MATHEMATICS 10C
MEASUREMENT
High School collaborative venture with
Harry Ainlay, Jasper Place, McNally, Queen Elizabeth,
Ross Sheppard and Victoria Schools
Harry Ainlay: Mathias Stewart, Colin Veldkamp, Cindy Wilson
Jasper Place: Lisa Lei, Clayton Maleski
McNally: Neil Peterson
Queen Elizabeth: Michael Freed, Scott Nytchay
Ross Sheppard: Silvia Fernandes-Isidoro, Clarence Harker, Dean Walls
Victoria: ,Shannon Sookochoff
Facilitator: John Scammell (Consulting Services)
Editor: Rosalie Mazurok (Contracted)
2009 - 2010
Mathematics 10C
Measurement
Page 2 of 47
TABLE OF CONTENTS
STAGE 1
DESIRED RESULTS
PAGE
Big Idea
4
Enduring Understandings
4
Essential Questions
4
Knowledge
5
Skills
6
Stage 2
ASSESSMENT EVIDENCE
Teacher Notes For Transfer Task
7
Transfer Task
Emergency Room Situation
Teacher Notes for Emergency Room Situation and Rubric
Transfer Task
Rubric
Possible Solution
8-9
10 - 14
15
16 -19
Stage 3 LEARNING PLANS
Lesson #1
A World Without Standard
20 - 23
Lesson #2
Explore Imperial
24 - 27
Lesson #3
Explore Metric
28 - 31
Lesson #4
Imperial to Metric…and Back
32 - 35
Lesson #5
Surface Area
36 - 38
Lesson #6
Volume
39 - 41
APPENDIX - Handouts
Measurement Unit Handouts
Mathematics 10C
43 - 47
Measurement
Page 3 of 47
Mathematics 10 Common
Measurement
STAGE 1
Desired Results
Big Idea:
Students will gain real and meaningful connections to the units of measure, providing
them with the capacity to describe the world.
Implementation note:
Post the BIG IDEA in a prominent
place in your classroom and refer to
it often.
Enduring Understandings:
Students will understand that…




Imperial and SI are related systems of measurement.
different situations require different units of measure and different measurement
tools.
estimating is useful to approximate and validate measures.
surface area and volume are related to the dimensions of 3-D objects.
Essential Questions:



What would the world be like without measurement?
How do we communicate measure?
o
Who keeps the standards?
In what circumstances is accuracy important?
o When is estimation good enough?
Implementation note:
Ask students to consider one of the
essential questions every lesson or two.
Has their thinking changed or evolved?
Mathematics 10C
Measurement
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Knowledge:
Enduring
Understanding
Specific
Outcomes
Knowledge that applies to this
Enduring Understanding
Students will understand that…
Students will know…
*M1
 Imperial and SI are related
systems of measurement.

the different units of measure for each
system.
*M2

Students will understand that…
 different situations require
different units of measure
and different measurement
tools.
that conversions within and between
systems exist.
Students will know…
*M1


Students will understand that…
the advantages and disadvantages of
various measurement tools in diverse
contexts.
appropriate units of measure for
varying lengths.
Students will know…
*M1
 estimating is useful to
approximate and validate
measures.

*M2
Students will know…
Students will understand that…
 surface area and volume
are related to the
dimensions of 3-D objects.
referents for common units of
measure.
*M3

the connections between objects, their
dimensions and the related formulas.
*M = Measurement
Mathematics 10C
Measurement
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Skills:
Enduring
Understanding
Specific
Outcomes
Students will understand that…
*M1
 Imperial and SI are related
systems of measurement.
*M2
Skills that apply to this
Enduring Understanding
Students will be able to…
 measure using referents or either of the
systems of standard measure.
 compare and convert measurements.
Students will understand that…
 different situations require
different units of measure
and different measurement
tools.
Students will be able to…
*M1
 justify choice of tools and units.
 use different measuring tools.
Students will understand that…
Students will be able to…
*M1
 estimating is useful to
approximate and validate
measures.
 choose a referent to estimate a measure
and explain the process used.
*M2
 use estimation to validate other types of
thinking.
Students will understand that…
 surface area and volume
are related to the
dimensions of 3-D objects.
Students will be able to…
*M3
 solve problems using some of the
following strategies:
o a provided formula
o deriving a formula
o manipulating a given formula
o drawing nets
o building models
*M = Measurement
Implementation note:
Teachers need to continually ask
themselves, if their students are
acquiring the knowledge and skills
needed for the unit.
Mathematics 10C
Measurement
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STAGE 2
1
Assessment Evidence
Desired ResultsDesired Results
Emergency Room Situation
Teacher Notes
There is one transfer task to evaluate student understanding of the concepts relating to
measurement. A photocopy-ready version of the transfer task is included in this section.
Each student will:

Estimate the surface area of his/her body using referents and/or geometric
calculations.
Implementation note:
Students must be given the transfer task & rubric at
the beginning of the unit. They need to know how
they will be assessed and what they are working
toward.
Mathematics 10C
Measurement
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Teacher Notes for Emergency Room Situation Transfer Task
The following website could be used to calculate and check the estimate of the surface area of
the body:
http://www.halls.md/body-surface-area/bsa.htm
Estimation tools
paper
hands
towels
cheese cloth
clothing
Suggestions for Differentiated Instruction
The students may choose to use a formula to actually calculate the surface area of their bodies.
http://en.wikipedia.org/wiki/Body_surface_area
Come up with a way to convert from Imperial square units to Metric square units.
Suggestions for Extensions
Volume

Calculate the volume of your body.
o Immerse your body in a tub full of water, calculate your overflow. You may use
composite shapes.
o Blood Volume Calculator
http://www.mbi.ufl.edu/~shaw/Blood.htm
Mathematics 10C
Measurement
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Teacher Notes for Rubric

No score is awarded for the Insufficient/Blank column , because there is no evidence of
student performance.

Limited is considered a pass. The only failures come from Insufficient/Blank.

When work is judged to be Limited or Insufficient/Blank, the teacher makes decisions
about appropriate intervention to help the student improve.
Implementation note:
Teachers need to consider what performances and
products will reveal evidence of understanding?
What other evidence will be collected to reflect
the desired results?
Mathematics 10C
Measurement
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Emergency Room Situation - Student Assessment Task
Scenario:
Sirens are blaring . . .
Nurse 1: “The ambulance is coming and there is a patient who has been burned from
head to toe.”
Nurse 2: “Quick! Call the skin bank and request 1000 square inches of skin”
The Doctor assesses the patient…
Doctor: (motions to you) “Hey, Intern! You are the exact same size as the patient.
Quick, calculate to see if they have ordered enough skin!!”
The following criteria must be considered:
Part A




Choose a referent to make an estimation of the SA, surface area of the human
body in square inches. Provide a full explanation of your results.
Imagine the body as a composite figure composed of standard 3-Dimensional
shapes that we will be examining in class. Provide a detailed calculation in square
inches.
Compare your initial estimation to your final answer.
Summarize your findings.
Part B
The patient has lost 30% of his/her bodily fluids . . . calculate the volume of
his/her body and find out how much fluid would be necessary to replenish
this amount.
Initial Skin Graft Preparation Form
Patient’s Name:
Height:
Weight:
Initial estimate of needed graft area:
Choose a referent to
make an estimation of
the SA of the patient in
square inches. Provide a
full explanation of your
results.
Gender:
Lab Work
Convert your dimensions from Imperial to Metric
Body Part
Dimensions (inches)
Conversions (centimetres)
Detailed Skin Graft Preparation Form
Detailed calculation of graft area:



Imagine the body as a composite figure composed of standard 3-dimensional shapes.
Provide a drawing/model.
Provide a detailed calculation.
Compare the estimate to calculation:
Other Research (if done):
Intern’s recommendation to the doctor:
Part B
Volume calculations:
Names: ________________________
________________________
Assessment
Mental Mathematics
and Estimation
Student has:
identified a referent
explained estimation
process
stated the resulting
estimation
Mathematics 10C
Emergency Room Transfer Task Rubric
Communication
Student communication
needs to be:
clear
detailed
Explanations need to
include:
calculations,
reasoning
labelled diagrams
conventional notation
appropriate
mathematical
terminology
Connections
Visualization
Problem Solving
Student demonstrates:
deep and rich
understanding of
surface area
conversions are
correct
formulas are
appropriately used
and modified when
necessary (ie.
duplications are
accommodated)
Student visual work
shows:
a detailed
consideration of the
surface area of the
human body
careful labelling
a variety of 3-D forms
in their composite
treatment of the body.
Student will:
identify a strategy
carry out the strategy
use appropriate
mathematics and tools
Excellent
4
Proficient
Proficient
Proficient
Adequate
Adequate
Adequate
Adequate
Adequate
Limited
Limited
Limited
Limited
Limited
Insufficient
Insufficient
Insufficient
3
2
1
0
Insufficient
Insufficient
/14
Emergency Room Situation
Sample Student Exemplar
Choose a referent to make
an estimation of the SA of
the patient in square inches.
Provide a full explanation of
your results
Mathematics 10C
Measurement
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Mathematics 10C
Measurement
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 Imagine the body as a composite figure composed of standard 3-dimensional shapes .
 Provide a drawing/model.
 Provide a detailed calculation.
154 in2
2902 in2
Mathematics 10C
Measurement
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Compare the estimate to calculation:
2902 in2.
Intern’s recommendation to the doctor:
Mathematics 10C
Measurement
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STAGE 3
Learning Plans
Lesson 1
A World Without Standard
STAGE 1
BIG IDEA:
Students will gain real and meaningful connections to the units of measure, providing them with the
capacity to describe the world.
ENDURING UNDERSTANDINGS:
ESSENTIAL QUESTIONS:
Students will understand that…
 What would the world be like without
measurement?
 different situations require different units of
measure and different measurement tools.
 estimating is useful to approximate and
validate measures.
 How do we communicate measure?
o Who keeps the standards?
 In what circumstances is accuracy important?
o When is estimation good enough?
KNOWLEDGE:
SKILLS:
Students will know…
Students will be able to…
 appropriate units of measure for varying
lengths.
 choose a referent to estimate a measure and
explain the process used.
 referents for common units of measure.
 justify choice of tools and units.
 use estimation to validate different ways of
measuring.
Implementation note:
Each lesson is a conceptual unit and is not intended to
be taught on a one lesson per block basis. Each
represents a concept to be covered and can take
anywhere from part of a class to several classes to
complete.
Mathematics 10C
Measurement
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Lesson Summary

Students will see relevance of numbers in measurement by trying to describe
objects without using numbers.

Measure objects using different referents. Discuss varied responses to show the
importance of standardization.
Lesson Plan
A World Without Numbers
Discuss what the world would be like without numbers. How would you describe
lengths? How would you compare? Consider sharing the story “Neil’s Numberless
World” by Lucy Coats.
Activate prior knowledge through discussion of situations where students may have
already measured without tools using a referent (e.g. football yards, golf estimates,
etc.)
The goal is to discuss the need for referents as an estimation tool.
Using Referents
Prepare an activity where students would measure various objects using referents of
their choice (e.g. body parts, common objects at hand, etc.). To differentiate you
could suggest 10 objects and ask students to choose 5 (see Going Beyond for
enrichment opportunities). Then compile results to investigate the need for
standardized measure. Once students choose a referent they should record it on the
My Referent Table handout (See Appendix).
Try to ensure students are measuring common objects with a
variety of lengths. This will lead to the need for a standard.
Mathematics 10C
Measurement
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The Need for Standards
A separate activity that could be included with the previous one is to have students
measure the same object using the same referent (hands, for example) and
investigate if this is standardized enough. If not, how could the system be improved?
Consider asking for the My Referent Table (See Appendix) as an exit slip.
Going Beyond
The choice of objects would be a great way to differentiate this lesson. To enrich you
could choose objects that are very small, or ones that are larger and/or slightly beyond
their reach. For example, the width of coins, the height of a wall or gym etc.
When completing the third column of the My Referent Table handout, encourage
examples of items not used during the classroom activity.
Resources
Foundations and Pre-calculus Mathematics 10 (Pearson: sec 1.1)
Math 10 (McGraw Hill: sec 1.1)
Neil’s Numberless World by Lucy Coats
My Referent Table (See Appendix)
A variety of objects to measure
Assessment
An Exit Slip - students should show their own systems of measurement.
This could be the completion of My Referent Table included in the Appendix.
Mathematics 10C
Measurement
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Glossary
exit slip – a task to be submitted to be able to leave at the end of class
referent – something that serves as a reference to which something else may be
compared
standard system – an authorized model used to define a unit of measurement
system of measurement – a system of measurement units such as the Metric
System or the Imperial System
Glossary hyperlinks redirect you to the Learn Alberta Mathematics Glossary
(http://www.learnalberta.ca/content/memg/index.html). Some terms can be found in
more than one division. Some terms have animations to illustrate meanings.
Mathematics 10C
Measurement
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Lesson 2
Explore Imperial
STAGE 1
BIG IDEA:
Students will gain real and meaningful connections to the units of measure, providing them with the
capacity to describe the world.
ENDURING UNDERSTANDINGS:
ESSENTIAL QUESTIONS:
Students will understand that…
 Imperial and SI are related systems of
measurement.
 How do we communicate measure?
o
Who keeps the standards?
 different situations require different units of
measure and different measurement tools.
 In what circumstances is accuracy important?
o
When is estimation good enough?
 estimating is useful to approximate and
validate measures.
KNOWLEDGE:
SKILLS:
Students will know…
Students will be able to…

the different units of measure for this system.

measure using referents and this system of
standard measure.

that conversions within these systems exist.

justify choice of tools and units.

the advantages and disadvantages of various
measurement tools in diverse contexts.

use different measuring tools.

appropriate units of measure for varying
lengths.

choose a referent to estimate a measure and
explain the process used.

referents for common units of measure.

use estimation to validate different ways of
measuring.
Mathematics 10C
Measurement
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Lesson Summary

Students will become familiar with units of Imperial and relate these to their
referents.

Students will be able to determine appropriate units to measure varying lengths.

Have students estimate and measure objects using Imperial measurement tools.
Lesson Plan
Imperial Standards
Measure a medium sized object (exactly 3 feet) using the student’s medium referent
from the previous day. Have students compare their results. Point out that “Sarah” is
queen and her referent is the correct one. After introducing this standard ask students
to try and relate their measures to hers. This leads nicely into the video on body
measures.
My Human Ruler
Introduce students to measuring tools that are in Imperial units focusing only on whole
numbers. Using appropriate tools have students develop a human ruler, deciding
what part of their body best compares with an inch, foot and yard. Record decisions
on My Human Ruler (see Appendix).
The intent here is to assist students to better estimate lengths with Imperial
units.
Mathematics 10C
Measurement
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Fraction Strip
Start a discussion around lengths that aren’t whole numbers? We can estimate these,
but how do we get exact lengths? Show students how to measure within an inch. A
suggestion would be to utilize fraction strips. Start with a strip of paper, define it has a
unit length, and then fold it in half to show measuring accurately to a half of an inch.
Then show folding it in half again to develop an accuracy of a quarter of an inch. Point
2
1
out that is equal to . Go back to fold it in half again creating an accuracy of an
4
2
2
1
4
1
eighth. Again help students see that
is equal to and is equal to . You could
8
4
8
2
1
1
carry it to
or
if necessary.
16
32
Practise Measuring
Have students measure a few objects; the objects from the previous day would be
ideal. If you have students measure the same objects as you could have them
compare the measurements between the referent and the Imperial System.
Build-a-box
A closing activity would have students demonstrate that they know how to measure
with Imperial measuring tools. For example, build a box that would be able to store a
certain object with little wasted space. Have a box that will store an object so that the
object is unable to move. Students will have to take measurements of the box and
then use their measurements to construct a replica of the box. Test the accuracy of
measurements by testing the fit of the object. Have students journal the steps they
took in creating the box to develop communication skills. Encourage students to
discuss the need for accuracy in their measurements.
The use of this box could be carried forward to future lessons regarding Metric
System, Surface Area and Volume.
Mathematics 10C
Measurement
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Going Beyond
Enrichment would come from the objects that students measure, both in size and
shape. With shapes, it would be interesting to see how students would measure the
perimeter of non-rectangular objects.
Challenge students to be precise and to refine their measurements. Provide students
with opportunities to compare measurements and share strategies to improve their
measurement accuracy
Resources
Math 10 (McGraw Hill: sec 1.2)
Foundations and Pre-calculus Mathematics 10 (Pearson: sec 1.2)
Imperial rulers
Imperial tape measures
sewing tape measure
yard stick
Video on Body Measures
http://videos.howstuffworks.com/hsw/5889-scientific-method-history-of-measurementvideo.htm
Assessment
Assessment will be combined with next lesson.
Glossary
foot – a unit of length equal to 30.48 centimetres or12 inches
Imperial System – in the United Kingdom, belonging or conforming to the non-metric
system of weights and measures that includes the foot, pound, and
gallon
1
inch – a unit of length equal to 2.54 centimetres or th of a foot
12
yard – a unit of length equal to 0.9144 metres or 3 feet
Mathematics 10C
Measurement
Page 27 of 47
Lesson 3
Explore Metric
STAGE 1
BIG IDEA:
Students will gain real and meaningful connections to the units of measure, providing them with the
capacity to describe the world.
ENDURING UNDERSTANDINGS:
ESSENTIAL QUESTIONS:
Students will understand that…
 Imperial and SI are related systems of
measurement.

How do we communicate measure?
o Who keeps the standards?
 different situations require different units of
measure and different measurement tools.

In what circumstances is accuracy important?
o When is estimation good enough?
 estimating is useful to approximate and
validate measures.
KNOWLEDGE:
SKILLS:
Students will know…
Students will be able to…
 the different units of measure for this system.
 that conversions within these systems exist.
 the advantages and disadvantages of various
measurement tools in diverse contexts.
 appropriate units of measure for varying
lengths.
 referents for common units of measure.
 measure using referents and this system of
standard measure.
 compare and convert measurements within
this systems.
 justify choice of tools and units.
 use different measuring tools.
 choose a referent to estimate a measure and
explain the process used.
 use estimation to validate different ways of
measuring.
Mathematics 10C
Measurement
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Lesson Summary

Introduce the Metric System by showing some challenges of the Imperial System.

Students will become familiar with the metric units and relate these to their
referents.

Students will be able to determine appropriate units to measure varying lengths.

Have students estimate and measure objects using metric measurement tools.
Lesson Plan
Imperial vs. Metric
Begin by highlighting some of the difficulties within the Imperial system. For example,
when dealing with the fractions of an inch, adding measurements together is difficult
for some. Conversions within the Imperial System are not straightforward and the
ratios would need to be memorized. See Conversion Chart in Appendix.
My Human Ruler
Introduce students to measuring tools (ruler, measuring tape, metre stick) that are in
metric units. Using appropriate measuring tools have students develop a human ruler,
deciding what part of their body best compares with a centimetre and metre. The
intent here is to assist students to be better able to estimate lengths. Have students
record their decisions on the My Human Ruler handout. (See Appendix)
Practise Measuring
Have students measure a few objects. The objects from the previous day would be
ideal. If you have students measure the same objects as they did using their referents
you could have them compare the measures between the referent, Imperial and the
Metric System.
Mathematics 10C
Measurement
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Measure-a-box
Prepare a closing activity that would have students demonstrate their ability to
measure. For example measure the dimensions of the box that was built in the last
lesson.
Why we need metric video (American Chopper) is a humorous look at the difficulties of
the Imperial System.
Going Beyond
Enrichment would come from the objects that students measure, both in size and
shape. With shapes it would be interesting to see how students would measure the
perimeter of non-rectangular objects.
Challenge students to be precise and to refine their measurements. Provide students
with opportunities to compare measurements and share strategies to improve their
measurement accuracy.
Students could explore the use of callipers and micrometers.
Resources
Foundations and Pre-calculus Mathematics 10 (Pearson: sec 1.3)
Math 10 (McGraw Hill: sec 1.3)
Conversions Chart (See Appendix)
meter stick
metric rulers
metric tape measures
sewing tape measure
Why we need metric video (American Chopper)
http://www.youtube.com/watch?v=Omh8Ito-05M
Metric & Standard Measures Video Clip
http://www.youtube.com/watch?v=DQPQ_q59xyw
Mathematics 10C
Measurement
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Assessment
Assess Metric and Imperial measuring skills through the “Build a Box” Activity (see
Lesson 2).
Glossary
1
metre
100
metre – the basic unit of length in the International System of Units (SI)
centimetre – a unit of measurement equalling
metric system – a decimal system of weights and measures based on units of 10
millimetre – a unit of measurement equalling
1
metre
1000
SI – International System of Units (Metric System)
Mathematics 10C
Measurement
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Lesson 4
Imperial to Metric…and Back
STAGE 1
BIG IDEA:
Students will gain real and meaningful connections to the units of measure, providing them with the
capacity to describe the world.
ENDURING UNDERSTANDINGS:
ESSENTIAL QUESTIONS:
Students will understand that…
 Imperial and SI are related systems of
measurement.
 How do we communicate measure?
o Who keeps the standards?
 different situations require different units of
measure and different measurement tools.
 In what circumstances is accuracy important?
o When is estimation good enough?
 estimating is useful to approximate and
validate measures.
KNOWLEDGE:
SKILLS:
Students will know…
Students will be able to…
 the different units of measure for this system.
 that conversions within this systems exist.
 the advantages and disadvantages of various
measurement tools in diverse contexts.
 appropriate units of measure for varying
lengths.

compare and convert measurements within
and between systems.

justify choice of tools and units.

choose a referent to estimate a measure and
explain the process used.

use estimation to validate different ways of
measuring.
 referents for common units of measure.
Lesson Summary


Explain the importance of equivalent measurements within and between different
systems. For example, 12 inches = 30 cm, 1000 m = 1 km.
Have students convert within each system and between the Metric and Imperial
Systems.
Mathematics 10C
Measurement
Page 32 of 47
Lesson Plan
Warm Up
Review base 10 multiplications / divisions with a sequence of warm up questions.





32 x 10
32 x 100
32 x 1000
32 / 10
32 / 100
Importance of Conversions
Discuss conversions within the systems to help students understand the process. To
help students understand the purpose behind conversions you can engage in a
discussion around 2-D and 3-D real life situations. For example, after purchasing a
shelving unit from “IKEA”, you see the box dimensions are 4 inches by 72 inches by
114 inches. If you are unfamiliar with the inch measurement, it is hard to judge
whether the carton will fit in the back of your car. If we could convert the inches to feet
it would make it easier to estimate.
Proportionality Activity – “How many … in a …”
To help students develop the comparison between measurements using their
referents, have each student determine how many “human inches” will fit in a “human
foot.” (Basically, compare how many thumb widths to their foot). In comparing
results, ideally students will come to a consensus that 12 inches will fit in a foot. Once
this has been established have students extend this knowledge to how many inches fit
in 2 feet or in 3 feet. What if it was 2.5 feet? After students have developed a strategy
for these conversions you could provide them with conversion factors (see conversion
chart in Appendix) for other lengths to practice with. The hope is that students will
discover the idea of proportionality.
Sample Problem
Another problem to present to students would be comparing two runners, one running
a mile in 15 minutes and the other running 1000 yards in 12 minutes. Which runner
ran further? Faster?
Mathematics 10C
Measurement
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Importance of Conversions Between
For conversions between imperial and metric you could begin by discussing the need
for this, and the need to communicate in a common language. Examples of this
include: Speed limits in different countries, lengths of material, volumes of quantities,
etc.
Ask students to explore the following proportions:




How many cm in an inch?
How many inches in a cm?
How many feet in a metre?
How many metres in a foot?
Follow up by illustrating the number of centimetres in an inch using the “Inch vs.
Centimetre Image” (see Appendix) and highlight known proportions on the
“Conversion Chart” (see Appendix).
Practise Conversions
Provide students with opportunities to practise conversions (refer to textbook).
Encourage the continued use of referents and estimation to verify the reasonableness
of all answers.
Tip: Check the reasonableness of answer by recognizing that a greater number of
smaller units is required to express an equivalent measure in larger units.
Going Beyond
Have students look up other units. The focus has been on linear units. Students could
look into 2-D and 3-D units (the names, the conversions).
Challenge students to do conversions of large numbers in scientific notation.
Mathematics 10C
Measurement
Page 34 of 47
Resources
Math 10 (McGraw Hill: sec 1.3)
Foundations and Pre-calculus Mathematics 10 (Pearson: sec 1.3)
Conversion Chart (See Appendix)
Objects to Measure
Inches to cm Image (see Appendix)
Assessment
Provide students with a list of measurements already converted. Make some with
mistakes so that they have to determine which are done correctly and which need to
be corrected.
Students should attempt some conversions and then check their answers using
referents and measurement tools.
Use the box that students created (See Lesson 2) and check the accuracy of their
Imperial and Metric measurements by converting both ways.
Glossary
conversion – a change from one measuring or calculating system to another,
or a calculation done to bring about the change
metric prefixes – relating to or using the metric system of measurement
proportional – possessing a constant ratio
Mathematics 10C
Measurement
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Lesson 5
Surface Area
STAGE 1
BIG IDEA:
Students will gain real and meaningful connections to the units of measure, providing them with the
capacity to describe the world.
ENDURING UNDERSTANDINGS:
ESSENTIAL QUESTIONS:
 What are meaningful applications of surface
area and volume?
Students will understand that…

surface area and volume are related to the
dimensions of 3-D objects.
.
o
o
o
o
KNOWLEDGE:
What are the advantages and
disadvantages of each shape?
What fascinates artists, mathematicians
and designers about the beauty of
shapes?
What is the importance of basic figures?
How do degree, exponents and
dimensions relate?
SKILLS:
Students will be able to…
Students will know…

the connections between objects, their
dimensions and the related formulas.
 solve problems using some of the following
strategies:
o a provided formula
o deriving a formula
o manipulating a given formula
o drawing nets
o building models
Lesson Summary

Review formulas from Junior High to determine surface area of prisms and
cylinders.

Apply this understanding to the surface area of pyramids, cones and spheres
through the use of nets and real world connections.

Given appropriate formulas, solve for an unknown dimension.
Mathematics 10C
Measurement
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Lesson Plan
Review Surface Area
Students should have an understanding of surface area of prisms and cylinders from
Junior High.
To begin this lesson it would be worthwhile to check the students’ understanding
through discussion, practice questions or providing real objects that students would
measure and then calculate the surface area. It may be worthwhile to investigate
student understanding of surface area. For example, some students may know it as
the application of a formula and others may understand that surface area can be
determined by combining the areas of all individual faces.
Review Idea: To review surface area of rectangular prism, have students calculate
the surface area of the box they created (See Lesson 2).
Importance of Surface Area
It may be worthwhile to facilitate a discussion around the meaningful applications of
surface area. Discussion topics may include:

What fascinates artists, mathematicians and designers about the beauty of
shapes?

What is the importance of basic figures?
Some examples of real world connections are: sod, wrapping paper, paint, wall paper,
flooring, sculpting, etc.
Surface Area of Pyramids, Cones and Spheres
Once all students seem to have arrived at similar understandings, have them apply
this knowledge to pyramids, cones and spheres. Using a net approach will be easy
for a pyramid. For a cone you would need to show  rs as the formula for calculating
the area of the sector. With a sphere, you can use an orange. Take the peelings and
piece it together making 4 circles that have the same radius as the radius of the
orange. For teacher reference see video: Surface Area of a Sphere
Missing Dimensions
After students have practiced determining surface area you would then need to give
them a surface area and ask them to determine a given dimension.
Mathematics 10C
Measurement
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Going Beyond
Have students discover/prove why  rs can be used to determine the area of the
sector which is the side of the cone.
Resources
Foundations and Pre-calculus Mathematics 10 (Pearson Publishers: sec 1.4, 1.7)
Math 10 (McGraw Hill: sec 2.1, 2.2)
Surface Area of a Sphere
http://www.youtube.com/watch?v=cAxHYFRx1Fs
Glossary
dimension – a measurement of something in one or more directions such as length,
width, or height
net – a set of polygons in a plane, all connected by certain edges such that when
"folded up" form a polyhedron
square centimetre – any area equivalent to the area formed by a 1 cm by 1 cm square
square metre – any area equivalent to the area formed by a 1 m by 1 m square
Mathematics 10C
Measurement
Page 38 of 47
Lesson 6
Volume
STAGE 1
BIG IDEA:
Students will gain real and meaningful connections to the units of measure, providing them with the
capacity to describe the world.
ENDURING UNDERSTANDINGS:
ESSENTIAL QUESTIONS:
 What are meaningful applications of surface
area and volume?
Students will understand that…

surface area and volume are related to the
dimensions of 3-D objects.
.
o
o
o
o
KNOWLEDGE:
What are the advantages and
disadvantages of each shape?
What fascinates artists, mathematicians
and designers about the beauty of
shapes?
What is the importance of basic figures?
How do degree, exponents and
dimensions relate?
SKILLS:
Students will be able to…
Students will know…

the connections between objects, their
dimensions and the related formulas.
 solve problems using some of the following
strategies:
o
o
o
o
o
a provided formula
deriving a formula
manipulating a given formula
drawing nets
building models
Lesson Summary
Students will develop formulas for and solve problems relating to the volumes of
prisms, pyramids, right cones, right cylinders, and spheres. An exploration of the
relationship between pyramids and prisms as well as that of cylinders and cones will
be done.
Mathematics 10C
Measurement
Page 39 of 47
Lesson Plan
Stacking Activity
Develop the volume of a prism by “stacking pancakes”.

By stacking various shapes students can see that the volume of a prism is the
“area of the base multiplied by the height”.

Discuss the relationship between degree, exponents and dimensions.
1
The “ ” Relationship
3
Explore the relationship between prisms and pyramids, cones and cylinders, with the
same base and height through the following two activities:

3-D Mystery Model Activity (See Appendix).

Prism Capacity Activity
o Students will try to fill, using rice, various prisms by using the corresponding
1
pyramid of that shape to discover the relationship.
3
o See YouTube Clips: Deriving the Formula – Volume of Cone and Deriving
the Formula – Volume of Pyramid .
.
Volume in the World
Discover Real World Connections of the Volumes of Shapes.

Some possible activities include a home project exploring the volume of concrete,
aquarium, dirt, mulch, etc.

Possible problems include a pirate ship that has a hole and will sink when 50% of
the ship is filled with water. If the ship fills at a certain rate, how long until the
ship sinks?
Mathematics 10C
Measurement
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Going Beyond
Explore building composite structures and the volume of material needed to construct
them.
Students may solve problems in Imperial and Metric Systems.
Resources
Math 10 (McGraw Hill: sec 2.3)
Foundations and Pre-calculus Mathematics 10 (Pearson: sec 1.5-1.7)
Deriving the Formula – Volume of Cone
(http://www.youtube.com/watch?v=QnVr_x7c79w)
Deriving the Formula – Volume of Pyramid
(http://www.youtube.com/watch?v=BjbilpBaA-U&feature=related)
Glossary
cubic centimetre – any volume equivalent to the volume formed by a 1 cm by 1 cm
by 1 cm cube
cubic metre – any volume equivalent to the volume formed by a 1 m by 1 m by 1 m
cube
exponent – the number in a power that represents how many times a base is used as
a factor
Mathematics 10C
Measurement
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Appendix
Handouts
Mathematics 10C
Measurement
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My Referent Table
When things are _______
Small
Medium
Large
I would use ______ as a
referent
to measure things like
________
My Human Ruler
When I want to estimate
using the units of ______
Inches
Feet
Yards
Centimetres
Meters
I compare to my _____________
CONVERSION CHART
Relationships between common
Imperial Units
Length
 1 mile = 1760 yards = 5280 feet
 1 yard = 3 feet = 36 inches
 1 foot = 12 inches
Relationships between Common Imperial Units
and Metric Units
1 inch = 2.54 cm
1 cm = 0.3937 inches
1 mile = 1.609 km
1 km = 0.6214 miles
1 yard = 0.9144 m
1 m = 1.0936 yards
1 foot = 0.3048 m
1 m = 3.2808 feet
Inch vs Centimetre Ruler
Here we can see that 1 inch = approximately 2.54 centimetres.
3-D MYSTERY MODEL ACTIVITY
Revised and used with permission from Bryan Quinn.
You will need one Pyramid A and four Pyramid Bs to complete this activity. Use the
nets given to cut out and make the five pyramids from cardstock (or paper). Cut on
solid lines and fold on the dotted lines and put glue on the tabs (or tape edges).
1. Without taping the pyramids together, arrange your 5 pyramids to make three
congruent pyramids in a row, as shown below.
2 Pyramid Bs
Pyramid A
2 Pyramid Bs
2. Start with your answer to #1 and tape together the five pyramids in such a way
that the taped edges act as hinges, so that the pieces of the 3-D model above
can be “folded up” to form a square prism
3. State the geometric property relating the volume of pyramids and prisms
demonstrated by this model. Can we extend this property to other volume of
prisms formulas?
Pyramid A
Glue Here
Pyramid B
Pyramid B
Pyramid B
Pyramid B
Glue Here