Abstract
Students learn about area and the units used to measure area using a variety of materials including computer applets.
Objectives
Upon completion of this lesson, students will:
- have practiced finding area of rectangular shapes and irregular shapes with right angles.
- understand why the area formula works for rectangular shapes.
Standards Addressed
Grade 3
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Geometry
- The student demonstrates an understanding of geometric relationships.
- The student solves problems using perimeter or area.
Grade 4
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Geometry
- The student demonstrates an understanding of geometric relationships.
- The student solves problems using perimeter or area.
Grade 5
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Geometry
- The student demonstrates an understanding of geometric relationships.
- The student solves problems (including real-world situations) using perimeter or area.
Third Grade
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Geometry
- Reason with shapes and their attributes.
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Measurement and Data
- Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
Sixth Grade
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Geometry
- Solve real-world and mathematical problems involving area, surface area, and volume.
Seventh Grade
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Geometry
- Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Grades 3-5
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Measurement
- Apply appropriate techniques, tools, and formulas to determine measurements
4th Grade
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Measurement
- Standard 4-5: The student will demonstrate through the mathematical processes an understanding of elapsed time; conversions within the U.S. Customary System; and accurate, efficient, and generalizable methods of determining area.
Student Prerequisites
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Technological:
Students must be able to:
- perform basic mouse manipulations such as point, click and drag
- use a browser for experimenting with the activities
Teacher Preparation
- access to a browser
- construction paper and pencil
- rulers and scissors
Key Terms
area
The number of square units needed to cover a surface
Lesson Outline
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Focus and Review
Review any pertinent vocabulary and tell the students that today they will be learning about area.
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Objectives
Students will acquire and demonstrate knowledge of area by calculating the area of computer generated shapes.
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Teacher Input
- Have all the students cut out one square. Do not specify the size. (You may want to remind the students that the corners of a square are right angles.)
- Once the students have completed their squares have them measure how many of their squares they could fit on top of their desk with out having the squares overlap.
- Record a few of the students' answers on the board.
- Tell the students there is a company which is willing to buy all the schools desks based on how many squares it takes to cover the desk's surface. Tell them the company is willing to pay 1 dollar per square.
- Discuss the answers on the board.
- Ask the students whose square the company would probably want to use to measure the desks.
- Ask the students which square the school would probably want the company to use.
- Discuss why this could be a problem and the possible solutions.
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Guided Practice
- Have the students tape two pieces of paper together so they are able to draw a 1 ft by 1 ft square on them.
- Tell the students to use their rulers to draw a 1 ft by 1 ft square on their paper. Convey to the students that it is important for their measurement to be precise.
- Once all of the students have constructed their squares explain to them that the squares they are holding are what a square foot looks like.
- Have the students measure their desks with their squares to see how many squares will fit on their desks.
- Ask a few of the students for their answers. (They should all be similar)
- Have the students calculate how many square inches there are in their desk top by using pre-cut squares.
- Have the students use the pre-cut square inches to calculate how many square inches there are in a square ft.
- Ask them if there are any short cuts they can figure out instead of having to lay out the squares on top of the desk.
- Have the students design different size rectangles and squares with their precut square inch pieces of paper.
- Have the students calculate the area of the shape they designed. Now have them trade places with their partner and calculate the area of their partner's shape.
- Have the students use their square inch pieces of paper to design a shape of their choice.
- Have the students calculate the area of their shape, trade places with their partner, and calculate the area of their partner's shape.
- Ask for the different methods the students used to calculate the area of the irregular shapes.
- Mention sectioning the shapes into smaller squares and rectangles to simplify the area calculation.
- Explain to the students that what they have been measuring is called area.
- Explain that area is measured in square units. These units can be square m, cm, in, ft, etc.
- Ask if anyone has discovered a way to calculate the area of a square or rectangle without actually having to count all the squares. If so have that person share their method. If no one mentions the length * width formula mention it to the class and have them try it.
- Show the students how to operate the Area Applet.
- You may want to specify certain perimeter settings for the students to use.
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Independent Practice
- Have the students work in pairs with the Area Applet.
- It is often helpful for students to copy down several of the problems from the activity onto graph paper they are either proud of or found challenging. This also provides something they can turn in to you at the end of class.
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Closure
- Review area measurement - both how and why it is measured with square units and ask for questions.
- Review the different ways the students used to calculate area.