Virginia - Mathematics Standards of Learning (2009): 3.9d, 5.8a,

Transcription

1 1 Lesson Plan Area and Perimeter (Meters) Age group: 4 t h Grade Virginia - Mathematics Standards of Learning (2009): 3.9d, 5.8a, 6.10c Virginia - Mathematics Standards of Learning (2016): 3.8.b, 4.7 Fairfax County Public Schools Program of Studies: 3.9.d.1, 3.9.d.2, 5.8.a.2, 5.8.a.3, 5.8.a.4, 5.8.a.7, 6.10.c.1 Online resources: F e nc e d I n Opening Teacher present s Students pract ice Ext ension Math Pract ice Closing 6 min 1 2 min 1 2 min 1 4 min 3 min M at h Obj ect ives E xpe ri e nc e a real-world example of perimeter and area P rac t i c e measuring lengths Learn to calculate perimeter and area De vel o p algebraic skills Ope ni ng 6 min

2 2 Ask the students to define perimeter and area. They should write their responses in their notebooks. When the students are done writing, share. What is the definition of perimeter? Perimeter is the distance around a shape. What is the definition of area? Area is the amount of space inside a shape. Display the following rectangle: How can we find the perimeter of this rectangle? We add 28 and 88 and double the result. Why do we double? We want the distance all the way around the rectangle. Adding 28 and 88 only gets us halfway around the rectangle. How do we find the area of this rectangle? We multiply 28 by 88. What unit would we use for the perimeter of this rectangle? We would use meters as the unit. What unit would we use for the area of this rectangle? We would use square meters.

3 3 Why do we use square meters? Area asks us how many small squares fit inside the rectangle. Each square in this case is 1 meter by 1 meter. We are asking how many 1 meter by 1 meter squares we can place inside the rectangle. Thus, the unit is square meters. T e ac he r prese nt s M at h game : F e nc e d I n - P e ri me t e r- Area: Level I (me t e rs) 12 min Present Matific s episode F e nc e d I n - P e ri me t e r- Area: Level I (me t e rs) to the class, using the projector. The goal of the episode is to calculate perimeter and area after measuring a rectangular piece of land. Example : Say: Please read the question. The question asks, How many meters of fence will you need to surround the park? What are we being asked to find? We are being asked to find the distance around the park, or the perimeter of the park.

4 4 How can we figure out the perimeter? We can measure the length and width of the park. Then we add those two numbers together and double the sum. What is the length of the horizontal side? Students can answer based on the episode. Move the tape measure to measure the vertical side. What is the length of the vertical side? Students can answer based on the episode. How many meters of fence do we need? Click on the to enter the students answer. If the answer is correct, the episode will proceed to the next question. If the answer is incorrect, the question will wiggle. The episode will present a total of six problems. The first four are about perimeter and the last two are about area. St ude nt s prac t i c e M at h game : F e nc e d I n - P e ri me t e r- Area: Level I (me t e rs) 12 min Have the students play F e nc e d I n - P e ri me t e r- Area: Level I (me t e rs) and F e nc e d I n - P e ri me t e r- Area: Level I I (me t e rs) on their personal devices. Circulate, answering questions as necessary. E xt e nsi o n M at h P rac t i c e : P e ri me t e r and Area Wo rkshe e t 14 min

5 5 Distribute graph paper. Display the following problems. Have students work in groups of four to solve. On the graph paper: 1. draw all the rectangles you can find (whose length and width are whole numbers) that have area: a. 15 square units b. 16 square units c. 20 square units d. 25 square units 2. find the perimeter of each of the rectangles you found in #1. 3. draw all the rectangles you can find (whose length and width are whole numbers) that have perimeter: a. 10 units b. 11 units c. 12 units d. 16 units 4. find the area of each of the rectangles you found in #3. Circulate, answering questions as necessary. When the students are done working, ask: How many rectangles did you find that have area 15? What are they? We found two rectangles. One is 1 unit by 15 units, and the other rectangle is 3 units by 5 units.

6 6 How do you know that you have found all possible rectangles? We used all the factors of 15. Fifteen has 4 factors: 1, 3, 5, and 15. How many rectangles did you find that have area 16? What are they? There are three rectangles. One is 1 unit by 16 units, another is 2 units by 8 units, and the last is 4 units by 4 units. What rectangles did you find that have area 20? We found a rectangle that is 1 unit by 20 units, another that is 2 units by 10 units, and a third that is 4 units by 5 units. What rectangles did you find that have area 25? There are two rectangles one is 1 unit by 25 units and the other is 5 units by 5 units. Say: Let s look at the perimeter of the rectangles you found. Display the following table:

7 7 Ask students for the perimeters of each rectangle and fill them into the table. If we know the area of a rectangle, do we know its perimeter?

8 8 No. A rectangle with area 20 could have perimeter 42, 24, or 18 units. How is it possible for us to have such different perimeters? The rectangles in the table vary from really skinny and long to square. The distance around these differently-shaped rectangles varies. Say: Now let s look at questions 3 and 4. Let s make another table and fill in. Display the following table: Ask students to fill in the table.

9 9 Why could we not find any rectangles that have perimeter 11? If the length and width of each rectangle must be a whole number, then the perimeter cannot be odd. To find perimeter, we add the length and the width and then double. When we double, we are multiplying a whole number by 2. Multiplying a whole number by 2 gives an even number. If we know the perimeter of a rectangle, do we know its area? No. We saw that there are four possible rectangles with perimeter 16. When we calculate the area of each, we get four different areas.

10 10 Cl o si ng 3 min Say: In this episode, we looked only at rectangles. Let s close by looking not only at rectangles but also at some other shapes. Display the following shapes: Say: Here are a few ways to arrange nine squares with the edges touching. So the area of each of the shapes is 9 square units. What is the perimeter of each? The first has a perimeter of 20 units. The second has a perimeter of 12 units. The third has a perimeter of 18 units. The fourth has a perimeter of 16 units.