Enhanced Instructional Transition Guide

Transcription

1 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Unit 09: Measurement (18 days) Possible Lesson 01 (5 days) Possible Lesson 02 (5 days) Possible Lesson 03 (5 days) Possible Lesson 04 (3 days) POSSIBLE LESSON 03 (5 days) This lesson is one approach to teaching the State Standards associated with this unit. Districts are encouraged to customize this lesson by supplementing with districtapproved resources, materials, and activities to best meet the needs of learners. The duration for this lesson is only a recommendation, and districts may modify the time frame to meet students needs. To better understand how your district is implementing CSCOPE lessons, please contact your child s teacher. (For your convenience, please find linked the TEA Commissioner s List of State Board of Education Approved Instructional Resources and Midcycle State Adopted Instructional Materials.) Lesson Synopsis: Students find perimeter, area, and volume by selecting and applying the appropriate formulas. Students use manipulatives, such as color tiles and centimeter cubes, to select, use, and connect the formulas for perimeter, area, and volume. Students use sketches and models of two-dimensional and three-dimensional figures in various problem-solving situations for perimeter, area, and volume. TEKS: The Texas Essential Knowledge and Skills (TEKS) listed below are the standards adopted by the State Board of Education, which are required by Texas law. Any standard that has a strike-through (e.g. sample phrase) indicates that portion of the standard is taught in a previous or subsequent unit. The TEKS are available on the Texas Education Agency website at Measurement.. The student applies measurement concepts involving length (including perimeter), area, capacity/volume, and weight/mass to solve problems. The student is expected to: 5.10B Connect models for perimeter, area, and volume with their respective formulas. Supporting Standard 5.10C Select and use appropriate units and formulas to measure length, perimeter, area, and volume. Readiness Standard Underlying Processes and Mathematical Tools TEKS: page 1 of 61

2 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days 5.14 Underlying processes and mathematical tools.. The student applies Grade 5 mathematics to solve problems connected to everyday experiences and activities in and outside of school. The student is expected to: 5.14A Identify the mathematics in everyday situations. 5.14D Use tools such as real objects, manipulatives, and technology to solve problems Underlying processes and mathematical tools.. The student communicates about Grade 5 mathematics using informal language. The student is expected to: 5.15A Explain and record observations using objects, words, pictures, numbers, and technology. 5.15B Relate informal language to mathematical language and symbols. Performance Indicator(s): page 2 of 61

3 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Grade 05 Unit 09 PI 03 Select and use appropriate formulas to find the following measures based on a real-life situation such as the following: A fish tank is shown below. The depth of the water in the fish tank is half of the height of the fish tank. The length of the fish tank is twice the height. Select and use appropriate formulas to determine: (1) the perimeter and the area of the bottom of the fish tank; (2) the volume of the entire fish tank; (3) the volume of the water in the fish tank; and (4) the difference between the volume of the water in the tank and the volume of the entire tank. Display all calculations and solution processes in a graphic organizer and justify in writing how each measure was determined. Standard(s): 5.10B, 5.10C, 5.14A, 5.14D, 5.15A, 5.15B ELPS ELPS.c.1C, ELPS.c.4F Key Understanding(s): Linear measurements may be used to calculate the perimeter, area, and volume of an object or geometric figure. The perimeter of a figure is a linear measure that can be determined by estimating each side length of the figure and expressing the total with appropriate units and calculated by adding the exact lengths of each side of the figure and expressing the total with appropriate units. The area of a rectangle is the space within an indicated figure and can be determined by finding the length and width of the figure and expressing the product of those dimensions in appropriate square units. The volume of a figure is the amount of space occupied in a three-dimensional figure which can be expressed with cubic units and determined by multiplying the area of each layer by the number of layers in the figure. page 3 of 61

4 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Misconception(s)/Underdeveloped Concept(s): None identified. Vocabulary of Instruction: area perimeter volume Materials List: cardstock (4 sheets per 2 students) centimeter cubes (75 per student) color tiles (36 per 2 students) dry erase marker (1 per student) math journal (1 per student) plastic zip bag (sandwich sized) (1 per 2 students) scissors (1 per teacher) STAAR Grade 5 Reference Materials (1 per student) whiteboard (student sized) (1 per student) yarn (36 cm) (1 per student) Attachments: All attachments associated with this lesson are referenced in the body of the lesson. Due to considerations for grading or student assessment, attachments that are connected with Performance Indicators or serve as answer keys are available in the district site and are not accessible on the public website. Perimeter and Area and Representation Cards KEY Perimeter and Area and Representation Cards page 4 of 61

5 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Centimeter Grid Paper Fencing in the Beetle Perimeter-Area-Volume Key Concept Table SAMPLE KEY Perimeter-Area-Volume Key Concept Table Kitchen Area Inch Grid Paper Finding Perimeter and Area of Irregular Figures Notes/Practice KEY Finding Perimeter and Area of Irregular Figures Notes/Practice Perimeter, Area, and Volume Relationships KEY Perimeter, Area, and Volume Relationships Jewelry Box KEY Jewelry Box Volume Practice-Problem Solving KEY Volume Practice-Problem Solving Measurement of Rectangular Prisms KEY Measurement of Rectangular Prisms Selecting Appropriate Measurement Formulas Practice KEY Selecting Appropriate Measurement Formulas Practice page 5 of 61

6 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days GETTING READY FOR INSTRUCTION Teachers are encouraged to supplement and substitute resources, materials, and activities to meet the needs of learners. These lessons are one approach to teaching the TEKS/Specificity as well as addressing the Performance Indicators associated with each unit. District personnel may create original lessons using the Content Creator in the Tools Tab. All originally authored lessons can be saved in the My CSCOPE Tab within the My Content area. Suggested Day Suggested Instructional Procedures Notes for Teacher 1 Topics: Introduction to perimeter and area Engage 1 Students use logic and reasoning skills to investigate the relationship and meaning of area and perimeter. Instructional Procedures: 1. Prior to instruction, create a card set: Perimeter and Area and Representation Cards for every 2 students by copying on cardstock, laminating, cutting apart, and placing in a plastic zip bag. 2. Place students in pairs. Distribute a card set: Perimeter and Area Representation Cards to each student pair and the STAAR Grade 5 Reference Materials to Spiraling Review ATTACHMENTS Teacher Resource: Perimeter and Area and Representation Cards KEY (1 per teacher) Card Set: Perimeter and Area and Representation Cards (1 set per 2 students) MATERIALS page 6 of 61

7 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures each student. Instruct student pairs to select a word problem card from the set of cards, identify the expression, formula, and model cards that match the word problem until all 8 word problem cards have been matched to the 3 representations. Encourage student pairs to use the formulas on their STAAR Grade 5 Reference Materials to guide them through selecting the appropriate representation. Allow time for students to complete the activity. Monitor and assess student pairs to check for understanding. Facilitate a class discussion to debrief student solutions. Ask: Notes for Teacher cardstock (4 sheets per 2 students) scissors (1 per teacher) plastic zip bag (sandwich sized) (1 per 2 students) STAAR Grade 5 Reference Materials (1 per student) math journal (1 per student) How did you know which representation to select for each problem? Answers may vary. The models represented the numbers in the problem by the way they were grouped, as well as the numbers in the expression matched the numbers in the problem; etc. How could you determine a solution for each of these problems? Answers may vary. Multiply or add each set of numbers the appropriate number of times; etc. TEACHER NOTE The STAAR Grade 5 Reference Materials should be made available to students at all times. 3. Instruct student pairs to solve each problem situation and record their solutions in their math journal. Allow time for students to complete the activity. Monitor and assess student pairs to check for understanding. Facilitate a class discussion to debrief student solutions. Topics: ATTACHMENTS Perimeter Area Explore/Explain 1 Handout: Centimeter Grid Paper (1 per student) Teacher Resource: Fencing in the Beetle (1 per teacher) page 7 of 61

8 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures Students explore perimeter and area in real-life problem situations. Students record the definition and formula for perimeter and area, as well as draw a model and provide an example of each type of measurement. Instructional Procedures: 1. Display teacher resource: Fencing in the Beetle. Ask: What do you need to know to solve this problem? (the area Marco has available, how much fencing he has, and how large an area he can fence in) How does the piece of yarn help you to solve this problem? Answers may vary. The string represents the total amount of fencing Marco has, or its perimeter; etc. Notes for Teacher Teacher Resource: Perimeter/Area/Volume Key Concept Table SAMPLE KEY (1 per teacher) Handout: Perimeter/Area/Volume Key Concept Table (1 per student) MATERIALS yarn (36 cm) (1 per student) math journal (1 per student) 2. Place students in groups of 4. Distribute a piece of yarn measuring 36 centimeters and handout: Centimeter Grid Paper to each student. Instruct students to use their handout: Centimeter Grid Paper and piece of yarn to create as many different rectangles as possible with whole number sides, and record the area and perimeter for each rectangle created in their math journal. Instruct student groups to discuss the area enclosed by each rectangle. Remind students that area is the amount of square units enclosed by a figure. Allow time for students to complete the activity. Monitor and assess student groups to check for understanding. Facilitate individual group discussions about the activity. Ask: How do you know if your shape is rectangular? (It has 4 sides and its opposite sides are equal in length.) TEACHER NOTE Many students may assume the areas will be the same for all rectangles created with the same 36 cm piece of yarn. TEACHER NOTE In order to reproduce materials consistent with intended measurements, set the print menu to print the handout at 100% by selecting None or Actual size under the Page Scaling/Size option. page 8 of 61

9 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures Is your shape rectangular? Answers may vary. How did you determine the perimeter? (add the length of each side) What is the perimeter of your shape? (36 cm) What is the area of your shape? Answers may vary. Notes for Teacher 3. Facilitate a class discussion to debrief student solutions. Ask: How many rectangles were you able to make with your string? (9) 4. Explain to students that although a 7 x 11 rectangle is oriented differently than an 11 x 7 rectangle, the perimeter and area would be the same, so only one needs to be listed. Ask: TEACHER NOTE Figures with the same perimeters can have different areas. Figures with the same areas can have different perimeters. Congruent figures have the same perimeters and the same areas. What do you notice about the perimeters of the rectangles you created? Why? Answers may vary. They are all the same, 36 centimeters, because the string I used to represent the fencing is 36 centimeters long; etc. Are the areas the same? Explain. (no) Answers may vary. As the shape of the rectangles changed, so did the lengths and widths. Therefore, the areas changed as well; etc. Which rectangle had the greatest area? Explain. (The 9 x 9 rectangle, or square, because the product of the length and width was the greatest.) 5. Instruct students to create a table in their math journal showing all the possible rectangles created with the string, and identify the perimeter and area for each rectangle. page 9 of 61

10 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures Notes for Teacher 6. Distribute handout: Perimeter/Area/Volume Key Concept Table to each student. Instruct students to only complete the Perimeter and Area sections of the table as independent practice and/or homework. 2 Topics: Perimeter Area Explore/Explain 2 Students explore perimeter and area in a real-life problem situation. Instructional Procedures: Spiraling Review ATTACHMENTS Teacher Resource: Kitchen Area (1 per teacher) Handout: Inch Grid Paper (1 per student) 1. Facilitate a class discussion to debrief and discuss the previously assigned handout: page 10 of 61

11 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures Perimeter/Area/Volume Key Concept Table as a class. Collect the handout from each student to redistribute and complete after further instruction. 2. Remind students that they investigated an application where the perimeter remained constant and the area changed. Ask: Notes for Teacher MATERIALS color tiles (36 per 2 students) math journal (1 per student) Is it possible to have a situation where the area remains the same, or constant, and the perimeter changes? Explain. (yes) Answers may vary. If you know the area of a figure, you can find more than one possible configuration using manipulatives or models; etc. 3. Place students in pairs. Distribute 36 color tiles to each student pair and handout: Inch Grid Paper to each student. 4. Display teacher resource: Kitchen Area. Ask: What do you need to know to solve this problem? (how many different rectangular arrangements of the 36 tiles can be made) How do the color tiles help you to solve this problem? Answers may vary. The tiles represent the kitchen tiles and can be manipulated to create the different rectangular arrangements; etc. TEACHER NOTE In order to reproduce materials consistent with intended measurements, set the print menu to print the handout at 100% by selecting None or Actual size under the Page Scaling/Size option. 5. Instruct student pairs to use their handout: Inch Grid Paper and color tiles to create as many different rectangles as possible with whole-number sides and record the area and perimeter for each rectangle created in their math journal. Encourage student pairs to page 11 of 61

12 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures discuss which rectangle might make the most useful kitchen floor. Allow time for students to complete the activity. Monitor and assess student groups to check for understanding. Facilitate individual discussions with students about the activity. Ask: Notes for Teacher How do you know if your shape is rectangular? (It has 4 sides and opposite sides are equal in length.) Is your shape rectangular? Answers may vary. How did you determine the perimeter? (add the length of each side) What is the perimeter of your shape? Answers may vary. What is the area of your shape? (36) 6. Facilitate a class discussion to debrief student solutions. Ask: How many rectangles were you able to make with your tiles? (5) 7. Explain to students that although a 4 x 9 rectangle is oriented differently than a 9 x 4 rectangle, the area and perimeter are the same so only one of these rectangles needs to be listed. Ask: What do you notice about the areas of the rectangles you created? Why? (They are all the same, 36 square centimeters, because I used 36 color tiles each time.) Are the perimeters the same? Explain. (no) Answers may vary. As the shape of the rectangles changed, so did the lengths and widths. Therefore, the perimeters changed page 12 of 61

13 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures as well; etc. Which rectangle had the greatest perimeter? Explain. (The 1 x 36 rectangle because the sum of the lengths and widths was the greatest.) Notes for Teacher 8. Instruct students to create a table showing all the possible rectangles created with the tiles in their math journal and identify the perimeter and area for each rectangle. Topics: ATTACHMENTS Perimeter and area of irregular figures Elaborate 1 Students apply concepts of measurement to find the perimeter and area of irregular figures. Instructional Procedures: 1. Facilitate a class discussion about perimeter and area. So far, you have found the perimeters and areas of figures that are squares or Teacher Resource: Finding Perimeter and Area of Irregular Figures Notes/Practice KEY (1 per teacher) Teacher Resource: Finding Perimeter and Area of Irregular Figures Notes/Practice (1 per teacher) Handout: Finding Perimeter and page 13 of 61

14 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures rectangles. How could you find the perimeter and area for a figure that is not a square or rectangle? Answers may vary. For perimeter, I could find the distance around of the sides of the figure and add them. For area, I could create a grid of square units and count how many square units cover the figure; etc. 2. Distribute a ruler and handout: Finding Perimeter and Area of Irregular Figures Notes/Practice to each student. 3. Display teacher resource: Finding Perimeter and Area of Irregular Figures Notes/Practice. Ask: What is a polygon? (A closed figure that has three or more sides.) What are the names of some polygons? Answers may vary. Triangle, square, rectangle, etc. 4. Explain to students that the irregular figures they will be working with today are polygons. Ask: What is the general rule or method for finding the perimeter of a polygon? (Add all the side lengths.) What should you do if you know the perimeter, but are missing one side length? Answers may vary. Add all the side lengths you have and subtract that sum from the perimeter to find the missing side length; etc. What should you do if you do not know the perimeter and are missing a side length? Answers may vary. Look at the sides opposite the missing side length and add Notes for Teacher Area of Irregular Figures Notes/Practice (1 per student) MATERIALS ruler (1 per student) TEACHER NOTE In order to reproduce materials requiring linear measure that are consistent with intended measurements noted on the KEY, set the print menu to print the handout at 100% by selecting "None" or "Actual size" under the Page Scaling/Size option. State Resources MTR 3-5: Fill Er Up!; Cover It Up!; Outline It!; Measurement Jeopardy TEXTEAMS: Rethinking Elementary Part I: Tiffany s Beanie Babies TEXTEAMS: Rethinking Elementary page 14 of 61

15 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures or use their measures to find the missing side length. Then find the perimeter by adding the lengths of all the sides; etc. 5. Using the displayed teacher resource: Finding Perimeter and Area of Irregular Figures Notes/Practice, demonstrate the solution process for examples 1 and 2. Instruct students to take notes, as needed, throughout the demonstration. 6. Place students in pairs. Instruct student pairs to complete the remainder of handout: Finding Perimeter and Area of Irregular Figures Notes/Practice. Allow time for students to complete the activity. Monitor and assess student pairs to check for understanding. Facilitate a class discussion to debrief student solutions. Notes for Teacher Part II: Tangram Task B: Measuring Tangrams; Area in Square Meters; Measurement Scavenger Hunt I & II 3 Topics: Perimeter Area Volume Explore/Explain 3 Students examine the relationships between perimeter, area, and volume. Instructional Procedures: 1. Explain to students that you need their help to measure the dimensions of the classroom (assuming your classroom is a rectangular prism). Ask: Spiraling Review ATTACHMENTS Teacher Resource: Centimeter Grid Paper (1 per teacher) Handout: Centimeter Grid Paper (1 per student) Teacher Resource: Perimeter, Area, and Volume Relationships KEY (1 per teacher) Handout: Perimeter, Area, and Volume Relationships (1 per page 15 of 61

16 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures How could you find the perimeter of the room? Answers may vary. Measure the 4 lengths of the walls in the room and label in feet or yards, then use the perimeter formula to find the perimeter; add the 4 lengths together, then label in feet or yards; etc. Why do you think perimeter is considered a measurement of the first dimension? (To find perimeter, you measure only the length of the sides of the figure, length being only one dimension of the figure.) How could you find the area of the room floor? Answers may vary. Multiply the length and width of the floor and label in square feet or square yards; etc. Why do you think area is considered a measurement of the second dimension? (To find area, you measure the length and the width of a figure; length being one dimension and width being the second dimension, then you calculate how much space is being covered over that area.) If you wanted to find the volume of the room, what could you do? Answers may vary. Measure the height of the room from floor to ceiling and then multiply the length, width, and height and label in either cubic feet or cubic yards; etc. If perimeter is a one-dimensional measurement and area is a two-dimensional measurement, what kind of measurement do you think volume is? Explain. (Volume is a three-dimensional measurement because you are measuring length, width, and height, three different dimensions.) Why is volume measured in cubic units? Answers may vary. Volume is a threedimensional measure and cubic units are three-dimensional units, each 1 cubic unit takes up 1 unit of length, width, and height; etc. 2. Display the following problem situation for the class to see: Kirsten and her father are ready to build a sandbox. What is the perimeter, area of the base, and Notes for Teacher student) Teacher Resource: Perimeter/Area/Volume Key Concept Table KEY (1 per teacher) MATERIALS centimeter cubes (75 per student) TEACHER NOTE In order to reproduce materials consistent with intended measurements, set the print menu to print page 16 of 61

17 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures volume of the sandbox? 3. Display teacher resource: Centimeter Grid Paper. 4. Distribute handout: Centimeter Grid Paper and 75 centimeter cubes to each student. Instruct students to use their grid paper to draw a 4 x 5 rectangle. Explain to students that this rectangle represents the base of the sandbox. 5. Using the displayed teacher resource: Centimeter Grid Paper, demonstrate drawing a 4 x 5 rectangle for the class to see. Notes for Teacher the handout at 100% by selecting None or Actual size under the Page Scaling/Size option. 7. Explain to students that each square centimeter = 1 square foot and that the rectangle is a model of the base of the sandbox Kirsten and her father are building. Ask: What is the perimeter of the sandbox? How do you know? (18 feet; because (2 x 5) + (2 x 4) = , or 18) 8. Instruct students to label the rectangle on their handout: Centimeter Grid Paper page 17 of 61

18 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures accordingly with the dimensions of the side lengths and then shade the inside of the rectangle to show the area of the rectangle. Ask: Notes for Teacher What is the area of the base of the sandbox? How do you know? (20 square feet; because 5 x 4 = 20) 9. Instruct students to label the rectangle on their handout: Centimeter Grid Paper accordingly with the area of the rectangle. 10. Instruct students to use their centimeter cubes to cover the rectangle on their handout: Centimeter Grid Paper. Ask: How many cubes did you place on your grid? (20 cubes) page 18 of 61

19 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures What is the length of the prism? Width? Height? (5; 4; 1 ft) If this prism represents the sandbox Kirsten and her dad built, what is the volume of the sandbox? (20 cubic feet) Looking at this figure, how could you use length, width, and height to find the total number of cubes (or the volume) without counting them? Answers may vary. I could multiply the length, the width, and the height to get the total number of cubes, or the volume, of the prism; etc. Notes for Teacher 11. Distribute handout: Perimeter, Area, and Volume Relationships to each student. Instruct students to use their centimeter cubes to determine the volume for each rectangular prism. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate a class discussion to debrief student solutions. 12. Redistribute handout: Perimeter/Area/Volume Key Concept Table to each student. Instruct students to complete the remainder of the handout as independent practice and/or homework. 4 Topics: Volume Explore/Explain 4 Students use problem-solving strategies and formulas to find the volume of objects in problems situations. Instructional Procedures: Spiraling Review ATTACHMENTS Teacher Resource: Jewelry Box KEY (1 per teacher) Teacher Resource: Jewelry Box (1 page 19 of 61

20 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures 1. Facilitate a class discussion to debrief and discuss the previously assigned handout: Perimeter/Area/Volume Key Concept Table. 2. Distribute a whiteboard, dry erase marker, and STAAR Grade 5 Reference Materials to each student. 3. Display teacher resource: Jewelry Box. Instruct students to create a sketch of the problem situation, solve the problem, and record their solution process on their whiteboard. Encourage students to reference their STAAR Grade 5 Reference Materials for the appropriate formula to solve the problem. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate a class discussion to debrief student solutions. Ask: How did you know to sketch a rectangular prism instead of a cube? Answers may vary. The dimensions (length, width, and height) are all different. If the figure had been a cube, each dimension would have been the same measure; etc. 4. Instruct students to sketch a cube on their whiteboard, label the length, width, height of the cube, and then find the volume of the cube. Allow time for students to complete the activity. Monitor and assess students to check for understanding. Facilitate a class discussion to debrief student solutions. Example: Notes for Teacher per teacher) Teacher Resource: Volume Practice/Problem Solving KEY (1 per teacher) Handout: Volume Practice/Problem Solving (1 per student) MATERIALS whiteboard (student sized) (1 per student) dry erase marker (1 per student) STAAR Grade 5 Reference Materials (1 per student) TEACHER NOTE Many students may have difficulty finding the length, width, and height on a model of a 3-dimensional figure especially if more than 3 measures are given. Instruct students to find a corner or point on the figure where 3 line segments intersect. They page 20 of 61

21 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures Notes for Teacher can use the 3 measures of these segments as their length, width, and height. Example: Ask: What is the length of your cube? The width? The height? Answers may vary. Why is the formula for finding the volume of a cube is s x s x s? Answers may vary. The length, width, and height are all the same measure; etc. 5. Distribute handout: Volume Practice/Problem Solving to each student. Instruct students to find the volume for each problem. Allow students to complete the handout as homework, as needed. 5 Topics: Measurements of rectangular prisms Elaborate 2 Students apply concepts of measurement to find the volume and missing dimensions of rectangular prisms. Instructional Procedures: 1. Debrief and discuss the previously assigned handout: Volume Practice/Problem Solving as a class. Ask: ATTACHMENTS Teacher Resource: Measurement of Rectangular Prisms KEY (1 per teacher) Handout: Measurement of Rectangular Prisms (1 per student) Teacher Resource (optional): Selecting Appropriate Measurement Formulas Practice KEY (1 per teacher) Handout (optional): Selecting page 21 of 61

22 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures How do the measurements of perimeter, area, and volume differ? Answers may vary. Perimeter is a one-dimensional measurement, area is a two-dimensional measurement, and volume is a three-dimensional measurement; etc. Notes for Teacher Appropriate Measurement Formulas Practice (1 per student) 2. Place students in groups of 4. Distribute handout: Measurement of Rectangular Prisms and the STAAR Grade 5 Reference Materials to each student. Instruct groups to use their STAAR Grade 5 Reference Materials to find the measurements for each rectangular prism. Allow time for students to complete the activity. Monitor and assess student groups to check for understanding. Facilitate a class discussion to debrief student solutions, as needed. MATERIALS STAAR Grade 5 Reference Materials (1 per student) ADDITIONAL PRACTICE Handout (optional): Selecting Appropriate Measurement Formulas Practice may be used to further facilitate understanding of perimeter, area, and volume. Evaluate 1 MATERIALS Instructional Procedures: 1. Assess student understanding of related concepts and processes by using the Performance Indicator(s) aligned to this lesson. STAAR Grade 5 Reference Materials (1 per student) Performance Indicator(s): page 22 of 61

23 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days Suggested Day Suggested Instructional Procedures Notes for Teacher Grade 05 Unit 09 PI 03 Select and use appropriate formulas to find the following measures based on a real-life situation such as the following: A fish tank is shown below. The length of the fish tank is twice the height. The depth of the water in the fish tank is half of the height of the fish tank. Select and use appropriate formulas to determine: (1) the perimeter and the area of the bottom of the fish tank; (2) the volume of the entire fish tank; (3) the volume of the water in the fish tank; and (4) the difference between the volume of the water in the tank and the volume of the entire tank. Display all calculations and solution processes in a graphic organizer and justify in writing how each measure was determined. Standard(s): 5.10B, 5.10C, 5.14A, 5.14D, 5.15A, 5.15B ELPS ELPS.c.1C, ELPS.c.4F page 23 of 61

24 Enhanced Instructional Transition Guide Grade 5/ Unit Unit 09: Suggested Duration: 5 days 05/10/13 page 24 of 61

25 Perimeter and Area Representation Cards KEY Grade 5 Word Problem Formula Expression Model Harold measured the 4 sides of his rectangular garden. His garden is 20 ft long and 8 ft wide. How much garden fencing will he need to place around his garden? P = (2 x l) + (2 x w) (2 x 20) + (2 x 8) 56 ft The sides of a square parking lot are each 75 feet. How much asphalt is needed to cover this parking lot? A = s x s 75 x sq ft A rectangular flag is 42 inches long and 24 inches wide. What is the area of the flag? A = l x w sq in A soccer field is 110 yd long and 70 yd wide. If Jeremy runs around the edges of this field once, how far will he have run? P = (2 x l) + (2 x w) (2 x 110) + (2 x 70) 360 yd Sheryl wants to sew lace around the edges of her scarf. Her scarf is a square that measures 75 centimeters on each side. How much lace will she need? P = 4 x s 4 x cm 75 Tony wants to glue trim around the edges of a square poster. The sides of the poster each measure 42 inches. How much trim will he need? P = 4 x s in. 42 A rectangular campsite measures 110 feet by 70 feet. What is the area of the campsite? A = l x w 110 x sq ft Jill is designing a cover for her brother s square sandbox which measures 7 feet on each side. What will the area of the cover be? A = s x s 7 x 7 49 sq ft , TESCCC 05/12/13 page 1 of 1

26 Perimeter and Area Representation Cards Grade 5 Harold measured the 4 sides of his rectangular garden. His garden is 20 ft long and 8 ft wide. How much garden fencing will he need to place around his garden? Sheryl wants to sew lace around the edges of her scarf. Her scarf is a square that measures 75 centimeters on each side. How much lace will she need? The sides of a square parking lot are each 75 feet. How much asphalt is needed to cover this parking lot? Tony wants to glue trim around the edges of a square poster. The sides of the poster each measure 42 inches. How much trim will he need? A rectangular flag is 42 inches long and 24 inches wide. What is the area of the flag? A rectangular campsite measures 110 feet by 70 feet. What is the area of the campsite? A soccer field is 110 yd long and 70 yd wide. If Jeremy runs around the edges of this field once, how far will he have run? Jill is designing a cover for her brother s square sandbox which measures 7 feet on each side. What will the area of the cover be? 2012, TESCCC 05/12/13 page 1 of 4

27 Perimeter and Area Representation Cards Grade 5 P = (2 x l) + (2 x w) P = 4 x s A = s x s P = 4 x s A = l x w A = l x w P = (2 x l) + (2 x w) A = s x s 2012, TESCCC 05/12/13 page 2 of 4

28 Perimeter and Area Representation Cards Grade 5 (2 x 20) + (2 x 8) 4 x x x 70 (2 x 110) + (2 x 70) 7 x , TESCCC 05/12/13 page 3 of 4

29 Perimeter and Area Representation Cards Grade , TESCCC 05/12/13 page 4 of 4

30 Centimeter Grid Grade , TESCCC 10/08/12 page 1 of 1

31 Grade 5 Fencing in the Beetle Marco has a pet beetle and plans to fence in a rectangular area of his desk for the beetle. Use this piece of string and centimeter grid paper to determine the shape and size of the area he could fence in. 2012, TESCCC 10/08/12 page 1 of 1

32 Perimeter/Area/Volume Key Concept Table SAMPLE KEY Grade 5 Complete the table by writing the definition, the formula, drawing a model, and providing an example of each type of measurement. Perimeter Area Volume Rectangle Square Rectangle Square Rectangular Prism Cube Definition The distance around a figure The number of square units that cover a figure The number of cubic units needed to fill a 3-dimensional figure Formula P = (2 x l) + (2 x w) P = 4 x s A = l x w A = s x s V = l x w x h V = s x s x s Model l w w s l w l s s l w h s s s Example Answers may vary. Answers may vary. Answers may vary. Answers may vary. Answers may vary. Answers may vary. Explain how you determine whether to use the formula for perimeter, area, or volume for a given situation. Possible answer: To find the distance around a rectangular figure, use the perimeter formula. To find the amount of space covered by a rectangular figure, use the area formula. To find how much space is enclosed by a solid rectangular figure, use the volume formula. 2012, TESCCC 04/29/13 page 1 of 1

33 Grade 5 Perimeter/Area/Volume Key Concept Table Complete the table by writing the definition, the formula, drawing a model, and providing an example of each type of measurement. Perimeter Area Volume Rectangle Square Rectangle Square Rectangular Prism Cube Definition Formula Model Example Explain how you determine whether to use the formula for perimeter, area, or volume for a given situation. 2012, TESCCC 10/08/12 page 1 of 1

34 Grade 5 Kitchen Area Greg has 36 kitchen tiles and wants to use them to make a rectangular kitchen floor. Use the tiles to find all the possible ways he can make the rectangular kitchen floor. Record your findings on inch grid paper. 2012, TESCCC 05/08/13 page 1 of 1

35 Inch Grid Paper Grade , TESCCC 04/26/12 page 1 of 1

36 Finding Perimeter and Area of Irregular Figures Notes/Practice KEY Perimeter Notes Grade 5 Sample 1 To find the perimeter of an irregular figure: Add all the side lengths = cm 2.5 cm The perimeter is 12 cm. 1.6 cm 2 cm 3.3 cm Sample 2 To find the length of an unknown side of an irregular figure when the perimeter is known: Find the length of side x if the perimeter of the figure equals 50 feet. P = sum of the side lengths x 50 = x = x = x x = 5; because = 50 Side x is 5 feet long. 19 ft 16 ft 4 ft 6 ft 2012, TESCCC 05/12/13 page 1 of 5

37 Finding Perimeter of Irregular Figures Notes/Practice KEY Grade 5 Perimeter and Area Notes Sample Find the perimeter and area of this polygon. 7 in. 15 in. 5 in. 11 in. 4 in.? First, find the unknown side length. Look at the sides opposite the unknown side. Their measures are 15 in. and 5 in. The unknown side is or 20 inches long. 7 in. 15 in. Find the perimeter using the sum of the side lengths. P = = 62 in. 4 in. 5 in. 11 in. 5 in in. = 20 in. The area of this figure can be found by calculating the area of the small rectangle and adding it to the large rectangle. A = (4 x 5) + (15 x 11) = 185 in 2 7 in. 5 in. 15 in. 15 x in. 4 in. 4 x 5 20 in. 2012, TESCCC 05/12/13 page 2 of 5

38 Finding Perimeter and Area of Irregular Figures Notes/Practice KEY Grade 5 Practice: Use the figure itself and the space next to each figure to show your work and explain your reasoning. (1) Find the perimeter of this figure. 13 m 24 m 45 m P = 13 m + 45 m + 43 m + 24 m = 125 m 43 m (2) What is the length of side x if the perimeter of this figure equals 941 mm? P = sum of the side lengths 218 mm 172 mm 941 = x = x = x x = 178; because = 941 x 183 mm Side x is 178 mm long. 190 mm (3) What is the perimeter of this polygon?? 6 yd 5 yd 11 yd 5 yd Look at the sides opposite the unknown side. Their measures are 5 yd and 7 yd, so, the unknown side is or 12 yards long. Find the perimeter using the sum of the side lengths. P = = 46 yd 7 yd 2012, TESCCC 05/12/13 page 3 of 5

39 Finding Perimeter and Area of Irregular Figures Notes/Practice KEY Grade 5 (4) What is the area of this polygon? Use the length of the side found in the problem above. 6 yd? Find the area using the sum of the area of the two rectangles that compose this shape. 5 yd 5 yd 7 yd 11 yd A = (12 x 6) + (5 x 7)=107 square yards or A=(6 x 5) + (7 x 11) = 107 square yards (5) What is the perimeter of this polygon?? 6 m 4 m 4m Look at the sides opposite the unknown side. Their measures are 4 m and 5 m, so, the unknown side is or 9 meters long. Find the perimeter using the sum of the side lengths. 5 m P = = 38 m 10 m (6) What is the area of this polygon? 6 m Use the length of the side found in the problem above.? 10 m 4 m 4m 5 m Find the area using the sum of the area of the two rectangles that compose this shape. A = (9 x 6) + (4 x 5)=74 square meters or A = (6 x 4) + (10 x 5) = 74 square meters 2012, TESCCC 05/12/13 page 4 of 5

40 Finding Perimeter and Area of Irregular Figures Notes/Practice KEY Grade 5 Use a ruler to determine the perimeter for each figure. (7) 81 ft 54 ft 54 ft 81 ft 1 inch = 27 feet Perimeter in yards: P = = 270 ft = 90 yards (8) 675 km 900 km 675 km 675 km 900 km 225 km 1 cm = 225 km 1,800 km Perimeter in meters: P = ,800 = 5,850 km 5,850 x 1000 = 5,850,000 m 2012, TESCCC 05/12/13 page 5 of 5

41 Finding Perimeter and Area of Irregular Figures Notes/Practice Perimeter Notes Grade 5 Sample 1 To find the perimeter of an irregular figure: Add all the side lengths = cm 2.5 cm The perimeter is 12 cm. 1.6 cm 2 cm 3.3 cm Sample 2 To find the length of an unknown side of an irregular figure when the perimeter is known: Find the length of side x if the perimeter of the figure equals 50 feet. P = sum of the side lengths x 50 = x = x = x x = 5; because = 50 Side x is 5 feet long. 19 ft 16 ft 4 ft 6 ft 2012, TESCCC 05/12/13 page 1 of 5

42 Finding Perimeter of Irregular Figures Notes/Practice Grade 5 Perimeter and Area Notes Sample Find the perimeter and area of this polygon. 7 in. 15 in. 5 in. 11 in. 4 in.? First, find the unknown side length. Look at the sides opposite the unknown side. Their measures are 15 in. and 5 in. The unknown side is or 20 inches long. 7 in. 15 in. Find the perimeter using the sum of the side lengths. P = = 62 in. 4 in. 5 in. 11 in. 5 in in. = 20 in. The area of this figure can be found by calculating the area of the small rectangle and adding it to the large rectangle. A = (4 x 5) + (15 x 11) = 185 in 2 7 in. 5 in. 15 in. 15 x in. 4 in. 4 x 5 20 in. 2012, TESCCC 05/12/13 page 2 of 5

43 Finding Perimeter and Area of Irregular Figures Notes/Practice Grade 5 Practice: Use the figure itself and the space next to each figure to show your work and explain your reasoning. (1) Find the perimeter of this figure. 13 m 24 m 45 m 43 m (2) What is the length of side x if the perimeter of this figure equals 941 mm? 218 mm 172 mm x 183 mm 190 mm (3) What is the perimeter of this polygon?? 6 yd 5 yd 11 yd 5 yd 7 yd 2012, TESCCC 05/12/13 page 3 of 5

44 Finding Perimeter and Area of Irregular Figures Notes/Practice Grade 5 (4) What is the area of this polygon?? 6 yd 5 yd 11 yd 5 yd 7 yd (5) What is the perimeter of this polygon? 6 m 4 m? 4m 5 m 10 m (6) What is the area of this polygon? 6 m 4 m? 4m 5 m 10 m 2012, TESCCC 05/12/13 page 4 of 5

45 Finding Perimeter and Area of Irregular Figures Notes/Practice Grade 5 Use a ruler to determine the perimeter for each figure. (7) 1 inch = 27 feet Perimeter in yards: (8) 1 cm = 225 km Perimeter in meters: 2012, TESCCC 05/12/13 page 5 of 5

46 Perimeter, Area, and Volume Relationships KEY Complete this table as you follow the steps below. Grade 5 Length (l) Width (w) Height (h) Perimeter of Base Figure 1 5 cm 3 cm 1 cm 16 cm Figure 2 5 cm 3 cm 2 cm 16 cm Figure 3 5 cm 3 cm 3 cm 16 cm Figure 4 5 cm 3 cm 4 cm 16 cm Figure 5 5 cm 3 cm 5 cm 16 cm Area of Base 15 square cm 15 square cm 15 square cm 15 square cm 15 square cm Total Number of Cubes Volume 15 cubic cm 30 cubic cm 45 cubic cm 60 cubic cm 75 cubic cm 1. Draw a 5 3 rectangle on centimeter grid paper. Place centimeter cubes on the rectangle as shown below. Record the perimeter of the base rectangle, area of the base rectangle, number of cubes you used to create the base rectangle, and volume of the rectangular prism in the table above for Figure 1. Figure 1 2. Add another layer to this prism so that it is 2 units in height as shown below. Record the perimeter of the base rectangle, area of the base rectangle, number of cubes you used to create the base rectangle, and volume of the rectangular prism in the table above for Figure 2. Figure 2 3. Add another layer to this prism so that it is 3 units in height. Record the perimeter of the base rectangle, area of the base rectangle, number of cubes you used to create the base rectangle, and volume of the rectangular prism in the table above for Figure Continue adding layers until the prism is 5 units tall. Record the perimeter of the base rectangle, area of the base rectangle, number of cubes you used to create the base rectangle, and volume of the rectangular prism in the table above for Figure 4 and Figure What did you notice about the perimeter and area of the base rectangle for each of the figures? The perimeter of the base and area of the base remained the same. 6. Based on the information in the table, how could you use the length, width, and height of a prism to find the total number of cubes without counting them? Write a formula you could use to show this. Answers may vary. We could multiply the length, the width, and the height to get the total number of cubes or the volume of the prism. V = l x w x h 2012, TESCCC 05/12/13 page 1 of 2

47 Perimeter, Area, and Volume Relationships KEY Grade 5 Use the table below to record your data and find the volume after building each rectangular prism listed below. Length (l) Width (w) Height (h) Perimeter of Base Figure 1 4 cm 2 cm 3 cm 12 cm Figure 2 5 cm 2 cm 5 cm 14 cm Figure 3 8 cm 4 cm 2 cm 24 cm Area of Base 8 square cm 10 square cm 32 square cm Total Number of Cubes Volume 24 cubic cm 50 cubic cm 64 cubic cm 7. Figure 1: Length = 4 cm, Width = 2 cm, Height = 3 cm 8. Figure 2: Length = 5 cm, Width = 2 cm, Height = 5 cm 9. Figure 3: Length = 8 cm, Width = 4 cm, Height = 2 cm 2012, TESCCC 05/12/13 page 2 of 2

48 Perimeter, Area, and Volume Relationships Grade 5 Complete this table as you follow the steps below. Figure 1 Length (l) Width (w) Height (h) Perimeter of Base Area of Base Total Number of Cubes Volume Figure 2 Figure 3 Figure 4 Figure 5 1. Draw a 5 3 rectangle on centimeter grid paper. Place centimeter cubes on the rectangle as shown below. Record the perimeter of the base rectangle, area of the base rectangle, number of cubes you used to create the base rectangle, and volume of the rectangular prism in the table above for Figure 1. Figure 1 2. Add another layer to this prism so that it is 2 units in height as shown below. Record the perimeter of the base rectangle, area of the base rectangle, number of cubes you used to create the base rectangle, and volume of the rectangular prism in the table above for Figure 2. Figure 2 3. Add another layer to this prism so that it is 3 units in height. Record the perimeter of the base rectangle, area of the base rectangle, number of cubes you used to create the base rectangle, and volume of the rectangular prism in the table above for Figure Continue adding layers until the prism is 5 units tall. Record the perimeter of the base rectangle, area of the base rectangle, number of cubes you used to create the base rectangle, and volume of the rectangular prism in the table above for Figure 4 and Figure What did you notice about the perimeter and area of the base rectangle for each of the figures? 6. Based on the information in the table, how could you use the length, width, and height of a prism to find the total number of cubes without counting them? Write a formula you could use to show this. 2012, TESCCC 05/12/13 page 1 of 2

49 Perimeter, Area, and Volume Relationships Grade 5 Use the table below to record your data and find the volume after building each rectangular prism listed below. Length (l) Width (w) Height (h) Perimeter of Base Area of Base Total Number of Cubes Volume Figure 1 Figure 2 Figure 3 7. Figure 1: Length = 4 cm, Width = 2 cm, Height = 3 cm 8. Figure 2: Length = 5 cm, Width = 2 cm, Height = 5 cm 9. Figure 3: Length = 8 cm, Width = 4 cm, Height = 2 cm 2012, TESCCC 05/12/13 page 2 of 2

50 Jewelry Box KEY Grade 5 The dimensions of a jewelry box are 6 inches by 3 inches by 2 inches. Sketch a model of the jewelry box, labeling each dimension. Then find the volume of the jewelry box. Sketches may vary in orientation, but dimensions should be the same. 6 x 3 x 2 = 36 cubic inches 2012, TESCCC 10/08/12 page 1 of 1

51 Grade 5 Jewelry Box The dimensions of a jewelry box are 6 inches by 3 inches by 2 inches. Sketch a model of the jewelry box, labeling each dimension. Then find the volume of the jewelry box. 2012, TESCCC 10/08/12 page 1 of 1

52 Volume Practice/Problem Solving KEY Grade 5 Find the volume of each figure in cubic units. (1) (2) (3) V = 6 cubic units V = 18 cubic units V = 8 cubic units Find the volume of each. Show your work. (4) rectangular prism l = 8 cm w = 2 cm h = 5 cm V = 80 cubic cm (8 x 2 x 5) (5) rectangular prism l = 4 m w = 2 m h = 5 m V = 40 cubic m (4 x 2 x 5) (6) cube s = 2 yd V = 8 cubic yd (2 x 2 x 2) (7) cube s = 16 ft V = 4096 cubic ft (16 x 16 x 16) (8) (9) 20 cm 20 cm 20 cm V = 8000 cubic cm (20 x 20 x 20) 18 in. 30 in. 8 in. V = 4320 cubic in. (30 x 8 x 18) (10) Maxine decorates boxes to sell at craft fairs. The boxes are in the shape of a cube measuring 7 inches on each side. What is the volume of each box? Show your work. 343 cubic in. (7 x 7 x 7) (11) Bernie has a yellow carton that measures 1 m 3 m 2 m, a white one that measures 1 m 2 m 1 m, and a brown one that measures 2 m 2 m 1 m. Order the cartons from least to greatest in volume. Show your work. White: 1 x 2 x 1 = 2 cubic m; Brown: 2 x 2 x 1 = 4 cubic m; Yellow: 1 x 3 x 2 = 6 cubic m 2012, TESCCC 05/12/13 page 1 of 2