as:

Would you measure the length of the room in finger-widths? (But don’t actually

have them do it).

Would it be reasonable to measure the top of the desk in paces?

Why are these not sensible measuring units? What units would be more

appropriate?

6. Provide the learner(s) with metric rulers and metre sticks. Briefly explain the markings

for centimetres and how to read the numbers of centimetres. You do not have to

provide in depth explanations at this point.

Provide the learner(s) with the Learner Activity Handout and My Body Part to Metric

Chart. Have the learners “calibrate” some parts of their bodies to actual metric

measurements.

Discuss the results. Talk about the size of the unit of measurement compared to what

was being measured.

7. Allow the learner(s) to take the measurement tools back to re-measure objects and

areas using the standardized tools.

8. After about 10 minutes, have a discussion on the results of this round as compared to

the first round. Are measurements more consistent? Which units of measure were used

for which measurements? Were the tools easier to use than body parts?

No Information Handouts Required for This Activity

Activity Answers

There are no set answers for this activity.

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This activity incorporates elements of the following Performance Descriptors associated with

the Task Group Level 1 Indicator. You and the learner could use this information along with

features of the activity to discuss performance, determine skill progression and identify some

possible next steps to further develop learner proficiency.

In this activity, the learner measures and makes simple comparisons and calculations (C3.1) by:

Adding and subtracting whole number measurements

Recognizing values in number and word format

Measuring distance, length, width, height, weight, liquid volume, angles and

temperature

Using common measuring tools, such as rulers, scales and thermometers

Understanding numerical order

Choosing appropriate units of measurement (e.g., centimetres, metres, kilometres)

Using common standard units (e.g., metres, inches) and non-standard units (e.g., paces,

cupsful, scoops)

Identifying and performing required operation

Interpreting and representing measures using whole numbers, decimals and simple,

common fractions (e.g., ¼, ½)

Following apparent steps to reach solutions

Rounding to the nearest whole unit (e.g., kilos)

Using strategies to check accuracy (e.g., estimating, using a calculator, repeating a

calculation, using the reverse operation)

This activity also incorporates elements of the following:

Competency A. Find and Use Information, Task Group A1. Read continuous text

In this activity, the learner reads texts to locate and connect ideas and information (A1.2) by:

Making connections between sentences and between paragraphs in a single text

Scanning text to locate information

Locating multiple pieces of information in simple texts

Reading more complex texts to locate a single piece of information

Making low-level inferences

Following the main events of informational texts

Obtaining information from detailed reading

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Competency A. Find and Use Information, Task Group A2. Interpret documents

In this activity, the learner interprets simple documents to locate and connect information

(A2.2) by:

Performing limited searches using one or two search criteria

Extracting information from tables and forms

Using layout to locate information

Making connections between parts of documents


Competency B. Communicate Ideas and Information, Task Group B1. Interact with others

In this activity, the learner participates in brief interactions to exchange information with one

other person (B1.1) by:

Conveying information on familiar topics

Showing an awareness of factors such as social, linguistic and cultural differences that

affect interactions in brief exchanges with others

Choosing appropriate language in exchanges with clearly defined purposes

Participating in short, simple exchanges

Competency B. Communicate Ideas and Information, Task Group B3. Complete and create

documents

In this activity, the learner makes straightforward entries to complete very simple documents

(B3.1a) by:

Making a direct match between what is requested and what is entered

Making entries using familiar vocabulary

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Learner Activity 1: Using Parts of Your Body as

Measuring Tools

Did you know that you are a human ruler?

Throughout history, people have been using themselves

to measure length. You can, too. You can easily use

some parts of your body as measures. You do not

always have a standard measuring tool, like a ruler,

metre stick or tape measure with you. You do have the

parts of your body with you. Before using parts of your

body as measuring tools, you should compare them to a

standard measure. To do this, you can use an "ordinary"

ruler. If you know their standard measurement, you will

always be able to measure things.

1. For this activity, you will measure body parts that you can easily use to measure

other objects and areas. You can use many body parts as measures. Some have

similar size (for example, hand and palm), so you can just choose which ones you

prefer. Maybe, those with easier to remember numbers might be best. For example,

my hand-span is 20 cm (centimetres). Yours may be different.

Use the My Body Part to Metric Chart to record your own body measurements. Feel

free to use other measures, or to modify these (like using your little finger rather

than middle finger). The important thing is to find ones that are easy to use and

useful to you.

Standard: well-known,

widely-accepted and

unchanging.

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My Body Part to Metric Chart

Measure Explanation My Metric Measurement

baby fingertip

width of just the tip of your baby finger Example –

about 1 cm

finger finger width

inch thumb width at joint

finger length

fingertip to knuckle

half finger fingertip to (middle of) second joint (choose a finger)

palm or hand

width of 4 extended fingers

hand length hand length, heel to fingertip

hand-span hand width, from outspread thumb to baby finger

foot foot-length, heel to toe - Good for walking short distances

cubit elbow to fingertip

fathom fingertip to fingertip, arms outstretched

height from the floor to the top of your head

step one step

pace

two steps (measured from the point at which the heel of one foot is raised to the point at which it is set down again after a step by the other foot). Good for walking longer distances

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Activity 2: Metric Games - Practitioner Notes

C3.1




Although not exactly goal-directed nor depending on authentic circumstances, group game

activities are a fun, non-intimidating way to help learners become familiar with metric

measurement. In this activity learners compete in a classroom game event, while learning

about the metric system. The activity can be adapted for different numbers, skill levels and

events.

Note: A number of versions of these games can be found online. We were unable to locate and

provide credit to the original source.


Understand numerical order and ordering terms (e.g., more, less, most, least)

Understand concepts of height, length, width, etc.

Add, subtract, multiply and divide whole numbers

Use a metric ruler and a Celsius thermometer

Round to the nearest whole unit (e.g., centimetre, metre)


Research by the USA National Council of Teachers of Mathematics (2000) shows that teachers

need to:

Help students understand that objects have measurable properties

Help students understand expressions referring to properties (i.e., "How long?" and

"How heavy?")

Help students understand and use terms of comparison (longer, heavier, shorter, wider)

Help students use appropriate units and processes for measurement

Help students use standard units of measurement

Help students create and use formulas to help count units

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Although that research was for a different age group, these critical steps are equally valid for

adult learners. Measurement is integrated into every part of adult life and is required for all

goal paths.

Once learners understand that objects have measureable properties, they have to learn to

measure concretely. Teaching the concepts of measurement without using some concrete

applications can be difficult for both you and the learner. Learners need many opportunities to

explore measuring and to discuss their experiences with others. Metric games give them those

chances to work with abstract mathematical quantities and to share math ideas with peers in

their everyday language. After learners thoroughly understand concrete measurement

experiences, they will be ready for further investigations with the mathematical concepts.

Games provide teachers the opportunity to put fun and humour into learning. Games work for

a variety of learning styles, as opposed to more traditional instruction.

It is a good idea to show the learners various measurement tools that will be used. It is

especially important to show comparisons between an imperial and metric ruler and/or a

metric and imperial thermometer.

Materials Required

Event Instruction Handout for each event station

Game equipment (you may vary this depending on stations): Cotton puffs, 4 or 5 plastic

straws, 2 or 3 paper plates, two bags of marbles, large sponge, a small bucket or large

bowl, water, 1 litre measuring cup, towels, small Post-It notes, box of salt, small bowl,

metric scale, 2-minute timer, stop watch, plastic bottle cap (e.g., pop or water bottle),

masking tape and sticky circle shape

Metric measuring equipment (may vary depending on stations): metric measuring tapes,

metre sticks, thermometer for liquids, small food or balance scale

Camera (digital or video) to record events, if the program has one, or someone can

volunteer to use theirs

Timer, stop-watch or other method of keeping time


Metric Games Scorecard for recording data

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Instructions

The learner may have help in reading the task instructions; however, this will affect the

Competency A. Find and Use Information elements of the task.

1. The handouts are set for six events; however, there are eight event suggestions from which

to choose (see the Event Instruction Handouts on the three pages following these

instructions for suggested events). This number can change depending on the type of

measurement you wish the learners to explore and the number of learners. You may also

adapt the events or create your own. This may be done with the learners’ help, if you wish.

The stations can be completed in one day, perhaps as a special celebration (Metric Day is

October 10th), or over several days, adjusting the number of “events” to be completed to

the time allowed.

2. Set up the event station for each event (e.g., cotton puff shot put, plastic straw javelin,

marble weight lifting). See the Event Instruction Handouts (on the following three pages) for

the details of each “event”.

3. Divide the learners into groups. We suggest 3 or 4 maximum in a group. Try to balance the

measurement and reading skill levels out amongst the teams. Each team will need a

captain, who will read the instructions, etc. This may be determined by you, by the learners

or by some non-judgemental method (e.g., birth date, alphabetically by name).

4. Establish fair ground rules before starting and be consistent with these rules throughout the

game. Some suggestions:

a. Measurement should be to the nearest whole unit (e.g., centimetres, degrees, grams).

b. How long will be allowed at a “station” and what method will announce when teams will

rotate to the next station.

c. The order of rotation through the event stations.

5. Provide the learners with the Learner Activity Handout along with the Games Measurement

Scorecard Handouts.

6. Assign each group to a starting event station.

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7. A “debriefing” after the activity has been completed is valuable. Discuss how the learners

felt about estimating and measuring. Ask what they used or thought about when making

their estimations. See if they felt there was any improvement in their estimation skills. Talk

about any challenges they had with the actual measurement.

8. You may present “awards” if you wish; however, this is meant to be a fun learning

opportunity, not a competition.


Activity Answers

There are no set answers for this activity.

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Measuring distance, length, width, height, weight, liquid volume, angles and

temperature



Making simple estimates



cupsful, scoops)


















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In this activity, the learner interprets very simple documents to locate specific details (A2.1) by:

Scanning to locate specific details

Interpreting brief text and common symbols

Locating specific details in simple documents, such as labels and signs

Identifying how lists are organized (e.g., sequential, chronological, alphabetical)


In this activity, the learner initiates and maintains interactions with one or more persons to

discuss, explain or exchange information and opinions (B1.2) by:

Showing an awareness of factors that affect interactions, such as differences in opinions

and ideas and social, linguistic and cultural differences

Demonstrating some ability to use tone appropriately

Using strategies to maintain communication, such as encouraging responses from

others and asking questions

Speaking or signing clearly in a focused and organized way

Rephrasing to confirm or increase understanding

Using and interpreting non-verbal cues (e.g., body language, facial expressions,

gestures)


documents


(B3.1a) by:



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Learner Activity 2: Metric Games

1. For this activity you will work in small teams.

2. Each team member will have their own Metric Games Scorecard.

3. Each team will have a team captain.

4. Each group will start at a different event station.

5. There are six event stations. Each event station has a different task.

6. There is a task card for each event station. This card has the instructions. Each

team’s captain will read the instructions to the team.

7. Before each event begins, each member of the team must estimate the

measurement he or she expects to achieve. Team members must record their

estimate on their own Metric Games Scorecard.

8. Before beginning each event, captains should check that all members on the team

have their estimation recorded for that activity.

9. After each team member performs the event activity, they should measure and

record the actual measurement achieved on their own Metric Games Scorecard.

10. Next, each member must calculate how much their estimate was off (the difference

between their estimated measurement and the actual measurement). This is their

individual “score” for the event station. Record this amount on the Metric Games

Scorecard.

11. After all the event stations have been completed, add the scores of all the events to

get your overall score.

12. On the back of your score sheet, gather the scores of all the team’s members. Add

them up to determine the team’s overall score.

Activity2: Metric Games

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Event Instruction Handouts

Event 1:

Plastic Straw Javelin Throw

1. Estimate in centimetres (cm) how far you can

throw the “straw javelin”.

2. Record your estimate on your record sheet.

3. Stand with your toes at the starting line.

4. Throw the plastic straw like a javelin (spear).

5. You are allowed only one throw each.

6. Measure your throw (the distance from the

starting line to your straw).

7. Record the distance of your throw.

Event 2:

Cotton Ball Shot Put

1. Estimate in centimetres (cm) how far you can throw

the “cotton ball (shot)”.



4. “Put” (throw) the cotton ball.

5. You are allowed only one “put” (throw) each.

6. Measure your “put” (the distance from the starting

line to your cotton ball).



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Event 3:

Marble Weight Lifting

1. Estimate how many grams (g) of marbles you can

pick up and hold for the count of 5, using just your

right hand.


3. Pick up a fistful of marbles.

4. Hold the marbles while you count to 5.

5. Put the handful of marbles on the scale.

6. Measure the weight of the lifted marbles using the

scale.

7. Record the weight of the lifted marbles.

Event 4:

Paper Plate Discus

1. Estimate in centimetres (cm) how far you can throw

the paper plate discus.



4. Throw the paper plate.

5. You are allowed only one throw each.

6. Measure your throw (the distance from the starting

line to your paper plate).



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Event 6:

Sponge Wrestling

1. Estimate in millilitres (ml) how much water you can

squeeze out of a sponge with your left hand.


3. Take the sponge in your left hand and fill it with

water from the bucket. Do not use your right hand.

4. Remove the sponge from the bucket and hold it over

the measuring cup.

5. Squeeze as much water out of the sponge and into

the measuring cup as you can. Use only 1 squeeze.

6. Measure how much water you “wrestled” out of the

sponge.

7. Record the amount of water.

Event 5:

High Jump

1. Estimate in centimetres (cm) how high you can

jump to put a Post-It note on the wall.


3. Stand facing the wall with your toes at the starting

line (20 cm from the wall).

4. Jump up and stick the Post-It note on the wall as

high as you can. You may not take a run at it.

5. You are allowed only one jump each.

6. Measure your high jump (the distance from the floor

to the lowest edge of the Post-It note).

7. Record the distance of your jump.


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Event 7:

Pinch in Time

1. Estimate in grams (g) how much salt you can move by

the pinch (picking it up between your thumb and first

finger) in 2 minutes.


3. Set the timer for 2 minutes. Move the salt from the bowl

to the scales by pinching it between your thumb and

finger. Stop when the time runs out.

4. You may not use any other means to move the salt.

5. Weigh the salt.

6. Record the weight of the salt you moved.

Event 8:

Bottle Cap Curling

1. Estimate in centimetres (cm) how close you can get the

bottle cap “curling rock” to the “button” dot-sticker, by

flicking it with your finger one metre down a table.


3. Place the bottle cap “rock” on the start point (called the

hack in curling) that is one metre from the “button” dot.

4. Using only your index (1st) finger, flick the cap towards

the “button” dot.

5. Measure how far your bottle cap “rock” is from the

“button” dot.

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Metric Games Scorecard

Name: ___________________________

Event 1 Event 2

Estimate: Estimate:

Actual: Actual:

Score: Score:

Event 3

Event 4

Estimate: Estimate:

Actual: Actual:

Score: Score:

Event 5

Event 6

Estimate: Estimate:

Actual: Actual:

Score: Score:

Overall Score (Total of scores of Events 1 to 6) _________________

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Activity 3: Redecorating Measures – Practitioner Notes

C3.1




In this activity, the learner will make linear measures in both imperial and metric systems. The

learner will also add and compare measures.



Understand concepts of height, length, width, depth, etc.

Add and subtract whole numbers

Use both a metric and an imperial tape measure

Round to the nearest whole or ½ unit

Understand properties of rectangular shapes, such as length and width


In Canada, both the metric and imperial measurement systems are used. The metric system is

more commonly in use for some purposes, now (e.g., metric Celsius for weather temperatures,

metric kilometres for driving distances and speeds). However, for many linear measurement

situations, a mix of systems is still the norm. This may be difficult for learners to understand and

adopt into real life practise. Using rulers, measuring sticks and tape measures that offer both

calibrations may help them to see the relationships. Being able to read one system separately

from the other is a skill that must be developed.

As we covered in Activity 1 of this module, it helps if the learner understands that all things

have measureable properties. The measurement tool may vary and standard tools offer

comparisons that are understood by many.

Materials Required


Measuring tape with both imperial and metric measurements

Extra paper for calculations

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Instructions

The learner may have help in reading the task instructions; however, this will affect the


Provide the learner with the tape measure. Ensure that the learner understands that there are

two different measuring systems incorporated on the tape and how to read each.

Provide the learner with the Learner Activity Handout.


Activity Answers

Activity answers will vary depending on the dimensions of the room and the width of the

door.

1. The learner should measure both the length and the width of the room correctly in feet

and round the measurements up to the nearest foot.

2. The learner should have added one length for every 12 feet or less width of room. (For

example, if the room is 15 feet wide and 16 feet long, you will need 2 lengths – one 12 feet

wide and one 3 feet wide to cover the 15 foot width (12+3=15). But the carpet only comes

in 12 foot widths, so you would have to order 16’ + 16’ = 32’ of carpet).

The learner does not have to do these formulas, but for purposes of showing the answer, we

can say, if l = the length of the room and w = the width of the room and c = carpet length

needed, then:

If w < 12’, then w=c

If w >12’ but < 24’, then w + w=c

If w >24, but < 36’, then w + w + w=c

3. The learner should accurately measure the length of one wall that has no doors or

windows. The measurement should have been done in inches and rounded to the nearest

½ inch.

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4. The task requires the learner to find the following sums (which would be through addition).

a. Sum of 3 boards that are each 96” wide equals_288_inches

b. Sum of 3 boards that are each 72” wide equals_216_inches

c. Sum of 3 boards that are each 60” wide equals___180__inches

d. Sum of 3 boards that are each 48” wide equals___144_inches

5. The learner should determine which option, a, b, c or d, would best fill the wall space

without being too large. To do this, the learner should determine which measurement (a,

b, c, or d) is the closest to the length of the wall measured in task 3 (without going over).

6. The learner has to measure the doorway width correctly, in centimetres, and then

compare that width to the dimensions of the completed desk. The doorway must be

greater than 78 cm for the pre-assembled desk to be ordered.








Measuring distance, length, width, height, weight, liquid volume, angles and temperature





cupsful, scoops)








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Learner Activity 3: Redecorating Measures

You are redecorating a rectangular room. You may choose the room you are in now or

you may choose another.

1. You are going to start with the carpet. To order the carpet you need to measure both

the length and width of the room. As carpet is sold in feet, you need to measure the

room in feet. Round up to the nearest foot.

Length _______________ Width ______________

2. The carpet you want only comes in 12 foot widths. Therefore, you will have to order

extra lengths if the room is wider than 12 feet. Calculate how long a carpet you must

order. Total length of carpet ________________

3. You need to order a set of three white boards for a large wall space that has no

doors or windows. The boards are sold in inches, so you should measure the wall in

inches. Round to the nearest ½ inch. The wall is ________inches.

4. The boards come in 4 sizes. Add up the 3 boards in each of the options below, to

determine how much space they will fill.

a. Sum of 3 boards that are each 96” wide equals __________ inches

b. Sum of 3 boards that are each 72” wide equals __________ inches

c. Sum of 3 boards that are each 60” wide equals __________ inches

d. Sum of 3 boards that are each 48” wide equals __________ inches

5. Determine which option a. b. c. or d. would best fill the wall space that

you measured in question 3, without being too large.

6. Next you need to order a desk. The desk is 78 cm tall, 165 cm wide and 90 cm deep.

You can purchase it pre-assembled or you can do it yourself (DIY), after delivery.

Measure the doorway of the room, in centimetres, to decide which you should

order. Door width _________ Order it Pre-assembled or Do It Yourself (DIY)

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Activity 4: Weather Forecasts - Practitioner Notes

C3.1




In this activity, the learner will interpret weather forecasts using metric measures for

temperature and precipitation.



Understand concepts of temperature and linear measure

Subtract integers (both positive and negative)


The same handout materials are used for both this activity and Activity 5: Comparing Weather

Forecasts (starting on page 41). This Activity 4 has level C3.1 tasks, while Activity 5 has level

C3.2 tasks. This may be useful to you when working with multi-level groups.

In Canada, the weather changes considerably, not only over the seasons, but also within days

and weeks. Being able to understand weather forecasts allows people to prepare for significant

weather events. Preparing for the weather is important for everyone in their personal life, but

for people working in many trades or outdoor jobs, it is critical.

Weather forecasts use terms that may not be familiar to learners. Some online glossaries for

weather terms, and other sites that explain weather forecasts that you may find useful, are:

Environment Canada:

o Weather Glossary (www.ec.gc.ca/meteo-

weather/default.asp?lang=En&n=B8CD636F-1)

o Weather Elements And When They Are Included In The Forecast

(www.ec.gc.ca/meteo-weather/default.asp?lang=En&n=2D8EBDE4-1)

o FAQs (www.ec.gc.ca/meteo-weather/default.asp?lang=En&n=108C6C74-1)

http://www.ec.gc.ca/meteo-weather/default.asp?lang=En&n=B8CD636F-1

http://www.ec.gc.ca/meteo-weather/default.asp?lang=En&n=B8CD636F-1

http://www.ec.gc.ca/meteo-weather/default.asp?lang=En&n=2D8EBDE4-1

http://www.ec.gc.ca/meteo-weather/default.asp?lang=En&n=108C6C74-1

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Weather Network.com

(http://past.theweathernetwork.com/index.php?product=help&pagecontent=faq&page

content=forecasts)

Time and Date.com Weather Glossary and Terminology

(www.timeanddate.com/weather/glossary.html)

To provide awareness and practice with understanding temperatures, you might find the

following to be useful:

Math Worksheets 4 Kids, Temperature Worksheets

(www.mathworksheets4kids.com/temperature.html)

Materials Required

Information Handout: Understanding Weather Forecasts (found on page 103)

Learner Activity Handouts

Weather Forecast Handouts (copied single-sided)

Instructions

Before doing this activity, go over the material in the Information Handout: Understanding

Weather Forecasts (found on page 103) with the learner. Use the sample forecasts found in the

Weather Forecast Handouts or use current forecasts found online (e.g., www.weather.com,

www.weathernetwork.com) using cell phone or tablet apps, or included in newspapers for

reference.

The learner may have help in reading the task instructions and locating information on the

weather forecast charts; however, this will affect the Competency A. Find and Use

Information elements of the task.

Provide the learner with the Learner Activity Handout and the Weather Forecast Handouts.

These should be printed single-sided to make it easier for the learner to find and use

information.

Information Handouts Required for This Activity:

Understanding Weather Forecasts Information Handout (found on page 103)

http://past.theweathernetwork.com/index.php?product=help&pagecontent=faq&pagecontent=forecasts

http://past.theweathernetwork.com/index.php?product=help&pagecontent=faq&pagecontent=forecasts

http://www.timeanddate.com/weather/glossary.html

http://www.mathworksheets4kids.com/temperature.html

http://www.weather.com/

http://www.weathernetwork.com/

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Activity Answers

1. In Forecast A,

a. The coldest forecasted temperature: 1C

b. The hottest forecasted temperature: 22C

c. If you might need to wear a jacket some of the time. Yes

d. Thursday, October 25, with a difference of 11C

e. The greatest precipitation, in the form of rain, forecasted for one day: 1-3 mm

f. No snow forecasted

2. In Forecast B,

a. The coldest forecasted temperature: -28C

b. The hottest forecasted temperature: -6C

c. If you might need to wear a jacket some of the time. Yes No

d. If you might only need to wear a short-sleeved or sleeveless shirt and shorts some of the

time. Yes No

e. Thursday, February 5, with a difference of 16C

f. Close to 5 mm forecasted for Saturday, February 7

g. The greatest precipitation, in the form of snow, forecasted for one day: 1-3 cm

3. In Forecast C,



c. Day(s): Wednesday, June 6, with a difference of 11C.

d. The greatest precipitation, in the form of rain, forecasted for one day: 1-3 mm

e. No snow forecasted

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4. In Forecast D,



c. If you might only need to wear a short-sleeved or sleeveless shirt and shorts some of the

time. Yes No

d. Day(s): Saturday, June 13 and Sunday, June 14 with a difference of 17C.

e. The greatest precipitation, in the form of rain, forecasted for one day: close to 10 mm

f. No snow forecasted

5. In Forecast E,

a. The coldest forecasted temperature: -29C




time. Yes No

e. Day(s): Wednesday, with a difference of 17C

6. In Forecast F,



c. If you might need to wear a jacket or sweater some of the time. Yes No


time. Yes No

e. Day(s): Tuesday, May 31 with a difference of 13C

f. The greatest precipitation, in the form of rain, forecasted for one day: close to 5 mm

g. No snow forecasted

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Beginning to interpret integers (e.g., temperature, elevation)


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Learner Activity 4: Weather Forecasts

Before doing this activity, you should review the Information Handout: Understanding

Weather Forecasts with your instructor.

Use the Weather Forecast Handouts to complete the following.

1. In Forecast A, determine:

a. The coldest forecasted temperature _______C.

b. The hottest forecasted temperature _______C.


d. The largest difference in one day’s low and high temperatures.

Day or days________________________________ Difference _____________

e. The greatest precipitation, in the form of rain, forecasted for one day _____.

f. The greatest precipitation, in the form of snow, forecasted for one day _____.

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2. In Forecast B, determine:




d. If you might only need to wear a short-sleeved or sleeveless shirt and shorts

some of the time. Yes No

e. The largest difference in one day’s low and high temperatures.


f. The greatest precipitation, in the form of rain, forecasted for one day _____.

g. The greatest precipitation, in the form of snow, forecasted for one day _____.

3. In Forecast C, determine:



c. The largest difference in one day’s low and high temperatures.


d. The greatest precipitation, in the form of rain, forecasted for one day _____.

e. The greatest precipitation, in the form of snow, forecasted for one day _____.

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4. In Forecast D, determine:



c. If you might only need to wear a short-sleeved or sleeveless shirt and shorts


d. The largest difference in one day’s low and high temperatures.


e. The greatest precipitation, in the form of rain, forecasted for one day _____.

f. The greatest precipitation, in the form of snow, forecasted for one day _____.

5. In Forecast E, determine:








6. In Forecast F, determine:



c. If you might need to wear a jacket or sweater some of the time. Yes No





f. The greatest precipitation, in the form of rain, forecasted for one day _____.

g. The greatest precipitation, in the form of snow, forecasted for one day _____.

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Weather Forecast Handouts

Forecast A.

Forecast B.

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Forecast C.

Forecast D.

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Forecast E.

Forecast F.

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Activity 5: Comparing Weather Forecasts

– Practitioner Notes

C3.2



Level 2: Use measures to make one-step calculations

In this activity, the learner will interpret and compare weather forecasts using metric measures

for temperature, precipitation and wind velocity.



Make comparisons using whole numbers, integers and percentages

Understand concepts of temperature, linear measure and rates of speed

Interpret rates

Add and subtract integers


This activity follows Activity 4: Weather Forecasts (starting on page 29) by taking the tasks up to

level 2. The same handout materials are used for both activities; however, Activity 4 has level

C3.1 tasks and Activity 5 has level C3.2 tasks. This may be useful to you when working with

multi-level groups.

See the information found in Activity 4: Weather Forecasts Background Information (on page

29) of this module.

Materials Required



Weather Forecast Handouts (starting on page 38) (copied single-sided)

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Instructions

The learner may have help in reading the information handout, task instructions and locating

information on the weather forecast charts; however, this will affect the Competency A. Find

and Use Information elements of the task.

Provide the learner with the Information Handout: Understanding Weather Forecasts (found on

page 103). Review the information with the learner to ensure understanding.

Provide the learner with the Learner Activity Handout and the Weather Forecast Handouts

(starting on page 38). These should be printed single-sided to make it easier for the learner to

find and use information.



Activity Answers

1. Forecast E. has the coldest overall forecasted temperature at -29C.

2. Forecasts D. and F. have the hottest overall forecasted temperatures at 31C.

3. The temperature range for each forecast period is:

a. Forecast A is 21C.

b. Forecast B is 22C.

c. Forecast C is 11C.

d. Forecast D is 22C.

e. Forecast E is 29C.

f. Forecast F is 18C.

4. Forecast E. has the largest forecasted range in temperatures, over the whole period, at

29C.

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5. Forecast C. has the smallest forecasted range in temperatures, over the whole period, at

11C.

6. Forecasts D. and E. have days with a difference of 17 between their low and high

temperatures.

7. Forecast D. has the greatest precipitation, in the form of rain, forecasted for one day at

close to 10 mm.

8. Forecast D. has the greatest overall precipitation forecasted at approximately 13 mm.

9. Forecast B. has the greatest precipitation, in the form of snow, forecasted for one day at

1-3 cm.

10. Forecast A. has the greatest P.O.P at 70%.

11. Forecast F. has the windiest day at 30 km/h.

12. Forecast F. has the greatest range in wind speeds at 25 km/h.





In this activity, the learner uses measures to make one-step calculations (C3.2) by:

Calculating using numbers expressed as whole numbers, fractions, decimals,

percentages and integers

Interpreting and applying rates (e.g., km/hr, km/l) and ratios (e.g., map scales)

Choosing and performing required operation(s); may make inferences to identify

required operation(s)

Selecting appropriate steps to solutions

Interpreting, representing and measuring using whole numbers, decimals, percentages,

ratios and simple, common fractions



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Competency C. Understand and Use Numbers, Task Group C4. Manage Data

In this activity, the learner makes low-level inferences to organize, make summary calculations

and represent data (C4.2) by:



Finding ranges for data sets




Recognizing patterns and beginning to identify trends in data

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Learner Activity 5: Comparing Weather Forecasts

Before doing this activity, you should read the Information Handout: Understanding

Weather Forecasts and review it with your instructor.

Use the Weather Forecast Handouts to complete the following.

1. Forecast A. B. C. D. E. F. has the coldest overall forecasted temperature

at _______C.

2. Forecast A. B. C. D. E. F. has the hottest overall forecasted

temperature at _______C.

3. Determine the temperature range for each forecast period:

a. The range for forecast A is __________C.

b. The range for forecast B is __________C.

c. The range for forecast C is __________C.

d. The range for forecast D is __________C.

e. The range for forecast E is __________C.

f. The range for forecast F is __________C.

4. Forecast A. B. C. D. E. F. has the largest forecasted range in

temperatures, over the whole period, at _______C.

5. Forecast A. B. C. D. E. F. has the smallest forecasted range in

temperatures, over the whole period, at _______C.

6. Determine which two forecasts have days with a difference of 17 between their low

and high temperatures. The two forecasts are _______________________.

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7. Forecast A. B. C. D. E. F. has the greatest precipitation, in the form of

rain, forecasted for one day at ____________.


rain, over the whole forecast period ____________ (Note: where there is a range

forecasted use the highest amount forecast in the day. For example, if 1-3 mm is

forecasted, use 3 mm.)


snow, forecasted for one day at ____________.

10. Only five forecasts show the Possibility of Precipitation (P.O.P.).

Forecast A. B. C. D. F. has the greatest P.O.P at __________.

11. Only five of the forecasts have wind rates listed. Forecast A. B. C. D. F.

has the windiest day at __________km/h.

12. Forecast A. B. C. D. F. has the greatest range in wind rates forecasted,

over the period of the forecast at ____________ km/h.

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Activity 6: EnerGuide kWh Labels – Practitioner Notes

C3.2






Have some understanding of metric measurement

Make comparisons using whole numbers

Add, subtract and multiply whole numbers

Interpret rates

Calculate percentages


EnerGuide is the official Government of Canada mark associated with the labelling and rating of

the energy consumption or energy efficiency of specific appliances. EnerGuide labelling exists

for appliances, heating and cooling equipment, houses and vehicles. For more information

about EnerGuide and appliance energy use costs, you may find the following websites useful:

Natural Resources Canada at www.nrcan.gc.ca/energy/products/energuide/12523

Yukon – Energy, Mines and Resources – Appliance Buying Tips at

www.energy.gov.yk.ca/em_appliance_buying_tips.html

Energuide, Brussels at www.energuide.be/en/questions-answers/how-much-energy-do-

my-household-appliances-use/71/

Materials Required

Information Handout: kWh EnerGuide Ratings (found on page 108)


EnerGuide Appliance Labels Handouts (found on page 55)

http://www.nrcan.gc.ca/energy/products/energuide/12523

http://www.energy.gov.yk.ca/em_appliance_buying_tips.html

http://www.energuide.be/en/questions-answers/how-much-energy-do-my-household-appliances-use/71/

http://www.energuide.be/en/questions-answers/how-much-energy-do-my-household-appliances-use/71/

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Instructions

The learner may have help in reading the information handout, task instructions and locating

information on the EnerGuide Labels; however, this will affect the Competency A. Find and

Use Information elements of the task.

Provide the learner with the Information Handout: kWh EnerGuide Ratings (found on page

108). Review the information with the learner to ensure understanding.

Provide the learner with the Learner Activity Handout and the EnerGuide Appliance Labels

Handouts.


Information Handout: kWh EnerGuide Ratings (found on page 108)

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Activity Answers

1. Of Appliances #1, 2 and 3:

a. Appliance #2 uses the least energy per year at 125 kWh.

b. Appliance #2 uses 360 kWh less energy than Appliance #3.

485 𝑘𝑊ℎ − 125 𝑘𝑊ℎ = 360 𝑘𝑊ℎ

c. It would cost $46.80 less. 360 𝑘𝑊ℎ × $0.13/𝑘𝑊ℎ = $46.80

d. Appliance #2 uses 74.23% less energy than #3. Since the percentage is expressed as

“less than #3”, appliance #3 is considered the “initial” or “old” amount and is used as

the divisor. The formula for percentage change is 100% × (new - old) / old.

∴ 100% × (485 − 125) ÷ 485 = 100% × 360 ÷ 485 = 74.23%

Note: Since two operations are used for task d., it is a transition activity towards level 3.

2. Of Appliances #4, 5 and 6:

a. Appliance #4 uses the least energy per year, at 385 kWh.

b. Appliance #4 uses 30 kWh less energy than Appliance #5.

415 𝑘𝑊ℎ − 385 𝑘𝑊ℎ = 30 𝑘𝑊ℎ

c. It would cost $3.90 less. 30 𝑘𝑊ℎ × $0.13/𝑘𝑊ℎ = $3.90

d. Appliance #4 uses 7.23% less energy than #5. Since the percentage is expressed as “less

than #5”, appliance #5 is considered the “initial” or “old” amount and is used as the

divisor. The formula for percentage change is 100% × (new - old) / old.

100% × (415 − 385) ÷ 415 = 100% × 30 ÷ 415 = 7.23%

Note: Since two operations are used for task d., it is a transition activity towards level 3.

3. The scale for televisions (Appliances #1, 2 and 3) is the largest, at 397 kWh.

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Converting units of measurement within the same system and between systems




Interpreting, representing and converting measures using whole numbers, decimals,

percentages, ratios and simple, common fractions (e.g., ½, ¼)












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Learner Activity 6: EnerGuide kWh Labels

You continue to pay for appliances, such as refrigerators, stoves, washers, dryers and

TVs, long after you purchase them. As major electricity users, they go on costing you,

month after month. This is important to consider when you are purchasing a new or

used appliance of any kind. It is even worth considering if you are deciding whether or

not to keep an old appliance that needs repair.

To help with these decisions, appliances in Canada usually have EnerGuide labels. These

labels show the number (or average number) of kWh that the labelled appliance

generally consumes in a year.

Before doing the activity, you should read the Information Handout: kWh EnerGuide

Ratings and/or discuss it with your instructor.

In this activity, you will compare and calculate using electric appliance EnerGuide labels.

Use the labels on the EnerGuide Appliance Labels Handout to complete the following

tasks. Show your calculation steps. You should round your answers to two decimal

places.

1. Use the labels for appliances 1, 2 and 3 to complete the following tasks:

a. Determine which of the appliances uses the least energy. Appliance #_____ uses

the least energy per year, at __________kWh.

b. Determine the difference in energy use between the appliance that uses the

most energy and the appliance that uses the least energy. Appliance # ______

uses less energy than Appliance # ____ by ________kWh.

c. If electricity costs you, on average, $0.13 per kWh, determine how much you

would save by using the most energy efficient appliance (use your answer from b

to multiply by the electricity cost rate). There would be a savings of

approximately $________per year.

d. Using your answer from b, determine what percentage less energy is used by the

appliance that uses the least energy. Appliance #____ uses ____% less energy

than Appliance # ____.

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2. Use the labels for appliances 4, 5 and 6 to complete the following tasks:

a. Determine which of the appliances uses the least energy. Appliance #_____ uses

the least energy per year, at __________kWh.

b. Determine the difference in energy use between the appliance that uses the

most energy and the appliance that uses the least energy. Appliance # ______

uses less energy than Appliance # ____ by ________kWh.

c. If electricity costs you, on average, $0.13 per kWh, determine how much you

would save by using the most energy efficient appliance (use your answer from b

to multiply by the electricity cost rate). There would be a savings of

approximately $________per year.

d. Using your answer from b, determine what percentage less energy is used by the

appliance that uses the least energy. Appliance #____ uses ____% less energy

than Appliance # ___.

3. Appliances 1, 2 and 3 are televisions and appliances 4, 5 and 6 are combined

refrigerator/freezers. Each type of appliance has a different scale of energy ratings.

Determine which group has the greatest range of energy consumption on their scale.

The scale for _____________________ is the largest, at _______kWh.

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EnerGuide Appliance Labels Handout

Appliance #1

Appliance #2

Appliance #3

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Appliance #4

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Activity 7: Comparing Fuel Consumption


C3.2






Have some understanding of metric measurement (distance and volume)

Make comparisons using whole numbers

Add, subtract and multiply whole numbers

Interpret rates

Calculate percentages


Being able to drive a car provides many learners with the mobility to reach their goals.

However, car ownership costs long after the initial purchase in the way of fuel consumption.

Materials Required

Information Handout: Fuel Consumption (found on page 110)


EnerGuide Fuel Consumption Label Handout

Computer with Internet access

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Instructions

The learner may have help in reading the information handout and task instructions, and in

locating information on the fuel consumption labels and on the Internet pages; however, this

will affect the Competency A. Find and Use Information elements of the task.

The learner may have help accessing the Internet sites and using the comparison tool;

however, this will affect the Competency D. Use Digital Technology elements of the task.

Provide the learner with the Information Handout: Fuel Consumption (found on page 110)

Review the information with the learner to ensure understanding.

Provide the learner with the Learner Activity Handout and the EnerGuide Fuel Consumption

Labels Handout. These should be printed single-sided to make it easier for the learner to find

and use information. Provide the learner with access to the Internet.


Information Handout: Fuel Consumption (found on page 110)

Activity Answers

1. Vehicle 4 has the lowest City Fuel Consumption rating.

2. Vehicle 6 has the lowest Highway Fuel Consumption rating.

3. City rate – Highway rate.

Vehicle 1 would need 4 litres more.

Vehicle 2 would need 2 litres more.

Vehicle 3 would need 2.1 litres more.




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Activity Answers

4. $2,918 Vehicle that uses the most – vehicle that uses the least.

$4,030 − $1,112 = $2,918

5. 72.4% the difference calculated in #4 ÷ the vehicle with the highest fuel consumption X

100 (for percent).

$2,918 ÷ $4,030 × 100% = 72.4%

6. No answer required. The learner should select 3 vehicles to compare.

7. Answers will vary depending on vehicles chosen.
















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In this activity, the learner interprets simple documents to locate and connect information (A2.2) by:







documents

In this activity, the learner decides what, where and how to enter information in somewhat complex documents (B3.3a) by:

Drawing from multiple sources as required (e.g., other documents and texts)

Managing unfamiliar elements (e.g., vocabulary, context, topic) to complete the task

Using layout to determine where to make entries

Making inferences to decide what, where and how to enter information

Competency D. Use Digital Technology

In this activity, the learner performs well-defined, multi-step digital tasks (D.2) by:

Selecting and following appropriate steps to complete tasks

Locating and recognizing functions and commands

Making low-level inferences to interpret icons and text

Beginning to identify sources and evaluate information

Performing simple searches using keywords (e.g., Internet, software help menu)

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Learner Activity 7: Comparing Fuel Consumption

Before doing this activity, you should read the Information Handout: Fuel Consumption

and/or review it with your instructor.

1. Compare the six labels on the EnerGuide. Determine which vehicle has the lowest

City Fuel Consumption rating.

Vehicle 1 Vehicle 2 Vehicle 3 Vehicle 4 Vehicle 5 Vehicle 6

2. Determine which has the lowest Highway Fuel Consumption.

Vehicle 1 Vehicle 2 Vehicle 3 Vehicle 4 Vehicle 5 Vehicle 6

3. Calculate how many more litres it will take for each vehicle to drive 100 km in the

city than on the highway. Write the value of the difference below.

Vehicle 1 would need _________litres more.






4. Using the Estimated Annual Fuel Costs on the labels, calculate how much you would

save a year if you drove the vehicle with the least fuel consumption instead of the

one with the most. $__________savings.

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5. Using your answer from #4, calculate the percentage savings this would be over

driving the vehicle with the highest fuel consumption. Please round your answer to

one decimal place. _____________% savings.

6. Go to the Natural Resources Canada fuel consumption ratings web tool found at

http://oee.nrcan.gc.ca/fcr-rcf/public/index-e.cfm. Choose three vehicles to

compare. You may get the information for each vehicle separately or you may

compare them all at one time. Ask your instructor for help with the web-search tool,

if you need it. If possible, print out the results of your search.

7. On the Blank EnerGuide Fuel Consumption Labels Handout, fill in the information

for each vehicle using the blank labels provided.

http://oee.nrcan.gc.ca/fcr-rcf/public/index-e.cfm

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EnerGuide Fuel Consumption Labels Handout

Vehicle 1 Vehicle 2

Vehicle 4

Vehicle 5 Vehicle 6

Vehicle 3

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Blank EnerGuide Fuel Consumption Labels Handout

Vehicle Name__________

Model ________________

Year _________________


Model ________________

Year _________________


Model ________________

Year _________________

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Activity 8: Measuring with an “App” – Practitioner Notes

C3.2




This activity is only for use with a Smart cell phone or a tablet. If neither the program nor the

learner has one, this activity is not appropriate.



Have some understanding of metric measurement

Add, subtract and multiply whole numbers and decimals

Interpret rates

Use a cell phone or tablet app (application)


Measuring has changed considerably in recent years. Often, instead of using tape measures,

squares, stop-watches, etc., professionals and home users will reach into their cell phone or

tablet “toolkit” when they want to measure something. One example of a mobile “toolkit” app

is Multi Measures (see the Information Handout: Multi Measures Application, found on page

112). We have chosen this application as it is available for iPhone, iPad and android mobiles, for

a reasonable cost. However, you and the learner may prefer other measuring apps.

Using mobile applications and measuring with a cell phone or tablet may be new to the learner.

It may even be new to you. Experiment with settings, try different tools and have some fun!

Materials Required

Information Handout: Multi Measures Application (found on page 112) - optional


Android cell phone, iPhone or tablet owned by the program or the learner

Access to Wi-Fi or Internet, if learner needs to investigate and download apps

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Instructions

The learner may have help in reading the information handout and task instructions;

however, this will affect the Competency A. Find and Use Information elements of the task.

The learner may have help accessing apps on the cell phone/tablet, downloading apps (if

required) and the Internet research; however, this will affect the Competency D. Use Digital

Technology elements of the task.

Provide the learner with the Information Handout: Multi Measures Application (found on page

112), if required. Review the information with the learner to ensure understanding.

Provide the learner with the Learner Activity Handout


Information Handout: Multi Measures Application (found on page 112) - optional

Activity Answers

1. For this task, the learner is measuring the area of objects using a metric system:

a. The learner can locate and/or download any app that measures areas of objects.

b. Answers will vary depending on desk or table measured, but should be in cm.

c. Answers will vary but should be in cm2. The formula for the surface area of a rectangle is

length X width.

2. Measuring the volume of a box:

a. Answers will vary but should be in cm.

b. Answers will vary but should be in cm3. The formula for the volume of a rectangular

prism is: length X width X height.

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3. Measuring a rectangular-shaped room:

a. The learner can locate and/or download any app that measures areas of objects.

b. Answers will vary depending on the room chosen, but measures should be in metres.

c. Answers will vary but should be the conversion to feet. 1 metre = 3.28 feet

d. Answers will vary but should be in ft2. The formula for the surface area of a rectangle is

length X width.

e. Answers will vary but should be in ft3. The formula for the volume of a rectangular prism

is: length X width X height.

4. Measuring sound:

a. The learner can locate and/or download any app that measures sound.

b. Answers will vary but should be in decibels.

c. Answers will vary but should be in decibels.

d. Answers will vary but should be in decibels.

e. Answers will vary but should be in decibels.

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Interpreting and representing area and volume using symbols and abbreviations (e.g.,

m3 )

Converting units of measurement within the same system and between systems

Understanding and using formulas for finding the perimeter, area and volume of simple,

common shapes


















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(A2.2) by:






Competency D. Use Digital Technology

In this activity, the learner performs well-defined, multi-step digital tasks (D.2) by:

Selecting and following appropriate steps to complete tasks

Locating and recognizing functions and commands

Making low-level inferences to interpret icons and text

Beginning to identify sources and evaluate information

Performing simple searches using keywords (e.g., Internet, software help menu)

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Learner Activity 8: Measuring with an “App”

In this activity, you will use applications on a “Smart” cell phone or tablet to measure a

variety of things.

1. Measuring the area of objects:

a. Locate and download an app (application) for your mobile device that acts like a

ruler and measures in centimetres.

b. Measure the desk or table you are sitting at to determine the metric

measurements in centimetres for the:

Width ___________, length ________ and height _________

c. Using your measurements in 1.b., and the formula for the area of a rectangle,

calculate the surface area of the table or desk. The surface area is

__________________cm2.

2. Measure the volume of a box:

a. Use the same ruler app as in #1 to measure a rectangular box to determine the

metric measurements in centimetres for the:

Width ___________, length ________ and height ___________

b. Using the measurements for 2.a. and the formula for the volume of a rectangular

prism, calculate the volume of the box. The volume is __________________cm3.

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3. Measuring a rectangular room:

a. Locate and download an app that measures distances in metres.

b. Measure a rectangle-shaped room to determine the metric measurements in

metres for the:

width __________, length _________ and height ___________

c. Convert the amounts in 3.b. to feet:

width __________, length _________ and height __________

d. Using the amounts in 3.c. and the formula for area of a rectangle, calculate the

floor area of the room. The floor area is ___________ft2.

e. Using the amounts in 3.c. and the formula for the volume of a rectangular prism,

calculate the volume of the room. The volume is ____________ft3.

4. Measuring sound:

a. Locate and download an app that measures sound in decibels.

b. Measure the sound of the room in decibels. ___________

c. Turn on a music source such as a radio or computer and measure the decibels.

_________________

d. If possible, stand around some loud machinery, such as a lawn tractor or

construction equipment, and measure the decibels. ____________

e. Compare the room’s sound, the music and the sound of the equipment to

determine which was the loudest and by how many decibels. The

_______________ sound was loudest by __________decibels.

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Activity 9: Increasing Gingerbread Measurements with Ratios


C3.3



Level 3: Use measures to make multi-step calculations; use specialized measuring tools

This activity has some fun with ratios and measurement by adjusting the recipe and pattern for

a gingerbread house.


Add, subtract, multiply and divide whole numbers, decimals and fractions

Make calculations that include exponents

Know formulas to determine the area of rectangular and triangular prisms

Convert within and between measuring systems

Make multiple-step calculations


Gingerbread isn’t just for Christmas anymore. Spooky spectaculars are popular at Halloween

and the Easter Bunny often comes to call at a spring gingerbread house. In fact, it seems that

anything a person wants to celebrate, from birthdays to new house purchases, is being

celebrated with gingerbread creations. It’s not just houses anymore. Ships, castles, woods

scenes, etc., are all showing up made out of the spicy dough. For those who don’t like ginger,

there are recipes using chocolate cookie dough instead.

Materials Required


Gingerbread Recipe Handout

Gingerbread House Pattern Handout

Ratios and Rates Information Handout (found on page 113)

Calculator

Paper for calculation steps

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Instructions

The learner may have help in reading the information handout and task instructions, and in

locating information on the diagrams; however, this will affect the Competency A. Find and

Use Information elements of the task.

Provide the learner with the Ratios and Rates Information Handout and the Learner Activity,

Gingerbread Recipe and Gingerbread House Pattern Handouts. These should be printed single-

sided to make it easier for the learner to find and use information. Provide the calculator and

extra paper.

Information Handouts Required for This Activity

Ratios and Rates Information Handout (found on page 113)

Activity Answers

The answers to 1 and 4 require changes to the recipe ingredients, as indicated below:

4 cups (1000 mL) flour 12 cups 1 tbsp (15 mL) cinnamon 3 tbsp 2 tsp (10 mL) baking powder 6 tsp 2 tsp (10 mL) ground cloves 6 tsp 2 tsp (10 mL) ground ginger 6 tsp 1 tsp (5 mL) nutmeg 3 tsp 1 tsp (5 mL) baking soda 3 tsp 1 tsp (5 mL) salt 3 tsp 1 cup (250 mL) shortening 3 cups 1 cup (250 mL) fancy molasses 3 cups 1 cup (250 mL) sugar 3 cups 2 egg yolks 6 egg yolks

2. The imperial conversions in the instructions should be from 180°C to 356°F or 350°F, and

the 1.24 cm to 0.49 inches or ½ inch.

3. The ratio of old recipe amounts to new recipe amounts is 1:3.

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5. Royal Icing adjusted using the ratio of 1:4 is:

2 cup (125 mL) pasteurized liquid egg whites

8 tsp (10 mL) cream of tartar

16 - 18 cups (1 - 1.125 L) icing sugar, sifted

6. The dimensions are:

a. The scaled-down size of the squares is 0.25 inches.

b. The distance each square represents, when it is not scaled down, is 1 inch.

c. The final house will be approximately 11 inches high. 2.75" × 4 = 11"

d. The final house width will be approximately 8 inches.

(𝐿𝑎𝑟𝑔𝑒 𝑠𝑖𝑑𝑒 + 𝑠𝑚𝑎𝑙𝑙 𝑠𝑖𝑑𝑒) × 4 ∴ (1.25" + approx. 0.75") × 4 = 2" × 4 = 8"

e. The depth of the final house will be approximately 6 inches. 1.5" × 4 = 6"

7. The ratio would be 1:6.

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In this activity, the learner uses measures to make multi-step calculations; uses specialized

measuring tools (C3.3) by:



Managing unfamiliar elements (e.g., context, content) to complete tasks

Making estimates involving many factors where precision is required

Choosing and performing required operations; making inferences to identify required

operations

Selecting appropriate steps to solutions from among options

Identifying a variety of ways to complete tasks


percentages, ratios and fractions













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(A2.2) by:







documents


(B3.1a) by:



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Learner Activity 9: Increasing Gingerbread

Measurements with Ratios

For this activity, you will be converting a recipe from metric to imperial measures. You

will also be adjusting the recipe’s quantities and the scale of a house pattern, using

ratios.

1. The recipes on the Gingerbread Recipe Handout are in metric measurements.

Convert the amount of each ingredient to imperial measures. Write the imperial

measures to the left of the current metric amounts.

2. In the recipe instructions, change the oven temperature and the thickness to roll out

the pieces from imperial measures to metric.

3. You want to make 3 houses, not just 1. The gingerbread recipe is only large enough

for one house. Determine what ratio you should use to change the recipe. ________

4. Using the ratio you determined in #3, calculate new imperial measurements for all

the ingredients in the recipe. Write the new amounts to the right of the ingredients.

5. The Royal Icing recipe will not make enough for all the decorating. Using the ratio of

1:4, adjust the ingredients in the recipe and write the new amounts to the right of the

ingredients.

6. Look at the Gingerbread House Pattern Handout. The handout is in a ratio of 1:4.

a. Measure the size of the squares in inches _______

b. Determine what distance each square represents when it is not scaled down.

______________inches

c. Determine approximately how high the final house will be. _________

d. Determine approximately how wide the final house will be (the width of both the

large and small sides). _________

e. Determine approximately how deep the final house will be. _________

7. Determine the ratio you would use if you wanted a house that was 16.5 inches tall.

The ratio would be ____________.

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Gingerbread Recipe Handout

1000 mL flour

15 mL cinnamon

10 mL baking powder

10 mL ground cloves

10 mL ground ginger

10 mL nutmeg

5 mL baking soda

5 mL salt

250 g shortening

250 mL fancy molasses

250 mL sugar

2 egg yolks

Combine the first 8 ingredients (flour through salt) in a bowl; set it aside. Put shortening,

molasses and sugar in another bowl. Using a mixer on low speed, beat mixture until

fluffy. Add egg yolks and continue beating until blended. Gradually beat in flour mixture

just until blended. Gather dough into a ball; divide in half. Flatten each half into a

rectangular shape. Wrap in plastic wrap and refrigerate for 1 hour before rolling out.

Preheat oven to 180ºC. Meanwhile, remove the dough from refrigerator and let stand at

room temperature for 5 minutes before rolling out. On parchment paper, roll out each

shape of dough to 6 mm thickness. Using pattern pieces and a sharp knife, cut out your

shapes.

For larger pieces, bake for 15 – 18 minutes or until lightly browned. For smaller pieces,

bake for 10 – 13 minutes or until lightly browned. Working with one gingerbread piece

at a time, immediately transfer hot pieces to a cutting board. Hold pattern pieces on top

using an oven mitt and trim gingerbread pieces using a sharp knife to match pattern

pieces. Cool trimmed gingerbread pieces completely on racks.

Royal Icing

½ cup (125 mL) pasteurized liquid egg whites 2 tsp (10 mL) cream of tartar 4 - 4½ cups (1 - 1.125 L) icing sugar, sifted

Using the high speed setting of an electric mixer, beat liquid egg whites until foamy. Add cream of tartar and continue beating until very stiff. Gradually beat in icing sugar until stiff peaks form. Spoon frosting into a pastry bag fitted with a large plain tip. Frosting becomes hard when left standing uncovered. May be refrigerated in an airtight container for up to 24 hours. Makes about 3 cups (750 mL).

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Gingerbread House Pattern Handout

Cut here after baking

Small Side

Scale: 1:4

Large Roof

(Cut 2)

Small End

(Cut 2)

Small Roof

(Cut 2)

Large Side

(Cut 2)

(Cut 2)

Porch roof

Large end

(Cut 2)

Chimney (Cut 2)

Door

(Cut 1)

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Activity 10: Volume of Prisms to Make a Concrete Pad


C3.3







Know formulas to determine the area of rectangular and triangular prisms

Convert within and between measuring systems



Applying mathematical theory to life applications is often difficult for learners. Not all learners

will be creating concrete pads, although some with apprenticeship, employment or even

independence goals, may. However, applying the formulas to life tasks allows all learners to see

relevance in learning formulas and theories.

This activity involves both rectangular and triangular prisms. For more information about these

shapes, there are a number of websites that you might be interested in reviewing, including:

www.mathsisfun.com/geometry/prisms.html

www.analyzemath.com/Geometry/3D_shapes_problems.html

www.onlinemathlearning.com/volume-rectangular-prism.html

www.mathcaptain.com/geometry/triangular-prism.html

www.mathscore.com/math/practice/Triangular%20Prisms

Practice activities are also available, if you require them, at:

http://ca.ixl.com/math/grade-6/volume-and-surface-area-of-triangular-prisms

http://imathworksheets.com/geometry-worksheets-2complementary-angles-

worksheets/volume-worksheets/volume-of-a-triangular-prism/

http://algebralab.org/practice/practice.aspx?file=Word_VolumePrisms.xml

http://www.mathsisfun.com/geometry/prisms.html

http://www.analyzemath.com/Geometry/3D_shapes_problems.html

http://www.onlinemathlearning.com/volume-rectangular-prism.html

http://www.mathcaptain.com/geometry/triangular-prism.html

http://www.mathscore.com/math/practice/Triangular%20Prisms

http://ca.ixl.com/math/grade-6/volume-and-surface-area-of-triangular-prisms

http://imathworksheets.com/geometry-worksheets-2complementary-angles-worksheets/volume-worksheets/volume-of-a-triangular-prism/

http://imathworksheets.com/geometry-worksheets-2complementary-angles-worksheets/volume-worksheets/volume-of-a-triangular-prism/

http://algebralab.org/practice/practice.aspx?file=Word_VolumePrisms.xml

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Materials Required


Calculator

Paper for calculation steps

Instructions

The learner may have help in reading task instructions and locating information on the

diagrams; however, this will affect the Competency A. Find and Use Information element of

the task.

Provide the learner with the Learner Activity Handout. This should be printed single-sided to

make it easier for the learner to find and use information. Provide a calculator and extra paper.


Activity Answers

1. The pad needs to be 1.5” higher at the garage end than the driveway end.

2 yards x1

4inch per foot ∴ 6 feet x 0.25

in

ft= 1.5 𝑖𝑛𝑐ℎ𝑒𝑠

2. a. Using the formula for the volume of a rectangular prism (Volume = L x W x D), the

volume is 45 ft3.

𝑣𝑜𝑙𝑢𝑚𝑒 = 𝐿 × 𝑊 × 𝐷

∴ 𝑣𝑜𝑙𝑢𝑚𝑒 = 10 𝑦𝑎𝑟𝑑𝑠 × 2 𝑦𝑎𝑟𝑑𝑠 × 6 𝑖𝑛𝑐ℎ𝑒𝑠 = 30′ × 6′ × 0.5′ = 90 𝑓𝑡3

b. Using the formula for the volume of a right-angle triangular prism [volume = ½(base x

width x height)], the volume is 11.25 ft3.

𝑣𝑜𝑙𝑢𝑚𝑒 =1

2(𝑏𝑎𝑠𝑒 × 𝑤𝑖𝑑𝑡ℎ × ℎ𝑒𝑖𝑔ℎ𝑡)

∴ 𝑣𝑜𝑙𝑢𝑚𝑒 =1

2(10 𝑦𝑎𝑟𝑑𝑠 × 2 𝑦𝑎𝑟𝑑𝑠 × 1.5 𝑖𝑛𝑐ℎ𝑒𝑠) = 0.5(30′ × 6′ × 0.125′) = 0.5 ×

22.5 𝑓𝑡3 = 11.25𝑓𝑡3

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3. The total volume of the pad is 101.25 ft3. 90𝑓𝑡3 + 11.25𝑓𝑡3 = 101.25𝑓𝑡3

4. The volume in cubic metres is 2.87 m3. 101.25 𝑓𝑡3 × 0.0283 𝑚3 1 𝑓𝑡3⁄ = 2.87 𝑚3

Or 101.25 ft2 x 1 m2/35 ft2= 2.87 m2









Understanding and using properties of angles and triangles to solve problems

Understanding and using formulas for finding the perimeter, area and volume of non-

rectangular, composite shapes




operations







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Identifying how lists are organized (e.g., sequential, chronological, alphabetical)


documents


(B3.1a) by:



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Learner Activity 10: Volume of Prisms to Make a

Concrete Pad

In this activity, you will calculate the volume of a concrete pad, to determine the

amount of concrete you will need. Show your calculation steps on a separate piece of

paper and round your answers to two decimal places.

You are planning a concrete pad to go in front of a two-bay garage to make it easier to

shovel snow. The length of the pad, from one side of the garage to the other, will be 10

yards. The pad cannot be less than 6” deep at any point, so it won’t crack under the

weight of vehicles.

1. To prevent water from running into the garage, the pad must slope away from the

garage and down to the driveway. For every foot the concrete pad comes out from

the garage you need to drop the slope by ¼ inch. The pad will be 2 yards wide

extending out from the garage. Calculate how much higher the pad needs to be at

the garage end than the driveway end.

2. To determine how much concrete you need, you must calculate the volume of the

pad. The easiest way to do this is to divide the pad into two sections. Consider the

diagram below.

width height

base

Rectangular Prism

L

D

W

Right-Angle Triangular Prism

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a. The bottom section is a 6” deep rectangular prism that is 10 yards wide and 2

yards long.

Using the formula for the volume of a rectangular prism (Volume = L x W x D),

calculate the volume of the bottom section. The volume is _________________.

b. The top section, created by the slope, is a right-angle triangular prism. The base

of the triangular prism is the same width as the pad (10 yards). The width is the

same as the width of the pad (2 yards) and the height is the value of your

calculation in #1.

Using the formula for the volume of a right-angle triangular prism [volume =

½(base x width x height)], calculate the volume of the top section of the pad.

The volume is ____________.

3. Calculate the total volume of the pad. The total volume of the pad is

______________.

4. In Ontario, suppliers usually sell concrete

in cubic metres or in mixes that are

estimated to cover a certain number of

cubic metres. Convert your answer in 2.c.

to cubic metres. The volume in cubic

metres is _____________.

1 cubic foot = 0.0283 cubic metres

or

1 cubic metre = 35.3 cubic feet

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Activity 11: Planter Volumes – Practitioner Notes

C3.3







Know formulas to determine the area of rectangular prisms, cones and cylinders


Convert measures within the metric system and between metric and imperial systems


In this activity, the learner uses formulas to determine the volume of differently shaped plant

containers, the amount of soil needed to fill them and the cost of the soil.


will be planting, although some with apprenticeship, employment or even independence goals,

may. However, applying the formulas to life tasks allows all learners to see relevance in learning

formulas and theories.

Materials Required


Conversion and Formulas Handout (optional)

Calculator

Extra paper

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Instructions

The learner may have help in reading task instructions; however, this will affect the


Provide the learner with the Learner Activity Handout, calculator and extra paper. If it is

suitable for you and the learner, you may also provide the Conversion and Formulas Handout

(found on page 92, following the Learner Activity Instructions). This will add elements of

Competency A. Find and Use Information, Task Group A2: Interpret Documents.


Activity Answers

1. The conversions from inches to centimetres are:

a. The cube shaped pot has sides measuring 50.8 cm.

b. The rectangular prism pot measures 71.12 cm long by 22.23 cm high by 25.4 cm wide.

c. The cylindrical pot measures 43.18 cm in diameter and 20.32 cm in height.

d. The truncated cone pot is 39.37 cm across the top, 31.75 cm in height and 33.02 cm

across the bottom.

2. a. It will take 131,096.51 cm3 of soil to fill one cube shaped planter.

Volume of cube = side³ ∴ 𝑣𝑜𝑙𝑢𝑚𝑒 = 50.8 𝑐𝑚3 = 131,096.51 𝑐𝑚3.

b. It will take 40,157.34 cc of soil to fill one rectangular prism shaped planter.

𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑎 𝑟𝑒𝑐𝑡𝑎𝑛𝑔𝑢𝑙𝑎𝑟 𝑝𝑟𝑖𝑠𝑚 = 𝐿 × 𝑊 × 𝐻

∴ 𝑉𝑜𝑙𝑢𝑚𝑒 = 71.12 𝑐𝑚 × 22.23 𝑐𝑚 × 25.4 𝑐𝑚 = 40,157.34 𝑐𝑚3

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c. It will take 29,741.33 cm3 of soil to fill one cylindrical shaped planter.

𝑅𝑎𝑑𝑖𝑢𝑠 =𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟

2 ∴ 𝑟 =

43.18 𝑐𝑚

2= 21.59 𝑐𝑚

𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑎 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟 = 𝜋 𝑟² ℎ

∴ 𝑣𝑜𝑙𝑢𝑚𝑒 = 3.14 × 21.592 × 20.32 = 3.14 × 466.13 × 20.32 = 29,741.33 𝑐𝑚3

d. It will take 32,849.44 cm3 of soil to fill one truncated cone shaped planter.

𝑅𝑎𝑑𝑖𝑢𝑠 =𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟

2 ∴ 𝑅 =

39.37

2= 19.69 𝑎𝑛𝑑 𝑟 =

33.02

2= 16.51

Volume of truncated cone= 𝜋

3(𝑅2 + 𝑟2 + 𝑅 × 𝑟)ℎ

∴ 𝑣𝑜𝑙𝑢𝑚𝑒 =𝜋

3(19.692 + 16.512 + 19.69 × 16.51)31.75

∴ 𝑣𝑜𝑙𝑢𝑚𝑒 =𝜋

3(387.7 + 272.58 + 325.08)31.75 =

𝜋

3(985.36)31.75

∴ 𝑣𝑜𝑙𝑢𝑚𝑒 = 1.05 × 985.36 × 31.75 = 32,849.44

3. The total amount of soil to fill all the planters is 233,844.62 cm3 (or cc).

131,096.51 𝑐𝑐 + 40,157.34 𝑐𝑐 + 29,741.33 𝑐𝑐 + 32,849.44 𝑐𝑐 = 233,844.62 𝑐𝑚3

4. You would need 2.75 bags, but would have to buy 3 bags of soil at 85 litres each.

1,000 𝑐𝑐 = 1 𝑙𝑖𝑡𝑟𝑒 ∴ 233,844.62 𝑐𝑐 = 233.84 𝑙𝑖𝑡𝑟𝑒

234.84 𝑙𝑖𝑡𝑟𝑒𝑠 ÷ 85 𝑙𝑖𝑡𝑟𝑒𝑠 𝑏𝑎𝑔⁄ = 2.75 𝑏𝑎𝑔𝑠

5. The potting soil to fill all the planters will cost $47.97.

3 𝑏𝑎𝑔𝑠 × $15.99 𝑏𝑎𝑔⁄ = $47.97

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This activity incorporates elements of the following Performance Descriptors associated with the Task Group Level 3 Indicator. You and the learner could use this information along with features of the activity to discuss performance, determine skill progression and identify some possible next steps to further develop learner proficiency.

In this activity, the learner uses measures to make multi-step calculations; uses specialized measuring tools (C3.3) by:

Calculating using numbers expressed as whole numbers, fractions, decimals, percentages and integers

Calculating the radius, diameter and circumference of circles

Understanding and using formulas for finding the perimeter, area and volume of non-rectangular, composite shapes


Choosing and performing required operations; making inferences to identify required operations



Interpreting, representing and converting measures using whole numbers, decimals, percentages, ratios and fractions

Using strategies to check accuracy (e.g., estimating, using a calculator, repeating a calculation, using the reverse operation)











Competency B. Communicate Ideas and Information, Task Group B3. Complete and create documents

In this activity, the learner makes straightforward entries to complete very simple documents (B3.1a) by:



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Learner Activity 11: Planter Volumes

For this activity you will be calculating how much soil you will need in order to fill a

number of planters (e.g., pots, window boxes) of various shapes. You will also determine

the overall cost of the soil. Show your calculation steps on a separate piece of paper.

Round all your calculations to two decimal places.

You have purchased four differently shaped planters:

a. A cube shaped box with 20” sides

b. A rectangular shaped box

measuring 28” long by 8 ¾”

high by 10” wide

c. A cylindrical shaped pot

measuring 17” in diameter

and 8” in height

d. A truncated cone shaped

pot measuring 15.5” across

the top, 12.5” in height and

13” across the bottom

1. Since soil is sold in metric measurement values, convert the measurements of all the

pots to centimetres.

a. The cube shaped planter box has sides measuring ___________ cm.

b. The one rectangular prism planter box measures _____ cm long by ______ cm

high by _____ cm wide.

c. The cylindrical planter pot measures ______ cm in diameter and ______ cm in

height.

d. The truncated cone planter pot has diameters of _____ cm across the top and

_____ cm across the bottom and it is______ cm in height.

Truncated Cone: a cone shaped object, which

has had the point (apex) cut off in a plane

that is usually parallel to the base.

Cone Point or Apex

removed

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2. Calculate how much soil in cubic centimetres it will take to fill each planter (each

planter’s volume).

a. It will take ________ cc of soil to fill the cube shaped planter.

b. It will take ________ cc of soil to fill the rectangular prism shaped planter.

c. It will take ________ cc of soil to fill the cylindrical shaped planter.

d. It will take ________ cc of soil to fill the truncated cone shaped planter.

3. Calculate the total amount of soil that you will need to fill all of the planters.

_________ cc of soil is needed to fill all the planters.

4. Potting soil comes in 85 litre bags. Calculate how many bags you will need to fill all

the planters. _________ 85 litre bags of soil are needed.

5. The bags of potting soil are selling for $15.99 a bag. Calculate how much the potting

soil will cost. The potting soil to fill all the planters will cost _____________.

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Conversion and Formulas Handout

1 inch = 2.54 centimetres

1 cubic centimetre = 1 millilitre (1,000 cc = 1 litre)

𝜋 = 𝑎𝑝𝑝𝑟𝑜𝑥𝑖𝑚𝑎𝑡𝑒𝑙𝑦 3.14159

Volume of a cube = side³

(All sides and bottom are equal)

Volume of a cylinder = π r² h

𝑟𝑎𝑑𝑖𝑢𝑠 =𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟

2

Volume of a truncated cone

𝜋

3(𝑅2 + 𝑟2 + 𝑅 × 𝑟)ℎ

(R is the top radius and r is the bottom radius)

Volume of a rectangular prism = L x W x H

h

r

R

h

d

L

H

W

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Activity 12: Shingling a Roof – Practitioner Notes

C3.3







Know formulas to determine the area of rectangles and triangles (Pythagorean theory)




will be shingling a roof in their future, although some with apprenticeship, employment or even

independence goals, may. However, applying the formulas to life tasks allows all learners to see

relevance in learning formulas and theories.

The imperial measurement system was used for this activity, since that is the system used by

most carpenters and roofers.

Materials Required


House Diagrams Handout

Calculator

Extra paper

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Instructions

The learner may have help in reading task instructions and locating information on the house

measurement diagrams; however, this will affect the Competency A. Find and Use

Information elements of the task.

Provide the learner with the Learner Activity Handout and the House Diagrams Handout. This

should be printed single-sided to make it easier for the learner to find and use information.


Activity Answers

1. a. The length of the house roof is 22’.

b. The length of the foyer roof is 5’.

2. The overhang of the roof is 1’ at each end.

3. On the foyer roof, there is only a 1’ overhang at one end, so the total overhang is 1’.

4. a. The rise of the house roof is 10’.

b. The rise of the foyer roof is 5’.

5. a. The run of the house roof is 17’.

b. The run of the foyer roof is 5’.

6. a. The travel of the roof is 19.72’.

Using the formula 𝑎2 + 𝑏2 = 𝑐2 or run2 + rise2= travel2

172 + 102 = 𝑡𝑟𝑎𝑣𝑒𝑙2 ∴ 289 + 100 = 𝑡𝑟𝑎𝑣𝑒𝑙2 ∴ 389 = 𝑡𝑟𝑎𝑣𝑒𝑙2 ∴ √389 = 𝑡𝑟𝑎𝑣𝑒𝑙

∴ 𝑡𝑟𝑎𝑣𝑒𝑙 = 19.72′

b. The travel of the foyer is 7.07’ using the same calculation method as in 6.a.

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7. The learner should have added the amounts calculated in 6.a. and b. to the House A

diagram, in the correct place along the slope of the roofs.

8. a. The area of the house roof is 867.68 ft2. Using the formula for the area of a rectangle:

(19.72′ × 22′) × 2 𝑠𝑖𝑑𝑒𝑠 = 433.84 𝑓𝑡2 × 2 = 867.68 𝑓𝑡2

b. The area of the foyer roof is 70.7 ft2. Using the same calculation method as 8.a.

9. It will be 9.38 squares. The area of the two roofs together is 938.38 ft2. Divide this by

100 ft2.

10. a. 29 bundles. This can be calculated in two ways.

Using the answer from 9, multiply the number of squares by 3, since there are 3

bundles to cover a square (9.38 𝑠𝑞𝑢𝑎𝑟𝑒𝑠 × 3 𝑏𝑢𝑛𝑑𝑙𝑒𝑠 𝑠𝑞𝑢𝑎𝑟𝑒⁄ = 28.14). So you

would have to order 29 bundles.

The other method divides the roof area from 8.a. and 8.b. by the square footage

coverage of a bundle (938.38 𝑓𝑡2 ÷ 33.3 𝑓𝑡2 𝑏𝑢𝑛𝑑𝑙𝑒⁄ = 28.18 𝑏𝑢𝑛𝑑𝑙𝑒𝑠), which

means you must order 29 bundles.

b. The cost is $673.96 for 29 bundles at $23.24 per bundle.

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11. The calculations for House B are:

a. The number of bundles needed for House B is 21:

House roof: Rise =9.5’, Run =½(24’ house depth + 2’ roof overhang) =13’

𝑡𝑟𝑎𝑣𝑒𝑙2 = 𝑟𝑢𝑛2 + 𝑟𝑖𝑠𝑒2

∴ 𝑡𝑟𝑎𝑣𝑒𝑙2 = 13𝑓𝑡2 + 9.5 𝑓𝑡2 = 169′ + 90.25′ = 259.25′

∴ 𝑡𝑟𝑎𝑣𝑒𝑙 = √259.25′ = 16.1′

𝐴𝑟𝑒𝑎 = 𝑤𝑖𝑑𝑡ℎ × 𝑡𝑟𝑎𝑣𝑒𝑙

∴ 𝐴𝑟𝑒𝑎 = 38′ × 16.1′ = 611.8 𝑓𝑡2

∴ 𝐴𝑟𝑒𝑎 𝑜𝑓 2 𝑠𝑖𝑑𝑒𝑠 𝑜𝑓 𝑟𝑜𝑜𝑓 = 611.8 𝑓𝑡2 𝑠𝑖𝑑𝑒⁄ × 2 𝑠𝑖𝑑𝑒𝑠 = 1,223.6 𝑓𝑡2

Garage roof: Rise = 8, Run = ½(15’ garage depth + 2’ roof overhang) = 8.5’

𝑡𝑟𝑎𝑣𝑒𝑙2 = 𝑟𝑖𝑠𝑒2 + 𝑟𝑢𝑛2

∴ 𝑡𝑟𝑎𝑣𝑒𝑙2 = 8 𝑓𝑡2 + 8.5 𝑓𝑡2 = 64′ + 72.25′ = 136.25′

∴ 𝑡𝑟𝑎𝑣𝑒𝑙 = √136.25′ = 11.67′

𝐴𝑟𝑒𝑎 = 𝑤𝑖𝑑𝑡ℎ × 𝑡𝑟𝑎𝑣𝑒𝑙

∴ 𝐴𝑟𝑒𝑎 = (8.5′𝑔𝑎𝑟𝑎𝑔𝑒 𝑤𝑖𝑑𝑡ℎ + 1′ 𝑜𝑣𝑒𝑟ℎ𝑎𝑛𝑔) × 11.67′ = 110.87 𝑓𝑡2

∴ 𝐴𝑟𝑒𝑎 𝑜𝑓 2 𝑠𝑖𝑑𝑒𝑠 𝑜𝑓 𝑟𝑜𝑜𝑓 = 110.87 𝑓𝑡2 𝑠𝑖𝑑𝑒⁄ × 2 𝑠𝑖𝑑𝑒𝑠 = 221.74 𝑓𝑡2

Area of two roofs: ℎ𝑜𝑢𝑠𝑒 𝑟𝑜𝑜𝑓 𝑎𝑟𝑒𝑎 + 𝑔𝑎𝑟𝑎𝑔𝑒 𝑟𝑜𝑜𝑓 𝑎𝑟𝑒𝑎 = 𝑡𝑜𝑡𝑎𝑙 𝑎𝑟𝑒𝑎 𝑠ℎ𝑖𝑛𝑔𝑙𝑒𝑑

∴ 1,223.6 𝑓𝑡2 + 221.74 𝑓𝑡2 = 𝑡𝑜𝑡𝑎𝑙 𝑎𝑟𝑒𝑎 𝑠ℎ𝑖𝑛𝑔𝑙𝑒𝑑 = 1,445.34 𝑓𝑡2

Number of bundles: 1,445.34 𝑓𝑡2 ÷ 33.3 𝑓𝑡2 𝑏𝑢𝑛𝑑𝑙𝑒⁄ = 43.4 𝑏𝑢𝑛𝑑𝑙𝑒𝑠

Therefore you would have to buy 44 bundles.

b. The cost before taxes is $1,022.56. 44 𝑏𝑢𝑛𝑑𝑙𝑒𝑠 × $23.24 𝑏𝑢𝑛𝑑𝑙𝑒⁄ = $1,022.56

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Understanding and using properties of angles and triangles to solve problems

Understanding and using formulas for finding the perimeter, area and volume of non-

rectangular, composite shapes




operations

















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(A2.2) by:






documents


(B3.1a) by:



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Learner Activity 12: Shingling a Roof

For this activity, you will be ordering shingles for a house that has two roofs – the main

roof on the house and a smaller roof on the foyer (entryway or vestibule). Show the

steps to your calculations on a separate piece of paper. In your calculations, round to 2

decimal places.

Use the House A diagram on the House Diagrams Handout to complete the following

tasks.

1. Locate the length value for each roof.

a. The length of the house roof is _________.

b. The length of the foyer roof is __________.

2. Notice that the length of the house roof is longer than the length of the house.

This is because it has an overhang at each end. Determine the overhang amount

at each end. ______________.

3. The foyer roof is attached to the house at its back, so we only have to account for

the overhang at the front. Determine the front overhang. _____________.

4. Find the rise (height) of each roof on the diagram.

a. The rise of the house roof is _________.

b. The rise of the foyer roof is _________.

5. Calculate the run of each roof.

a. The run of the house roof is ½ of the total of the width of the house plus

the overhang. _________ .

b. The run of the foyer roof is ½ of the total of the width of the foyer plus the

overhang. _________.

Rise

Run

Travel

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6. Notice that the rise, run and travel (sloping

side of roof) create a right-angle triangle.

Knowing this, you can use the Pythagorean

Theorem to determine the travel of the

roof (the hypotenuse, c). Use the rise and

run measurements that you located in

#4 and #5 as the two sides, a and b, of

the Pythagorean Theorem.

a. The travel of the house roof is

____________.

b. The travel of the foyer roof is

_______.

7. Add the travel values to the diagram.

8. Calculate the area of each roof.

a. The house roof area is __________.

b. The foyer roof area is ___________.

9. Roofers usually calculate the amount of roofing materials needed in “squares” of

100 ft2. Calculate how many squares of shingles you will need for the two roofs.

10. You look up the shingles you wish to order and see that they are $23.24 for a

bundle. The bundle coverage is 33.3 square feet or 1/3 of a square (100 ft2 ÷ 3 =

33.3 ft2). Calculate:

a. The number of bundles you should order _____. Note: You cannot order

part bundles.

b. The total cost before taxes ________________.

11. Use the House B diagram on the House Diagrams Handout to calculate the

number of bundles of shingles needed. _________ Then calculate the total cost

before taxes to shingle House B. _________

90°

a

b c

Pythagorean Theorem states that a2

+ b2=c2 (also written as a^2 + b^2 =

c^2). In this formula, a and b are the

shorter two sides (the base and

vertical side) of a right angle

triangle, and c is the longer side, the

hypotenuse. For example, if the

horizontal width is 10 feet and the

height is 5 feet, the hypotenuse is

11.18 feet -- 102+ 52 = 125. The

square root of 125 is 11.18.

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House Diagrams Handout

House A

House B

10’ 5’

5’

22’ 34’

10’

20’

32’

4’ 8’

House Roof

Foyer Roof

Rise

9.5’

24’ Depth 36’ Width

8.5’

Width

1’ roof over-hang

all around

Garage depth

15’

Garage roof

rise 8’

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Measures Information Handouts

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Information Handout: Understanding Weather Forecasts

Don’t forget to check the weather forecast before heading outdoors. Changes in

weather conditions can happen gradually throughout the day. Weather may even

change quickly, as with sudden blizzards, dangerous thunderstorms, freezing cold or

high heat. Your local weather forecasters can usually provide advanced weather

warnings. If you pay attention to the forecast, you can be prepared for the day’s

weather.

To accurately predict and report the weather, forecasters use computer data, satellite

images and their own current observations and measurement readings. Weather

forecasts usually include temperature, sky or precipitation conditions, and wind

information.

Temperature

Forecasters usually provide two temperatures: a high and a low. These are simply the

highest and lowest temperatures expected to occur during that day. A day is normally a

24 hour period, 12 midnight to 12 midnight. They may provide more information to

explain when these may occur or the trend throughout the day. Many forecasts will give

a day and night temperature.

Temperatures in Canada are forecasted in degrees Celsius (C). The Celsius system is

based on two main temperatures, the freezing point of water (0C) and the boiling point

of water (100C).

Water will always be ice below 0C, liquid from 1 to 99C, and steam from 100C

upwards. Temperatures between the freezing and boiling points of water fall

somewhere in between on the scale of 100, depending on how hot they are.

Temperatures below the freezing point of water are shown as negative numbers, for

example -5C is 5 Celsius degrees below zero.

0C = water freezes and water boils = 100C

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This chart adapted from Think Metric (www.thinkmetric.org.uk/temperature.html)

shows some guidelines to Celsius temperatures:

Temperature °C

What might be at this temperature

How it feels

-30 (30 below zero)

Ice, freezer Very cold if you are outside in this temperature, unbearable to most

-10 Ice Very cold still, but bearable in lots of warm clothes

0 Water freezes, ice melts

Cold

4 Fridge Cold

10 Cold

15 Cool

20 Room indoors Warm

25 Warm room Warm to hot (Typical Ontario summer temperature)

30 Hot day Feeling hot (Hot in Ontario, typical temperature for hotter countries)

37 Body temperature Very hot (Average human body temperature)

40 Washing machine setting for clothes for normal wash

Very hot (If you are outside in this temperature you will feel hot, but more so if humidity is high. If your internal body temperature reaches this level, you are in danger of death.)

50 Extremely hot (Not many places get this high in temperature, and in this heat you would need to find shade, drink water and stay cool.)

60 Washing machine setting for hot wash

Too hot to live in (This temperature kills most bacteria)

90 Washing machines’ hottest water setting

Too hot to live in

100 Water boils Water turns to steam

1000 Lava from a volcano

5500 Surface of the Sun

http://www.thinkmetric.org.uk/temperature.html

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Sky Conditions

Sky Conditions indicate how much sun or cloud there will be in the sky. Sky Condition is

replaced by the following terms when they are forecasted: fog, ice fog, blowing snow,

local blowing snow, blizzard, or snow squalls. Sky Conditions are also replaced by

precipitation amounts when there is a significant chance of precipitation.

Precipitation

Precipitation is included in the forecast when

the Possibility of Precipitation (POP) or

Chance of Precipitation (COP) is 30 per cent

or more.

When the precipitation is rain, amounts are recorded and forecast in millimetres (mm).

Precipitation in the form of snow, ice pellets or a combination of snow and ice pellets is

recorded and forecast in centimetres (cm).

The term “risk” is often used along with the terms thunderstorm, thundershower, hail,

freezing rain and freezing drizzle.

Wind

Wind forecasts vary more than other factors. When wind is included, it is forecast as a

speed in kilometers per hour (km/h) and usually includes the direction of the wind. In

some forecasts, wind isn’t reported until the average speed is expected to be 20 km/h

or more. Wind speed changes may be reported. Two examples are “Wind south 20 km/h

increasing to 40 this evening,” or if the wind is decreasing, “Wind west at 20 km/h

becoming light this evening.” The term “windy” is used when the average wind speed is

expected to be 40 km/h or more, or when gusts of 50 km/h or more are expected. A

wind chill warning will also be mentioned in the forecast, if there is a chance of it.

Notices

Forecasts will also provide notice of other weather events that may occur, such as frost,

limited visibility (due to snow or fog), wind chill, high humidex (humidity that increases

the feeling or effects of temperature) and UV index (ultraviolet sunlight that causes skin

to burn or become damaged).

The Possibility of Precipitation (POP) or

Chance of Precipitation (COP) is the

chance that measurable precipitation

(0.2 mm of rain or 0.2 cm of snow) will

fall on “any random point of the

forecast region” during the forecast

period.

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Information Handout: Checking Your Calculations

We all make mistakes. When you are using numbers to complete tasks, it is easy to

make calculation errors. That’s why it is always important to check your results. There

are a number of ways to check your answers and some ways are better for different

situations and times.

Reasonable

You should always be considering if your answer is reasonable. Does your answer make

sense? For example:

If you are calculating how many seats are in a stadium and you get an answer of 15, that

isn’t reasonable. A stadium would have seats in the hundreds or thousands.

If you were calculating the hours you did something in a day and you came up with an

answer over 24, you would know that isn’t possible since a day only has 24 hours.

Calculator

Of course, if you have one, a calculator is a good way to check your mental calculations.

Do remember, though, that calculators will only give you the right answer if you key in

the right information.

Repeating

One of the easiest ways to check your calculations is to do them again. It is possible to

make the same mistake twice, but those silly little mistakes often happen only once. If

you get a different answer the second time around, try it again until you get the same

answer more than once. This is especially useful in checking calculations done on a

calculator since it is easy to make a keying mistake and you often can’t see what

numbers you actually typed in.

When repeating mental addition, it is sometimes a good idea to do it in the reverse

order. If you did it from top to bottom, try going from bottom to top.

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Reverse (or Inverse) Operation

Operation is the word used for any mathematical process. The most common are add,

subtract, multiply and divide(+, −,×,÷), but there are many others. A reverse or inverse

operation reverses the effect of another operation. Examples:

Addition and subtraction are reverse operations of each other.

5 + 8 = 13 to check we can subtract 13 − 8 = 5 or 13 − 5 − 8 = 0

562 − 96 = 466 to check we can add 466 + 96 = 562

Multiplication and division are reverse operations of each other.

10 × 9 = 90 to check we can divide 90 ÷ 10 = 9

105 ÷ 7 = 15 to check we can multiply 7 × 15 = 105

Estimating

You can get a rough idea if your answer is right by estimating approximately what the

answer should be. For example:

If the problem is 304 x 10,109, you know that your answer has to be a little more

than 300 x 10,000, or 3,000,000. If you answered with a smaller number or a

much higher number, you have made an error.

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Information Handout: kWh EnerGuide Ratings

Calculating how much electricity, an appliance uses and how much it will cost to use the

appliance can be confusing. Your electricity is billed to you based on the number of

kilowatt-hours (kWh) that you use in a period, usually a month. On the other hand,

appliances are rated in watts.

Watts (W), Kilowatts (kW) and Kilowatt-hours (kWh)

Watt (W) is a unit measuring the rate of energy

transfer of an appliance. It is a measure of an

appliance's power.

Kilowatts (kW) - A kilowatt is 1000 watts (W).

Some equipment or appliances consume electricity

at a rate specified in kW, for example, a generator.

A 60 watt light bulb would equal 0.06 kW.

Kilowatt-hours (kWh) is the amount of electricity

produced or consumed. Watts and kilowatts are

“power” ratings, while kilowatt-hours (kWh) is an

“energy” rating of “power” used over “time”. The

total energy in kilowatt-hours is the product of the

power in kilowatts and the time in hours (kW x

hrs). Your electric bill will charge you for the

number of kilowatt-hours you used.

EnerGuide Labels

In Canada, many appliances are required to have a clearly displayed EnerGuide label

during their sale. These labels show a rating number based on their average annual

energy consumption (sample label on next page).

To calculate how much it will cost you to run an appliance over a year, you can take the

EnerGuide rating (in kWh) and multiply it by the rate your electricity company (hydro

company) charges you per kWh. For example:

If your electricity provider charged you $0.15 per kWh, then a refrigerator that has

an EnerGuide rating of 400kWh would cost you:

o $0.15/kWh 400 kWh per year = $60.00 per year

Converting watts to

kilowatts

1kW = 1000W

We can use the formula:

W / 1000 = kW

One kilowatt hour is equal to

1,000 watt-hours. This is the

reason for the name

“kilowatt-hours”.

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Sample EnerGuide Label for Appliances

There are five things displayed

on the label:

1. The EnerGuide symbol

2. Annual energy

consumption of the model

in kilowatt hours (kWh)

3. Energy consumption

indicator, which positions

the model on a scale

compared with the most

efficient (in this sample 491

kWh) and least efficient

models (in this sample 703

kWh) in the same class

4. The model number

5. Type and capacity of models that make up this class

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Information Handout: Fuel Consumption

Fuel—whether gas, diesel, propane or electricity—is

a major expense. When you are making decisions

about keeping, buying or leasing a vehicle, it is

important to consider its “fuel consumption”.

The amount of fuel a vehicle uses to travel a set

distance is its “fuel consumption”. In Canada, this is usually rated by the amount of fuel

needed to drive one hundred kilometres, for example, 6.9 L/100 km. Even though

distances in Canada are measured in kilometres, we still often refer to fuel consumption

as mileage. Other terms, like fuel economy and fuel efficiency are also common.

Each year, Natural Resources Canada, publishes a Fuel Consumption Guide. This guide

has estimated fuel consumption details on all new, light-duty vehicles (cars and small

trucks, like pick-ups) sold in Canada. The guides for 2012 and up are online at

www.nrcan.gc.ca/energy/efficiency/transportation/cars-light-trucks/buying/7487.

To compare the estimated annual fuel consumption of any 1995 to 2015 vehicles, you

can use the fuel consumption ratings web tool found at http://oee.nrcan.gc.ca/fcr-

rcf/public/index-e.cfm.

How and where each person drives also affects fuel consumption. Quick acceleration

and lots of braking increases fuel consumption. City driving uses more fuel than highway

driving.

In Canada, all new vehicles must have an EnerGuide fuel consumption label (see sample

on next page) on their window during sale. Many used car dealers also report the fuel

consumption information when selling a car. The EnerGuide label’s fuel-pump logo

makes it easy to spot! The label provides the estimated fuel consumption for that model

of car. It also has the estimated annual fuel cost for the vehicle. You can use the

EnerGuide label to compare new vehicle fuel consumption.

Choosing the most fuel-efficient and appropriate size of vehicle, driving in a fuel-

efficient manner, using your vehicle only when needed, and following the

manufacturer’s operation and maintenance recommendations for your vehicle can save

you fuel and money, and reduce your greenhouse gas emissions.

The fuel consumption of an

automobile is the relationship

between the distance traveled

and the amount of fuel used

or “consumed” by the vehicle.

http://www.nrcan.gc.ca/energy/efficiency/transportation/cars-light-trucks/buying/7487



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Use the EnerGuide label to compare the fuel consumption and the estimated annual

fuel cost of different vehicles.

1. EnerGuide is the official Government of Canada mark for rating and labelling the

energy consumption or energy efficiency of specific products.

2. The number to call to order your free copy of the Fuel Consumption Guide.

3. City fuel consumption ratings in L/100 km. Look at these to find out which vehicle

on your list will consume the least amount of fuel. It takes more fuel to drive in

the city, due to the constant stop and start of traffic.

4. Highway fuel consumption ratings in L/100 km. Look at these to find out which

vehicle on your list will consume the least amount of fuel. It takes less fuel to

drive since the car only has to do a major acceleration once and then has

momentum.

5. Estimated annual fuel cost – This estimate is based on an annual distance

travelled of 20,000 km, with 55 percent city and 45 percent highway driving, at a

price of 58¢/L for regular unleaded gasoline, 67¢/L for premium unleaded

gasoline and 55¢/L for diesel fuel.

5 4

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Information Handout: Multi Measures Application

Multi Measures is an application for mobile devices, such as an iPhone or iPad, or any

Android cell phone or tablet. Multi Measures is one of several measurement toolkits

that include a number of different measurement tools. Multi Measure includes:

Ruler – The ruler helps you precisely know the lengths of objects around you, such

as pens, tables or pictures. The ruler includes instructions for measuring large

objects and the option to use various different units.

Compass – A compass can help you with navigation, traveling and direction

reference purposes.

Sound Meter – This tool can precisely measure the sound pressure levels around

you. It can measure how quiet your room is, or how loud a piece of machinery, a

rock concert or sporting event is.

Teslameter – This takes advantage of your mobile device’s built-in magnetometer to

monitor the strength of a magnetic field. There is a range of real-life applications for

this, such as, metal detector, AC magnetic fields or finding high- or low-magnetic

areas.

Timing Devices – Included are a timer, stopwatch and metronome, each of which

has a number of useful options.

Seismometer – By using your mobile device’s built-in accelerometer, this tool

detects and visualizes any vibrations. It isn’t only useful for earthquakes; some other

uses are: as an alarm to tell you if your device is moved or to test how smooth the

car is on a test drive.

Plumb Bob – A plumb bob is an instrument to check if something is perfectly vertical

(plumb). It can be used when hanging objects or when doing carpentry work, brick

laying or building construction.

Levels – The toolkit includes two kinds of levels, a surface level and a spirit/bubble

level. These levels help you determine if an object is perfectly horizontal or what the

slope of the surface is. These are useful during construction, furniture and appliance

set-up, hanging pictures, etc.

Protractor – This tool measures any kind of angle in real life.

Multi Measures is available from both the app stores on iTunes or Google Play for a low

cost.

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Information Handout: Ratios and Rates

Ratio

A ratio is the number-based relationship of two or more things. For example, if you need

2 batteries for one flashlight, you would say the ratio of batteries to flashlights is 2 to 1.

Ratios are often used in life and work. For example:

Fuel has to be mixed at the right ratio of gas and oil for weed-eaters and other small 2-

cycle engines.

Cement must be the correct mixture so it will be sturdy.

Finance companies and businesses use ratios as in income to expense ratio, partnership

ratio, price to earnings ratio, etc.

Artists use ratios to mix colours and keep objects, body parts, etc., in proper perspective

in their art.

Cooks work with recipes containing ratios, such as a teaspoon of one ingredient per cup

of another.

Health workers calculate ratios of body weight to medications.

Ratios may be written in several ways. You can write the example of 2 batteries to 1

flashlight by using the word “to” (2 to 1), or using a colon (2:1), or as a fraction (2/1).

The relationship between the numbers always stays the same. If you change the first

number (the antecedent) by multiplying or dividing, you must also change the other

numbers in the ratio (the consequents) the same way. In our flashlight example, if you

need batteries to flashlights in a ratio of 2:1 then you will need:

4 batteries for 2 flashlights (multiply both numbers by 2, so 2:1 becomes 4:2)



10 batteries for 5 flashlights, etc.

Ratios can also be expressed as a fraction. If you have a group of 20 people and 12 of

them are men and 8 are women, the ratio is 12 men to 8 women, or 12:8. As a fraction,

it would be 12/8. You can also say that 12 out of the 20 people are men, writing it as

12/20. Eight out of 20 are women, or 8/20.

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As with other fractions, you usually express ratios in their “simplest” form. To “simplify” a

fraction or ratio, divide each number by the highest number that can divide into both

numbers exactly. Our batteries to flashlights ratio is in its simplest form at 2:1. With the

example of 12 men to 8 women in a group of 20 our ratio is not in its simplest form because

both 12 and 8 can be divided by 4. This would make our ratio of men to women 3:2.

12:8 = 3:2 or 12/8 = 3/2

Read as 12 to 8 = 3 to 2

When rewriting or converting ratios to a simpler or different form, it is important that

you do not change the order. The antecedent must stay as the first number or the top

number of a fraction, and the consequent number(s) must follow, in order or be on the

bottom of the fraction as the denominator. For example, if you say the mix of frozen

juice to water is 1 can of juice to 3 cans of water, you would write the ratio as 1:3. On

the other hand, if you said 3 cans of water to 1 can of juice, you would have to write it

as 3:1. If you get confused and reverse the order, you will have either very strong or

very weak juice.

Rates

When the things being compared are measured in different units, the term rate is

usually used instead of ratio. For example a 2014 KIA Cadenza is rated to use gas at a

rate of 7.4 litres per 100 kilometres of highway driving.

The mathematics of rates is the same as the mathematics of ratios. For example:

If you travel 240 kilometres in 3 hours, this can be written mathematically as a rate of:

240 km/3 hrs, and read as 240 kilometres per 3 hours

If we reduce the fraction to its simplest form by dividing both the numerator and

denominator by 3, then it is:

80 km/hr, and read as 80 kilometres per hour

If you pay $2.99 for 10 pounds of potatoes:

10 lbs/$2.99, and read as 10 pounds for $2.99

If we reduce the fraction by dividing both the numerator and denominator by 10,

we would get 1 pound/$0.30, which is read as one pound for 30 cents.

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However, for ease of calculation, we often use unit rates. A unit rate is when you

compare variable quantities of one thing against one unit of another. For example:

Speed is measured in the number of kilometres travelled in one hour, or per

hour.

In hockey, you might speak of the number of shots on goal per game.

When invoicing for parts or service, the price for one part is provided.

To compare food items in the grocery store, the price of one unit may be on the

shelf sticker. Meat and produce are usually sold as price per kilogram or per

pound.

Gas is sold by the price per litre.

Currency exchange rates are based on price per unit, which is the price of a

currency in terms of another currency. For more information on working with

currency exchange rates, see the Foreign Exchange Information Handout.

When we are talking about or writing rates, we may use the word “per”, which means

“for each”, or just the word “for”. The forward slash symbol “/” is often used to replace

the word “per”, especially when writing it in a formula.

The benefit of using the unit rate is that you simply take the quantity you have and

multiply it by the unit rate to determine the answer.

Example:

Unit Rate: Boneless, skinless chicken breasts sell for $10.98/kilogram.

Quantity: You purchase 3.2 kg.

How much will the chicken cost?

$10.98/1 kg X 3.2 kg = $35.14