Возрастная группа: 4 t h Grade Virginia - Mathematics Standards of Learning (2009): 3.10a, 3.9d,

Transcription

1 1 План урока Inches, Feet and Yard s in Perimeter and Area Возрастная группа: 4 t h Grade Virginia - Mathematics Standards of Learning (2009): 3.10a, 3.9d, 5.8a, 6.10c Virginia - Mathematics Standards of Learning (2016): 3.8.a, 4.7 Fairfax County Public Schools Program of Studies: 3.10.a.1, 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 Онлайн ресурсы: F e nc e d I n Opening Teacher present s Students pract ice Class discussion Closing 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 convert between inches, feet, and yards De vel o p multiple methods to convert square units

2 2 Ope ni ng 6 Display the following problem: Sara and Sam are comparing their heights. Sara is 4 feet 8 inches tall and Sam is 5 feet 2 inches tall. How many inches taller is Sam than Sara? How do you know? Have students write the answer in their notebook. When they are done writing, share. Ask: What is the height difference between the two students? How do you know? The difference is 6 inches. We could find this answer two ways: 1. We could convert both heights to inches and then subtract. So 4 feet 8 inches is equal to 56 inches, and 5 feet 2 inches is equal to 62 inches. When we subtract 56 from 62, we get 6 inches. 2. We could subtract without converting. To do this, we would have to borrow from the 5 feet. Instead of writing 5 feet 2 inches, we can write 4 feet 14 inches. Then we can subtract 4 feet 8 inches from 4 feet 14 inches to get 6 inches. Say: Today we re going to look at pe ri me t e r and area. Pay attention to the units in the questions. We will need to convert between inches and feet. T e ac he r prese nt s M at h game : F e nc e d I n - I nc he s and F e e t 12 Using Presentation Mode, present Matific s episode F e nc e d I n - I nc he s and F e e t to the class, using the projector. The goal of the episode is to measure a rectangular piece of land, convert between feet and inches, and calculate perimeter and area.

3 3 Example : Say: Please read the question. The question asks, How many inches of fence will you need to surround the purple flowerbed? Ask: What are we being asked to find? We are being asked to find the distance around the flowerbed, or the perimeter of the flowerbed. Ask: How can we figure out the perimeter? We can measure the length and width of the flowerbed. Then we add those two numbers together and double the sum. Move the tape measure to measure the horizontal side of the purple flowerbed. Ask: What is the length of the horizontal side of the flowerbed? Include units in your answer. The flowerbed is 3 feet wide. Say: In what unit do we want our answer? Our answer needs to be in inches. Ask: How many inches wide is the flowerbed?

4 4 It is 36 inches wide. Move the tape measure to measure the vertical side of the purple flowerbed. Ask: What is the length of the vertical side of the flowerbed? Include units in your answer. The flowerbed is 2 feet long. Say: We want our answer in inches. How many inches is it? It is 24 inches long. Ask: How many inches 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 four problems. The first two are perimeter problems and the second two are area problems. When prompting the students to solve the area problems, encourage them to convert the dimensions of the rectangles to the correct unit before multiplying. St ude nt s prac t i c e M at h game : F e nc e d I n - I nc he s and F e e t 14 Have the students play F e nc e d I n - I nc he s and F e e t and F e nc e d I n - F e e t and Yards on their personal devices. Circulate, answering questions as necessary. Cl ass di sc ussi o n 10

5 5 Display the following problem: Ask students to look over the problem and the work that both Marty and Maddy did. They should think to themselves for a minute, and then turn to a partner to discuss the problem. Once the students have had a chance to talk to their partners, share. Ask: What did Marty and Maddy do differently? Marty and Maddy converted to inches at different times in the problem. Marty found the area first and then converted to inches. Maddy converted to inches first and then found area. Ask: Who is correct? How do you know? Maddy is correct. There are no flaws in Maddy s calculations. Marty made an error when he converted from square feet to square inches. While there are 12 inches in a foot, there are not 12 square inches in a square foot. A square foot is a square with that is 1 foot long and 1 foot wide. So another way to describe that square would be 12 inches long and 12 inches wide. So its

6 6 area is 144 square inches. So 1 square foot is equal to 144 square inches. So when Marty converts at the end, instead of multiplying the number of square feet by 12, he should multiply the number of square feet by 144. Multiplying the number of square feet by 144 does indeed give 1728 square inches, which is Maddy s answer. Say: So when we convert from feet to inches, we multiply by 12. But when we convert from square feet to square inches, we multiply by 144. Display the following rectangle: Say: Name two ways we could find the area of this rectangle in square inches. We could multiply 5 by 8 to find the area in square feet. So the rectangle is 40 square feet. We can then convert to square inches by multiplying 40 by 144. We get 5760 square inches. The second way to solve the problem is to convert the dimensions to inches first. So 5 feet is equal to 60 inches, and 8 feet is equal to 96 inches. Now we can multiply 60 by 96 to get the answer, 5760 square inches. Display the following rectangle: Say: Name two ways we could find the area of this rectangle in square feet.

7 7 We could multiply 24 by 48 to get 1152 square inches. To convert to feet, we divide by 144. Dividing 1152 by 144 gives 8. The answer is 8 square feet. The other way to solve the problem would be to convert to feet first. The rectangle is 24 inches by 48 inches. That is the same as 2 feet by 4 feet. Then we can multiply 2 by 4 to get the answer, 8 square feet. Ask: If we convert 5 feet to inches, what do we get? We get 60 inches. Ask: And if we convert 5 square feet to square inches, what do we get? We get 720 square inches. Ask: If we convert 108 inches to feet, what do we get? We get 9 feet. Ask: If we convert 288 square inches to square feet, what do we get? We get 2 square feet.

8 8 Cl o si ng 5 Display the following diagram. Ask students to find its perimeter in inches and its area in square inches. Have students work independently, showing their work in their notebooks. When the students are done working, share. Ask: What is the perimeter of the polygon in inches? How do you know? The perimeter is 384 inches. The right side of the polygon is 6 feet long. The bottom is 10 feet long. To find the perimeter, we add the lengths of all the edges: 3 plus 6 plus 3 plus 4 plus 6 plus 10. That adds to 32 feet. Then we need to convert to inches. There are 12 inches in a foot, so we multiply 32 by 12 to get 384 inches. Ask: What is the area of the polygon in square inches? How do you know? The polygon has area 6048 square inches. One way to solve this is to draw a horizontal line within the figure to create a rectangle that is 3 feet by 4 feet and a rectangle that is 3 feet by 10 feet. Then we convert all the measurements to inches. So now we have a rectangle that is 36 inches by 48 inches and a rectangle that is 36 inches by 120 inches. To find the area of each, we multiply. The smaller rectangle has area 1728 square inches, and the larger rectangle has area 4320 square inches. We add the two areas together to get the total area, which is 6048 square inches.

9 9