Lesson Plan Garden Grade 6 Area and Perimeter

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1 CCSSM: Grade 6 Domain: Expressions and Equations Cluster: Reason about and solve one-variable equations and inequalities. Standard: 6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q, and x are all nonnegative rational numbers. CCSSM: Grade 4 DOMAIN: Measurement and Data Cluster: Solve problems involving measurement and conversion of measurements for a larger unit to a smaller unit. Standard: 4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical problems. Clarification: The clarification is an explanation of the indicator and objective and how these math concepts appear in the puzzle. Materials and/or Set Up: Welcome to Farmer Joe s Farm; Farmer Joe s Rabbit Pen; Finding Area and Perimeter; Finding Area and Perimeter Answers; Interactive Resource 1; Work Order for Interactive Resource 1; Interactive Resource 2; Work Order for Interactive Resource 2; Interactive Resource 2 Answers; Square blocks; Interactive Resource 3 Levels 1, 2, and 3; Work Orders for Interactive Resource 3 Levels 1, 2, and 3 Interactive Resource 3 Levels 1, 2, 3 Answers Relevant Vocabulary: area, dimension, formula, length, perimeter, width Note to Teacher Students should have attempted levels 1, 2 and 3 of the Garden puzzle before this lesson is implemented. In the implementation of this lesson, it is recommended that the Interactive Resources be projected to encourage a rich and active discussion of math strategies and concepts. Activities: 1. After students have played levels 1, 2, and 3 of the Garden puzzle, ask them to share their experiences and insights into the relationships between area and perimeter. 2. Pair students and have them work with a partner to complete #1 on Welcome to Farmer Joe s Farm. Ask students to share their findings. Record the results. (1 by 8; 2 by 7; 3 by 6; 4 by 5) 3. Have students recognize that there are 4 possible rectangles that can be formed using 18 pieces of fence. Ask students: What is the distance around each of the possible Copyright 2012 Maryland Public Television Page 1 of 24

2 rectangles? (18 meters) What is the term used to name the distance around a rectangle? (perimeter) 4. Using Farmer Joe s Rabbit Pen, work as a class to complete #2 (14 rabbits). Discuss with students how they determined their answer. (The number of square meters would be 14. Multiply length by width or draw a picture and count the number of squares). 5. Explain to students that the area of a rectangle is the number of square units that cover the rectangle. Ask students: What would the area of a 3 meter by 6 meter rectangle be? (18 m 2 ) What about a 4 meter by 5 meter pen? (20 m 2 ) Of the four rectangles with a perimeter of 18, which rectangle has the largest area? (The 4 meter by 5 meter rectangle) 6. Have students work with their partner to complete #3 on Welcome to Farmer Joe s Farm. (14 meters of fencing; 3 meters by 4 meters) 7. Ask the students to define perimeter to a partner. Ask students: How is the perimeter of a rectangle determined? Discuss the various forms of the perimeter formula as a class. [P = l + w + l + w or P = 2l + 2w or P = 2(l + w)]. Ask the students: How could you find the area of a rectangle, given the length and width of the rectangle? (The area is the number of squares that cover a region. Area can be found by counting the squares in the rectangle or by multiplying the length and the width.) Discuss the area formula, A = lw. 8. Using Finding Area and Perimeter, complete Section A as a class. Have students complete Section B with a partner and Section C independently. 9. Display Interactive Resource 1 and distribute Work Order for Interactive Resource 1. Ask the students to locate the work order for Blotchweed. (Number of Blotchweed plants is 16; fencing units is 20.) Facilitate a class discussion to determine the dimensions of the rectangular plot for the Blotchweed (2 units by 8 units.) Discuss ways in which the dimensions could be determined. (Square tiles could be used to represent the garden plots. A list could be generated of all possible dimensions for the perimeter and then checked to determine which dimensions also work for the area. A list could be generated of all possible dimensions for the area and then checked to determine which dimensions also work for the perimeter. The perimeter could be divided by two to determine the sum of the length and width. Factors of this sum could be found that yield the area.) 10. Ask the students to find the dimensions of the Prickletoe plot. (Work order says 28 plants and 22 fence lengths; dimension of the plot is 7 units by 4 units). Discuss the various places that this plot could go without encompassing any garden trolls. (This plot could be placed vertically in the middle of the screen at the top of the garden to the right of the group of 8 garden trolls, or horizontally in the middle left of the screen under the group of 8 garden trolls.)ask students: What would happen if a garden troll is enclosed in the garden? (On level 1, each garden troll takes the place of one plant and when enclosed will eat part of the crops) 11. Facilitate a discussion to guide students to complete the remaining work orders. Name of Plant Number of Plants Number of Fence Lengths Dimensions of Garden Plot Blotchweed x 8 Prickletoe x 7 Slugroot x 6 Fungwort x 2 Copyright 2012 Maryland Public Television Page 2 of 24

3 Purple Night x Display Interactive Resource 2A and distribute Work Order for 2B. Have students work with a partner to follow the work order to determine the dimensions and placement of each plot. Display Interactive Resource 2B Answers and discuss. Ask students how this work plan differs from the last one. (This puzzle is a level 2 puzzle which means the placement of each plot is more challenging than in level 1. The garden trolls still eat the plants if they are enclosed in a plot.) Name of Plant Number of Plants Number of Fence Lengths Dimensions of Garden Plot Blotchweed x 8 Prickletoe x 7 Slugroot x 4 Fungwort x 4 Purple Night x 7 Differentiation Suggestions: 1. For students who need additional assistance with the concepts: Give students a set of 12 square blocks. Instruct them to look at one block. Ask students: What is the perimeter (4) and what is the area (1)? Pose a series of questions, changing the dimensions and size of the figure by adding to the number of blocks you use. Ask students what perimeter and area of each figure is. Discuss patterns. Ask students: What is the shape that you can make that has the largest area for 12 blocks? (Dimensions of 3 x 4). What is the perimeter of this shape? (14) Ask students to each make a different-shaped figure that uses all 12 blocks. Ask them to determine the perimeter and area of each figure. As an alternative, use graph paper, with shading figures or geo boards. 2. Display Interactive Resource 3A (Level 1, Level 2 or Level 3) and distribute Work Order for 3B (Level 1, Level 2, or Level 3.) Have the students work in pairs or individually to find the dimensions of each of the five plots and determine the appropriate placement for each plot. Use level 1 for students who may need more assistance or time; level 2 for students who are more comfortable with the material, and level 3 for students who are ready for a challenge. Encourage the students to show their work. Have students share their answers and display Interactive Resource 3B Answers for Levels 1, 2, and/or 3 so that students can see garden configurations. (Answers: Level 1, Dimensions of Garden Plot: Blotchweed, 6 x7; Prickletoe, 2 x 3; Slugroot, 2 x 4; Fungwort, 1 x 12; Purple Night, 2 x 2 Level 2, Dimensions of Garden Plot: Blotchweed, 3 x 4; Prickletoe, 2 x 10; Slugroot, 2 x 3; Fungwort 4 x 4; Purple Night, 5 x 6 Level 3, Dimensions of Garden Plot: Blotchweed, 3 x 8 with 2 gnomes enclosed; Prickletoe, 2 x 7; Slugroot, 4 x 4 with 3 gnomes enclosed; Fungwort, 2 x 3; Purple Night, 1 x 4 with 2 gnomes enclosed) Copyright 2012 Maryland Public Television Page 3 of 24

4 Assessment Follow Up: Distribute Assessment resource sheet. Answers: units Have the students return to the puzzle to apply what they learned in the lesson. Ask: Did the lesson help you to clarify the math in the puzzle? How? What other strategies could you have used to help you solve the puzzle? Additionally, check teacher stats in the game to determine students level of understanding. Provide the students with this scenario: The perimeter of a vegetable garden is 24 units and the length is twice the width. What are the dimensions of this garden? What is the area? Use what you know about area to explain how you determined the dimensions and the area. Use words, numbers, and/or symbols in your explanation. (Since the length is twice the width, let the width be represented as w and the length 2 x w, or 2w. In order to find the perimeter, add all of the sides which would be: w + 2w + w + 2w = perimeter 6w = 24 6w w = 4 and l = 8 or Real World Connection: Given that the perimeter was 24 units, make a list of all possible dimensions of a rectangle with this perimeter. (1 x 11; 2 x 10; 3 x 9; 4 x 8; 5 x 7; 6 x 6) After making the list, examine the relationship between the length and the width. (Only the 4 x 8 rectangle has a length that is twice its width.) Provide students with this scenario: Ms. Buckley buys a rug for her rectangular classroom. The rug covers the entire room perfectly! The area of the rug is 140 square feet. If the width of the classroom is 10 feet, what is the perimeter of the classroom? (48 feet) Copyright 2012 Maryland Public Television Page 4 of 24

5 Welcome to Farmer Joe s Farm Lesson Plan 1. Farmer Joe is planning to build a rabbit pen. He has 18 sections of fence, each 1 meter long. What are the various sizes of rectangular pens that Farmer Joe can make using all 18 units of fence? Show your work here: 2. One rabbit needs 1 square meter of space to live comfortably. For example, if Farmer Joe decided to build a pen that is 1 meter wide by 8 meters long, the pen would enclose eight square meters and eight rabbits could live in it. How many rabbits would be able to fit into a pen that is 2 meters by 7 meters? Use numbers, symbols and/or words to explain how you determined the answer. Show your work here: 3. Farmer Joe s brother, Farmer Frank, would like to make a rectangular pen for his 12 rabbits. He would like to buy the fewest meters of fencing and build a pen that can comfortably house his rabbits. Remember, each rabbit needs 1 square meter of space. How many meters of fencing should he buy? What are the dimensions of the pen he should make? Show your work here: Copyright 2012 Maryland Public Television Page 5 of 24

6 Farmer Joe s Rabbit Pen 1 meter 8 meters Each rabbit needs one square meter of space inside the pen! Copyright 2012 Maryland Public Television Page 6 of 24

7 Finding Area and Perimeter Lesson Plan Directions: Find Area and Perimeter, as indicated, in each figure below. Section A 1. Find the Perimeter of the rectangle below. Area = 36 in 2 Length = 9 inches Width =? Perimeter = 2. Find the Area of the square below. Side = 4 cm Area = Section B 3. Find the Perimeter of the square below, given that the Area = 25 m 2. Area = 25 m 2 Perimeter = 4. Find the Area of the rectangle below, given that the perimeter is 30 cm. width = 4 cm Area = length =? Section C 5. Find the Perimeter of the rectangle below. Area = 15 in 2 Perimeter = Length = 5 in 6. Find the Area of the square below, given that the perimeter is 40 feet. Area = Copyright 2012 Maryland Public Television Page 7 of 24

8 Finding Area and Perimeter Answers Lesson Plan Directions: Find Area and Perimeter, as indicated, in each figure below. Section A 1. Find the Perimeter of the rectangle below. Area = 36 in 2 Length = 9 inches Width =? Perimeter = 26 inches 7. Find the Area of the square below. Side = 4 cm Area = 16 cm 2 Section B 8. Find the Perimeter of the square below, given that the Area = 25 m 2. Area = 25 m 2 Perimeter = 20 m 9. Find the Area of the rectangle below, given that the perimeter is 30 cm. width = 4 cm Area = 44 cm 2 length =? Section C 10. Find the Perimeter of the rectangle below. Area = 15 in 2 Perimeter = 16 inches Length = 5 in 11. Find the Area of the square below, given that the perimeter is 40 feet. Area = 100 ft. 2 Copyright 2012 Maryland Public Television Page 8 of 24

9 Copyright 2012 Maryland Public Television Page 9 of 24

10 Work Order for Interactive Resource 1 Name of Plant Blotchweed Prickletoe Slugroot Fungwort Purple Night Number of Plants Number of Fence Lengths Dimensions of Garden Plot Copyright 2012 Maryland Public Television Page 10 of 24

11 Copyright 2012 Maryland Public Television Page 11 of 24

12 Work Order for Interactive Resource 2 Lesson Plan Name of Plant Number of Plants Number of Fence Lengths Blotchweed Dimensions of Garden Plot Prickletoe Slugroot Fungwort 8 12 Purple Night Copyright 2012 Maryland Public Television Page 12 of 24

13 Interactive Resource 2 - Answers Copyright 2012 Maryland Public Television Page 13 of 24

14 Copyright 2012 Maryland Public Television Page 14 of 24

15 Work Order for Interactive Resource 3 Level 1 Name of Plant Number of Plants Number of Fence Lengths Blotchweed Dimensions of Garden Plot Prickletoe 6 10 Slugroot 8 12 Fungwort Purple Night 4 8 Copyright 2012 Maryland Public Television Page 15 of 24

16 Interactive Resource 3 Level 1 Answers (Other possible configurations exist, but the dimensions of each plot should be the same as below) Copyright 2012 Maryland Public Television Page 16 of 24

17 Copyright 2012 Maryland Public Television Page 17 of 24

18 Work Order for Interactive Resource 3 Level 2 Name of Plant Number of Plants Number of Fence Lengths Blotchweed Dimensions of Garden Plot Prickletoe Slugroot 6 10 Fungwort Purple Night Copyright 2012 Maryland Public Television Page 18 of 24

19 Interactive Resource 3 Level 2-Possible Answers (Different configurations can exist but the dimensions should remain the same) Copyright 2012 Maryland Public Television Page 19 of 24

20 Interactive Resource 3 Level 2-Possible Answers (Different configurations can exist but the dimensions should remain the same) Copyright 2012 Maryland Public Television Page 20 of 24

21 Copyright 2012 Maryland Public Television Page 21 of 24

22 Work Order for Interactive Resource 3 Level 3 Name of Plant Number of Plants Number of Fence Lengths Blotchweed Dimensions of Garden Plot Prickletoe Slugroot Fungwort 6 10 Purple Night 2 10 Copyright 2012 Maryland Public Television Page 22 of 24

23 Interactive Resource 3 Level 3 - Possible Answers Copyright 2012 Maryland Public Television Page 23 of 24

24 Assessment 1. The area of a rectangle is 30 square units. What is the largest possible perimeter of the rectangle? a. 62 units b. 34 units c. 26 units d. 22 units 2. The front door of a house is broken and needs to be replaced. The perimeter of the door is 26 feet. If the width of the door is 3 feet, what is the door s area in square feet? Copyright 2012 Maryland Public Television Page 24 of 24

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