Prior to this lesson, students should have familiarity with the following concepts and skills:
- The relationship between fractions, decimals and percents
- Calculation and interpretation of measures of central tendency (mean, median, mode)
- Creating data representations using box-and-whisker plots
- Geographical awareness about the United States and Canada
- Basic understanding of both metric and customary systems of measurement
Prior to conducthing this lesson with students, open the State Data Map and Canada Data Map, to familiarize yourself with the activities. You may also wish to bookmark the activities for easy access by students.
Know Thy Neighbor: An Introduction for American (or non-Canadian) Classes
with a discussion of what your students know about Canada. You might
prepare some interesting facts to share, including a list of famous
Canadians, such as Avril Lavigne, Wayne Gretzky, Steve Nash, Justin
Bieber, Michael J. Fox, Nelly Furtado, Alexander Graham Bell, Kiefer
Sutherland, Pamela Anderson, Shania Twain, Keanu Reeves, Alanis
Morissette, Neil Young, Jim Carrey, William Shatner (Captain Kirk). For
fun, present the list without introduction, and then ask students what
all of these people have in common. Students might be also interested
to know that the following originated from Canadian inventors:
- IMAX technology
- Blackberry® PDAs
- the telephone
- Trivial Pursuit®
Students should also know that Canada consists of 10 provinces and 3 territories.
Use this introduction as an opportunity to introduce the "Rough
Rule of 10" — that is, population‑related quantities in the United
States tend to be roughly 10 times larger than those in Canada.
However, do not refer to it as the Rough Rule of 10 yet! Students will
discover this rule on their own. Ask students what the U.S. population
is (approximately 309 million). Have students guess what the Canadian
population is (approximately 34 million).
Distribute the Rough Rule
activity sheet. (As this is meant to be a quick introduction to the
lesson, you can save paper by displaying the same information on a
chalkboard, overhead projector, or interactive whiteboard instead of
making copies for all students.) Working in pairs, students should
calculate values for the last two columns. To save time, you could have
different parts of the room complete a different row, have a
representative report their answer, and then aggregate the data. The
completed table is shown below.
|Year||Canadian Population (millions)||U.S. Population (millions)||Canadian Population as Share of U.S. Population (decimal form)||Canadian Population as Share of U.S. Population (Percentage)|
Ask students if they can develop a rule for comparing the U.S. and
Canadian populations using their conclusions from the table. Students
should recognize that for the last 40 years, the Canadian population
has been roughly 1/10 the U.S. population. For the remainder of the
lesson, this concept can be referred to as the "Rough Rule of 10."
Conduct a discussion about the introductory activity. Ask students
if the Rough Rule of 10 over or underestimates the Canadian population,
if the U.S. population is known? What if they had the actual Canadian
population and used the rule to estimate the U.S. population? Is the
rule likely to under or overestimate the population, according to what
was observed in the data?
Tell students that the rule can be extended in a few other
cases, including the size of the economy. Introduce students to the
concept of the gross domestic product, known by its acronym GDP. Simply
put, GDP measures the total sale of all goods and services within an
economy, including everything that consumers, businesses and
governments purchase as well as net exports from trade and investment
spending. (You might point out that this is the final sale of goods and
services so that the measurement avoids double or triple counting.)
Inform students that 2009 U.S. GDP was $14.3 trillion. Using
the Rough Rule of 10, ask students to predict the Canadian GDP
for 2009. Canadian GDP for 2009 was $1.3 trillion. (Note that both the
U.S. and Canadian GDP are given in U.S. dollars.) Student estimates
should be close to this number.
Explain to students that per capita means "per
person." Using the population data and GDP data, ask questions that
allow students to articulate how to calculate the per capita GDP. This
will help them later when working with the data maps. Ask students if
it would make sense to use the Rough Rule of 10 for per capita numbers,
such as when calculating per capita GDP, and to explain their
reasoning. Students should realize this estimation rule only works to
estimate a rough magnitude of quantifiable characteristics which are
likely to be similar in U.S. and Canada. To reinforce this idea you
could provide a list of quantifiable categories, such as fast food
consumption or home heating expenditures, and ask them if they think
the rule would apply. Ask them who might be interested in estimating
this type of information.
Where is Everybody? Population Density in Canada and the United States
Distribute a copy of the Where is Everybody Activity Sheet
activity sheet to each student. Students can work in pairs, and one
method to randomly assign partners is to write a simple equation or
expression in one corner of each activity sheet. When students solve
the equation or simplify the expression, students with the same
solution become partners. Have the students find their match.
Alternatively, if the computers are numbered, the solution could be the
computer number, which would tell students immediately where to go if
the handouts are distributed as they enter the computer lab. In
general, students can be paired either randomly or deliberately, but
when choosing a pairing strategy, the following questions should be
considered: Are my students always working with the same partners? Is
there a benefit or downside to grouping by ability in this activity?
How much time do I have to organize the groups?
Once students are in pairs and at a computer, they should open the State Data Map and Canada Data Map so that they can easily navigate between the two maps.
Have students observe the Canada Data Map. Using a projector,
demonstrate that students can find data sets in the upper left corner.
Have them select the Land Area map. Ask them what province has the
largest land area in Canada. [Nunavut.] If you are in a non-Canadian
classroom have a list of provinces with their abbreviations in a place
where all students can see it so the students can readily identify the
Canadian provinces and increase their geographical awareness. Have the
students select the Population map and ask them which province is the
most populated. [Ontario.]
Before switching to the Population Density map, ask students
to predict which province has the greatest population density. Students
may need to have the term population density defined for
them. Explain that population density is a measure of the number of
people per unit area, and it is commonly measured as people per square
mile or people per square kilometer. Once students understand the
concept, ask them again to predict which province will have the
greatest population density. Without judging their responses, ask them
to select the Population Density map from the Canada Data Map. Then ask
students which province has the greatest population density. [Prince
Edward.] Ask them to explain why there was a different province to the
answer for the questions about population, area, and density. This
introduction will provide students with an understanding of population
density and familiarize them with the activity so that they can
continue to work on the activity sheet.
Circulate as students work through the activity sheet,
inquiring how students arrived at their answers and asking probing
questions if they are stuck, such as, "How can the mean be used to help
you find the total population?"
Check that students are using precise mathematical language.
For example, encourage them to use the word denominator instead of
"bottom" in their responses. If a students' language or calculations
are inaccurate, have them rewrite a correct response. Use questioning
to help them identify where they might have gone wrong. For example,
when working with the U.S. data maps, a student may perform
calculations with 50 rather than 51, overlooking the fact that
Washington, DC, is included in the set. Asking, "How many data points
are there?" might help the student realize the mistake without
explicitly explaining where they went wrong.
Questions for Students
1. Notice that the population data is from different years. Is it
reasonable to use these data sets to make comparisons between U.S. and
[Yes. The population data from the U.S. and Canada only
differs by a couple years, and population doesn't change quickly enough
to have a great influence on the results.]
2. When using the computer activity, the sum of all data points was not
displayed. How can you quickly calculate the sum of all data points
without adding them together?
[Take the number of data points, and multiply by the average.]
- What was the level of student engagement in this activity? Could
the activity have been structured differently to increase engagement?
- Were the students sufficiently prepared to be successful in this activity?
- What areas of strength or weaknesses did you observe among your students during this lesson?
- Make estimates about real-life data
- Work flexibly with fractions, decimals and percents to solve problems and make comparisons
- Develop number sense
- Find, use and interpret measures of center and spread
- Discuss and understand the correspondence between data sets and their graphical representations
Common Core State Standards – Mathematics
Grade 6, Ratio & Proportion
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, ''The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.'' ''For every vote candidate A received, candidate C received nearly three votes.''
Grade 6, Stats & Probability
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
Grade 6, Stats & Probability
Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
Grade 7, The Number System
Solve real-world and mathematical problems involving the four operations with rational numbers.
Grade 7, Expression/Equation
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
Common Core State Standards – Practice
Make sense of problems and persevere in solving them.
Model with mathematics.
Use appropriate tools strategically.
Look for and make use of structure.