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

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1 1 U n t er r ich t splan More Area and Perimeter (Yard s) Altersgruppe: Grade 4 Virginia - Mathematics Standards of Learning (2009): 3.10a, 3.9d, 5.8a, 6.10c Virginia - Mathematics Standards of Learning (2016): 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 Online-Ressourcen: F e nc e d I n Opening Teacher present s Students pract ice Math Pract ice Worksheet 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 calculate perimeter and area De vel o p algebraic skills

2 2 Ope ni ng 6 Ask the students to solve the following problem by working in their notebooks: Find the perimeter and area of this rectangle. When the students are done working, share. Ask: What is the perimeter of the rectangle? How do you know? The rectangle is 5 units by 3 units. To find perimeter, we add the lengths of the edges of the polygon. So here, we add 5 plus 3 plus 5 plus 3 and get 16 units. The perimeter is 16 units. Ask: What is the area of the rectangle? How do you know? The rectangle has area 15 square units. We can either count the number of small squares to see that there are 15 of them, or we can multiply the length by the width. If we multiply, we are multiplying 5 by 3, so we get 15 square units. Ask: Why in our answer to perimeter, we say 16 units, but in our answer to area, we say 15 square units? Why are the units different? For perimeter, we are asking for the total distance around the shape. Distance is one-dimensional. So we just use units. For area, we are asking how many small squares fit inside the shape. The small squares are two-dimensional. So we use square units. 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 I I (yards) 12

3 3 Present Matific s episode F e nc e d I n - P e ri me t e r- Area: Level I I I (yards) to the class, using the projector. The goal of the episode is to answer perimeter and area questions after measuring a rectangular piece of land. Example : Say: Please read the question. The question asks, How many yards of fence will you need to surround the park? Ask: What are we being asked to find? We are being asked to find the distance around the park, or the perimeter of the park. Ask: 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. Ask: Why do we double the sum? The rectangle has 4 sides. To get the perimeter, we need to add all four sides. If we just add the length and the width, we have found the combined distance of two of the four sides. Since the opposite sides of a rectangle are equal, we can double the sum of the length and the width to get the total distance around the

4 4 rectangle. Ask: What is the length of the horizontal side? Students can answer based on the episode. Move the tape measure to measure the vertical side. Ask: What is the length of the vertical side? Students can answer based on the episode. Ask: How many yards 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 two are perimeter problems, the third is an area problem, and the last three are multi-step problems that alternate between perimeter and 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 I I (yards) 14 Have the students play F e nc e d I n - P e ri me t e r- Area: Level I I I (yards) and F e nc e d I n - P e ri me t e r- Area: Level I V (yards) on their personal devices. Circulate, answering questions as necessary. M at h P rac t i c e : M o re Area and P e ri me t e r (Yards) Wo rkshe e t 12

5 5 Distribute the following problems. Have students work in pairs. 1. Consider the following rectangles: a. Each rectangle has a perimeter of 42 yards and an area of 90 yards. When we place the rectangles next to each other, we get the following larger rectangle. What is its perimeter and area? b. How do the perimeter and area of this rectangle relate to the perimeter and area of the two rectangles above? Why does this make sense? 2. Find the area of the shaded regions: 3. A rectangular pool is 10 feet by 20 feet. You wish to build a deck around the pool that is 4 feet wide on all sides using tile that is 1 foot by 2 feet long. How many tiles do you need to purchase?

6 6 When the students are done working, review solutions. Discuss any questions the students may have. Cl o si ng 3 Ask: True or False? The area of a polygon is the amount of space inside the polygon. True, the area of a polygon is the amount of space inside the polygon. Ask: True or False? To find perimeter of a rectangle, add the length and the width. False. To find the perimeter of a rectangle, double the sum of the length and the width. Ask: True or False? If we combine two rectangles, the area of the combined rectangle is equal to the sum of the areas of the two smaller rectangles. True, the area of two combined rectangles is equal to the sum of the areas of the individual rectangles.

7 7 Ask: True or False? If we combine two rectangles, the perimeter of the combined rectangle is equal to the sum of the perimeters of the two smaller rectangles. False. When we combine two rectangles, the outside edges of the combined rectangle do not include all the edges of the original two rectangles. Two of the edges of the smaller rectangles do not appear in the larger rectangle because they are in the middle of the larger rectangle and therefore are not counted when calculating the perimeter. Display the following two polygons: Ask: How do the perimeters of these two polygons compare? How do their areas compare? How do you know? The perimeters of the two polygons are the same. Perimeter is the distance around a shape. Here, we could move the horizontal lines on the staircase up so that they are aligned with the top stair. Likewise, we could move the vertical parts of the stairs left so that they aligned with the vertical part of the bottom stair. Moving the parts does not alter their length, so the perimeter remains unchanged. Once we move the parts, we can see that the figure on the right looks identical to the figure on the left, so their perimeters must be equal. The area of the square is larger than the area of the staircase. If we move the entire staircase to its left until it overlaps with the square, we can see that the staircase fits inside the square and therefore takes up less space.

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