AREA and PERIMETER. Integrated Math 1 Grade 9 / Minute Periods 10 Day Lesson. Geo Boards TI 83 Plus. I2T2 Project. Kaye Lynn Spencer Sue Draper

Transcription

1 AREA and PERIMETER Integrated Math 1 Grade 9 / Minute Periods 10 Day Lesson Geo Boards TI 83 Plus I2T2 Project Kaye Lynn Spencer Sue Draper 1

2 Overview Much of what the students will be covering in this unit has been taught to them previous. We will be using geo boards and the TI 83 Plus calculator in this unit to show more concrete evidence of what has been learned about perimeter and area. I will be combining pages of unit 6 in the Cognitive Tutor Integrated Math 1 book by the Carnegie Learning program with worksheets from Learning Resources Dot Paper Geometry with or without a geo board book by Charles Lund (2002, 1980). I will also be creating a project at the end of the unit for the students to complete. The students will be working as a class, in pairs, and individually. We will be using pp. 49, 50, and 51 for perimeter and pp. 31, for area. 2

3 Objectives: The students will recognize various geometric shapes by their definitions The students will be able to write the definition of each geometric shape The students will write the area formula of each geometric shape The students will write the perimeter formula of each geometric shape The students will understand the mathematical concepts of perimeter and area New York Standards: 5A Apply formulas to find measures such as length, areas, volume, weight, time, and angle in real world context 5F Apply proportions to scale drawings and direct variations 5I Use geometric relationships in relevant measurement problems involving geometric concepts NCTN Standards Geometry Analyze characteristics and properties of two- and threedimensional geometric shapes and develop mathematical arguments about geometric relationships Use visualization, spatial reasoning, and geometric modeling to solve problems Measurement Apply appropriate techniques, tools, and formulas to determine measurements 3

4 Problem Solving Apply and adapt a variety of appropriate strategies to solve problems Monitor and reflect on the process of mathematical problem solving Communication Communicate their mathematical thinking coherently and clearly to peers, teachers, and others Materials and Equipment: TI 83 Plus Application program for the calculator; Area formula Graph paper UCSMP Algebra Book Carnegie Learning Cognitive Tutor Integrated Math 1 book; unit 6 pages Geo boards, rubber bands Worksheets from Learning Resources book Dot Paper Geometry Transparencies of dot paper Overhead projector and markers 4

5 Day One Unit 6 Pages 8 12 Students will be able to determine perimeter of given picture Students will be able to make shapes on geo boards for specific perimeter given Students will come in and follow directions on the board to make a square on the geo board. Students will also write the Essential Question for the day and answer it for their Ticket out the Door. EQ. What is perimeter? I will define that perimeter is the distance around the outside of a figure. I will show what 1 length is on the overhead geo board. I will create 4 figures on the overhead and show them how to calculate the perimeter of the first one and then the whole class together will do the remaining 3. I will then give a specified number of units for perimeter and create a figure to show that perimeter. The whole class will do 2 more together. Dot paper worksheet on perimeter 5

6 Day Two Unit 6 Pages 8 12 Students will be able to understand the concept of area Students will be able to calculate area of a base figure (square) and form a figure (square) on the geo board with specified area given Students will use their geo board to create a square or rectangle. Students will also write the Essential Question for the day and answer it for the ticket out the door. EQ. What is area? I will define area is the number of square units contained in the interior of a figure. I will show what 1-sq. unit is on the overhead geo board. I will create a figure (square) and show how to determine the area. I will then show 2 more for the class to do together. I will then give a specified area and create a figure to that area. I will do one more with the entire class. Dot paper worksheet on area 6

7 Day Three Unit 6 Pages Students will better understand area of a rectangle and be able to apply information from Day 1 and Day 2. Students will complete 1a. on page 13. I will introduce the formula for perimeter and area of squares and rectangles. The students will be paired and complete pages in class. None 7

8 Day Four Unit 6 Pages Students will know how to find the height of a parallelogram Students will be able to calculate the area of a parallelogram given board Students will be given directions to create a parallelogram on the geo I will define altitude as the height of the parallelogram. I will then have the students determine the height of their parallelogram. Students will complete pages as a whole class with me. None 8

9 Day Five Unit 6 Pages triangles Students will be able to use the geo board and formulas to find areas of Students will come in and create a triangle on the geo board. They will give the altitude and what they think the estimated area is. I will use geo board to show students how to estimate area of triangles using chop strategy. Students will be paired and use the geo board to complete pager Pages (Carn. Book) 9

10 Day Six square The students will be able to recognize the definition of a rectangle, and a Materials: Notebook, TI 83 Plus, pencil or pen and graph paper Student will come in and start on the warm-up on the board. Correct each of the following statements: 1. The area of a rectangle is measured is cubic units. 2. The formula for finding the area of a square is A = l+ w. 3. There are 2 right angles in a rectangle. After discussing the warm-up with the class, the students will retrieve their IT 83 Plus calculators. The students will start the application program called areaform. They will then select a mode. We will start with number one: definition and formulas. They will then select the rectangle. The students will copy the picture and definition of a rectangle in their notebooks. They will then select area at the bottom of the screen. They will add this information to the definition. Now continuing with the example the students will use their graph paper and duplicate what is on their screen. They will do this for 4 examples. The students will now go back to the menu and select the next shape a square. They will continue as they did with the rectangle. 10

11 Closing Activity: The students will return their calculators to the bin and then turn to page 76 in their text. The students will now complete numbers 4 and 6. These answers will be entered in their notebooks. The student will do problems numbers 7, 16a, 17a, 18a,b,c and

12 Day Seven The students will be able to recognize the definition of a parallelogram, and a triangle Materials: Notebook, TI 83 Plus, pencil or pen and graph paper Student will come in and start on the warm-up on the board Using your notebook find the following: 1. Area = 7 km * 2 km 2. Area = 8 in. * 3 in. 3. What is the definition of a rectangle? 4. Define a square. After discussing the warm-up with the class, the students will retrieve their IT 83 Plus calculators. The students will start the application program called areaform. They will then select a mode. We will start with number one: definition and formulas. They will then select the parallelogram. The students will copy the picture and definition of a parallelogram in their notebooks. They will then select area at the bottom of the screen. They will add this information to the definition. Now continuing with the example the students will use their graph paper and duplicate what is on their screen. They will do this for 4 examples. The students will now go back to the menu and select the next shape, a triangle. They will continue as they did with the parallelogram 12

13 Closing Activity: The students will explain what the similarities and differences between a rectangle, square, parallelogram and triangle. These answers will be entered into their notebooks. The student will find something in their house that has the shape of a square, rectangle, parallelogram and a triangle. They will find the area of each figure and draw a scaled representation on graph paper. 13

14 Day Eight circle. The students will be able to recognize the definition of a trapezoid and a Materials: Notebook, TI 83 Plus, pencil or pen and graph paper Student will come in and start on the warm-up on the board Using your notebook find the following: 1. What is the definition of a parallelogram? 2. What is the area formula for a parallelogram? 3. What is the definition of a triangle? 4. What is the area formula for a triangle? After discussing the warm-up with the class, the students will retrieve their IT 83 Plus calculators. The students will start the application program called areaform. They will then select a mode. We will start with number one: definition and formulas. They will then select the trapezoid. The students will copy the picture and definition of a trapezoid in their notebooks. They will then select area at the bottom of the screen. They will add this information to the definition. Now continuing with the example the students will use their graph paper and duplicate what is on their screen. They will do this for 4 examples. The students will now go back to the menu and select the next shape, a circle. They will continue as they did with the trapezoid. 14

15 Closing Activity: The students will explain what the differences are between a trapezoid and a parallelogram. These answers will be entered into their notebooks. The student will find something in their house that has the shape of a trapezoid and a circle. They will find the area of each figure and draw a scaled representation on graph paper. If the are unable to find a trapezoid the will manufacture one on their own. 15

16 Day Nine shapes. The students will be able to solve area problems of various geometric Materials: Notebook, TI 83 Plus, pencil or pen and graph paper Student will come in and start on the warm-up on the board Using your notebook find the following: 1. How any sides are parallel in a trapezoid? 2. Draw a trapezoid with base 1 = 3 units and base 2 = 6 units. 3. What is the area formula for a trapezoid? 4. What is the definition of a circle? 5. What is the area formula of a circle? After discussing the warm-up with the class, the students will retrieve their IT 83 Plus calculators. The students will start the application program called areaform. They will then select a mode. We will start with number two; area quiz. They will select level one. The students will do 20 problems recording each problem in their notebook and calculating a response. They will keep tract of all correct and incorrect responses. 16

17 Closing Activity: The students will compile the problems into each geometric shape we have discussed. Then the students will count the number of wrong for each category. I will tally this information on the board so we can see where we have made the most errors. The student will correct the problems the got wrong during the lesson. 17

18 Day Ten shapes. The students will be able to solve area problems of various geometric Materials: Notebook, TI 83 Plus, pencil or pen and graph paper Student will come in and start on the warm-up on the board Using your notebook find the area of the following: 1. Parallelogram: h= 4ft. b= 12ft. 2. Circle: r= 7m. 3. Rectangle: l= 4ft. w= 3ft. 4. Square: s= 8km. 5. Triangle: b= 4cm. h= 3cm. 6. Trapezoid: b1= 4mm. h= 4mm b2= 10mm After discussing the warm-up with the class, the students will retrieve their IT 83 Plus calculators. The students will start the application program called areaform. They will then select a mode. We will start with number two; area quiz. They will select level two. I will reward the student with the fewest wrong an no homework pass. The students will do 20 problems recording each problem in their notebook and calculating a response. They will keep tract of all correct and incorrect responses. 18

19 Closing Activity: The students will compile the problems into each geometric shape combination we have discussed. Then the students will count the number of wrong for each category. I will tally this information on the board so we can see where we have made the most errors. The student with the fewest wrong will receive a no homework pass. The student will correct the problems the got wrong during the lesson. 19