STRAND 1: Number Sense and Operations
CONCEPT 2 Numerical Operations
GRADE 5
PO 3 Divide multi - digit whole numbers by
whole number divisors with and without
remainders.
STRAND 2: Data Analysis, Probability,
and Discrete Mathematics
CONCEPT 1 Data Analysis
GRADE 4
PO 1 Collect, record, organize, and display
data using double bar graphs, single line
graphs, or circle graphs .
GRADE 5
PO 1 Collect, record, organize, and display
data using multi-bar graphs or double line
graphs.
Overview
Math manipulatives (or Legos) help the
kinesthetic learner to understand geographic
concepts and see spatial patterns. This lesson
will help students formulate a mental map of
U.S. regions in terms of population density and
elevation of land.
Purpose
Students will learn how the elevation of land
can directly relate to the population density of
the region. Students will also practice the math
skills of division and creating double-bar
graphs.
Materials
• Several thousand math blocks or Legos
bricks that will be divided into small plastic
bags. Each bag should contain 84 Legos,
unifix cubes, centimeter cubes, or base ten
cubes: 42 each of TWO colors . Each bag
will be enough for one student or a group of
students as the teacher decides.
• Small plastic resealable bags
• If using Legos bricks, green Lego base
material cut into 10 inch by 1 1/8 inch strips
glued to Masonite board for stability and
durability is desirable
• Graph paper provided in this lesson
• Colored pencils, crayons, or markers
• Comparing U .S. Elevation to Population
Density student worksheet
• Answer key for Comparing U.S. Elevation
to Population Density Worksheet
• Ups and Downs of Population and Regions
map
• Ups and Downs of Population and Regions
map (no labels) for assessment
• Overhead of Physical Regions of the United
States map
• Overhead of answer key for graph work
• Physical map of U.S. without region names
• Calculators for students needing adaptations
Objectives
The student will be able to:
1. Create a double bar graph of geographic
concepts.
2. Practice division of whole numbers.
3. Analyze data that shows elevation of land as
it relates to population density.
Procedures
Prerequisite math skills: the ability to graph,
complete long division problems, and round off
numbers to the 100th place.
Prerequisite geography skills: knowledge of
vocabulary words: elevation, sparse, dense, and
population density, and some familiarity with
the physical regions of the U.S.
SESSION ONE
1. Introduce the lesson with a mental mapping
exercise. Have the students study the map of
Physical Regions of the United States briefly.
level (straight out from the side of the body).
Tell them their arm is at sea level—the eastern
shore of the United States. Explain that they will
be moving their arm from its position at the
right of the body to their left as we trace in the
air (from east to west) across the U.S. according
to how high above sea level they think this
region will be. Have students begin with the
Atlantic Coastal Plain. Is it sea level or
higher? Next, the Appalachian Mountains.
Have students move their arms to the west and
raise it as high as they think the Appalachian
region will be. After that, have students move
their arms west for the Mississippi River/Great
Lakes region. Students should move their arms
up or down for the elevation of this region.
Continue to have the students move their arms
to the west and estimate the elevation of the:
Great Plains, Rocky Mountains and Plateaus,
Great Basin, Sierra Nevada and Cascade
Mountains, and Pacific Coast.
3. Next explain the idea behind this lesson.
Students just estimated the elevation of the
physical regions of the U.S. Now they are going
to analyze data and discover how elevation
relates to population density. Review what
population density means: the AVERAGE
number of people living in a square mile . Have
the students estimate the population density for
their region of the country,.
4. Distribute the worksheets . Have the students
work in groups or individually to complete the
math problems for U.S. Elevation and
Population Density. Have them check their
work by displaying the overhead of the answer
key. Gather their papers and record their scores.
SESSION TWO
1. Distribute bags of the Legos (and their bases)
or the math linking blocks, the graph paper, and
colored pencils or markers. Pass back their
corrected papers from SESSION ONE.
Ups and Downs of Population and Region
2. Have the students select which of the 2
colored blocks will be elevation and which will
be population density. Model for them how to
stack the first double-bar graph. Teacher should
choose whether to begin at the west with Pacific
Coast or begin on the right with the Atlantic
Coastal Plain, but the regions must be kept in
order from west to east.
Pacific Coast =
2 blocks for elevation
8 blocks for population density
Sierra Nevada/Cascade Mountains =
7 blocks for elevation
2 blocks for population density
Continue until all regions are displayed.
(Note: there will be blocks left over of the elevation color.)
3. Now have the students use the graph paper to
create the same double-bar graph that the
manipulatives are showing. Be sure to remind
them that the graph needs a title. The class
could brainstorm a good title or the teacher can
print the title on the whiteboard: Comparing
U.S. Elevation to Population Density. Have the
students label the two axes. One should be
labeled in numbers (500 to 5000) and the other
should be labeling the regions (Pacific Coast to
Atlantic Coastal Plain).
4. Students should separate the blocks or Legos
and return them to the bags. All materials
should be gathered and returned to the teacher.
5. Students should complete the questions at the
bottom of the worksheet. This can be done as
homework.
6. Have the students share answers on the
worksheet to reinforce geography concepts. Ask
what two other concepts could be graphed that
would show the relationship to either elevation
(number of animal species, amount of mining,
number of trees) or population density (number
of cars, number of economic activities, number
of schools).
Assessment
The student worksheet can be graded for
comprehension of geography knowledge. Each
question will equal 1 point except for the “Why
do you think so?” questions. These can be worth
more points. Mastery is considered 80% or
higher.
The graph can be graded for math (32 points),
title (10 points), correctly labeled regions (8
points), key to the colors on the graph (10
points), general neatness (14 points) and correct
spelling (10). The final 16 points will come
from the worksheet division problems. Mastery
is considered 80% or higher.
Extensions
Have the students think of two topics that have a
relationship to each other, research the data, and
complete another double-bar graph.
Students can read the land section in the
National Geographic Society Reading
Expeditions Series: Travels Across America (all
five titles: The West, The Southeast, The
Southwest, The Midwest, and the Northeast)
Order #JB41237 and create a summary of what
are the specific physical features of this region.
After studying the Physical Regions of the
United States map, students can label a map of
the U.S with the names of the eight regions used
in the lesson as a quiz.
Technology Standard can be applied if the
computer is used to do the graphing:
3T-E2 Use a variety of technology tools for data
collection and analysis
PO1 Use technology device(s) to collect and
record data
PO2 Create and use a spreadsheet to analyze
data (e.g., use formulas, create charts and
graphs )
Sources
Adapted from original lesson by John Daly
Wayland Middle School, Wayland, MA
