Mathematics Success Level C

Transcription

1 T761 [OBJECTIVE] The student will compare and contrast rectangles with the same perimeter and different areas, and same area with different perimeters. [PREREQUISITE SKILLS] finding perimeter and area of rectangles, multiplying one-digit and two-digit numbers [MATERIALS] Student pages S253 S265 Transparencies T773, T775, T777, T780, T782, T784, and T787 Centimeter cubes (40 per student pair) [ESSENTIAL QUESTIONS] 1. What conclusion can you draw about the area of rectangles with the same perimeter? 2. What conclusion can you draw about the perimeter of rectangles with the same area? 3. What is the largest perimeter rectangle you can create if the area is 50 cm 2? [WORDS FOR WORD WALL] area, perimeter, dimensions [GROUPING] Cooperative Pairs (CP), Whole Group (WG), Individual (I) *For Cooperative Pairs (CP) activities, assign the roles of Partner A and Partner B to students. This allows each student to be responsible for designated tasks within the lesson. [LEVELS OF TEACHER SUPPORT] Modeling (M), Guided Practice (GP), Independent Practice (IP) [MULTIPLE REPRESENTATIONS] SOLVE, Algebraic Formula, Verbal Description, Graphic Organizer, Pictorial Representation, Concrete Representation

2 T762 Mathematics Success Level C [WARM-UP] (5 minutes IP, WG, I) S253 (Answers are on T772.) Have students turn to S253 in their books to begin the Warm-Up. Students will answer questions based on area and perimeter. Monitor students to see if any of them need help during the Warm-Up. Give students 3 minutes to complete the problems and then spend 2 minutes reviewing the answers as a class. {Pictorial Representation, Algebraic Formula, Verbal Description} [HOMEWORK] (5 minutes) Take time to go over the homework from the previous night. [LESSON] (60 minutes M, GP, IP, CP, WG) SOLVE Problem (3 minutes WG, GP) T773, S254 (Answers on T774.) Have students turn to S254 in their books, and place T773 on the overhead. The first problem is a SOLVE problem. You are only going to complete the S step with students at this point. Tell students that during the lesson they will learn about the relationship between perimeter and area. They will use this knowledge to complete this SOLVE problem at the end of the lesson. {SOLVE, Graphic Organizer} Comparing Areas when Perimeter Stays the Same (15 minutes M, GP, WG, CP, IP) T773, T775, S254, S255 (Answers on T774, T776.) 9 minutes M, GP, WG, CP: Have students turn to S254 in their books, and place T773 on the overhead. Pass out centimeter cubes to student pairs. Have students work in cooperative pairs, and designate Partner A and Partner B. {Concrete Representation, Pictorial Representation, Algebraic Formula, Graphic Organizer, Verbal Description}

3 T763 MODELING Comparing Areas when Perimeter Stays the Same Step 1: Direct students attention to the word problem on the bottom half of S254 (T773). Read the problem together. Partner A, identify a math term that we use when talking about a length of fence. (perimeter) Partner B, explain how to find the area of a rectangle. (Multiply the length and width of the rectangle.) Step 2: Explain to students that they will be using the concepts of perimeter and area to create rectangles that will represent the puppy pens. They will use centimeter cubes to build the puppy pens and each cm will represent one foot in real life. Step 3: Look at the chart together and identify each column. Partner A, what information is given in the chart? (perimeter) Partner B, compare the perimeter in every row of the chart. (24 cm) Have partners discuss possible explanations for the consistent measurement of 24 cm. (There are 24 feet of fence, so every rectangle we make has to have a perimeter of 24.) Step 4: Model for the students how to find the dimensions of the first rectangle. Partner A, identify the smallest possible width for the rectangle. (1 cube or 1 cm) Partner B, place a 1 cm cube on the graph paper on S255 and determine the perimeter. (4 cm) Partner A, add a second cube next to the first cube and determine the perimeter with 2 cubes. (6 cm) Partner B, add a third cube and determine the perimeter with 3 cubes. (8 cm) Continue modeling and have partners place additional cubes in the row and count the perimeter until there is a perimeter of 24 cm. How many cm cubes are in the row? (11)

4 T764 Mathematics Success Level C Step 5: Write 11 and 1 for the length and width on the graphic organizer as students record their findings. Model for students how to trace the cubes on the graph paper on T775 (S255), and write the dimensions 11 and 1 along the length and width. Step 6: Have partners discuss how they can use the cm cubes to determine the area. (by counting the number of squares that contained a cm cube on the traced drawing or using the formula A = l w) Record in the Area column of the graphic organizer. [11(1) = 11 cm 2 ] Step 7: Ask students to help you find the dimensions for the next rectangle using their cubes. Partner A, identify the next bigger width for the rectangle. (2 cubes or 2 cm) Partner B, place 2 cm cubes in one column on the graph paper on S255 and determine the perimeter. (6 cm) Partner A, add a second group of 2 cubes next to the first group and determine the perimeter with 4 cubes. (8 cm) Partner B, add a third group of 2 cubes and determine the perimeter with 6 cubes. (10 cm) Continue modeling and have partners place additional cubes in the row and count the perimeter until there is a perimeter of 24 cm. How many cm cubes are in the rows? (20) Step 8: Write 10 and 2 for the length and width on the graphic organizer as students record their findings. Model for students how to trace the cubes on the graph paper on T775 (S255), and write the dimensions 10 and 2 along the length and width. Step 9: Have partners discuss how they can use the cm cubes to determine the area. (by counting the number of squares that contained a cm cube on the traced drawing or using the formula A = l w) Record in the Area column of the graphic organizer. (10 2 = 20 cm 2 )

5 T765 4 minutes IP, CP: Have students use the cm cubes and graph paper to construct the remaining rectangles for the chart on S254. Students should fill in the information for the length, width, and area of each rectangle. {Pictorial Representation, Algebraic Formula, Graphic Organizer, Verbal Description} 2 minutes WG: Go over the rectangles dimensions and areas on S254 to complete the chart. {Pictorial Representation, Algebraic Formula, Graphic Organizer, Verbal Description} More Comparing Areas when Perimeter Stays the Same (13 minutes M, GP, WG, CP, IP) T773, T775, T777, S254, S255, S256, S257 (Answers on T774, T776, T778, T779.) 3 minutes M, GP, WG, CP: Have students refer to the questions below the graphic organizer on S254, and place T773 on the overhead. {Concrete Representation, Pictorial Representation, Algebraic Formula, Graphic Organizer, Verbal Description} MODELING More Comparing Areas when Perimeter Stays the Same Step 1: Use the graphic organizer on S254 to answer the following questions. Partner A, examine the length and width of each rectangle. Identify the sum of the length and width in each row. (12 cm) Partner B, what can you conclude about the sum of the length and width? (The sum of the length and width is half of the perimeter.) Record. Partner A, identify the dimensions that give the puppy pen the smallest area? (11 cm by 1 cm) Record. Partner B, identify the dimensions that give the puppy the largest area? (6 cm by 6 cm) Record. Look at the areas in the chart. Discuss with your partner and conclude what happens to the area as the dimensions of the rectangle get closer to a square. (The area gets larger.) Record.

6 T766 Mathematics Success Level C 8 minutes IP, CP: Have students turn to S256 and apply what they have just learned to solve the area/perimeter problem. Tell students that Partner A should use the graph paper to show the first rectangle, and explain it. Then Partner B should use the graph paper to show the second rectangle and explain it continuing to take turns until student pairs have formed all of the rectangles. Partners should then answer Questions 1 5 below the graphic organizer. {Pictorial Representation, Algebraic Formula, Graphic Organizer, Verbal Description} 2 minutes WG: Go over the rectangles and questions on S256 and S257 using the answers on T778 and T779. Be sure to ask the students how they determined the dimensions on the rectangles and the answers to the questions. {Pictorial Representation, Algebraic Formula, Graphic Organizer, Verbal Description} Comparing Perimeters When Area Stays the Same (10 minutes M, GP, WG, CP, IP) T780, T782, S258, S259 (Answers on T781, T783.) 7 minutes M, GP, WG, CP: Have students turn to S258 in their books, and place T780 on the overhead. Students will be using centimeter cubes again. Have students work in cooperative pairs, and designate Partner A and Partner B. {Concrete Representation, Pictorial Representation, Algebraic Formula, Graphic Organizer, Verbal Description}

7 T767 MODELING Comparing Perimeters When Area Stays the Same Step 1: Direct students attention to the word problem and read the problem together. Partner A, identify a math term that we use when talking about the number of squares to cover the dance floor. (area) Partner B, explain how to find the perimeter of a rectangle. (Add the length and width of the rectangle and multiply by two.) Step 2: Explain to students that they will be using the concepts of perimeter and area to create rectangles that will represent the dance floor. They will use centimeter cubes to build the dance floor. Each cm cube will represent one square foot in real life. Step 3: Look at the chart together and identify each column. Partner A, what information is given in the chart? (area) Partner B, compare the area in every row of the chart. (It is 20 cm 2.) Have partners discuss possible explanations for the consistent measurement of 20 cm 2. (There are 20 squares to make the dance floor, and we know that each square is represented using a cm cube with a side measure of 1 cm for a total of 20 cm 2.) Step 4: Model for the students how to find the dimensions of the first rectangle. Partner A, identify the smallest possible width for the rectangle. (1 cube or 1 cm) Partner B, place a 1 cm cube on the graph paper on S259 and continue adding cubes until the rectangle has an area of 20 cubes. Determine the length if the width is 1 cm. (20 cm because A = lw) Step 5: Write 20 and 1 for the length and width on the graphic organizer as students record their findings. Model for students how to trace the cubes on the graph paper on T782 (S259), and write the dimensions 20 and 1 along the length and width.

8 T768 Mathematics Success Level C Step 6: Have partners discuss how they can use the cm cubes to determine the perimeter. [By counting the distance around the rectangle that contained the cm cubes on the traced drawing or using the formula, P = 2(l + w).] Record in the Perimeter column of the graphic organizer. [2(20 + 1) = 2(21) = 42 cm] Step 7: Ask students to help you find the dimensions for the next rectangle using their cubes. Partner A, identify the next biggest width for the rectangle. (2 cubes or 2 cm) Partner B, place 2 cm cubes in one column on the graph paper on S259 and determine the area. (2 cm 2 ) Partner A, add a second group of 2 cubes next to the first group and determine the area with 4 cubes. (4 cm 2 ) Partner B, add a third group of 2 cubes and determine the area with 6 cubes. (6 cm 2 ) Continue modeling and have partners place additional cubes in the row until there is a total area of 20 cm 2. Determine the length if the width is 2. (10 cm) Step 8: Write 10 and 2 for the length and width on the graphic organizer as students record their findings. Model for students how to trace the cubes on the graph paper on T782 (S259), and write the dimensions 10 and 2 along the length and width. Step 9: Have partners discuss how they can use the cm cubes to determine the perimeter. [by counting the distance around the rectangle that contained the cm cubes on the traced drawing or using the formula, P = 2(l + w)] Record in the Perimeter column of the graphic organizer. [2(10 + 2) = 2(12) = 24 cm]

9 T769 2 minutes IP, CP: Have students use the cm cubes and graph paper to construct the remaining rectangle for the chart on S259. Students should fill in the information for the length, width, and perimeter of the rectangle. {Pictorial Representation, Algebraic Formula, Graphic Organizer, Verbal Description, Concrete Representation} 1 minute WG: Go over the rectangles dimensions and perimeters on S259 to complete the chart. {Pictorial Representation, Algebraic Formula, Graphic Organizer, Verbal Description, Concrete Representation} More Comparing Perimeter when Area Stays the Same (12 minutes M, GP, WG, CP, IP) T780, T782, T784, S258, S259, S260, S261 (Answers on T781, T783, T785, T786.) 3 minutes M, GP, WG, CP: Have students refer to the questions below the graphic organizer on S258, and place T780 on the overhead. Have students work in cooperative pairs, and designate Partner A and Partner B. {Concrete Representation, Pictorial Representation, Algebraic Formula, Graphic Organizer, Verbal Description} MODELING More Comparing Areas when Perimeter Stays the Same Step 1: Use the graphic organizer on S258 to answer the following questions. Partner A, examine the length and width of each rectangle. Identify the dimensions that give the smallest perimeter. (5 cm by 4 cm) Record. Partner B, examine the length and width of each rectangle. Identify the dimensions that give the largest perimeter. (20 cm by 1 cm) Record. Partner A, explain what happens to the perimeter as the dimensions of the rectangle get closer to a square. (The perimeter gets smaller.) Record. Look at the areas in the chart. Discuss with your partner and conclude why this happens. (The longer the row of cubes the larger the perimeter.) Record.

10 T770 Mathematics Success Level C 7 minutes IP, CP: Have students turn to S260 and apply what they have just learned to solve the area/perimeter problem. Tell students that Partner A should use the graph paper to show the first rectangle and explain it. Then Partner B should use the graph paper to show the second rectangle and explain it continuing to take turns until they have used all of the rectangles. Partners should then answer the questions below the graphic organizer on S260. {Pictorial Representation, Concrete Representation, Algebraic Formula, Graphic Organizer, Verbal Description} 2 minutes WG: Go over the rectangles and questions on S260 and S261. The answers are on T785 and T786. Be sure to ask students how they arrived at their rectangles and the answers to the questions. {Pictorial Representation, Concrete Representation, Algebraic Formula, Graphic Organizer, Verbal Description}

11 T771 SOLVE Problem (5 minutes GP, WG) T787, S262 (Answers on T788.) Remind students that the SOLVE problem is the same one from the beginning of the lesson. Complete the SOLVE problem with your students. Ask them for possible connections from the SOLVE problem to the lesson. (They have to be able to answer questions about the relationship between perimeter and area.) {SOLVE, Graphic Organizer, Verbal Description} If time permits (10 minutes IP, CP) S263 (Answers on T789.) Have students complete the perimeter and area problem on S263. [CLOSURE] (2 minutes) To wrap up the lesson, go back to the essential questions and discuss them with students. What conclusion can you draw about the area of rectangles with the same perimeter? (The closer the rectangle is to a square, the larger the area.) What conclusion can you draw about the perimeter of rectangles with the same area? (The closer the rectangle is to a square, the smaller the perimeter.) What is the largest perimeter rectangle you can create if the area is 50 cm 2? (102 centimeters a 1 by 50 rectangle.) [HOMEWORK] Assign S264 and S265 for homework. (Answers on T790 and T791.) [QUIZ ANSWERS] T792 T794 The quiz can be used at anytime as extra homework or to assess how students progress on comparing perimeter and area in rectangles.