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