# Grade 5 supplement. Set D1 Measurement: Area & Perimeter. Includes. Skills & Concepts

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1 Grade 5 supplement Set D1 Measurement: Area & Perimeter Includes Activity 1: Measuring Area D1.1 Activity 2: Measuring Perimeter D1.5 Activity 3: The Ladybugs Garden D1.9 Activity 4: Hexarights D1.15 Independent Worksheet 1: Area & Perimeter Review D1.23 Independent Worksheet 2: Measuring Rectangles D1.27 Skills & Concepts H determine area by finding the total number of same-sized units of area that cover a shape without gaps or overlaps H select appropriate units, strategies, and tools for solving problems that involve estimating or measuring perimeter and/or area H find the areas of complex shapes by dividing those figures into basic shapes (e.g., rectangles, squares) H understand that rectangles with the same area can have different perimeters and that rectangles with the same perimeter can have different areas H measure necessary attributes of shapes to use perimeter and area formulas to solve problems P0509

2 Bridges in Mathematics Grade 5 Supplement Set D1 Measurement: Area & Perimeter The Math Learning Center, PO Box 12929, Salem, Oregon Tel by The Math Learning Center All rights reserved. Prepared for publication on Macintosh Desktop Publishing system. Printed in the United States of America. P0509 The Math Learning Center grants permission to classroom teachers to reproduce blackline masters in appropriate quantities for their classroom use. Bridges in Mathematics is a standards-based K 5 curriculum that provides a unique blend of concept development and skills practice in the context of problem solving. It incorporates the Number Corner, a collection of daily skill-building activities for students. The Math Learning Center is a nonprofit organization serving the education community. Our mission is to inspire and enable individuals to discover and develop their mathematical confidence and ability. We offer innovative and standards-based professional development, curriculum, materials, and resources to support learning and teaching. To find out more, visit us at

3 Set D1 Measurement: Area & Perimeter Set D1 H Activity 1 Activity Measuring Area Overview Students review the term area and work together to generate a formula for determining the area of rectangles and squares. In the process, they have an opportunity to see and handle a square inch and a square foot. Then they apply the information as they work in pairs to find the area of various items around the classroom. Skills & Concepts H determine area by finding the total number of samesized units of area that cover a shape without gaps or overlaps H select appropriate units, strategies, and tools for solving problems that involve estimating or measuring perimeter and/or area You ll need H Measuring Area (page D1.4, run a class set) H one 12" 12" piece of red construction paper H 10" 18" blue construction paper (1 piece for every 4 students) H square inch tile (class set) H rulers (class set) H yardsticks and measuring tapes H masking tape H calculators (optional, class set) H Student Math Journals H Word Resource Cards (area, dimension) H measure necessary attributes of shapes to use perimeter and area formulas to solve problems Instructions for Measuring Area 1. Post the Word Resource Card for area on the board. Ask students to pair-share what they know about this term. After a minute or two, invite volunteers to share their ideas with the class. As the discussion unfolds, review the following concepts: area is a measure of how much surface something takes up. area is measured in square units such as square inches, square feet, or square miles. area 2. Hold up a single tile and ask students to report its area in square inches. If necessary, have a volunteer measure the dimensions of the tile and work with the class to establish the fact that it s exactly 1 square inch. Use a loop of masking tape to fasten the tile to the board. Work with class input to label its dimensions and area. 3. Distribute sets of tile. Ask students to work in groups of four to build a square with an area of exactly 144 square inches. After they ve had a few minutes to work, have them share and compare their results. Bridges in Mathematics Grade 5 Supplement D1.1

5 Set D1 Measurement: Area & Perimeter Activity 1 Measuring Area (cont.) 18" It s 10 tiles along the side and 18 along the top. 10 rows of 18 is " If you count by 10 s it s " x 18" = 180 sq. in. 8. Chances are, some students will have compared the paper rectangle to the tile square at their table to find the side lengths, and then used some kind of counting strategy to find the area. Others may have done the same but multiplied the dimensions to find the area. Still others may have measured the dimensions with their rulers and multiplied. If the third strategy doesn t come from the students, tape one of the 10" 18" pieces of paper to the board and model it yourself. 9. Post the Word Resource Card for dimension on the board. Explain that to find the area of a square or a rectangle, we measure its dimensions and multiply the 2 numbers. Press students to explain how and why this works, and then work with input from the class to write the general formula: area = length width or A = lw. 3 dimension Explain that in a minute, students will be working in pairs to measure the area of some things around the classroom. Ask them to look around. Can they spot anything they d measure in square inches? What about the calendar grid pocket chart or the whiteboard? Would they find the area of these in square inches or square feet? Students I d use square inches to find out the area of small stuff like my math journal or probably my desk. I d maybe use square feet instead of square inches to get the area of the calendar chart. I d definitely use square feet to measure the area of the rug or the whole room. 11. Give students each a copy of the Measuring Area worksheet. Examine the chart together and explain the tasks as needed. Make sure they know where to find the yardsticks and measuring tapes as they need them. Then ask them to work in pairs to complete the sheet. Note Advise students to work to the nearest inch in measuring the dimensions of the items listed on the worksheet. Bridges in Mathematics Grade 5 Supplement D1.3

6 Set D1 Measurement: Area & Perimeter Blackline Run a class set. name date Measuring Area Find the area of each item listed below. example A piece of blue construction paper Dimensions (Measure to the nearest inch and show your units: inches or feet) Length = 18 Width = 10 Area (Show your work and label the answer with the correct units.) 18 x 10 = 180 sq. in. 1 Your math journal 2 Your desk or table 3 A geoboard 4 Calendar Grid pocket chart 5 The top of a bookshelf 6 The front of a chapter book 7 A Calendar Grid marker 8 A work table larger than the one where you sit 9 The whiteboard 10 The classroom D1.4 Bridges in Mathematics Grade 5 Supplement

7 Set D1 Measurement: Area & Perimeter Set D1 H Activity 2 Activity Measuring Perimeter Overview Students review the terms area and perimeter, and find the perimeter of a rectangular and a square piece of construction paper. Together, they generate formulas for determining the perimeter of rectangles and squares. Then they apply the information as they work in pairs to find the perimeter of various items around the classroom. Skills & Concepts H select appropriate units, strategies, and tools for solving problems that involve estimating or measuring perimeter and/or area H measure necessary attributes of shapes to use perimeter and area formulas to solve problems You ll need H Measuring Perimeter (page D1.8, run a class set) H 9" 12" green construction paper (half class set) H one 12" 12" piece of red construction paper H base 10 mats available H geoboards available H rulers (class set) H yardsticks and measuring tapes H Student Math Journals H Word Resource Cards (area, perimeter) Recommended Timing Anytime after Set D1 Activity 1 Instructions for Measuring Perimeter 1. Post the Word Resource Cards for area and perimeter on the board. Ask student pairs to compare and contrast the two terms. How are they alike? How are they different? After a minute or two, invite volunteers to share their ideas with the class. As the discussion unfolds, review the following concepts: area and perimeter are both measurements. area is a measure of how much surface something takes up. area is measured in square units such as square inches, square feet, or square miles. perimeter is a measure of the total distance around something. perimeter is measured in linear units such as inches, feet, yards, or miles. area perimeter 2. Explain that you ll be working with perimeter today. Have students pair up or assign partners, and ask them to get out their rulers and math journals. Give each pair a 9" 12" sheet of construction paper without mentioning the dimensions. Ask them to use the inch side of their ruler to find the perimeter, or the total distance around the paper. Have them each record the answer, along with any computations they made, in their journals. Bridges in Mathematics Grade 5 Supplement D1.5

9 Set D1 Measurement: Area & Perimeter Activity 2 Measuring Perimeter (cont.) 9. Give students each a copy of the Measuring Perimeter worksheet. Examine the chart together and explain the tasks as needed. Ask students if they need to measure the length of every side in order to find the perimeter of their math journal or their desk. Why not? Make sure they know where to find the yardsticks and measuring tapes as they need them. Then ask them to work in pairs to complete the sheet. Note Advise students to work to the nearest inch in measuring the side lengths of the items listed on the worksheet. Bridges in Mathematics Grade 5 Supplement D1.7

10 Set D1 Measurement: Area & Perimeter Blackline Run a class set. name date Measuring Perimeter Find the perimeter of each item listed below. example A piece of green construction paper 1 Your math journal 2 Your desk or table Side Lengths (Include units: inches, feet, or yards) 9 and 12 Circle the formula you need to find the perimeter. P = 2w + 2l P = 4s P = 2w + 2l P = 4s P = 2w + 2l P = 4s 3 A geoboard P = 2w + 2l 4 Calendar Grid pocket chart 5 The top of a bookshelf P = 4s P = 2w + 2l P = 4s P = 2w + 2l P = 4s 6 A base 10 mat P = 2w + 2l P = 4s 7 The whiteboard P = 2w + 2l P = 4s 8 The classroom P = 2w + 2l P = 4s Perimeter (Show your work and label the answer with the correct units.) (2 x 9) + (2 x 12) = 42 D1.8 Bridges in Mathematics Grade 5 Supplement

14 Set D1 Measurement: Area & Perimeter Blackline Run 1 copy on a transparency. The Ladybugs Garden 1 The Ladybugs are planning to plant a garden this spring. They want it to be rectangular. They have exactly 24 centimeters of fencing put around the perimeter of their garden. Sketch a plan for them on your grid paper. 2 Now sketch as many different rectangles as you can find that have a perimeter of 24 centimeters. Label each one with its perimeter and area, along with equations to show how you got the answers. 3 All of your rectangles have a perimeter of 24 centimeters. Do they all have the same area? Why or why not? 4 Which rectangle would work best for the Ladybugs garden? Explain your answer. D1.12 Bridges in Mathematics Grade 5 Supplement

15 Set D1 Measurement: Area & Perimeter Blackline Run a class set. name date Centimeter Grid Paper Bridges in Mathematics Grade 5 Supplement D1.13

16 D1.14 Bridges in Mathematics Grade 5 Supplement

17 Set D1 Measurement: Area & Perimeter Set D1 H Activity 4 Activity Hexarights Overview Students continue to investigate relationships between area and perimeter as they measure and construct polygons called hexarights (hexagons with pairs of adjacent sides that meet at right angles). Skills & Concepts H determine area by finding the total number of samesized units of area that cover a shape without gaps or overlaps H select appropriate units, strategies, and tools for solving problems that involve estimating or measuring perimeter and/or area H find the areas of complex shapes by dividing those figures into basic shapes (e.g., rectangles, squares) H understand that rectangles with the same area can have different perimeters and that rectangles with the same perimeter can have different areas H measure necessary attributes of shapes to use perimeter and area formulas to solve problems Recommended Timing Anytime after Set D1 Activity 2 You ll need H Introducing Hexarights (page D1.18, 1 copy on a transparency) H Measuring Hexarights (page D1.19, run a half-class set, cut in half) H Hexarights, Perimeter = 24 cm (page D1.20, run a class set) H Centimeter Grid Paper (page D1.21, run a class set, plus a few extra) H piece of paper to mask parts of the overhead H 2 or 3 transparencies and overhead pens H rulers marked with both centimeters and inches (class set) Instructions for Hexarights 1. Show the top portion of Introducing Hexarights at the overhead, masking the rest with a piece of paper. Give students a minute to pair-share any observations they can make. Then invite volunteers to share their thinking with the class. Record some of their ideas in the space to the left of the shape. 2. Then reveal the definition below the shape, still keeping the rest of the overhead covered. Read and discuss it with the class. As you do so, review the meanings of the terms hexagon, perpendicular, and right angles. Set D1 Measurement: Area & Perimeter Blackline Run 1 copy on a transparency. Introducing Hexarights 1 Describe this shape. has 6 sides has 5 maybe 6 right angles has parallel lines some of the lines are perpendicular kind of like 2 rectangles stuck together none of the lines are the same length This shape is a hexagon because it has 6 sides, but let s call it a hexaright. A hexaright is a hexagon in which every pair of sides that touch each other is per - pendicular. (That is, they meet at right angles.) 2 Bridges in Mathematics Grade 5 Supplement D1.15

18 Set D1 Measurement: Area & Perimeter Activity 4 Hexarights (cont.) 3. Next, reveal the two counter-examples show in the middle of the overhead. Can students explain why neither of these are hexarights? Have them share at the overhead so their classmates can see what they re talking about. Set D1 Measurement: Area & Perimeter Blackline Run 1 copy on a transparency. Introducing Hexarights 1 Describe this shape. has 6 sides has 5 maybe 6 right angles has parallel lines some of the lines are perpendicular kind of like 2 rectangles stuck together none of the lines are the same length This shape is a hexagon because it has 6 sides, but let s call it a hexaright. A hexaright is a hexagon in which every pair of sides that touch each other is per - pendicular. (That is, they meet at right angles.) 2 Here are 2 examples of shapes that are not hexarights. Can you see why? a b 3 Find the area and perimeter of the hexarights below. Students Shape a isn t a hexaright because there are 2 angles that aren t right angles. I thought they were wrong about shape b because it s all right angles, but then I realized there are 10 sides! A hexaright can only have 6 sides. 4. Now show the 2 hexarights at the bottom of the overhead and briefly discuss strategies for finding the area and perimeter of each. Then give students each a copy of the Measuring Hexarights half-sheet. Ask them to experiment with both the inch side and the centimeter side of their rulers. Which unit of measure works best? Students will quickly discover that most of the measurements don t come out evenly unless they use centimeters. 5. Solicit agreement from the class that they ll work in centimeters and square centimeters rather than inches and square inches, and let them get started. Encourage them to share and compare their strategies and solutions as they work. 6. When most students have finished finding the perimeter and area of at least one of the hexarights, place a blank transparency on top of the overhead and invite volunteers to share their work with the class. Move or replace the transparency each time a new volunteer comes up to the overhead to accommodate several different presentations. At the top of the next page is an example of the sort of work you might expect from students, although some will divide the hexarights differently. D1.16 Bridges in Mathematics Grade 5 Supplement

19 Set D1 Measurement: Area & Perimeter Activity 4 Hexarights (cont.) 3 Find the area and perimeter of the hexarights below. a 6 cm 2 cm 3 cm 2 x 3 = 6 sq cm 2 cm 3 x 4 = 12 sq cm 3 cm 4 cm = 20 cm P = 20 cm A = 18 sq cm 1 cm b 8 cm 1 x 7 = 7 sq cm 7 cm 3 cm = 24 cm P = 24 cm A = 11 sq cm 1 x 4 = 4 sq cm 4 cm 1 cm 7. As students share, discuss the methods they re using to find the area and perimeter of these shapes. Did they use the perimeter formulas they developed during Measurement Area Perimeter Activity 2? Why not? (Because these are irregular polygons. All you can do is simply add all the different side lengths.) Did they use the area formula they developed during Measurement Area Perimeter Activity 1? How? (To find the area without covering the shape with centimeter square units or drawing them in, you need to divide each hexaright into 2 rectangles. Then you can use A = lw to find the area of each and add them.) 8. After 2 or 3 strategies have been shared for each hexaright, explain that there is more than one hexaright with a perimeter of 24 centimeters. Give students each a copy of Hexarights, Perimeter = 24 cm. Review the instructions together and clarify as needed. Place a small stack of the Centimeter Grid Paper on each table and give students the remainder of the math period to work. Encourage them to share and compare their strategies for finding other hexarights with perimeters equal to 24 centimeters. What are some of the areas that result? Are they all equal? Set D1 Measurement: Area & Perimeter Blackline Run a class set. NAME DATE Hexarights, Perimeter = 24 cm 1 Draw 2 different hexarights with a perimeter of 24 cm, and find the area of each. Then draw a third hexaright with a perimeter of 24 cm. This time, make the area as large as possible. 2 You can use the space below and the back of this sheet. Or, you can draw your hexarights on centimeter grid paper, cut them out, and glue them to this sheet. Use your ruler to help make the lines straight and accurate. 3 Label your hexarights with their dimensions, perimeter, and area. Use num - bers, sketches, and/or words to show how you found the perimeter and area of each hexaright. 4 On the back of the sheet, write at least 2 sentences to describe what you found out about the areas of hexarights with a perimeter of 24 cm. Reconvene the class to share strategies and solutions either at the end of the period or at another time. Note Hexaright is not some long-forgotten concept from your high school geometry days. It is a made-up term borrowed from Measuring Up: Prototypes for Mathematics Assessment (Mathematical Sciences Education Board National Research Council, Washington, DC: National Academy Press). You may want to let students know this so that they won t expect to see, or use it on standardized texts. Bridges in Mathematics Grade 5 Supplement D1.17

20 Set D1 Measurement: Area & Perimeter Blackline Run 1 copy on a transparency. Introducing Hexarights 1 Describe this shape. This shape is a hexagon because it has 6 sides, but let s call it a hexaright. A hexaright is a hexagon in which every pair of sides that touch each other is perpendicular. (That is, they meet at right angles.) 2 Here are 2 examples of shapes that are not hexarights. Can you see why? a b 3 Find the area and perimeter of the hexarights below. a b D1.18 Bridges in Mathematics Grade 5 Supplement

21 Set D1 Measurement: Area & Perimeter Blackline Run a half-class set and cut the sheets in half. name date Measuring Hexarights Find the area and perimeter of the hexarights below. Show all your work. name Measuring Hexarights date Find the area and perimeter of the hexarights below. Show all your work. Bridges in Mathematics Grade 5 Supplement D1.19

22 Set D1 Measurement: Area & Perimeter Blackline Run a class set. name date Hexarights, Perimeter = 24 cm 1 Draw 2 different hexarights with a perimeter of 24 cm, and find the area of each. Then draw a third hexaright with a perimeter of 24 cm. This time, make the area as large as possible. 2 You can use the space below and the back of this sheet. Or, you can draw your hexarights on centimeter grid paper, cut them out, and glue them to this sheet. Use your ruler to help make the lines straight and accurate. 3 Label your hexarights with their dimensions, perimeter, and area. Use numbers, sketches, and/or words to show how you found the perimeter and area of each hexaright. 4 On the back of the sheet, write at least 2 sentences to describe what you found out about the areas of hexarights with a perimeter of 24 cm. D1.20 Bridges in Mathematics Grade 5 Supplement

23 Set D1 Measurement: Area & Perimeter Blackline Run a class set, plus a few extras. name date Centimeter Grid Paper Bridges in Mathematics Grade 5 Supplement D1.21

24 D1.22 Bridges in Mathematics Grade 5 Supplement

25 Set D1 Measurement: Area & Perimeter Blackline Use anytime after Set D1, Activity 2. Run a class set. name date Set D1 H Independent Worksheet 1 Independent Worksheet Area & Perimeter Review Perimeter is the distance all the way around a figure. Perimeter is measured in linear units like centimeters, meters, inches, feet, and yards. Area is the amount of surface a figure covers. Area is measured in square units like square centimeters, square meters, square inches, square feet, and square yards. Perimeter Area 1 Use the centimeter side of your ruler to measure the dimensions (the length and width) of each rectangle on the next page. Then find its area and perimeter using the formulas below. Show your work. Perimeter = (2 the width) + (2 the length) or P = (2 w) + (2 l) Area = length width or A = l w example 12 cm 3 cm 36 sq. cm Perimeter: (2 x 3) + (2 x 12) = 30 cm Area: 12 x 3 = 36 sq. cm (Continued on back.) Bridges in Mathematics Grade 5 Supplement D1.23

26 Set D1 Measurement: Area & Perimeter Blackline Run a class set. Independent Worksheet 1 Area & Perimeter Review (cont.) 1a b Perimeter: Area: c Perimeter: Area: d Perimeter: Area: Perimeter: Area: 2 Jamie says you only need to measure one side of a square to find its perimeter. Do you agree with her? Why or why not? Use numbers, labeled sketches, and words to explain your answer. (Continued on next page.) D1.24 Bridges in Mathematics Grade 5 Supplement

27 Set D1 Measurement: Area & Perimeter Blackline Run a class set. name Independent Worksheet 1 Area & Perimeter Review (cont.) date 3 Hector says you have to measure the length of every side of this figure to find its perimeter. Do you agree with him? Why or why not? Use numbers, labeled sketches, and words to explain your answer. 5 Mr. Hunter is trying to find the distance from one end of his whiteboard to the other. Mr. Hunter is measuring: whiteboard the board s area the board s length the board s perimeter 6 Which of these situations is about perimeter? determining the number of tiles needed to cover a floor 4 Which equation shows how to find the perimeter of this rectangle? 8 ft. determining how many feet of fencing is needed to surround a rectangular yard determining the width of a table 3 ft. 3 8 = 24 ft. (2 3) + 8 = 14 ft. (2 3) + (2 8) = 22 ft = 12 ft. 7 Beckett and his mom are going to paint the living room. They need to measure the room so they know how much paint to buy. They should measure the wall in: square centimeters square feet square inches square miles (Continued on back.) Bridges in Mathematics Grade 5 Supplement D1.25

28 Set D1 Measurement: Area & Perimeter Blackline Run a class set. Independent Worksheet 1 Area & Perimeter Review (cont.) 8 This rectangle has an area of 45 square feet. What is the missing measure? Show your work.? ft. 5 ft. 45 sq. ft. 9 Tom wants to find the area of his school s basketball court. Which formula should he use? (circle one) A = l + w A = l w A = l w A = (2 w) + (2 l) 10 Alexandra and her dad build a deck in their backyard. It had an area of 48 square feet and a perimeter of 28 feet. Circle the drawing that shows the deck they built. Use numbers, labeled sketches, and words to explain your answer. 6 ft. 5 ft. 9 ft. 8 ft. 4 ft. 12 ft. D1.26 Bridges in Mathematics Grade 5 Supplement

29 Set D1 Measurement: Area & Perimeter Blackline Use anytime after Set D1 Activity 2. Run a class set. name date Set D1 H Independent Worksheet 2 Independent Worksheet Measuring Rectangles 1a Which formula shows how to find the area of this rectangle? 6 ft. 4 ft. Area = (2 width) + (2 length) or A = 2w + 2l Area = length + width or A = l + w Area = length width or A = l w b Use the formula you selected to find the area of the rectangle. Show your work. 2a Which formula shows how to find the perimeter of this rectangle? 8 cm 2 cm Perimeter = (3 width) + (3 length) or P = 3w + 3l Perimeter = length + width or P = l + w Perimeter = length width or P = l w Perimeter = (2 width) + (2 length) or P = 2w + 2l (Continued on back.) Bridges in Mathematics Grade 5 Supplement D1.27

30 Set D1 Measurement: Area & Perimeter Blackline Run a class set. Independent Worksheet 2 Measuring Rectangles (cont.) 2b Use the formula you selected to find the perimeter of the rectangle. Show your work. 3a Which formula shows how to find the area of this rectangle? 4 meters 3 meters Area = length width A = l w Area = length width A = l w Area = length width A = l w Area = length + width A = l + w b Use the formula you selected to find the area of the rectangle. Show your work. (Continued on next page.) D1.28 Bridges in Mathematics Grade 5 Supplement

31 Set D1 Measurement: Area & Perimeter Blackline Run a class set. name Independent Worksheet 2 Measuring Rectangles (cont.) date 4a Which formula shows how to find the perimeter of this rectangle? 40 ft. 20 ft. Perimeter = (2 width) + (2 length) P = 2w + 2l Perimeter = length width height P = l w h Perimeter = length width P = l w Perimeter = (2 width) length P = 2w l b Use the formula you selected to find the perimeter of the rectangle. Show your work. Bridges in Mathematics Grade 5 Supplement D1.29

32 D1.30 Bridges in Mathematics Grade 5 Supplement

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