Riverside USD Scope and Sequence: 3.M D.5 a [3.9], 3.M D.5 b

Transcription

1 1 U n t er r ich t splan Introduction to Perimeter Altersgruppe: Grade 4, Grade 3 Texas - TEKS: G3.7.GM.B, G4.5.AR.C, G4.5.AR.D, G5.4.AR.H Riverside USD Scope and Sequence: 3.M D.5 a [3.9], 3.M D.5 b [3.9] Oklahoma Academic Standards Mathematics: 3.GM.2.8 Virginia - Mathematics Standards of Learning (2009): 3.10a, 3.9d, 5.8a Common Core: 3.M D.C.5 a, 3.M D.C.5 b Mathematics Florida Standards (MAFS): 3.M D.3.5 a, 3.M D.3.5 b Alaska: 3.M D.10, 3.M D.D, 4.M D.3 Minnesota: , , , Fairfax County Public Schools Program of Studies: 3.10.a.1, 3.9.d.1, 3.9.d.2, 5.8.a.1 Nebraska Mathematics Standards: M A f South Carolina: 3.M DA.6, 4.M DA.3 Indiana: 3.M.5, 3.M.7, 4.M.4, 5.M.3 Georgia Standards of Excellence: M GSE 3.M D.5 a, M GSE 3.M D.5 b Virginia - Mathematics Standards of Learning (2016): 3.8.a Online-Ressourcen: B ac k t o Sq uare One Opening Teacher present s Students pract ice Math Pract ice Worksheet Closing M at h Obj ect ives

2 2 E xpe ri e nc e building polygons P rac t i c e calculating perimeter and area Learn that area does not detere perimeter De vel o p geometry skills

3 3 Ope ni ng 6 Display the following polygons. What is the same in all of the polygons? They all contain six small squares. Yes, these shapes all take up the same amount of space. Mathematically, we say that they all have the same area. If each small square is considered to be one square unit, then the area of each of these polygons is six square units. Display the following polygons. These polygons have different areas. However, they do share a common trait. What is it? What is the same for all of these rectangles? Answers may vary, but students should be encouraged to recognize that the outside edges of the rectangles are the same length, 16. Yes, the distance around each of these rectangles is the same. Mathematically, we say that they all have the same pe ri me t e r. The perimeter for each of them is 16 units.

4 4 T e ac he r prese nt s M at h game : B ac k t o Sq uare One - Co mpo se Shape s: P e ri me t e r 10 Present Matific s episode B ac k t o Sq uare One - Co mpo se Shape s: P e ri me t e r to the class, using the projector. The goal of the episode is to explore perimeter by building polygons to certain specifications. Example : Please read the instruction at the bottom of the screen. Students can read the instruction. So we are looking for perimeter. What is perimeter? Perimeter is the distance around the edge of a shape. Drag one square up. If each side of this square is one unit, what is the perimeter of the square? The perimeter is four units. Drag another square up and attach it to the first square. What is the perimeter of this rectangle that is made up of two squares? The perimeter is six units.

5 5 Since we are using two squares, why is the perimeter not eight, twice the perimeter of one square? Perimeter measures the outside edges of a shape. When two squares are attached, two edges are now on the inside of the rectangle. Those edges are not counted when finding perimeter. Drag two more squares up and attach them to the first two in a row so that they form a 1 by 4 rectangle. What is the perimeter of this rectangle? The perimeter is 10 units. Now move two of the squares to change the rectangle into a 2 by 2 square. What is the perimeter of this square? The perimeter is eight units. When we consider area, the shape of the polygon is unimportant. Four little squares have an area of four, regardless of the placement of the squares. But when we consider perimeter, the placement of the squares matters. Drag all four squares to the trash can. Return the students attention to the instruction at the bottom of the screen. How many squares do I need and how should I place them in order to obtain the perimeter that we want? Drag and move the squares as the students indicate. Then click. If the answer is correct, the episode will proceed to the next situation. If the answer is incorrect, the number will enlarge, and the instructions will wiggle. The episode will present a total of six questions.

6 6 St ude nt s prac t i c e M at h game : B ac k t o Sq uare One - Co mpo se Shape s: P e ri me t e r 12 Have the students play B ac k t o Sq uare One - Co mpo se Shape s: P e ri me t e r on their personal devices. Circulate, answering questions as necessary. M at h P rac t i c e : I nt ro duc t i o n t o P e ri me t e r Wo rkshe e t 15 Have the students work in groups of four. Distribute graph paper to each group. Ask the students to complete the following assignment. 1. Draw all rectangles with area 20 square units. (Do not repeat rectangles. This rectangle is the same as this rectangle.) 2. Find the perimeters of each of the rectangles you drew for #1. 3. Draw all rectangles with perimeter 12 units. 4. Find the area of each of the rectangles you drew for #3. When the students have completed the assignment, discuss. How many rectangles can you draw with an area of 20 square units? What are the lengths of the sides? There are three possible rectangles: 1 unit by 20 units, 2 units by 10 units, and 4 units by 5 units. How do we know we have found all the rectangles with area 20? We have used all the pairs of numbers that multiply to 20.

7 7 What are the perimeters of the rectangles you drew? The perimeters are 42, 24, and 18 units. How many rectangles can you draw with a perimeter of 12 units? What are the lengths of the sides? There are three possible rectangles: 1 unit by 5 units, 2 units by 4 units, and 3 units by 3 units. How do we know we have found all the rectangles with perimeter 12? We have found all the pairs of numbers that add to six. (We need the numbers that add to six, not 12, because in finding perimeter, we add the width and the length twice. P = 2(l + w). So the sum of the length and the width must equal half the perimeter.) What are the areas of the rectangles you drew? The areas are 5, 8, and 9 square units. If we know the area of a rectangle, do we know its perimeter? If we know its perimeter, do we know its area? No. A rectangle s area does not detere its perimeter. Likewise, its perimeter does not detere its area. Cl o si ng 4 Display the following rectangle. What is the area of this rectangle? Its area is 12 square units. Can we draw a different rectangle that still has area 12 square

8 8 units? What would the lengths of its sides be? Yes, there are two possible rectangles: 1 unit by 12 units and 2 units by 6 units. How many little squares do we need to make those two other rectangles? We still need 12 little squares for each of them. What is the perimeter of this rectangle? Its perimeter is 14 units. Can we draw a different rectangle that still has perimeter 14 units? What would the lengths of its sides be? Yes, there are two possible rectangles: 1 unit by 6 units and 2 units by 5 units. Do we still need 12 little squares to form those two rectangles? No. A rectangle that is 1 unit by 6 units requires six little squares. A rectangle that is 2 units by 5 units requires 10 little squares. True or False? When we keep the area the same but change the shape, the number of little squares changes. False. The area is the total number of little squares. If we keep the area the same, then we keep the number of little squares the same. True or False? When we keep the perimeter the same but change the shape, the number of little squares may change. True. If we keep the perimeter but change the shape, the area may change. Thus, the number of little squares may change

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