Enhanced Instructional Transition Guide
Grade 5/Mathematics
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 http://www.tea.state.tx.us/index2.aspx?id=6148
5.10
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 Enhanced Instructional Transition Guide
Grade 5/Mathematics
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.
5.15
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 Enhanced Instructional Transition Guide
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
Grade 05 Mathematics 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 Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
Enhanced Instructional Transition Guide
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 Mathematics 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 Enhanced Instructional Transition Guide
Grade 5/Mathematics
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 Enhanced Instructional Transition Guide
Grade 5/Mathematics
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
1
Suggested Instructional Procedures
Notes for Teacher
Topics:
Spiraling Review
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 Mathematics Reference Materials to
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 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
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 Mathematics 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:
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.
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 Mathematics
Reference Materials (1 per student)
math journal (1 per student)
TEACHER NOTE
The STAAR Grade 5 Mathematics 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:
Perimeter
Area
Explore/Explain 1
ATTACHMENTS
Handout: Centimeter Grid Paper (1
per student)
Teacher Resource: Fencing in the
Beetle (1 per teacher)
page 7 of 61 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
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.
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:
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)
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.
How do you know if your shape is rectangular? (It has 4 sides and its opposite
sides are equal in length.)
page 8 of 61 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
Notes for Teacher
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.
3. Facilitate a class discussion to debrief student solutions.
Ask:
How many rectangles were you able to make with your string? (9)
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.
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:
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 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
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:
Spiraling Review
Perimeter
Area
Explore/Explain 2
Students explore perimeter and area in a real-life problem situation.
Instructional Procedures:
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 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
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:
TEACHER NOTE
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.
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 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
Notes for Teacher
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:
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 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
Notes for Teacher
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.)
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:
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
ATTACHMENTS
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 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
Suggested Instructional Procedures
Notes for Teacher
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.
Area of Irregular Figures
Notes/Practice (1 per student)
MATERIALS
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.
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.
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
State Resources
MTR 3-5: Fill “Er Up!; Cover It Up!; Outline It!;
Measurement Jeopardy
TEXTEAMS: Rethinking Elementary Mathematics
Part I: Tiffany’s Beanie Babies™
TEXTEAMS: Rethinking Elementary Mathematics
page 14 of 61 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
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.
Notes for Teacher
Part II: Tangram Task B: Measuring Tangrams;
Area in Square Meters; Measurement Scavenger
Hunt I & II
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.
3
Topics:
Spiraling Review
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:
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 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
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.
Notes for Teacher
student)
Teacher Resource:
Perimeter/Area/Volume Key
Concept Table KEY (1 per teacher)
MATERIALS
centimeter cubes (75 per student)
TEACHER NOTE
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
In order to reproduce materials consistent with
intended measurements, set the print menu to print
page 16 of 61 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
volume of the sandbox?
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
Notes for Teacher
the handout at 100% by selecting “None” or “Actual
size” under the Page Scaling/Size option.
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.
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) = 10 + 8, or 18)
8. Instruct students to label the rectangle on their handout: Centimeter Grid Paper
page 17 of 61 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
Notes for Teacher
accordingly with the dimensions of the side lengths and then shade the inside of the
rectangle to show the area of the rectangle.
Ask:
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 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
Notes for Teacher
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.
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:
Spiraling Review
Volume
Explore/Explain 4
Students use problem-solving strategies and formulas to find the volume of objects in problems situations.
Instructional Procedures:
ATTACHMENTS
Teacher Resource: Jewelry Box
KEY (1 per teacher)
Teacher Resource: Jewelry Box (1
page 19 of 61 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
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 Mathematics 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 Mathematics 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.
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 Mathematics
Reference Materials (1 per student)
TEACHER NOTE
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:
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 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
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 Enhanced Instructional Transition Guide
Suggested
Day
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
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.
2. Place students in groups of 4. Distribute handout: Measurement of Rectangular Prisms
and the STAAR Grade 5 Mathematics Reference Materials to each student. Instruct groups
to use their STAAR Grade 5 Mathematics 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.
Notes for Teacher
Appropriate Measurement
Formulas Practice (1 per student)
MATERIALS
STAAR Grade 5 Mathematics
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
Instructional Procedures:
MATERIALS
STAAR Grade 5 Mathematics
Reference Materials (1 per student)
1. Assess student understanding of related concepts and processes by using the
Performance Indicator(s) aligned to this lesson.
Performance Indicator(s):
page 22 of 61 Enhanced Instructional Transition Guide
Suggested
Day
Suggested Instructional Procedures
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
Notes for Teacher
Grade 05 Mathematics 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 Enhanced Instructional Transition Guide
Grade 5/Mathematics
Unit Unit 09:
Suggested Duration: 5 days
05/10/13
page 24 of 61 Grade 5
Mathematics
Unit: 09 Lesson: 03
Perimeter and Area Representation Cards KEY
Word Problem
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?
Formula
(2 x 20) + (2 x 8)
P = (2 x l) + (2 x w)
8
20
75
75 x 75
A rectangular flag is 42 inches long and
24 inches wide. What is the area of the
flag?
A=lxw
75
5625 sq ft
42
42 × 24
1008 sq in.
24
110
(2 x 110) + (2 x 70)
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)
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=4xs
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=4xs
©2012, TESCCC
8
56 ft
A=sxs
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?
Model
20
The sides of a square parking lot are
each 75 feet. How much asphalt is
needed to cover this parking lot?
A rectangular campsite measures 110
feet by 70 feet. What is the area of the
campsite?
Expression
70
70
360 yd
110
4 x 75
75
300 cm
4 × 42
42
168 in.
110
110 x 70
A=lxw
7700 sq ft
70
7
7x7
A=sxs
49 sq ft
05/12/13
7
page 1 of 1
Grade 5
Mathematics
Unit: 09 Lesson: 03
Perimeter and Area Representation Cards
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 A rectangular campsite measures
110 feet by 70 feet. What is the
and 24 inches wide. What is the
area of the campsite?
area of the flag?
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?
©2012, TESCCC
05/12/13
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?
page 1 of 4
Grade 5
Mathematics
Unit: 09 Lesson: 03
Perimeter and Area Representation Cards
P = (2 x l) + (2 x w)
P=4xs
A=sxs
P=4xs
A=lxw
A=lxw
P = (2 x l) + (2 x w)
A=sxs
©2012, TESCCC
05/12/13
page 2 of 4
Grade 5
Mathematics
Unit: 09 Lesson: 03
Perimeter and Area Representation Cards
(2 x 20) + (2 x 8)
4 x 75
75 x 75
4 × 42
42 × 24
110 x 70
(2 x 110) + (2 x 70)
7x7
©2012, TESCCC
05/12/13
page 3 of 4
Grade 5
Mathematics
Unit: 09 Lesson: 03
Perimeter and Area Representation Cards
20
8
75
8
75
20
110
42
70
24
70
110
75
42
7
110
70
©2012, TESCCC
7
05/12/13
page 4 of 4
Grade 5
Mathematics
Unit: 09 Lesson: 03
Centimeter Grid
©2012, TESCCC
10/08/12
page 1 of 1
Grade 5
Mathematics
Unit: 09 Lesson: 03
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
Grade 5
Mathematics
Unit: 09 Lesson: 03
Perimeter/Area/Volume Key Concept Table SAMPLE KEY
Complete the table by writing the definition, the formula, drawing a model, and providing an example of each type of measurement.
Perimeter
Rectangle
Definition
Formula
Area
Square
The distance around a figure
P = (2 x l) + (2 x w)
Rectangle
w
Square
The number of square units that cover a
figure
P=4xs
A=lxw
l
Model
Volume
A=sxs
s
w
Answers may vary.
V=lxwxh
V=sxsxs
w
l
Answers may vary.
s
h
s
l
Example
Cube
The number of cubic units needed to fill
a 3-dimensional figure
s
l
w
Rectangular Prism
Answers may vary.
Answers may vary.
Answers may vary.
s
s
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
Grade 5
Mathematics
Unit: 09 Lesson: 03
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
Rectangle
Area
Square
Rectangle
Volume
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
Grade 5
Mathematics
Unit: 09 Lesson: 03
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
Grade 5
Mathematics
Unit: 09 Lesson: 03
Inch Grid Paper
©2012, TESCCC
04/26/12
page 1 of 1
Grade 5
Mathematics
Unit: 09 Lesson: 03
Finding Perimeter and Area of Irregular Figures
Notes/Practice KEY
Perimeter Notes
Sample 1
To find the perimeter of an irregular figure:
•
2.6 cm
Add all the side lengths.
2.5 cm
2.6 + 2.5 + 2 + 3.3 + 1.6 = 12
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 + 16 + 6 + 4 + 19
50 = x + 45
50 – 45 = x
x = 5; because 45 + 5 = 50
19 ft
16 ft
Side x is 5 feet long.
4 ft
©2012, TESCCC
05/12/13
6 ft
page 1 of 5
Grade 5
Mathematics
Unit: 09 Lesson: 03
Finding Perimeter of Irregular Figures
Notes/Practice KEY
Perimeter and Area Notes
Sample
15 in.
Find the perimeter and area of this polygon.
7 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 15 + 5 or 20 inches
long.
15 in.
7 in.
5 in.
Find the perimeter using the sum of the
side lengths.
11 in.
4 in.
P = 4 + 5 + 7 + 15 + 11 + 20 = 62 in.
5 in. + 15 in. = 20 in.
•
15 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
7 in.
2
5 in.
4 in.
15 x 11
11 in.
4x5
20 in.
©2012, TESCCC
05/12/13
page 2 of 5
Grade 5
Mathematics
Unit: 09 Lesson: 03
Finding Perimeter and Area of Irregular Figures
Notes/Practice KEY
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
45 m
P = 13 m + 45 m + 43 m + 24 m = 125
m
24 m
43 m
(2)
What is the length of side x if the
perimeter of this figure equals 941
mm?
218 mm
P = sum of the side lengths
172 mm
183 mm
x
941 = x + 218 + 172 + 183 + 190
941 = x + 763
941 – 763 = x
x = 178; because 763 + 178 = 941
Side x is 178 mm long.
190 mm
(3)
What is the perimeter of this polygon?
?
Look at the sides opposite the unknown
side. Their measures are 5 yd and 7 yd, so,
the unknown side is 5 + 7 or 12 yards long.
6 yd
11 yd
5 yd
Find the perimeter using the sum of the
side lengths.
P = 6 + 12 + 11 + 7 + 5 + 5 = 46 yd
5 yd
7 yd
©2012, TESCCC
05/12/13
page 3 of 5
Grade 5
Mathematics
Unit: 09 Lesson: 03
Finding Perimeter and Area of Irregular Figures
Notes/Practice KEY
(4)
What is the area of this polygon?
Use the length of the side found in the
problem above.
?
Find the area using the sum of the area of
the two rectangles that compose this
shape.
6 yd
A = (12 x 6) + (5 x 7)=107 square
yards or
11 yd
5 yd
5 yd
A=(6 x 5) + (7 x 11) = 107 square
yards
7 yd
(5)
What is the perimeter of this polygon?
6m
Look at the sides opposite the unknown
side. Their measures are 4 m and 5 m, so,
the unknown side is 4 + 5 or 9 meters long.
Find the perimeter using the sum of the
side lengths.
4m
4m
?
5m
P = 6 + 4 + 4 + 5 + 10 + 9 = 38 m
10 m
(6)
What is the area of this polygon?
Use the length of the side found in the
problem above.
6m
Find the area using the sum of the area of
the two rectangles that compose this
shape.
4m
4m
?
5m
10 m
©2012, TESCCC
A = (9 x 6) + (4 x 5)=74 square meters
or
A = (6 x 4) + (10 x 5) = 74 square
meters
05/12/13
page 4 of 5
Grade 5
Mathematics
Unit: 09 Lesson: 03
Finding Perimeter and Area of Irregular Figures
Notes/Practice KEY
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 = 54 + 54 + 81 + 81 = 270 ft
270 ÷ 3 = 90 yards
(8)
m
5k
90
0k
m
67
675 km
900 km
675 km
225 km
1,800 km
1 cm = 225 km
Perimeter in meters:
P = 900 + 675 + 675 + 675 + 900 + 225 + 1,800 = 5,850 km
5,850 x 1000 = 5,850,000 m
©2012, TESCCC
05/12/13
page 5 of 5
Grade 5
Mathematics
Unit: 09 Lesson: 03
Finding Perimeter and Area of Irregular Figures
Notes/Practice
Perimeter Notes
Sample 1
To find the perimeter of an irregular figure:
•
2.6 cm
Add all the side lengths.
2.5 cm
2.6 + 2.5 + 2 + 3.3 + 1.6 = 12
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.
x
P = sum of the side lengths
50 = x + 16 + 6 + 4 + 19
50 = x + 45
50 – 45 = x
x = 5; because 45 + 5 = 50
19 ft
16 ft
Side x is 5 feet long.
4 ft
©2012, TESCCC
05/12/13
6 ft
page 1 of 5
Grade 5
Mathematics
Unit: 09 Lesson: 03
Finding Perimeter of Irregular Figures
Notes/Practice
Perimeter and Area Notes
Sample
15 in.
Find the perimeter and area of this polygon.
7 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 15 + 5 or 20 inches
long.
15 in.
7 in.
5 in.
Find the perimeter using the sum of the
side lengths.
11 in.
4 in.
P = 4 + 5 + 7 + 15 + 11 + 20 = 62 in.
5 in. + 15 in. = 20 in.
•
15 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
7 in.
2
5 in.
4 in.
15 x 11
11 in.
4x5
20 in.
©2012, TESCCC
05/12/13
page 2 of 5
Grade 5
Mathematics
Unit: 09 Lesson: 03
Finding Perimeter and Area of Irregular Figures
Notes/Practice
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
45 m
24 m
43 m
(2)
What is the length of side x if the
perimeter of this figure equals 941
mm?
218 mm
172 mm
183 mm
x
190 mm
(3)
What is the perimeter of this polygon?
?
6 yd
11 yd
5 yd
5 yd
7 yd
©2012, TESCCC
05/12/13
page 3 of 5
Grade 5
Mathematics
Unit: 09 Lesson: 03
Finding Perimeter and Area of Irregular Figures
Notes/Practice
(4)
What is the area of this polygon?
?
6 yd
11 yd
5 yd
5 yd
7 yd
(5)
What is the perimeter of this polygon?
6m
4m
4m
?
5m
10 m
(6)
What is the area of this polygon?
6m
4m
4m
?
5m
10 m
©2012, TESCCC
05/12/13
page 4 of 5
Grade 5
Mathematics
Unit: 09 Lesson: 03
Finding Perimeter and Area of Irregular Figures
Notes/Practice
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
Grade 5
Mathematics
Unit: 09 Lesson: 03
Perimeter, Area, and Volume Relationships KEY
Complete this table as you follow the steps below.
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
15
30
45
60
75
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 3.
4. 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 5.
5. 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
Grade 5
Mathematics
Unit: 09 Lesson: 03
Perimeter, Area, and Volume Relationships KEY
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
24 cubic
cm
50
50 cubic
cm
64
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
Grade 5
Mathematics
Unit: 09 Lesson: 03
Perimeter, Area, and Volume Relationships
Complete this table as you follow the steps below.
Length
(l)
Width
(w)
Height
(h)
Perimeter
of Base
Area of
Base
Total
Number of
Cubes
Volume
Figure 1
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 3.
4. 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 5.
5. 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
Grade 5
Mathematics
Unit: 09 Lesson: 03
Perimeter, Area, and Volume Relationships
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
Grade 5
Mathematics
Unit: 09 Lesson: 03
Jewelry Box KEY
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
Grade 5
Mathematics
Unit: 09 Lesson: 03
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
Grade 5
Mathematics
Unit: 09 Lesson: 03
Volume Practice/Problem Solving KEY
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
(5)
rectangular prism
l=4m
w=2m
h=5m
V = 80 cubic cm (8 x 2 x 5)
V = 40 cubic m (4 x 2 x 5)
(6)
(7)
cube
s = 2 yd
cube
s = 16 ft
V = 8 cubic yd (2 x 2 x 2)
V = 4096 cubic ft (16 x 16 x 16)
(8)
(9)
20 cm
20 cm
18 in.
20 cm
V = 8000 cubic cm (20 x 20 x 20)
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
Grade 5
Mathematics
Unit: 09 Lesson: 03
Volume Practice/Problem Solving KEY
Use the diagram of the cereal box shown to answer the following questions.
(12)
What is the volume of the cereal box shown?
480 cubic in. (10 x 3 x 16)
Cereal
16 in.
Cereal level
(13)
What is the volume of the cereal in the box?
150 cubic in. (10 x 3 x 5)
5 in.
3 in.
10 in.
(14)
How could you find the volume of the box that is not filled with cereal? What is this
volume? Find the height of the box that does not have cereal (16 – 5 = 11 in.)
and use that in the volume formula for height. 10 x 3 x 11 = 330 cubic inches of
the box is not filled with cereal; OR Subtract the volume of the cereal from the
box’s total volume (480 – 150 = 330 cubic inches of empty box).
====================================================================
Use the table below to help solve this problem.
Janet has an oddly-shaped gift to wrap. The dimensions of the gift are about 14 inches long,
4 inches wide, and 5 inches high. She needs a rectangular box that is little bit bigger than
the dimensions of the gift because she needs to put packing material around the gift. The
packing and shipping store had the following display for the sizes of boxes available. All the
boxes were rectangular prisms.
.
Dimensions and Volume of Various Size Boxes
Box
Length
(inches)
Width
(inches)
Height
(inches)
Volume
(cubic inches)
A
14
5
4
280
B
16
4
5
320
C
15
6
3
270
D
15
5
6
450
E
4
4
15
240
(15) What process was used to determine the volume of each box? Explain.
The volume formula: Volume = length x width x height
(16) Which box should Janet choose for her gift? Why?
Janet’s gift has a volume of 280 cubic inches (14 x 4 x 5). Janet should choose
box D because all of the box dimensions are a little bit bigger than the dimensions
of her gift. So, her gift would fit in this box along with the packing material.
©2012, TESCCC
05/12/13
page 2 of 2
Grade 5
Mathematics
Unit: 09 Lesson: 03
Volume Practice/Problem Solving
Find the volume of each figure in cubic units.
(1)
(2)
V = _______________
V = _______________
Find the volume of each. Show your work.
(4)
rectangular prism
l = 8 cm
w = 2 cm
h = 5 cm
(3)
(5)
V = _______________
rectangular prism
l=4m
w=2m
h=5m
V = ____________________________
V = ____________________________
(6)
(7)
cube
s = 2 yd
cube
s = 16 ft
V = ____________________________
V = ____________________________
(8)
(9)
20 cm
20 cm
18 in.
20 cm
V = ____________________________
30 in.
8 in.
V = ____________________________
(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.
(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.
©2012, TESCCC
05/12/13
page 1 of 2
Grade 5
Mathematics
Unit: 09 Lesson: 03
Volume Practice/Problem Solving
Use the diagram of the cereal box shown to answer the following questions.
(12)
What is the volume of the cereal box shown?
Cereal
16 in.
Cereal level
(13)
What is the volume of the cereal in the box?
5 in.
3 in.
10 in.
(14)
How could you find the volume of the box that is not filled with cereal? What is this
volume?
===================================================================
Use the table below to help solve this problem.
Janet has an oddly-shaped gift to wrap. The dimensions of the gift are about 14 inches long,
4 inches wide, and 5 inches high. She needs a rectangular box that is little bit bigger than
the dimensions of the gift because she needs to put packing material around the gift. The
packing and shipping store had the following display for the sizes of boxes available. All the
boxes were rectangular prisms.
Dimensions and Volume of Various Size Boxes
Box
Length
(inches)
Width
(inches)
Height
(inches)
Volume
(cubic inches)
A
14
5
4
280
B
16
4
5
320
C
15
6
3
270
D
15
5
6
450
E
4
4
15
240
(15) What process was used to determine the volume of each box? Explain.
(16) Which box should Janet choose for her gift? Why?
©2012, TESCCC
05/12/13
page 2 of 2
Grade 5
Mathematics
Unit: 09 Lesson: 03
Measurement of Rectangular Prisms KEY
Use the appropriate formulas to complete the chart below.
Length
Width
Height
Perimeter of Base
Area of Base
Volume
(1)
6 ft
4 ft
2 ft
20 ft
24 sq ft
48 cu ft
(2)
5 ft
4 ft
2 ft
18 ft
20 sq ft
40 cu ft
(3)
4 ft
4 ft
5 ft
16 ft
16 sq ft
80 cu ft
(4)
3 ft
5 ft
4 ft
16 ft
15 sq ft
60 cu ft
(5)
7 ft
6 ft
3 ft
26 ft
42 sq ft
126 cu ft
(6)
3 ft
6 ft
10 ft
18 ft
18 sq ft
180 cu ft
(7)
How is the area of the base of each rectangle related to the volume?
The volume is the area of the base (l x w) times the height.
(8)
How could you find the height of a rectangular prism if you knew the volume, the length, and the
width?
Find the area of the base (l x w) and divide the volume by this number.
©2012, TESCCC
10/08/12
page 1 of 1
Grade 5
Mathematics
Unit: 09 Lesson: 03
Measurement of Rectangular Prisms
Use the appropriate formulas to complete the chart below.
Length
Width
(1)
6 ft
4 ft
(2)
5 ft
4 ft
(3)
4 ft
(4)
3 ft
(5)
3 ft
Perimeter of Base
Area of Base
Volume
20 ft
24 sq ft
48 cu ft
16 ft
16 sq ft
2 ft
5 ft
5 ft
6 ft
(6)
Height
60 cu ft
3 ft
126 cu ft
10 ft
18 ft
18 sq ft
(7)
How is the area of the base of each rectangle related to the volume?
(8)
How could you find the height of a rectangular prism if you knew the volume, the length, and the
width?
©2012, TESCCC
10/08/12
page 1 of 1
Grade 5
Mathematics
Unit: 09 Lesson: 03
Selecting Appropriate Measurement Formulas Practice KEY
Determine whether you need to find perimeter, area, or volume for each problem. Then use
your STAAR Grade 5 Mathematics Reference Materials to solve each problem. Show your
work.
1. Marsha wants to make a frame for a print that is 26 inches long and 18 inches wide. She
found a piece of metal trim that she would like to use. How much of the metal trim will she
need to make the frame?
Perimeter: P = (2 x 26) + (2 x 18)
P = 52 + 36
P = 88 inches of metal trim needed
2. Lindsey is covering the bottom of her jewelry box with velvet. Her jewelry box is a
rectangular prism that is 8 inches long, 7 inches wide, and 4 inches high. How much velvet
does Lindsey need?
Area: A = 8 x 7
A = 56 sq inches of velvet needed
3. Mr. Gomez bought a freezer for his restaurant. The freezer’s dimensions were 70 inches
long, 24 inches wide, and 36 inches high. If Mr. Gomez fills the freezer completely, how
many cubic inches will it hold?
Volume: V = 70 x 24 x 36
V = 60,480 cubic inches
4. A rectangular playhouse floor is 7.5 feet long and 6.5 feet wide. How many feet of trim would
be needed to go around the playhouse floor?
Perimeter: P = 7.5 + 7.5 + 6.5 + 6.5
P = 15 + 13
P = 28 feet of trim needed
©2012, TESCCC
05/12/13
page 1 of 2
Grade 5
Mathematics
Unit: 09 Lesson: 03
Selecting Appropriate Measurement Formulas Practice KEY
Determine whether you need to find perimeter, area, or volume for each problem. Then use
your STAAR Grade 5 Mathematics Reference Materials to solve each problem. Show your
work.
5. Antonio is helping his father paint the side of their garage. The side of the garage is 10 feet
high and 15 feet wide. If each can of paint covers 80 square feet, how many cans of paint
will Antonio and his father need?
Area: A = 10 x 15
A = 150 sq feet of paint needed
150 ÷ 80 = 1 remainder 70. So, at least 2 cans will be needed. OR 80 x 2 = 160→
which is approximately equal to 150. They will need 2 cans of paint.
6. Jared wants to calculate how much rice he needs to refill an empty rectangular container.
The dimensions of the rectangular container are: 6 inches long, 8 inches high, and 2 inches
wide. How much rice would refill the container?
Volume: V = 6 x 8 x 2
V = 96 cubic inches
7. Cooper wants to put wood trim around the top edge of his rectangular fish tank. The
dimensions of the rectangular fish tank are shown below. How much wood trim does he
need?
5 in.
12 in.
15 in.
Perimeter: P = (2 x 15) + (2 x 12)
P = 30 + 24
P = 54 inches of wood trim needed
©2012, TESCCC
05/12/13
page 2 of 2
Grade 5
Mathematics
Unit: 09 Lesson: 03
Selecting Appropriate Measurement Formulas Practice
Determine whether you need to find perimeter, area, or volume for each problem. Then use
your STAAR Grade 5 Mathematics Reference Materials to solve each problem. Show your
work.
1. Marsha wants to make a frame for a print that is 26 inches long and 18 inches wide. She
found a piece of metal trim that she would like to use. How much of the metal trim will she
need to make the frame?
2. Lindsey is covering the bottom of her jewelry box with velvet. Her jewelry box is a
rectangular prism that is 8 inches long, 7 inches wide, and 4 inches high. How much velvet
does Lindsey need?
3. Mr. Gomez bought a freezer for his restaurant. The freezer’s dimensions were 70 inches
long, 24 inches wide, and 36 inches high. If Mr. Gomez fills the freezer completely, how
many cubic inches will it hold?
4. A rectangular playhouse floor is 7.5 feet long and 6.5 feet wide. How many feet of trim would
be needed to go around the playhouse floor?
©2012, TESCCC
10/08/12
page 1 of 2
Grade 5
Mathematics
Unit: 09 Lesson: 03
Selecting Appropriate Measurement Formulas Practice
Determine whether you need to find perimeter, area, or volume for each problem. Then use
your STAAR Grade 5 Mathematics Reference Materials to solve each problem. Show your
work.
5. Antonio is helping his father paint the side of their garage. The side of the garage is 10 feet
high and 15 feet wide. If each can of paint covers 80 square feet, how many cans of paint
will Antonio and his father need?
6. Jared wants to calculate how much rice he needs to refill an empty rectangular container.
The dimensions of the rectangular container are: 6 inches long, 8 inches high, and 2 inches
wide. How much rice would refill the container?
7. Cooper wants to put wood trim around the top edge of his rectangular fish tank. The
dimensions of the rectangular fish tank are shown below. How much wood trim does he
need?
5 in.
12 in.
15 in.
©2012, TESCCC
10/08/12
page 2 of 2