MEASUREMENT: FINDING AREAS OF RECTANGLES
Grades 4 - 5
The students will construct the formula for the area of a rectangle
by viewing a video revolving around two students, their lawn mowing business
and their need to charge by the square meter. The extension exercises will
allow the students to explore the connection between lawn care, science
and math.
Math Talk: Measurement: Scooping out the Area - Measuring Area
(Children's Television Workshop)
Students will be able to:
- relate square units to measuring area;
- estimate area;
- develop the formula for area of a rectangle;
- caluculate area in real world situations using the formula;
- use cooperative learning strategies;
- use calculator skills to multiply decimals;
- use the scientific process to perform experiments including the collection
and analysis of data.
Each pair of students will need:
- a pad of square-shaped post-its,
- rulers,
- a measurement tool (paper made) the length of a post-it
- a calculator,
- a dictionary,
- a meter stick,
- replicas of a square inch (paper) and a square foot,
- a plastic garbage bag cut to measure one meter square.
- area
- perimeter
- square units
- formula
- estimate
- odometer
List these words on the board as they come up during the lesson. Their definitions
will be part of the discovery section in the video and lesson.
Review linear measurement by asking students to find the length
and width of their desks or any other objects in the room. Discuss the importance
of the placement of the measuring device and what unit of measure should
be used. Suggest that the choice of measuring device depends on the size
of the object being measured. Ask students what unit of measure they would
select to measure a paper clip, the room, the height of a desk. Ask how
they could measure the distance from home to school .
Estimate an inch, a foot and a meter by using body parts as a bench mark.
The focus for viewing is a specific responsibility or task(s)
students are responsible for during or after watching the video to focus
and engage students' viewing attention. Tell the students to imagine themselves
in place of Shirley and Bobby in the following video segment and pretend
that their desks are Mr. Freeman's lawn. Ask them, "Would you do things
differently? If so, how?"
BEGIN the video Math Talk: Scooping Out The Area:
Measuring Area and PAUSE after Mr. Freeman says, "I'm
Buddy Biggs and I'd like to cut your lawn for a penny a square meter."
Ask the students, "What is a square meter?" Have a meter stick
available and hold it up for the class. Ask the class if someone can show
you what a square meter looks like.
RESUME the tape. PAUSE it after Shirley and Bob say, "A
formula?" Ask the students, "What is a formula?" If the discussion
doesn't generate a suitable definition, ask a student to look it up in the
dictionary. Students need work in reading written words as a form of communication.
This is an opportunity to strengthen that.
RESUME the tape. PAUSE after the narrator says, "How
could you measure that?" Ask the students, "What is a rectangle?"
Tell them to write down in their own words the definition of a rectangle.
Ask them to compare it to their partner's and agree on one definition. Come
to an agreement as a class and write the definition on the board.
Ask the students, "Where around the room do you see rectangles and
how do they fit our definition?" Make a list of the rectangles around
the room.
RESUME the video. PAUSE after Shirley says, "You can
count how many square meters it takes to cover a lawn." Ask the students
to use their post-its to measure how many square units cover their desks.
Circulate around the room while the students do this activity. Do some assessing.
Carry a check list including cooperative learning skills, measurement skills
and problem solving skills that you want to assess.
RESUME the video. PAUSE the video after Shirley says, "How
did that tell him square meters?" Show the students the large plastic
sheet and compare it to the meter stick. Give the students a measuring device
the same length as one of the post-its. Ask them to discuss with their partners
how they could find the area of their desk in the same way that Buddy Biggs
managed to determine the area of the lawn.
Tell the students, "See if what you and your partner talked about matches
what Shirley and Bobby are about to discuss." RESUME the video
and continue it to the end. STOP when the narrator says, "You
always measure area in square units."
Have the students determine the area of their desk by using
the formula: A = L x W. Write the formula on the board and ask students
to tell you what each letter represents. Point out that the reason we are
using letters (variables) is that the area of any rectangular surface can
be found using this formula.
Point out to the students the two things that have been discovered so far:
1.) What a square meter is and 2.) how a square meter or a square anything
can cover a surface. Ask the students what the narrator meant when he said
a square anything. For instance, what are the other square measurements
that are commonly used? (square inches, square feet) If the students can't
see that at this point, demonstrate a square foot with a ruler and have
them draw a square inch on one of their post-its.
Consider the list (on the board) of rectangles in the classroom. Ask the
students to first estimate the areas and then measure the area of rectangles
that would be suitable for this exercise.
- Visit the Chamber of Commerce and offer the service of planning and
planting a flower garden. Visit the site and measure square footage to determine
the specifics of cost and materials needed.
- Research the steps and costs of the "Adopt a Highway Program."
- Dig up a square foot of lawn to find out how many insects were in
the lawn and predict the number of insects in the whole lawn based on the
area. Go to the library and try to classify the insects found. Invite an
entomologist or an expert from one of the local lawn care businesses to
help identify the insects and talk about their behaviors.
- Survey local lawn care businesses to determine price per square meter
for lawn care services. Develop a survey containing questions such as: How
much extra do they charge for insect control and how do they determine the
extent of the insect population? How much extra do they charge for weed
control and how do they measure the extent of that problem? What other measurements
do they need to consider before determining the price of their service?
Do the number of trees, bushes, a pool, hills or flat lands play a part?
Math:
Write down that Buddy Biggs charged one cent per square meter to mow a lawn.
Using a calculator find out how much it would cost the customer to mow the
following lawn sizes: 75 square meters, 200 square meters, 500 square meters.
Ask, "At today's prices, how much would you charge to mow a lawn? If
you were paid $10 to mow a lawn, what area would Buddy Biggs say the lawn
had to cover?"
Math:
Have the students determine what they would charge to mow a lawn the size
of their own front lawn. Measure the lawn and determine the cost per square
meter. Make a chart of the class' findings.
Outdoor Activity:
Design an experiment to answer the question "Is mowing the lawn the
best way to control weeds?" Be sure to get their parents' permission
before you begin. Hint: Try varying the depth of the cut. For example, try
cutting the grass really short, say 1/2 inch for two or three weeks. Cordon
off one square meter in three different places on the lawn and calculate
the average number of weeds per square meter. Discuss the importance of
taking the count from different parts of the lawn. During the next two or
three weeks, cut it to the depth of two inches and calculate the average
number of weeds per square meter.
Science:
Discuss the role the weather might play in this experiment.
Writing:
Ask the students to imagine that their parents plan to redecorate their
bedroom. Tell them to describe specifically what they would have to do to
find the area of the bedroom and why.
Master Teacher: Mary Ellen Baron
Springfield School Department, Springfield, MA
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