# Perimeter, Area and Volume What Do Units Tell You About What Is Being Measured? Teacher Materials

Save this PDF as:

Size: px
Start display at page:

Download "Perimeter, Area and Volume What Do Units Tell You About What Is Being Measured? Teacher Materials"

## Transcription

1 Lesson 1 Perimeter, Area and Volume What Do Units Tell You About What Is Being Measured? Teacher Materials Perimeter: The Line Club T1: Before class: Copy one set of student pages for each student in the class. Make the following 8 rectangles on the classroom floor using narrow masking tape. Spread them out around the room to allow students room to work in groups around each rectangle. Metric units can be used as well, but don t intermix the two types of units. A B C D E F G H 6ft x 5ft 3ft x 4ft 1ft x 6ft 4ft x 4ft 8 in x 5 in 10 in x 2 in 6 in x 6 in 7 in x 3 in Prepare class charts for Perimeter Tool, Rectangle A, and Rectangles A-H. (See teacher masters #1, 2, & 3) 1. With your partner, make a list of situations where a series of straight lines forms a boundary around a space or object. Example: a fence around a garden T2: Possible answers: fences, edges of a deck, molding around a room, ribbon around a package, picture frame, window frame, etc. Discussion questions: Are we measuring a line or the space between the lines? How do you know? 2. What kind of tools could be used to measure straight lines? How could you use the tools to find the amount of tape used to form the rectangle you are looking at on the floor? Record your ideas on the chart below. Tool How would you use the tool? Units? What Do Units Tell You About What Is Being Measured? Teacher Material Page 1 of 29

2 T3: Focus on the idea of a line without measurable width. Use of a string to trace the outline of the rectangle might help students see this. Additional appropriate tools can replace or be added to this list. When students are measuring with their foot, it is important they place their feet heel to toe to get accurate data. This is also true for the ruler and yardstick as they move it around the perimeter. After all data and units are compiled, ask students to compare advantages & disadvantages of each tool drawing upon their experience and the data results across the class. Students should notice a wide range of measurements using feet because of different sizes of feet. They should see more variability with a ruler than a yardstick because of having to move the ruler along the perimeter, but the answers should be closer among the groups. The yardstick requires less moves around the perimeter, but students may have difficulty with the partial measurements of a yard along some sides. The tape measure should give the most consistent measurements because it does not require them to move it along a side. Summary question: How can we all get the same measurements? (idea of standard units & tools) Hopefully students will see the value of using a standard unit of measure to get consistent results and also see the value of the longer extension of the tape measure. 3. Work with your group to measure the total distance around each rectangle (A H). Rectangle Length 1 Length 2 Width 1 Width 2 Total (with units) A 6ft 6ft 5ft 5ft 22ft B 3ft 3ft 4ft 4ft 14ft C 6ft 6ft 1ft 1ft 14ft D 4ft 4ft 4ft 4ft 16ft E 8in 8in 5in 5in 16in F 10in 10in 2in 2in 24in G 6in 6in 6in 6in 14in H 7in 7in 2in 2in 18in What Do Units Tell You About What Is Being Measured? Teacher Material Page 2 of 29

4 4. The total measurement of the straight lines enclosing a figure is called the. (perimeter) 5. How do you measure the perimeter? ( length + length + width + width = perimeter) 6. What kind of units are used? Why?_(length units of inches or feet because they measure a line and perimeter is a series of connecting lines enclosing an area) T6: Students could work in pairs on the following problems. Struggling students: Suggest they trace the perimeter of each rectangle with their pencil as they calculate the perimeter. Students needing additional challenge: Change the numbers to include decimal or fractional parts. Change the shape of the figure to a triangle or other polygon. Would their procedure still work? Why or why not? Would they have to change anything to make it work? Why or why not? Create additional perimeter story problems to be used as entry warm-ups or extra practice items for students needing additional help. Students love to see their work identified by name. Find the perimeter for the following rectangles. Include appropriate units. 10 feet inches 4 feet 4 ft 6 inches 10 ft. 2 in. Perimeter = Perimeter = (28 feet) (16 inches) What Do Units Tell You About What Is Being Measured? Teacher Material Page 4 of 29

5 9. 15 inches inches 5 feet 5 feet Perimeter = Perimeter = (36 inches) (20feet) 11. Pleasant Valley Middle School is painting tetherball courts on their playground. Each tetherball court forms a rectangle with a length of 12 feet and a width of 10 feet. What is the perimeter of each tetherball court? Include appropriate units. Show your work using words, numbers and/or diagrams. The perimeter of the tetherball court will be. (44 feet) What Do Units Tell You About What Is Being Measured? Teacher Material Page 5 of 29

6 T7: Use this exit ticket to assess individual student understanding of the attribute of perimeter, determining its value and assigning appropriate units. Use this assessment to determine if reteaching is required. Exit Ticket Lesson 1 Name: Stacy and Eddie want to put a rectangular fence around their pool to make it safer for small children in the neighborhood. They want the fence to be 30 feet long and 25 feet wide. What will be the total length of the new fence? Show your work using words, numbers and/or pictures. The total length of the new fence will be. (110 feet) What Do Units Tell You About What Is Being Measured? Teacher Material Page 6 of 29

7 Name: Lesson 2 Area: The Square Club T1: Before class: Copy student set of pages for each student in the class. Make class poster of master #5 Tools for Area. Make four sets of 30 1ft x 1ft squares for rectangles A D. Make four sets of 40 1in x 1in squares for rectangles E H or use 1in tiles. Make class poster of master #6 Areas of Rectangles A H. T2: Students generate a summary of yesterday s learning about perimeters. Use the charts created with the class. Create the definition for perimeter with the students and add it to the master #4 chart from yesterday. T3: Ask students to think about the area or space inside the perimeter of a rectangle and generate a list of places in real life they might see such an area. Some possible ideas: garden, picture, carpet, football field, door, etc 1. With your partner, make a list of situations where the space or area inside the perimeter of a rectangle is used. Example: a garden T4: Give them the following questions to think about with their partner. H ow would they measure these kinds of areas? Some possible ideas: lines placed side by side across the inside of the perimeter, line from corner to corner, winding string back and forth across the space, flat piece of paper cut to size, strips of paper, squares of paper, triangles, etc There could be many polygons that would cover the area, but help students realize that squares are probably the easiest because of their attributes (90 angles, parallel sides, etc.) Ask them if this area can be covered by a line or does it require something different? Remind them to think about what they learned yesterday about perimeters. Perimeters are lines, so a line measures a line not an area. Could they use the same procedures and tools? Why or why not? What Do Units Tell You About What Is Being Measured? Teacher Material Page 7 of 29

8 2. With your partner, generate some ideas about how you could measure this area. T5: Give students a few minutes to turn and talk with their partners about the following questions and then generate a chart with their ideas as a class. In this case, define tools as something used with which to measure a flat surface. Help them think about tools that would cover the surface of the rectangles. Examples students might develop would be strips of tape or string with units of inches or feet, but help them see these would not cover the surface very well. Another example might be circles of paper with each circle being 1 unit, but there would be gaps between the circles. Students should realize squares would work since they fit together without gaps and cover the surface completely. Help them to see the unit for a square is 1 unit on each side called a square unit. Ask students if their idea covers the entire space completely? Are their ideas efficient? What kind of units would be used for each idea? 3. What kind of tools could be used to measure this area? How could you use the tools to find the amount of area? Tool How would you use the tool? Units 4. Which tool would work best to cover the area inside the perimeter of a rectangle? Explain why? What Do Units Tell You About What Is Being Measured? Teacher Material Page 8 of 29

9 T6: Introduce square units after students generate the idea of squares fitting neatly next to one another to cover the area inside the perimeter. Give each student a square and have them place it side by side inside the perimeter of rectangle A until the entire area is covered. Why does this choice measure the space well? (it covers the entire space.) Why is it easy to use and count? (The square covers a piece of the interior of the rectangle and it is easy to keep adding squares until the whole interior of the rectangle is covered.) How can we measure these squares? (1 foot on each side makes a square a foot from top to bottom and a foot from side to side.) Linear units, such as a foot, measures what? (A line) Are we measuring lines? (no) How could we show these units are not lines, but squares covering one foot from top to bottom and one foot from side to side? (Square foot ( 1 ft² )) Students may suggest marking the square with one foot on each side or four feet of perimeter. Focus them on the fact that the perimeter measures lines and we are measuring an area one foot in each direction. Students are not expected to use exponents on the 6 th grade WASL. They are allowed to use the term square units or square feet. When we cover the area inside the perimeter with square units it creates rows and columns of squares. How many rows and how many columns? 6 rows and 5 columns How this is related to the total number of squares it takes to fill the entire area? (5 x 6 = 30 square units) T7: As students work together, circulate and record their ideas and strategies to find the area of the rectangles. Decide which strategies you want to discuss as a whole class and in which order you want them to appear in the discussion to build the concept of what the attribute of area represents, how to measure it and what kind of units are necessary. Struggling students: Some students may be hesitant to continue to use the physical square units if the group begins to move to a more conceptual understanding. Encourage struggling students to continue physically using the square units to fill the area and to physically count the total number of square units. Take this into consideration when making groups for this activity if you foresee a group of students needing this accommodation. Placing a couple of similar students together in a group may help them find support for this problem solving strategy.. Students needing more challenge: Ask if they think the same strategies would work with rectangles where the length of one side is 4 ½? 3 ¾? Why or why not? What would you have to do to prove your idea? What Do Units Tell You About What Is Being Measured? Teacher Material Page 9 of 29

10 3. Work with your group of 4 students to measure the total area inside rectangles (A H). Rectangle Count total # squares # of # of Area of rows columns rectangle Units A Square feet B Square feet C Square feet D Square feet E Square inches F Square inches G Square inches H Square inches T8: Use the class chart from master #8 to summarize group data. Have students turn and talk with partners about patterns they see in the data. How are these patterns related to the number of squares it takes to cover the inside of the perimeter? (number of rows multiplied by the number of columns is equal to the total number of squares needed to cover the entire area inside the perimeter of any rectangle). 4. The total number of squares contained within the perimeter of a rectangle is called the. (area) T9: Generate discussion about how to measure area. Students may say they need to count every square needed. Ask them if they will always have squares with them to use? (No) Students may say they need to count the number of rows of squares and the number of columns of squares to get the total number of squares needed. Ask them how they could find that out without putting squares along the perimeter? Notice the number of rows of squares is the same as the length of one side of the perimeter and the number of columns of squares is the same as the width of one side of the perimeter. What Do Units Tell You About What Is Being Measured? Teacher Material Page 10 of 29

11 Have students draw pictures or use Rectangle A on the floor to demonstrate this idea. What Do Units Tell You About What Is Being Measured? Teacher Material Page 11 of 29

12 5. How do you measure the total area of a rectangle? (# of rows x # of columns) 6. What kind of units are used? Why? (square units because they cover the area) T10: Have students work in pairs to find the area of these rectangles. Struggling students: May still need to use the 1 foot and the 1 inch squares to solve these problems. Another strategy for students still struggling with visualizing the covering of the area with square units is to have students create a grid across each rectangle to help them find the area. Grid paper could be used for all these problems if you think all your students will require this adaptation. Students needing more challenge: Change the numbers to include decimal or fractional parts. You could also change the shape of the figure to a triangle or other polygon. Would their procedure still work? Why or why not? Would they have to change anything to make it work? Why or why not? Also ask them to create additional area story problems to be used as entry warmups or extra practice items for students needing additional help. Students love to see their work identified by name. What Do Units Tell You About What Is Being Measured? Teacher Material Page 12 of 29

13 Find the area for the following rectangles. Include appropriate units feet 2 inches 8. 4 feet 4 feet 6 inches 6 inches 10 feet 2 inches Area = Area = (40 square feet) (12 square inches) inches inches 5 feet 5 feet Area = Area = (45 square inches) (25 square feet²) What Do Units Tell You About What Is Being Measured? Teacher Material Page 13 of 29

14 11. Pleasant Valley Middle School is painting tetherball courts on their playground. Each tetherball court forms a rectangle with a length of 12 feet and a width of 10 feet. What is the total area of each tetherball court? Include appropriate units in your answer. Show your work using words, numbers and/or pictures. The total area of the new court will be. (120 square feet) What Do Units Tell You About What Is Being Measured? Teacher Material Page 14 of 29

15 T11 Use this exit ticket to assess individual student understanding of the attribute of area, their ability to determine its value and assign appropriate units. Use this assessment to determine if reteaching is required. Exit Ticket Lesson 2 Na me : Sta cy and Eddie want to put a rectangular fence around their pool to make it safer for small c hildren in the neighborhood. They want the fence to be 30 feet long and 25 feet wide. What will be the total area inside the fence? Include appropriate units in your answer. Show your work using words, numbers and/or pictures. The total area inside the fence will be. (750 square feet) What Do Units Tell You About What Is Being Measured? Teacher Material Page 15 of 29

16 Name: Lesson 3 Volume: The Cubic Club T1: Before class: Copy student set of pages for each student in the class. Make class poster of master #7 Tools for Volume. Make or find a 2ft X 3ft X 2ft box for rectangular prism A Make twelve 1ft cubes for rectangular prism A. Use master #9. Make one set of prisms (B-H) for each pair of students leaving one end open for filling. Use master # 9. Students could also be given the nets to create the prisms. Gather a set of 50 on- inch cubes for each pair of students. Centimeter cubes could also be used if metric measurements have been introduced to students. Make class poster of master #8 Volumes of Rectangular Prisms A H. T2: Summarize the area lesson Which tool would work best to cover the area inside the perimeter of a rectangle? (Squares) What is the total number of squares contained within the perimeter of a rectangle called? (area) How do you measure the total area of a rectangle? ( count the squares) What formula could be used to find the area? (L x W = A) What kind of units are used? (square units) Why? (cover the area) T3 : Possible examples of space inside a rectangular prism: (box of candy, swimming pool, storage unit, a planter box, etc.) 1. With your partner, make a list of examples where the space inside a rectangular prism (box) might need to be found. T4: Students may generate the following ideas: Pieces of paper the size of the bottom stacked up, squares covering the bottom stacked up, filling the box with Styrofoam peanuts, filling with blocks, etc. Measuring the all edges of the box and adding them up Measuring the all edges of the box and multiplying them Show the 2ft x 3ft x 2ft box as an example. What Do Units Tell You About What Is Being Measured? Teacher Material Page 16 of 29

17 2. With your partner, generate some ideas about how you could measure this space. 3. What kind of tools could be used to measure this space? How could you use the tools to find the amount of space? Tool How would you use the tool? Units T5: Ask the following questions to summarize their ideas: Would the lines we used for perimeter work to measure the space inside the box? (N o, only measur es length.) Would the squares we used for area work to measure the space inside the box? (No, only measures area which has a length and a width.) What would work? (cubes) Why? (Stack side by side and on top without spaces between) How is this related to the previous units we used for perimeter and area? (Area is 2- D with length and width. Volume is 3-D with length, width and height.) Show a cube and label the length, width and height. Have 12 students each place one cube into the 2ft x 3ft x 2ft box. Count as each cube is placed in. Which tool would work best to measure the space inside the rectangular prism (box)? Explain why? What Do Units Tell You About What Is Being Measured? Teacher Material Page 17 of 29

18 3. Work with your prisms (A H). group of 4 students to measure the volume inside the rectangular Rectangle # of # of # of Total # Units Prism rows of columns layers of of cubes on of cubes cubes cubes the on the high is bottom bottom Volume A cubic feet (ft³) B cubic inches (in³) C cubic inches (in³) D cubic inches (in³) E cubic inches (in³) F cubic inches (in³) G cubic inches (in³) H cubic inches (in³) T6: Summarize student data from the above chart. What patterns do you see from your data? (# rows on the bottom multiplied by the # or columns on the bottom is the same as the area of the rectangle making the bottom of the box. The area (L x W) x H is equal to the number of cubes to fill the rectangular prism.) What s the unit used to measure volume? (Cubes and in these cases cubic feet and cubic inches) Point out if students don t generate the idea that there are 3 measurements L x W x H so ft³ or in³. 5 th and 6 th grade students are not required to use exponents on the WASL, but point out the exponent represents 3 measurements (length, width & height) Point out again the idea of a line measuring length only thus feet (ft) for perimeter A square measures length and width thus square feet (ft²) for area A cube measures length, width and height thus cubic feet (ft³) for volume. 4. The total number of cubes contained within the rectangular prism is called the. What Do Units Tell You About What Is Being Measured? Teacher Material Page 18 of 29

19 (volume) 5. How do you measure the volume of a rectangular prism? (# of rows x # of columns to form the base x # of layers) (LxWxH) 6. What kind of units are used? Why? (cubes because they fill the prism) T7: Students can work in pairs to find the volume of the following prisms. Watch for students using incorrect notation like 30²ft instead of 30ft² if they chose to use exponents in their answers. Remind students to label each of their measurements with units in their work. Struggling students: May still need to use the 1 inch cubes to solve these problems. You may want to change the measurements for each prism to inches to help with this need. An example of using squares on the bottom of the box might help students see the connection to area an d help them see that flat squares won t fill the box like cubes. The cubes could even be placed directly over the squares to visualize the connection. Students needing more challenge: Change the numbers to include decimal or fractional parts. You could also change the shape of the figure to a triangle or other polygon. Would their procedure still work? Why or why not? Would they have to change anything to make it work? Why or why not? Also ask them to create additional volume story problems to be used as entry warm-ups or extra practice items for students needing additional help. Students love to see their work identified by name. What Do Units Tell You About What Is Being Measured? Teacher Material Page 19 of 29

20 Find the volume of the following rectangular prisms. Include appropriate units in your answer feet 6 inches 3 feet 2 inches 10 feet 2 inches Volume = Volume = (120 cubic feet) (24 cubic inches) inches 5 feet 3 inches 5 feet 2 inches 5 feet Area = Area = (90 cubic inches) (125 cubic feet) What Do Units Tell You About What Is Being Measured? Teacher Material Page 20 of 29

21 11. Pleasant Valley Middle School is constructing tetherball courts on their playground. Each tetherball pole will be set in a concrete prism 18 inches long, 15 inches wide and 12 inches high. What is the volume of concrete needed to make each prism for the tetherball poles? Include appropriate units in your answer. Show your work using words, numbers and/or pictures. The volume of concrete needed for each prism will be. (3240 cubic inches) What Do Units Tell You About What Is Being Measured? Teacher Material Page 21 of 29

22 T8: Use this exit ticket to assess individual student understanding of the attribute of volume, their ability to determine its value and assign appropriate units. Use this assessment to determine if reteaching is required. Exit Ticket Lesson 3 Name: Miguel is mailing a package to his uncle for his birthday. He has two boxes he can use and he wants to send the box with the largest volume. The first box is 24 inches long, 10 inches wide and 12 inches high. The second box is 20 inches long, 15 inches wide and 11 inches high. Explain which box you think he should use and why. Include appropriate units in your answer. Show your work using words, numbers and/or pictures. Box #1 Box #2 ( Miguel should us e box #2 because it has a volume of 3300 cubic inches. Box #1 only has an area of 2880 cubic inches. The volume of box #2 is 420 cubic inches larger than the volume of box #1.) What Do Units Tell You About What Is Being Measured? Teacher Material Page 22 of 29

23 Vocabulary Prior vocabulary Vocabulary in lesson Future vocabulary centimeter area estimate foot column exponent height inch length linear units perimeter ruler rectangle square width cubic units edge face hypothesis row rectangular prism side square units volume surface area What Do Units Tell You About What Is Being Measured? Teacher Material Page 23 of 29

24 Ma terials Manipulatives Copies Tools Supplies inch tiles or cm tiles student lessons rulers/yardsticks empty box (60 per group of 4) (one per student (one per student) 2ft x 3ft x 2ft or 160 inch squares for each lesson) tape measures for class demonstration cut from paper (one per group) inch cubes or cm net patterns on calculators poster paper cubes tag board (one (one per student) for class charts (60 per group of 4) set per student) foot cubes (12) gold tickets (2 per class) felt pens (various colors per group of 4) one foot squares cut from paper (120) classroom charts (one per class for each teacher master) vocabulary (one per student) exit tickets (one per student for each lesson) unit assessment (one per student) inch grid paper or cm grid paper several sheets per student) ball of string small white boards (two per group) dry erase pens (one per student) kleenex (one per student for erasing) scotch tape (roll per table) masking tape narrow width scissors (one per student) snack size candy bars (one per student) transparencies if overhead is used What Do Units Tell You About What Is Being Measured? Teacher Material Page 24 of 29

25 Name: Perimeter, Area & Volume Pre-Test 1. Sandra wants to build a fence around her vegetable garden. Which of the following will she need to determine in ord er to know how long her fence needs to be? a. area b. perimeter c. volume d. surface area 2. Alejandro is buying new carpet for his bedroom. Which of the following will he need to determine in order to buy the correct amount of carpet? a. perimeter b. volume c. height of the room d. area 3. How many faces does a rectangular prism (box) have? a. 6 b. 5 c. 8 d Wh ich of the following can be used to find the perimeter of a rectangle? a. L x W b. L + W + H c. L x W x H d. L + L + W + W 5. Which of the following can be used to find the area of a rectangle? a. L x W b. L + W + H c. L x W x H d. L + L + W + W 6. Which of the following can be used to find the volume of a rectangular prism? a. L x W b. L + W + H c. L x W x H d. L + L + W + W What Do Units Tell You About What Is Being Measured? Teacher Material Page 25 of 29

26 7. Which of the following measurements could be used to describe the area of a rectangle? a. 10 inches b. 10 square inches c. 10 cubic inches d. 10 quadruple inches 8. Which of the following measurements could be used to describe the perimeter of a rectangle? a. 10 inches b. 10 square inches c. 10 cubic inches d. 10 quadruple inches 9. Which of the following measurements could be used prism? to describe the volume of a a. 10 inches b. 10 square inches c. 10 cubic inches d. 10 quadruple inches 10. Yessica is painting her family room floor and putting molding around the edge of the floor. What is the area of the floor she needs to paint How much molding will she need to buy? 14 feet 10 feet The area of the floor is Yessica needs to buy of molding. 11. Tyler has built a sandbox for his younger brother for Christmas. The sandbox is 5 feet long, 2 feet high, and 6 feet wide. What is the volume of sand he will need to buy to completely fill the sandbox? Tyler needs to buy of sand. What Do Units Tell You About What Is Being Measured? Teacher Material Page 26 of 29

27 Name: Perimeter, Area & Volume Pre-Test Rubric 1. Sandra wants to build a fence around her vegetable garden. Which of the following will she need to determine in ord er to know how long her fence needs to be? a. area b. perimeter c. volume d. surface area 2. Alejandro is buying new carpet for his bedroom. Which of the following will he need to determine in order to buy the correct amount of carpet? a. perimeter b. volume c. height of the room d. area 3. How many faces does a rectangular prism (box) have? a. 6 b. 5 c. 8 d Which of the following can be used to find the perimeter of a rectangle? a. L x W b. L + W + H c. L x W x H d. L + L + W + W 5. Which of the following can be used to find the area of a rectangle? a. L x W b. L + W + H c. L x W x H d. L + L + W + W 6. Which of the following can be used to find the volume of a rectangular prism? a. L x W b. L + W + H c. L x W x H d. L + L + W + W What Do Units Tell You About What Is Being Measured? Teacher Material Page 27 of 29

28 7. Which of the following measurements could be used to describe the area of a rectangle? a. 10 inches b. 10 square inches c. 10 cubic inches d. 10 quadruple inches 8. Which of the following measurements could be used to describe the perimeter of a rectangle? a. 10 inches b. 10 square inches c. 10 cubic inches d. 10 quadruple inches 9. Which of the following measurements could be used to describe the volume of a prism? a. 10 inches b. 10 square inches c. 10 cubic inches d. 10 quadruple inches 10. Yessica is painting her family room floor and putting molding around the edge of the floor. What is the area of the floor she needs to paint and how much molding will she need to buy? 14 feet 10 feet The area of the floor is _( 140 square feet)_ Yessica needs to buy (48 feet) of molding. 11. Tyler has built a sandbox for his younger brother for Christmas. The sandbox is 5 feet long, 2 feet high, and 6 feet wide. What is the volume of sand he will need to buy to completely fill the sandbox? Tyler needs to buy (60 cubic feet) of sand. What Do Units Tell You About What Is Being Measured? Teacher Material Page 28 of 29

29 What Do Units Tell You About What Is Being Measured? Teacher Material Page 29 of 29

### Perimeter, Area, and Volume

Perimeter is a measurement of length. It is the distance around something. We use perimeter when building a fence around a yard or any place that needs to be enclosed. In that case, we would measure the

### Assessment Management

Areas of Rectangles Objective To reinforce students understanding of area concepts and units of area. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family

### Perimeter, Area and Volume What Do Units Tell You About What Is Being Measured? Overview

Perimeter, Area and Volume What Do Units Tell You About What Is Being Measured? Overview Summary of Lessons: This set of lessons was designed to develop conceptual understanding of the unique attributes

### Formulas for Area Area of Trapezoid

Area of Triangle Formulas for Area Area of Trapezoid Area of Parallelograms Use the formula sheet and what you know about area to solve the following problems. Find the area. 5 feet 6 feet 4 feet 8.5 feet

### Lesson 3: Area. Selected Content Standards. Translating Content Standards into Instruction

Lesson 3: Area Selected Content Standards Benchmark Assessed: M.3 Estimating, computing, and applying physical measurement using suitable units (e.g., calculate perimeter and area of plane figures, surface

### Area and Circumference of Circles

Teacher Created Materials 21208 Focused Mathematics Student Guided Practice Book of Circles Learning Objectives Geometry Know the formulas for the area and circumference of a circle and use them to solve

### Grade 4 Mathematics Measurement: Lesson 2

Grade 4 Mathematics Measurement: Lesson 2 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside

### Number Models for Area

Number Models for Area Objectives To guide children as they develop the concept of area by measuring with identical squares; and to demonstrate how to calculate the area of rectangles using number models.

### WHAT IS AREA? CFE 3319V

WHAT IS AREA? CFE 3319V OPEN CAPTIONED ALLIED VIDEO CORPORATION 1992 Grade Levels: 5-9 17 minutes DESCRIPTION What is area? Lesson One defines and clarifies what area means and also teaches the concept

### Lesson 13: The Formulas for Volume

Student Outcomes Students develop, understand, and apply formulas for finding the volume of right rectangular prisms and cubes. Lesson Notes This lesson is a continuation of Lessons 11, 12, and Module

### Unit 6 Measurement and Data: Area and Volume

Unit 6 Measurement and Data: Area and Volume Introduction In this unit, students will learn about area and volume. As they find the areas of rectangles and shapes made from rectangles, students will need

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

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

### 1. Kyle stacks 30 sheets of paper as shown to the right. Each sheet weighs about 5 g. How can you find the weight of the whole stack?

Prisms and Cylinders Answer Key Vocabulary: cylinder, height (of a cylinder or prism), prism, volume Prior Knowledge Questions (Do these BEFORE using the Gizmo.) [Note: The purpose of these questions is

### Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms.

Volume of Right Prisms Objective To provide experiences with using a formula for the volume of right prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game

### MD5-26 Stacking Blocks Pages 115 116

MD5-26 Stacking Blocks Pages 115 116 STANDARDS 5.MD.C.4 Goals Students will find the number of cubes in a rectangular stack and develop the formula length width height for the number of cubes in a stack.

### Linear, Square and Cubic Units Grade Five

Ohio Standards Connection Measurement Benchmark F Analyze and explain what happens to area and perimeter or surface area and volume when the dimensions of an object are changed. Indicator 4 Demonstrate

### Lesson 18: Determining Surface Area of Three Dimensional Figures

Lesson 18: Determining the Surface Area of Three Dimensional Figures Student Outcomes Students determine that a right rectangular prism has six faces: top and bottom, front and back, and two sides. They

### Solving Geometric Applications

1.8 Solving Geometric Applications 1.8 OBJECTIVES 1. Find a perimeter 2. Solve applications that involve perimeter 3. Find the area of a rectangular figure 4. Apply area formulas 5. Apply volume formulas

### VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.

Math 6 NOTES 7.5 Name VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. **The formula for the volume of a rectangular prism is:** l = length w = width h = height Study Tip:

### Mathematics and Science

Mathematics and Science Table of Contents FORWARD KEVA Planks are great for: Basic Instructions for Building Team Building and Incentives For Young Children MATH AND SCIENCE 1 Counting with KEVA 2 Number

### Geometry Notes PERIMETER AND AREA

Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter

### Archdiocese of Washington Catholic Schools Academic Standards Mathematics

5 th GRADE Archdiocese of Washington Catholic Schools Standard 1 - Number Sense Students compute with whole numbers*, decimals, and fractions and understand the relationship among decimals, fractions,

### Unit 6 Geometry: Constructing Triangles and Scale Drawings

Unit 6 Geometry: Constructing Triangles and Scale Drawings Introduction In this unit, students will construct triangles from three measures of sides and/or angles, and will decide whether given conditions

### *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles.

Students: 1. Students understand and compute volumes and areas of simple objects. *1. Derive formulas for the area of right triangles and parallelograms by comparing with the area of rectangles. Review

### Free Pre-Algebra Lesson 3 page 1. Example: Find the perimeter of each figure. Assume measurements are in centimeters.

Free Pre-Algebra Lesson 3 page 1 Lesson 3 Perimeter and Area Enclose a flat space; say with a fence or wall. The length of the fence (how far you walk around the edge) is the perimeter, and the measure

### EXPLAINING AREA AND CIRCUMFERENCE OF A CIRCLE

EXPLAINING AREA AND CIRCUMFERENCE OF A CIRCLE 7.G.4 CONTENTS The types of documents contained in the unit are listed below. Throughout the unit, the documents are arranged by lesson. LEARNING MAP INFORMATION

### Geometry Notes VOLUME AND SURFACE AREA

Volume and Surface Area Page 1 of 19 VOLUME AND SURFACE AREA Objectives: After completing this section, you should be able to do the following: Calculate the volume of given geometric figures. Calculate

### Mathematics as Reasoning Students will use reasoning skills to determine the best method for maximizing area.

Title: A Pen for Penny Brief Overview: This unit is a reinforcement of the concepts of area and perimeter of rectangles. Methods for maximizing area while perimeter remains the same are also included.

### IWITNESS NEWS: BREAKING IN TO GEOMETRY ASHLEY BAILEY, BEAR CREEK MIDDLE SCHOOL

IWITNESS NEWS: BREAKING IN TO GEOMETRY ASHLEY BAILEY, BEAR CREEK MIDDLE SCHOOL Unit Overview In this interactive geometry unit, students work in differentiated groups to master finding the area and volume

### Integrated Algebra: Geometry

Integrated Algebra: Geometry Topics of Study: o Perimeter and Circumference o Area Shaded Area Composite Area o Volume o Surface Area o Relative Error Links to Useful Websites & Videos: o Perimeter and

### 5E Lesson Plan Perimeter and Area

5E Lesson Plan Perimeter and Area teachhouston Student Name: Mentor Teacher Name: Grade Level: 4th Lesson Teaching Date: Concept(s): Perimeter is the distance around the outside of a shape. Area is the

3 rd Grade Mathematics Unit #3 : Relating Area to Multiplication and Division Pacing: 29 Days Unit Overview In this unit, students extend their understanding of multiplication and division (Unit 2) by

### CALCULATING PERIMETER. WHAT IS PERIMETER? Perimeter is the total length or distance around a figure.

CALCULATING PERIMETER WHAT IS PERIMETER? Perimeter is the total length or distance around a figure. HOW DO WE CALCULATE PERIMETER? The formula one can use to calculate perimeter depends on the type of

### Hint for success: When tested in groups of students grade 3 and younger, this activity worked best as a centers activity.

Activities Grades 3 5 www.exploratorium.edu/geometryplayground/activities MAKING A TRANSLATION TESSELLATION Background: What is a tessellation? Suppose you wanted to cover a floor with tiles. You could

### Area of Circles. 2. Use a ruler to measure the diameter and the radius to the nearest half centimeter and record in the blanks above.

Name: Area of Circles Label: Length: Label: Length: A Part 1 1. Label the diameter and radius of Circle A. 2. Use a ruler to measure the diameter and the radius to the nearest half centimeter and recd

### Round Rock ISD Lesson 1 Grade 3 Measurement Kit. Broken Rulers and Line It Up!* - A Length Measurement Lesson

Round Rock ISD 2008-09 Lesson 1 Grade 3 Measurement Kit Broken Rulers and Line It Up!* - A Length Measurement Lesson tech *Lesson is adapted from two activities in Sizing Up Measurement: Activities for

### GEOMETRY CIRCLING THE BASES

LESSON 3: PRE-VISIT - PERIMETER AND AREA OBJECTIVE: Students will be able to: Distinguish between area and perimeter. Calculate the perimeter of a polygon whose side lengths are given or can be determined.

### Measuring with Yards and Meters

Measuring with Yards and Meters Objectives To provide review for the concept of nonstandard units of measure; and to introduce yard and meter. www.everydaymathonline.com epresentations etoolkit Algorithms

### Polygon of the Day Discovering Area Formulas

Polygon of the Day Discovering Area Formulas Utilizing Technology and Manipulatives Cuisenaire pop-cubes Geometry tiles GSP triangles tool Trapezoid magnets Sixth Grade 6-day Unit Plan (40 minute classes)

### Title: Measurement Conversion

Title: Measurement Conversion Brief Overview: Students will explore the relationship between various units of measurement including inches to feet, feet to yards, and inches to yards. They will develop

### STATE GOAL 7: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable

C 1 Measurement H OW MUCH SPACE DO YOU N EED? STATE GOAL 7: Estimate, make and use measurements of objects, quantities and relationships and determine acceptable levels of accuracy Statement of Purpose:

### CC Investigation 4: Measurement

Content Standards 6.G., 6.G. CC Investigation : Measurement Mathematical Goals At a Glance PACING 3 days DOMAIN: Geometry Find the volume of a right rectangular prism with fractional edge lengths by packing

### Area Long-Term Memory Review Review 1

Review 1 1. To find the perimeter of any shape you all sides of the shape.. To find the area of a square, you the length and width. 4. What best identifies the following shape. Find the area and perimeter

### Unit 8 Geometry. Introduction. Materials

Unit 8 Geometry Introduction In this unit, students will learn about volume and surface area. As they find the volumes of prisms and the surface areas of prisms and pyramids, students will add, subtract,

### Area of Parallelograms, Triangles, and Trapezoids (pages 314 318)

Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base

### Assessment Management

Area Objectives To provide experiences with the concept of area, distinguishing between area and perimeter, and finding areas of rectangular figures by partitioning and counting squares. www.everydaymathonline.com

### Area, Perimeter, Surface Area and Change Overview

Area, Perimeter, Surface Area and Change Overview Enduring Understanding: (5)ME01: Demonstrate understanding of the concept of area (5)ME02: Demonstrate understanding of the differences between length

### MATH STUDENT BOOK. 6th Grade Unit 8

MATH STUDENT BOOK 6th Grade Unit 8 Unit 8 Geometry and Measurement MATH 608 Geometry and Measurement INTRODUCTION 3 1. PLANE FIGURES 5 PERIMETER 5 AREA OF PARALLELOGRAMS 11 AREA OF TRIANGLES 17 AREA OF

### Georgia Department of Education Common Core Georgia Performance Standards Framework Fourth Grade Mathematics Unit

Fourth Grade Mathematics Unit Constructing Task: Area and Perimeter Adapted from Fixed Perimeters and Fixed Areas in Teaching Student-Centered MATHEMATICS Grades 3-5 by John Van de Walle and LouAnn Lovin.

### Measurement. Volume It All Stacks Up. Activity:

Measurement Activity: TEKS: Overview: Materials: Grouping: Time: Volume It All Stacks Up (7.9) Measurement. The student solves application problems involving estimation and measurement. The student is

### Area and Perimeter Man

Area and Perimeter Man MA.C.3.2.1.3.1 and.2; MA.B.3.2.1.3.3 LESSON FOCUS Using counting procedures to determine perimeter and area of rectangles, squares, and other figures. COMPANION ANCHORS LESSONS Perimeter;

### 9-10. NCSC Sample Instructional Unit. Investigating Measurement in the Real World. Mathematics: Measurement

Mathematics: Measurement NCSC Sample Instructional Unit 9-10 Investigating Measurement in the Real World The contents of this product were developed under a grant from the Department of Education (PR/Award

### Objective To introduce a formula to calculate the area. Family Letters. Assessment Management

Area of a Circle Objective To introduce a formula to calculate the area of a circle. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment

### Volume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms.

Volume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts

### Author(s): Hope Phillips

Title: Fish Aquarium Math *a multi-day lesson Real-World Connection: Grade: 5 Author(s): Hope Phillips BIG Idea: Volume Designing and building aquariums includes mathematical concepts including, but not

### CARMEL CLAY SCHOOLS MATHEMATICS CURRICULUM

GRADE 4 Standard 1 Number Sense Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers 1 and decimals relate to simple fractions. 4.1.1 Read and write

### Lesson 11: Volume with Fractional Edge Lengths and Unit Cubes

Lesson : Volume with Fractional Edge Lengths and Unit Cubes Student Outcomes Students extend their understanding of the volume of a right rectangular prism with integer side lengths to right rectangular

### b = base h = height Area is the number of square units that make up the inside of the shape is a square with a side length of 1 of any unit

Area is the number of square units that make up the inside of the shape of 1 of any unit is a square with a side length Jan 29-7:58 AM b = base h = height Jan 29-8:31 AM 1 Example 6 in Jan 29-8:33 AM A

### I Perimeter, Area, Learning Goals 304

U N I T Perimeter, Area, Greeting cards come in a variety of shapes and sizes. You can buy a greeting card for just about any occasion! Learning Goals measure and calculate perimeter estimate, measure,

### Name: Date: Geometry Solid Geometry. Name: Teacher: Pd:

Name: Date: Geometry 2012-2013 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 1-7 HW: Pgs: 8-10 DAY 2: SWBAT: Calculate the Volume of

### Activity Set 3. Trainer Guide

Geometry and Measurement of Plane Figures Activity Set 3 Trainer Guide GEOMETRY AND MEASUREMENT OF PLANE FIGURES Activity Set 3 Copyright by the McGraw-Hill Companies McGraw-Hill Professional Development

### Signs, Signs, Every Place There Are Signs! Area of Regular Polygons p. 171 Boundary Lines Area of Parallelograms and Triangles p.

C H A P T E R Perimeter and Area Regatta is another word for boat race. In sailing regattas, sailboats compete on courses defined by marks or buoys. These courses often start and end at the same mark,

### Measuring with a Ruler

Measuring with a Ruler Objective To guide children as they measure line segments to the nearest inch, _ inch, _ inch, centimeter, _ centimeter, and millimeter. www.everydaymathonline.com epresentations

### Warning! Construction Zone: Building Solids from Nets

Brief Overview: Warning! Construction Zone: Building Solids from Nets In this unit the students will be examining and defining attributes of solids and their nets. The students will be expected to have

### Family Letters. Assessment Management. Playing Fraction Of

Formula for the Area of a Parallelogram Objectives To review the properties of parallelograms; and to guide the development and use of a formula for the area of a parallelogram. www.everydaymathonline.com

### Geometry: Chapter Questions. 1. How is the formula for area of a parallelogram related to area of a rectangle?

Geometry: Chapter Questions. How is the formula for area of a parallelogram related to area of a rectangle?. How is the formula for area of a triangle related to area of a rectangle?. How do you find the

### Shape, space and measures 1

Shape, space and measures 1 contents There are three lessons in this unit, Shape, space and measures 1. S1.1 Lines, length and perimeter 3 S1.2 Area of a rectangle 6 S1.3 Solving problems 9 Resource sheets

### 17.1 INVESTIGATE. Model Perimeter. Are You Ready? Lesson Opener Making Connections. Resources. Texas Essential Knowledge and Skills.

. INVESTIGATE? Essential Question How can you find perimeter? How can you find perimeter? Lesson Opener Making Connections Invite students to tell you what they know about the distance around objects.

### Lesson 3. Measuring Volume

Math 5 Lesson 3 Measuring Volume Shipping Cars Each day cars are packed into containers and placed on large ships to be delivered to places all over the world. It is really important to get as many cars

### Area and Perimeter. Name: Class: Date: Short Answer

Name: Class: Date: ID: A Area and Perimeter Short Answer 1. The squares on this grid are 1 centimeter long and 1 centimeter wide. Outline two different figures with an area of 12 square centimeters and

### 4. Molly walked all the way around the edge of her yard. The distance she walked is the yard's

Name: Date: 1. Derrius has 24 feet of fencing to use for a rectangular dog pen. Which dimensions would give him the most room (area) for his dog? A. 1 foot by 11 feet B. 3 feet by 9 feet C. 4 feet by 8

### Demystifying Surface Area and Volume Teachers Edition

Demystifying Surface and Volume Teachers Edition These constructions and worksheets can be done in pairs, small groups or individually. Also, may use as guided notes and done together with teacher. CYLINDER

2009 Leaders Notes Grade 8 Module 3 page 1 General Materials and Supplies: Handouts 10 and 11 8 ½ x 11 paper white boards markers chalk tape tape measure ruler yard stick meter stick tennis balls in the

### Planning Guide. Grade 5 Volume. Shape and Space (Measurement) Specific Outcome 4

Mathematics Planning Guide Grade 5 Volume Shape and Space (Measurement) Specific Outcome 4 This Planning Guide can be accessed online at: http://www.learnalberta.ca/content/mepg5/html/pg5_volume/index.html

### ME3-11 Measuring Perimeter

ME3-11 Measuring Perimeter Goals: Students will estimate and measure perimeters using non-standard units. Prior Knowledge Required: What measurement means Practice and comfort with other forms of linear

### Grade 5 supplement. Set C1 Geometry: Triangles & Quadrilaterals. Includes. Skills & Concepts

Grade 5 supplement Set C1 Geometry: Triangles & Quadrilaterals Includes Activity 1: Classifying Triangles C1.1 Activity 2: Sorting & Classifying Quadrilaterals C1.13 Activity 3: Finding the Perimeter &

### Sort It Out Student Materials Page 1 of 8

Nick s favorite candy is red licorice and he decides that using licorice would be a great addition to put on the edge of the frosting around his birthday cake. How much licorice will he need if his cake

### Exploring Length, Area, and Attributes

Explorations Exploring Length, Area, and Attributes Objectives To guide children as they measure lengths and distances to the nearest inch and centimeter, explore area by tiling surfaces, and sort attribute

### Overview. Essential Questions. Grade 8 Mathematics, Quarter 4, Unit 4.3 Finding Volume of Cones, Cylinders, and Spheres

Cylinders, and Spheres Number of instruction days: 6 8 Overview Content to Be Learned Evaluate the cube root of small perfect cubes. Simplify problems using the formulas for the volumes of cones, cylinders,

### Show that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square.

Week & Day Week 6 Day 1 Concept/Skill Perimeter of a square when given the radius of an inscribed circle Standard 7.MG:2.1 Use formulas routinely for finding the perimeter and area of basic twodimensional

### Volume of Pyramids and Cones

Volume of Pyramids and Cones Objective To provide experiences with investigating the relationships between the volumes of geometric solids. www.everydaymathonline.com epresentations etoolkit Algorithms

### Covering and Surrounding: Homework Examples from ACE

Covering and Surrounding: Homework Examples from ACE Investigation 1: Extending and Building on Area and Perimeter, ACE #4, #6, #17 Investigation 2: Measuring Triangles, ACE #4, #9, #12 Investigation 3:

### Student Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes)

Student Outcomes Students give an informal derivation of the relationship between the circumference and area of a circle. Students know the formula for the area of a circle and use it to solve problems.

### Height. Right Prism. Dates, assignments, and quizzes subject to change without advance notice.

Name: Period GL UNIT 11: SOLIDS I can define, identify and illustrate the following terms: Face Isometric View Net Edge Polyhedron Volume Vertex Cylinder Hemisphere Cone Cross section Height Pyramid Prism

### Chapter 4: The Concept of Area

Chapter 4: The Concept of Area Defining Area The area of a shape or object can be defined in everyday words as the amount of stuff needed to cover the shape. Common uses of the concept of area are finding

### Area and Perimeter: The Mysterious Connection TEACHER EDITION

Area and Perimeter: The Mysterious Connection TEACHER EDITION (TC-0) In these problems you will be working on understanding the relationship between area and perimeter. Pay special attention to any patterns

### Such As Statements, Kindergarten Grade 8

Such As Statements, Kindergarten Grade 8 This document contains the such as statements that were included in the review committees final recommendations for revisions to the mathematics Texas Essential

### Surface Area and Volume

1 Area Surface Area and Volume 8 th Grade 10 days by Jackie Gerwitz-Dunn and Linda Kelly 2 What do you want the students to understand at the end of this lesson? The students should be able to distinguish

### Imperial Length Measurements

Unit I Measuring Length 1 Section 2.1 Imperial Length Measurements Goals Reading Fractions Reading Halves on a Measuring Tape Reading Quarters on a Measuring Tape Reading Eights on a Measuring Tape Reading

### BALLPARK FIGURES. Problems #1-7 will be worked out as a class 1. Definition of Perimeter. 2. Formula or method for finding Perimeter

BALLPARK FIGURES Name: Date: Goal of lesson: This lesson will lead you through a number of activities (based on the theme of a baseball field) to build your understanding, through experience, of situations

### Measuring Prisms and Cylinders. Suggested Time: 5 Weeks

Measuring Prisms and Cylinders Suggested Time: 5 Weeks Unit Overview Focus and Context In this unit, students will use two-dimensional nets to create threedimensional solids. They will begin to calculate

### Area of Parallelograms (pages 546 549)

A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular

### MATH STUDENT BOOK. 7th Grade Unit 9

MATH STUDENT BOOK 7th Grade Unit 9 Unit 9 Measurement and Area Math 709 Measurement and Area Introduction 3 1. Perimeter 5 Perimeter 5 Circumference 11 Composite Figures 16 Self Test 1: Perimeter 24 2.

### Describing and Solving for Area and Perimeter

Grade 3 Mathematics, Quarter 2,Unit 2.2 Describing and Solving for Area and Perimeter Overview Number of instruction days: 8-10 (1 day = 90 minutes) Content to Be Learned Distinguish between linear and

### Name: Date: Geometry Honors Solid Geometry. Name: Teacher: Pd:

Name: Date: Geometry Honors 2013-2014 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 1-6 HW: Pgs: 7-10 DAY 2: SWBAT: Calculate the Volume

### Grade 2 Math Expressions Vocabulary Words

Grade 2 Math Expressions Vocabulary Words Unit 1, Book 1 Understanding Addition and Subtraction OSPI word: number pattern, place value, value, whole number Link to Math Expression Online Glossary for some

### Area and Perimeter. one-inch squares. There are one-inch squares covering Rectangle X. row(s) of one-yard squares. one-yard squares.

12 CHAPTER Area and Perimeter Lesson 12.1 Area of a Rectangle Find the area of each figure. 1. 1 in. 1 in. X There are Each row has rows of one-inch squares. one-inch squares. There are one-inch squares