measurement and data 1 108me0a08surmsn80u 4...108me0a08surmsn80u. perimeter. is the distance around...

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Objective

Common Core State Standards

■ 4.MD.3

1Measurement and Data

Perimeter and AreaPerimeter is the distance around a figure, so it is a length measured in linear units such as inches. Area is a measure of the surface covered by a figure, so it is measured in square units such as square inches. Students can develop (or verify) formulas for determining the perimeter and area of a rectangle.

Talk About ItDiscuss the Try It! activity.

■ Ask: What is the perimeter of a rectangle with dimensions 5 units by 3 units? Students can count units around the rectangle to get 16, or they can add: 5 + 3 + 5 + 3 = 16. Say: Now write a formula for the perimeter of a rectangle with dimensions a units by b units. Students write P = a + b + a + b, or P = 2a + 2b, or P = 2(a + b).

■ Ask: What is the area of a rectangle with dimensions 5 units by 3 units? Students can count the square units that make up the rectangle to get 15, or they can multiply: 5 × 3 = 15. Say: Now write a formula for the area of a rectangle with dimensions a units by b units. Students write A = ab.

Solve ItReread the problem with students. By completing the worksheet, students find all the possible 16-block routes for Lisa, starting with 7 blocks east, then 6, 5, 4, 3, 2, and 1. When comparing areas, students see that rectangles with the same perimeter can have different shapes and therefore different areas. Also, the rectangle with the greatest area is the square.

More IdeasFor other ways to teach about perimeter and area—

■ Have students use Centimeter Cubes or Color Tiles to build all the possible rectangles with an area of 24 square units. Compare the perimeters. Ask: Which rectangle has the least perimeter?

■ Students can use a Geoboard and rubber bands for this activity. Step 1: Make a square with side length 2 units. Find its area and perimeter (2-by-2 square, A = 4 and P = 8). Step 2: Make a rectangle that has the same area as your square, but different perimeter (1-by-4 rectangle, A = 4 and P = 10). Step 3: Make a rectangle that has the same perimeter as your square, but different area (1-by-3 rectangle, A = 3 and P = 8).

Formative AssessmentHave students try the following problem.

A rectangle has a perimeter of 28 feet. What is the greatest possible area?

A . 56 sq ft. B . 49 sq ft. C . 48 sq ft. D . 40 sq ft.

Measurement and Data

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Materials• Color Tiles (100 per group)• 4-Column Recording Chart (BLM 6; 1 per group)• pencils (1 per group)• paper (1 sheet per group)

Try It! 30 minutes | Groups of 4

Here is a problem about perimeter and area.

Each morning, Lisa walks 16 blocks for exercise. She always walks east, turns right

and walks south, turns right and walks west, then turns right and walks north

back to home. Find all the possible 16-block routes that Lisa can take. Compare

the areas of the rectangles formed by the routes. Every block is the same length.

Introduce the problem. Then have students do the activity to solve the problem. Distribute Color Tiles, recording charts, and pencils. Have students fill in the recording chart with the following headings: Dimensions, Perimeter, Area.

1. Have students line up 7 Color Tiles left to right. Ask: What are the dimensions of the rectangle you made with the tiles? Have students draw and label a copy of the rectangle. Ask: What is the perimeter of the rectangle? Have a student draw arrows on the diagram to show Lisa’s route.

3. Say: Now consider the areas of the rectangles that are enclosed by the routes. Add the area of each rectangle to the recording chart. Have students finish by adding the 5-by-3, 6-by-2, and 7-by-1 routes to the chart.

2. Say: Use tiles to build a route in which Lisa first walks 6 blocks east. Students form a 2-by-6 rectangle. Say: Continue building rectangles that decrease by one block east each time until you have built a square route. Students form 3-by-5 and 4-by-4 rectangles. Have them fill in the dimensions and perimeters on the recording chart. Keep the models of the rectangles.

Students might think that since the length of the route is 16 blocks, they will use 16 tiles to build the rectangle that shows the route. This is not the case, because the route is found along the outside edge of the rectangle. Two sides of one tile are counted at each corner.

Name Measurement and DataLesson

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Hands-On Standards, Common Core Edition

1

Use Color Tiles to build each rectangle. Find the perimeter and area.

Find the perimeter and area of each rectangle.

1.

perimeter ______________

area ______________

2.

perimeter ______________

area ______________

5. 2

8

P = _____

A = ____

7. length: 12 units, width: 3 units

P = _________ A = ________

6.

6

2 P = _______

A = _______


P = _________ A = ________

Use Color Tiles to build a rectangle with the given perimeter and area. Sketch the model.

3 . perimeter: 16 units

area: 15 units2


area: 30 units2

Answer Key

Download student pages at hand2mind.com/hosstudent.

(Check students’ work.)

18 20

18 24

Check students’ models. Check students’ models.

20

30 32

16

36 63

16

12

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Challenge! Can you find rectangles with the same areas, but with different perimeters? Draw your solutions.

Answer Key

Download student pages at hand2mind.com/hosstudent.

Challenge: (Sample) Yes, for example a figure that is 4-cm by 4-cm has a perimeter of 16 cm and an area of 16 square cm. A figure that is 2-cm by 8-cm also has an area of 16 square cm, but its perimeter is 20 cm.

Name Measurement and DataLesson

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1

Use Color Tiles to build each rectangle. Find the perimeter and area.

Find the perimeter and area of each rectangle.

1.

perimeter ______________

area ______________

2.

perimeter ______________

area ______________

5. 2

8

P = _____

A = ____


P = _________ A = ________

6.

6

2 P = _______

A = _______


P = _________ A = ________

Use Color Tiles to build a rectangle with the given perimeter and area. Sketch the model.


area: 15 units2


area: 30 units2

www.hand2mind.com

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Name

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Hands-On Standards, Common Core Editionwww.hand2mind.com

Challenge! Can you find rectangles with the same areas, but with different perimeters? Draw your solutions.

measurement and data 1 108me0a08surmsn80u 4...108me0a08surmsn80u. perimeter. is the distance around...

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