Altersgruppe: Grade 4 Virginia - Mathematics Standards of Learning (2009): 3.10a, 3.9d,

Transcription

1 1 U n t er r ich t splan Meter and Centimeter in Perimeter and Area Altersgruppe: Grade 4 Virginia - Mathematics Standards of Learning (2009): 3.10a, 3.9d, 5.8a, 6.10c Virginia - Mathematics Standards of Learning (2016): 3.8.a 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 Online-Ressourcen: 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 converting between meters and centimeters Learn to convert between square units De vel o p multiple methods to find area

2 2 Ope ni ng 6 Ask the students to copy and complete the following in their notebooks: 1 m = cm 4 m = cm 500 cm = m 7000 cm = m 15 m = cm 20 m = cm 300 cm = m When the students are done working, review. How many centimeters are in a meter? There are 100 centimeters in a meter. How do we convert from meters to centimeters? How do we convert from centimeters to meters? To convert from meters to centimeters, we multiply by 100. To convert from centimeters to meters, we divide by 100. So let s fill in the remaining blanks. Ask different students for the missing numbers in the remaining equalities above.

3 3 T e ac he r prese nt s M at h game : F e nc e d I n - M e t e rs and Ce nt i me t e rs 12 Using Presentation Mode, present Matific s episode F e nc e d I n - M e t e rs and Ce nt i me t e rs to the class, using the projector. The goal of the episode is to measure a rectangular piece of land, convert between meters and centimeters, and calculate perimeter and area. Example : Please read the question. The question asks, How many meters of fence will you need to surround the purple flowerbed? What are we being asked to find? We are being asked to find the distance around the flowerbed, or the perimeter of the flowerbed. 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.

4 4 What is the length of the horizontal side of the flowerbed? Include units in your answer. The flowerbed is 200 centimeters wide. In what unit do we want our answer? Our answer needs to be in meters. How many meters wide is the flowerbed? It is 2 meters wide. Move the tape measure to measure the vertical side of the purple flowerbed. What is the length of the vertical side of the flowerbed? Include units in your answer. The flowerbed is 200 centimeters long. We want our answer in meters. How many meters is it? It is 2 meters long. How many meters of fence do we need to surround the purple flowerbed? 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.

5 5 St ude nt s prac t i c e M at h game : F e nc e d I n - M e t e rs and Ce nt i me t e rs 14 Have the students play F e nc e d I n - M e t e rs and Ce nt i me t e rs on their personal devices. Circulate, answering questions as necessary. Cl ass di sc ussi o n 10 Display the following problem: Ask students to look over the problem and the work that both Tony and Tina did. They should think to themselves for a ute, and then turn to a partner to discuss the problem. Once the students have had a chance to talk to their partners, share. What did Tony and Tina do differently?

6 6 Tony and Tina converted to centimeters at different times in the problem. Tony converted to centimeters first and then found the area. Tina found the area first and then converted to centimeters. Who is correct? How do you know? Tony is correct. There are no flaws in Tony s calculations. Tina made an error when she converted from square meters to square centimeters. While there are 100 centimeters in a meter, there are not 100 square centimeters in a square meter. A square meter is a square that is 1 meter long and 1 meter wide. So another way to describe that square would be 100 centimeters long and 100 centimeters wide. So its area is 10,000 square centimeters. So 1 square meter is equal to 10,000 square centimeters. So when Tina converts at the end, instead of multiplying the number of square meters by 100, she should multiply the number of square meters by 10,000. Multiplying the number of square meters by 10,000 does indeed give 350,000 square centimeters, which is Tony s answer. So when we convert from meters to centimeters, we multiply by 100. But when we convert from square meters to square centimeters, we multiply by 10,000. Display the following rectangle: Name two ways we could find the area of this rectangle in square centimeters. We could multiply 6 by 9 to find the area in square meters. So the rectangle is 54 square meters. We can then convert to square centimeters by multiplying 54 by 10,000. We get 540,000 square centimeters. The second way to solve the problem is to convert the dimensions to centimeters first. So 6 meters is equal to 600

7 7 centimeters, and 9 meters is equal to 900 centimeters. Now we can multiply 600 by 900 to get the answer, 540,000 square centimeters. Display the following rectangle: Name two ways we could find the area of this rectangle in square meters. We could multiply 200 by 400 to get 80,000 square centimeters. To convert to meters, we divide by 10,000. Dividing 80,000 by 10,000 gives 8. The answer is 8 square meters. The other way to solve the problem would be to convert to meters first. The rectangle is 200 centimeters by 400 centimeters. That is the same as 2 meters by 4 meters. Then we can multiply 2 by 4 to get the answer, 8 square meters. If we convert 8 meters to centimeters, what do we get? We get 800 centimeters. And if we convert 5 square meters to square centimeters, what do we get? We get 50,000 square centimeters. If we convert 200 centimeters to meters, what do we get? We get 2 meters. If we convert 600,000 square centimeters to square meters, what do we get? We get 60 square meters.

8 8 Cl o si ng 5 Display the following diagram. Ask students to find its perimeter in centimeters and its area in square centimeters. Have students work independently, showing their work in their notebooks. When the students are done working, share. What is the perimeter of the polygon in centimeters? How do you know? The perimeter is 4000 centimeters. The right side of the polygon is 8 meters long. The bottom is 12 meters long. To find the perimeter, we add the lengths of all the edges: 4 plus 7 plus 4 plus 5 plus 8 plus 12. That adds to 40 meters. Then we need to convert to centimeters. There are 100 centimeters in a meter, so we multiply 40 by 100 to get 4000 centimeters. What is the area of the polygon in square centimeters? How do you know? The polygon has area 680,000 square centimeters. One way to solve this is to draw a horizontal line within the figure to create a rectangle that is 4 meters by 5 meters and a rectangle that is 4 meters by 12 meters. Then we convert all the measurements to centimeters. So now we have a rectangle that is 400 centimeters by 500 centimeters and a rectangle that is 400 by 1200 centimeters. To find the area of each, we multiply. The smaller rectangle has area 200,000 square centimeters, and the larger rectangle has area 480,000 square centimeters. We add the two areas together to get the total area, which is 680,000 square

9 9 centimeters.