Math Journal - Chapter 10 - Perimeter, Area and Volume

10.01 The perimeter of a regular heptagon in 63 cm. Create a flow map to show how to find the
length of each side.
10.02 Create a model to demonstrate that the area of a triangle is 1/2 of the area of a
quadrilateral with the same base and height.
10.03 Use a rule to create an irregular polygon. Create a flow map to show the sequence of
steps required to find the area and perimeter of your polygon.
10.04 As you saw during the guided practice, the effects of doubling or halving the dimensions
of a polygon have a mathematical root. Write a paragraph to explain why you think this is
true. (I do not expect a correct answer - just a well thought out argument)

10.05 Write a narrative story (3 paragraphs) to tell a fifth grade student about today's
discovering pi activity. Open with expectations and a hook. Discuss the activity and
close your narrative by telling them what you discovered and/or why they should try it out
for themselves.
10.06 Use graph paper to recreate the nets on page 529. Attempt to create a solid figure with
each net.
10.07 Write a comparison/contrast piece to discuss how finding the surface area of a
rectangular pyramid is different from finding the surface area of a rectangular prism.

10.08 Finding the volume of pyramids isn't really harder than finding the volume of a prism, you
just have to use a different formula. The formula for finding the volume of a square
pyramid is S*S*H÷3. Why do you think that finding the volume of prisms is considered a
sixth grade objective while finding the volume of pyramids is saved for higher math?

10.09 Finding the volume of cones isn't really harder than finding the volume of a cylinder, you
just have to use a different formula. The formula for finding the volume of a cone is
π*d*d*h÷12. Why do you think that finding the volume of cylinders is considered a sixth
grade objective while finding the volume of cones is saved for higher math?

General Scoring Rubric:

0 No Response
1 Wrong response
2 Weak response
3 Showed understanding
4 Showed understanding and cited an example
5 Showed understanding, cited examples and communicated effectively enough to enable
others to understand.

© 2007 – Norm Mitchell (Math6.org) – All Rights Reserved

Freely reproducible for “non profit” educational purposes – visit http://www.math6.org/legal.htm for more details concerning “non-profit”.
 Name ______________
Word List – 3 Column Notes
Word Definition Example

area The amount of surface that an object covers. LxW

(measured in square units).
base

center

circle

circumference

cone

cylinder

diameter

edge

face

net

perimeter

pi

polyhedron

prism

pyramid

radius

surface area

vertex

volume

© 2007 – Norm Mitchell (Math6.org) – All Rights Reserved

Freely reproducible for “non-profit” educational purposes – visit http://www.math6.org/legal.htm for more details concerning “non-profit”.
 Name ______________
Matching
Perimeter, Area, and Volume – Matching
________1) area A. the middle of a circle.
the point that is equidistant to all the points in a circle.
________2) base
B. the number of cubic units needed to fill the space of a solid.
________3) center (measured in cubes)
C. the ratio that compares the circumference and diameter of any
________4) circle
circle.
________5) circumference D. a pattern made when the surface of a solid is laid out flat (2d).
E. a figure that is the set of all points that are the same distance
________6) cone
from a given point.
________7) cylinder F. a polyhedron with two congruent and parallel bases.
(made of bases and rectangles)
________8) diameter
G. the sum of the areas of all of the surfaces of a solid figure.
________9) edge H. a flat surface(s) of a solid for which the solid is named.
I. a line segment with one endpoint at the center of a circle and
________10) face
the other endpoint on the circle.
________11) net J. a chord that passes through the center of a circle.
K. a 3 dimensional object, or solid figure, with flat surfaces
________12) perimeter
L. a point at which three or more edges of a polyhedron meet.
________13) pi M. the measure of the distance around a figure.
N. the flat surface of any polyhedron.
________14) polyhedron
O. a polyhedron with a single polygon shaped base.
________15) prism (made of a base and triangles)
P. formed when two faces of a solid figure share a side.
________16) pyramid
Q. a solid that has a single circle for a base and a single triangle
________17) radius that comes to a point.
R. a solid that has two congruent circles as bases and a single
________18) surface area
rectangle to connect them.
________19) vertex S. the amount of surface that an object covers.
(measured in square units)
________20) volume
T. the measure of the distance around a circle.
(perimeter of a circle)

© 2007 – Norm Mitchell (Math6.org) – All Rights Reserved

Freely reproducible for “non-profit” educational purposes – visit http://www.math6.org/legal.htm for more details concerning “non-profit”.
 Name ______________
Matching
---------Key----------

1) S

2) H

3) A

4) E

5) T

6) Q

7) R

8) J

9) P

10) N

11) D

12) M

13) C

14) K

15) F

16) O

17) I

18) G

19) L

20) B

© 2007 – Norm Mitchell (Math6.org) – All Rights Reserved

Freely reproducible for “non-profit” educational purposes – visit http://www.math6.org/legal.htm for more details concerning “non-profit”.
 Math Objectives
2.02
The student will be able to solve problems
involving perimeter/circumference and area of
plane figures.
Instructor: _______________ Time Frame: 80 minutes
Subject: Math Grade 6 Date: _______________
Finding Perimeter
Essential Question: Over the next two days, we will be working with unmarked side lengths. Students
have a great deal of difficulty using spatial reasoning to figure out the length of
unmarked sides of a polygon. Teachers have tried for years to figure out why and
how to teach it. Can you come up with a plan to help your classmates realize and
determine unmarked side lengths?
Objective (s) Numbers: 2.02
Outcomes: The student will be able to solve problems involving perimeter/circumference and area of
plane figures.

Materials: Textbook pages 500-503; 10.1 Practice A and B

Anticipatory Set: Today we will learn to find the perimeter and missing side lengths of a polygon.
During the Lesson

Presentation of Information:
Integration of Other Subjects: Writing (sequencing)
Reading (vocabulary, problem solving, analyzing expectation)
Integration of Reading: Reading for information and interpretation.
Integration of Technology: Computer, Projector, PowerPoint, Internet

Modeling: Review perimeter. Discuss the 5th grade pitfalls of perimeter as it relates to
rectangles and squares (2 and 1 value given respectively.)

Differentiation: 504 modifications ET and RA. Additional student and teacher modeling will help to
guide
id allll students to reach expected outcomes.

Guided Practice: Use 10.1 Practice A and B as guided practices for finding the missing side lengths in
polygons.

After the Lesson

Independent Practice Text page 502-503 {1–13, 16, 17, 23–30}

AIG: {8–30}
Assign workbook page 10.1

Closure / Assessment: The perimeter of a regular heptagon in 63 cm. Create a flow map to show how to find
the length of each side.

Reflection:

Integration with School-wide Focus: Improve mathematics computation and problem solving.
Name Date Class

LESSON Practice A
10-1 Finding Perimeter
Find the perimeter of each figure.
1. 3 in. 2. 6 cm
2 in. 4 cm
1 in.
5 in. 7 cm

3. 5m 4. 14 ft
7m 9 ft
2m
10 ft
3m 4m 8 ft
8m 12 ft

Find the perimeter P of each rectangle.

5. 6. 7.
3 yd 9 mi 17 ft

6 yd
12 mi
20 ft

Find the unknown measure.

8. What is the length of side b if the 9. What is the length of side s if the
perimeter equals 30 in.? perimeter equals 45 yd?
6 in.
b
20 yd
10 yd
7 in.
8 in. s

10. A triangular rug has sides that measure

13 feet, 16 feet, and 12 feet. What is the
perimeter of that rug?
11. The perimeter of a rectangular swimming
pool is 140 meters. The pool is 20 meters
wide. How long is the pool?

Copyright © by Holt, Rinehart and Winston.

All rights reserved. 8 Holt Middle School Math Course 1
Name Date Class

LESSON Practice B
10-1 Finding Perimeter
Find the perimeter of each figure.
1. 15 in. 2.
26 cm 37 cm
11 in. 16 in.
48 cm
23 in.

3. 41 m 4. 1.6 ft 1.2 ft
15 m 17 m
8.3 ft 9.4 ft

18 m 12 m
14 ft
38 m

Find the perimeter P of each rectangle.

5. 6. 7.
16 yd 19 mi 1.7 ft

32 mi 2.8 ft
24 yd

Find the unknown measure.

8. What is the length of side b if the 9. What is the length of side s if the
perimeter equals 47 in.? perimeter equals 119 yd?
13 in. 22 yd s
7 in. 11 in. 59 yd

10. Benjamin is putting a fence around his rectangular-

shaped yard. The yard is 38 feet long and 27 feet
wide. How many feet of fencing does Benjamin need
to surround his entire yard?
11. If you drove from Bakersville to Salem and then to San
Mateo, your entire 81-mile journey would form a triangle.
The distance from Salem to San Mateo is 24 miles.
The distance from Bakersville to San Mateo is 40 miles.
How many miles is it from Salem to Bakersville?
Copyright © by Holt, Rinehart and Winston.
All rights reserved. 9 Holt Middle School Math Course 1
 Math Objectives
1.04d; 2.01; 2.02
The student will be able to judge the
reasonableness of solutions; estimate and measure
length, perimeter, area, angles, weight, and mass
of two
two- and three
three-dimensional
dimensional figures using
appropriate tools and solve problems involving
perimeter/circumference and area of plane
figures.
Instructor: _______________ Time Frame: 80 minutes
Subject: Math Grade 6 Date: _______________
Estimating and Finding Area
Essential Question: Students have a great deal of difficulty using spatial reasoning to figure out the length
of unmarked sides of a polygon. Teachers have tried for years to figure out why and
how to teach it. Can you come up with a plan to help your classmates realize and
determine unmarked side lengths?
Objective (s) Numbers: 1.04d; 2.01; 2.02
Outcomes: The student will be able to judge the reasonableness of solutions; estimate and measure
length, perimeter, area, angles, weight, and mass of two- and three-dimensional figures using
appropriate tools and solve problems involving perimeter/circumference and area of plane
figures.

Materials: Textbook pages 504-507; 10.2 Practice A and B

Anticipatory Set: Today we will learn to estimate the area of irregular figures and find the area of
rectangles, triangles, and parallelograms.
Presentation of Information:
Integration of Other Subjects: Writing (presentation/display)
Reading (vocabulary, problem solving, analyzing expectation)
Integration of Reading: Reading for information and interpretation.
Integration of Technology: Computer, Projector, PowerPoint, Internet

Modeling: Review and discuss using formulas for the area of triangles and quadrilaterals.

Differentiation: 504 modifications ET and RA. Additional student and teacher modeling will help to
guide all students to reach expected outcomes.

Guided Practice: Use 10.2 Practice A and B as guided practices for estimating and finding the area of
regular polygons.
After the Lesson

Independent Practice Text page 506-507 {1–6, 9–14, 17, 21–26}

AIG: {4–6, 9–14, 17–26}
Assign workbook page 10.2

Closure / Assessment: Create a model to demonstrate that the area of a triangle is 1/2 of the area of a
quadrilateral with the same base and height.

Reflection:

Integration with School-wide Focus: Improve mathematics computation and problem solving.
Name Date Class

LESSON Practice A
10-2 Estimating and Finding Area
Estimate the area of each figure.
1. 2.

ⴝ 1 ft2

ⴝ 1 in2

3. 4.

ⴝ 1 m2

ⴝ 1 yd2

Find the area of each rectangle.

5. 6.
4 yd 2 in.
7 in.
6 yd

7. 8.
3 mi 3 ft

5 mi 4 ft

9. A square room has sides that each 10. A rectangular coffee table is 2 feet
measure 5 feet. How many square wide and 4 feet long. How many
feet of carpet is needed to cover square feet of glass is needed to
the room’s entire floor? cover the entire table top?

Copyright © by Holt, Rinehart and Winston.

All rights reserved. 17 Holt Middle School Math Course 1
Name Date Class

LESSON Practice B
10-2 Estimating and Finding Area
Estimate the area of each figure.
1. 2.

ⴝ 1 ft2 ⴝ 1 m2

Find the area of each rectangle.

3. 4.
7 yd 8 mi

9 yd 12 mi

Find the area of each parallelogram.

5. 6.
2.1 in.
18 ft
5 in.
16 ft

Find the area of each triangle.

7. 8.
4 yd
25 yd
4 ft
3.5 ft

9. A section of a stained-glass window 10. Your rectangular yard is 10 feet wide

is shaped like a parallelogram. Its and 26 feet long. How many square
base is 6.5 inches, and its height is feet of grass do you need to plant if
4 inches. How much glass is needed you want to cover the entire yard?
to cover the section completely?

Copyright © by Holt, Rinehart and Winston.

All rights reserved. 18 Holt Middle School Math Course 1
 Math Objectives
2.01; 2.02
The student will be able to estimate and measure
length, perimeter, area, angles, weight, and mass
of two- and three-dimensional figures using
appropriate tools and solve problems involving
perimeter/circumference and area of plane
figures.
Instructor: _______________ Time Frame: 80 minutes
Subject: Math Grade 6 Date: _______________
Problem Solving: Break into Simpler Parts
Essential Question: Consider your response to yesterday's essential question. Do you think that students
have an easier time determining unmarked side lengths or finding the area of
irregular polygons? (Explain)
Objective (s) Numbers: 2.01; 2.02
Outcomes: The student will be able to estimate and measure length, perimeter, area, angles, weight, and
mass of two- and three-dimensional figures using appropriate tools and solve problems
involving perimeter/circumference and area of plane figures.
Materials: Textbook pages 508-510; 10.3 Practice A and B
Anticipatory Set: Today we learn to break a polygon into simpler parts to find its area.

During the Lesson

Presentation of Information:
Integration of Other Subjects: Writing (sequencing)
Reading (vocabulary, problem solving, analyzing expectation)
Integration of Reading: Reading for information and interpretation.
Integration of Technology: Computer, Projector, PowerPoint, Internet

Modeling: Irregular figures and polygons require an irregular approach to finding the area. An
easy way is to break the polygon into simpler parts for which you know mathematical
formulae for area computation.

Differentiation: 504 modifications ET and RA.RA Additional student and teacher modeling will help to
guide all students to reach expected outcomes.

Guided Practice: Use 10.3 Practice A and B as guided practice for breaking irregular polygons into
simpler parts.
After the Lesson

Independent Practice Text page 509-510 {1–2, 4–5, 7a–7b, 10–14}

AIG: {1–2, 4–5, 7, 10–14}
Assign workbook page 10.3

Closure / Assessment: Use a rule to create an irregular polygon. Create a flow map to show the sequence of
steps required to find the area and perimeter of your polygon.
Reflection:

Integration with School-wide Focus: Improve mathematics computation and problem solving.
Name Date Class

LESSON Practice A
10-3 Break into Simpler Parts
Find the area of each polygon.
1. 2. 1 cm
1 in.
1 cm

2 in.
2 cm
2 in.
3 cm

3. 4. 3m
1 ft
2m
2 ft

4 ft 2m
3m

5. 2 yd 6. 1 mi
4 yd
4 yd 5 mi
2 mi
4 yd
6 mi

7. A rectangular painting is made up of two congruent squares with

sides that measure 2 feet. What is the area of the entire
painting?

8. A carpet is made up of two congruent triangles. The base of

each triangle is 3 feet and the height is 6 feet. What is the area
of the entire carpet?

Copyright © by Holt, Rinehart and Winston.

All rights reserved. 27 Holt Middle School Math Course 1
Name Date Class

LESSON Practice B
10-3 Break into Simpler Parts
Find the area of each polygon.
1. 2. 4 cm
2 in.
4 cm
3 in. 8 cm
4 cm
9 in.
12 cm

3. 4.5 ft 4. 2 yd

3 ft
4 yd
2 ft
4.5 ft
4 yd
4.5 ft

5. 6.
6m
2.5 mi
6m
1 mi 2.5 mi 1 mi
6m 6m

7. Three paintings are shaped like an 8-foot square, a 7-foot by

4-foot rectangle, and a triangle with a 6-foot base and a height
of 7 feet. If those paintings are hung together on the outside of
a building, how much of the building’s wall will they cover
altogether?

8. Two diagonals divide a square carpet into 4 congruent triangles.

The base of each triangle is 5 feet and the height is 2.5 feet.
What is the area of the entire carpet?

Copyright © by Holt, Rinehart and Winston.

All rights reserved. 28 Holt Middle School Math Course 1
 Math Objectives
2.01; 2.02
The student will be able to estimate and measure
length, perimeter, area, angles, weight, and mass
of two- and three-dimensional figures using
appropriate tools and solve problems involving
perimeter/circumference and area of plane
figures.
Instructor: _______________ Time Frame: 80 minutes
Subject: Math Grade 6 Date: _______________
Comparing Area and Perimeter
Essential Question: Examine the table from our Guided Practice. Do you see a pattern that could be used
as an algorithm? (Describe)

Objective (s) Numbers: 2.01; 2.02

Outcomes: The student will be able to estimate and measure length, perimeter, area, angles, weight, and
mass of two- and three-dimensional figures using appropriate tools and solve problems
involving perimeter/circumference and area of plane figures.

Materials: Textbook pages 511-513

Anticipatory Set: Today we make a models to explore how area and perimeter are affected by changes
in the dimensions of a figure.

During the Lesson

Presentation of Information:
Integration of Other Subjects: Writing (opinion)
Reading (vocabulary, problem solving, analyzing expectation)
Integration of Reading: Reading for information and interpretation.
Integration of Technology: Computer, Projector, PowerPoint, Internet

Modeling: Examine the effects (on area and perimeter) when the dimensions of a triangle are
halved and doubled. Repeat with a rectangle.

Differentiation: 504 modifications ET and RA. Additional student and teacher modeling will help to
guide all students to reach expected outcomes.

Guided Practice: Set up a table: Dimensions, Perimeter, Area, Doubled, Area, Perimeter, Percent
Change, Percent Change. Using a 2x12, 3x8 and 4x6 rectangles - complete the table
and discuss the effects on the new area and perimeter. Repeat with a triangle with
similar dimensions.
After the Lesson
Independent Practice Text page 512-513 {1–5, 7, 11–14}
AIG: {5–14}
Assign workbook page 10.4

Closure / Assessment: As you saw during the guided practice, the effects of doubling or halving the
dimensions of a polygon have a mathematical root. Write a paragraph to explain why
you think this is true. (I do not expect a correct answer - just a well thought out
argument)
Reflection:

Integration with School-wide Focus: Improve mathematics computation and problem solving.
 Math Objectives
2.02; 3.02
The student will be able to solve problems
involving perimeter/circumference and area of
plane figures, identify the radius, diameter, chord,
center
center, and circumference of a circle and
determine the relationships among them.
Instructor: _______________ Time Frame: 80 minutes
Subject: Math Grade 6 Date: _______________
Circles
Essential Question: If pi is a constant (though irrational) number, why did our "discoveries" vary? (Explain
and give examples)

Objective (s) Numbers: 2.02; 3.02

Outcomes: The student will be able to solve problems involving perimeter/circumference and area of
plane figures, identify the radius, diameter, chord, center, and circumference of a circle and
determine the relationships among them.

Materials: Textbook pages 514-520; compasses, rulers, protractors, string, various circular objects,
Discovering Pi Practice 10.5 (from Math6.org)

Anticipatory Set: Today we will learn to identify the parts of a circle and find the circumference and
area of a circle.
During the Lesson

Presentation of Information:
Integration of Other Subjects: Writing (narrative)
Reading (vocabulary, problem solving, analyzing expectation)
Integration of Reading: Reading for information and interpretation.
Integration of Technology: Computer, Projector, PowerPoint, Internet

Modeling: The students will use the compasses to draw circles and model each of the
vocabulary terms; center, radius, diameter, chord, circumference, pi
Differentiation: 504 modifications ET and RA. Additional student and teacher modeling will help to
guide all students to reach expected outcomes.

Guided Practice: Students will use string to measure the circumference of various circles, then use
calculators to find the relationship between the circumference and the diameter.
Students will complete the worksheet - Discovering Pi Practice 10.5. Students will be
shown memorization techniques to memorize circle formulas: D=2R, C=πD; A=πRR

After the Lesson

Independent Practice Text page 518-519 {1–3, 6–9, 13–15, 17, 23–30}
AIG: {1–3, 6–9, 16–17, 19–20, 23–30}
Assign workbook page 10.5

Closure / Assessment: Write a narrative story (3 paragraphs) to tell a fifth grade student about today's
discovering pi activity. Open with expectations and a hook. Discuss the activity and
close your narrative by telling them what you discovered and/or why they should try it
out for themselves.
Reflection:

Integration with School-wide Focus: Improve mathematics computation and problem solving.
Activity Sheet
10.5 Circles
Write a defining sentence for each of the following words.

Circle Radii
Circumference
Center Chord
Pi
Radius Diameter

Create a poster to model each of the words from above (you may choose radius or radii)
Rewrite and memorize each of the following equations.

Diameter = 2 * R
Circumference = D * π A=π *R*R
Radius = D ÷ 2
22
Circumference = π * 2R A = π R2
Pi ≈ 3.14 or /7

Activity Sheet
10.5 Circles
Write a defining sentence for each of the following words.

Circle Radii
Circumference
Center Chord
Pi
Radius Diameter

Create a poster to model each of the words from above (you may choose radius or radii)
Rewrite and memorize each of the following equations.

Diameter = 2 * R
Circumference = D * π A=π *R*R
Radius = D ÷ 2
22
Circumference = π * 2R A = π R2
Pi ≈ 3.14 or /7

© 2005 – Norm Mitchell (Math6.org) – All Rights Reserved

Freely reproducible for “non profit” educational purposes – visit http://www.math6.org/legal.htm for more details concerning “non profit”.
 Discovering Pi Practice

Add your items to the table below.

Use a ruler to measure the diameter of your item.
Use the string to measure the circumference of your item.
Use you calculator to divide circumberence by diameter.

Item Diameter Circumference Relationship

Discovering Pi Practice

Add your items to the table below.

Use a ruler to measure the diameter of your item.
Use the string to measure the circumference of your item.
Use you calculator to divide circumberence by diameter.

Item Diameter Circumference Relationship

 Math Objectives
2.01
The student will be able to estimate and measure
length, perimeter, area, angles, weight, and mass
of two- and three-dimensional figures using
appropriate tools.
tools
Instructor: _______________ Time Frame: 80 minutes
Subject: Math Grade 6 Date: _______________
Solid Figures
Essential Question: For some reason, students really struggle to remember that pyramids have 1 base
while prisms have 2. Can you develop a plan to help all students easily remember
these facts?
Objective (s) Numbers: 2.01
Outcomes: The student will be able to estimate and measure length, perimeter, area, angles, weight, and
mass of two- and three-dimensional figures using appropriate tools.

Materials: Textbook pages 524-529; graph paper

Anticipatory Set: Today we will learn to name solid figures.

During the Lesson

Presentation of Information:
Integration of Other Subjects:
Reading (vocabulary, problem solving, analyzing expectation)
Integration of Reading: Reading for information and interpretation.
Integration of Technology: Computer, Projector, PowerPoint, Internet

Modeling: Use 3 column notes to present and practice the vocabulary for today's lesson.
{polyhedron, face, edge, vertex, prism, base, pyramid, cylinder, cone}

Differentiation: 504 modifications ET and RA. Additional student and teacher modeling will help to
guide all students to reach expected outcomes.

Guided Practice: Have students set up a table to show Name, Bases, Total Faces, Edges, Vertices.
Complete the table for each regular pyramid and prism.

After the Lesson

Independent Practice Text page 526-527 {1–3, 7–9, 20–23, 29–36}

AIG: {1–3, 7–9, 20–23, 29–36}
Assign workbook page 10.6

Closure / Assessment: Use graph paper to recreate the nets on page 529. Attempt to create a solid figure
with each net.
Reflection:

Integration with School-wide Focus: Improve mathematics computation and problem solving.
.
 Math Objectives
2.02
The student will be able to solve problems
involving perimeter/circumference and area of
plane figures.
Instructor: _______________ Time Frame: 80 minutes
Subject: Math Grade 6 Date: _______________
Surface Area
Essential Question: To find the surface area of a solid, you must break it into all of it pieces, find their area
and then add all of the faces together. Do you find it easier to find the surface area of
pyramids, prisms or cylinders. (Explain)
Objective (s) Numbers: 2.02
Outcomes: The student will be able to solve problems involving perimeter/circumference and area of
plane figures.

Materials: Textbook pages 530-533; 10.7 Practice A and B

Anticipatory Set: Today we will learn to find the surface areas of prisms, pyramids, and cylinders.
During the Lesson

Presentation of Information:
Integration of Other Subjects: Writing (compare/contrast)
Reading (vocabulary, problem solving, analyzing expectation)
Integration of Reading: Reading for information and interpretation.
Integration of Technology: Computer, Projector, PowerPoint, Internet

Modeling: The surface area of a solid figure is the sum of the areas of each of its faces. An
easy way to help you find surface area is to create a simple net to model each face.

Differentiation: 504 modifications ET and RA.RA Additional student and teacher modeling will help to
guide all students to reach expected outcomes.

Guided Practice: Practice identifying solids and then creating nets to model the 3D in 2D. Apply area
formulas to find the total surface area of each solid.
Use 10.7 Practice A and B as guided practices and further experiences with surface
area.
After the Lesson

Independent Practice Text page 532-533 {1–15, 27–32}

AIG: {13–32}
Assign workbook page 10.7

Closure / Assessment: Write a comparison/contrast piece to discuss how finding the surface area of a
rectangular pyramid is different from finding the surface area of a rectangular prism.

Reflection:

Integration with School-wide Focus: Improve mathematics computation and problem solving.
Name Date Class

LESSON Practice A
10-7 Surface Area
Find the surface area S of each net.
1. 2.

ⴝ 1 ft2
ⴝ 1 in2

3. 4.

ⴝ 1 yd2

ⴝ 1 m2

Find the surface area S of each prism.

5. 6.

s ⴝ 2 in. 1 ft
1 ft
3 ft

Copyright © by Holt, Rinehart and Winston.

All rights reserved. 65 Holt Middle School Math Course 1
Name Date Class

LESSON Practice B
10-7 Surface Area
Find the surface area S of each prism.
1. 2.

s ⴝ 10 in. 10 ft
3 ft
8 ft

Find the surface area S of each pyramid.

3. 4.

12 m 16 m

9m 6m

Find the surface area S of each cylinder. Use 3.14 for ␲.

5. 6.
7 cm 4 in.

6 cm 9 in.

7. Why can you find an exact surface area measurement for

a prism and pyramid but not for a cylinder?

8. The surface area of a rectangular prism is 48 square feet.

The area of its front is 4 square feet, and the area of one side is
10 square feet. What is the area of the top of the prism?

Copyright © by Holt, Rinehart and Winston.

All rights reserved. 66 Holt Middle School Math Course 1
 Math Objectives
2.01
The student will be able to estimate and measure
length, perimeter, area, angles, weight, and mass
of two- and three-dimensional figures using
appropriate tools.
tools
Instructor: _______________ Time Frame: 80 minutes
Subject: Math Grade 6 Date: _______________
Finding Volume
Essential Question: Over the next two days you will be adding several more formulas to the pile of
formulas you must memorize and master. Some students fail to memorize the many
formulas that they will need to solve the different geometry problems that they will
face in life and on the EOG. The state uses the EOG to rank students and to
determine which students are capable of moving to the next grade. Do you think the
state is correct in believing that memorizing formulas is part of being a good math
student or should the state provide the formulas on the test? (Explain - and don't say
provide just because you don't feel like memorizing formulas!)

Objective (s) Numbers: 2.01

Outcomes: The student will be able to estimate and measure length, perimeter, area, angles, weight, and
mass of two- and three-dimensional figures using appropriate tools.

Materials: Textbook pages 534-537

Anticipatory Set: Today we will learn to estimate and find the volumes of rectangular prisms and
triangular prisms.
During the Lesson

Presentation of Information:
Integration of Other Subjects: Writing (opinion)
Reading (vocabulary, problem solving, analyzing expectation)
Integration of Reading: Reading for information and interpretation.
Integration of Technology: Computer, Projector, PowerPoint, Internet

Modeling: Volume is the number of cubic units needed to fill a space. It is particularly easy to do
with rectangular and triangular prisms. Simply find the area of the base times the
third dimension Height (H). This formula will work with any prism.
Differentiation: 504 modifications ET and RA. Additional student and teacher modeling will help to
guide all students to reach expected outcomes.

Guided Practice: Model finding the area of triangular prisms. (3.4 x 2.6 x 3) (6 x 4.4 x 7.1)
Model finding the area of rectangular prisms. (6 x 4 x 2.5) (8 x 8 x 8)
Model finding the area of cylinders. (D=6 H=5) (D=5 H=3)....r*r*π*h

After the Lesson

Independent Practice Text page 536-537 {1–6, 8–13, 27–33}
AIG: {11–13, 15–23, 27–33}
Assign workbook page 10.8

Closure / Assessment: Finding the volume of pyramids isn't really harder than finding the volume of a prism,
you just have to use a different formula. The formula for finding the volume of a
square pyramid is S*S*H÷3. Why do you think that finding the volume of prisms is
considered a sixth grade objective while finding the volume of pyramids is saved for
higher math?
Reflection:

Integration with School-wide Focus: Improve mathematics computation and problem solving.
 Math Objectives
2.01; 2.02
The student will be able to estimate and measure
length, perimeter, area, angles, weight, and mass
of two- and three-dimensional figures using
appropriate tools and solve problems involving
perimeter/circumference and area of plane
figures.
Instructor: _______________ Time Frame: 80 minutes
Subject: Math Grade 6 Date: _______________
Volume of Cylinders
Essential Question: Some students fail to memorize the many formulas that they will need to solve the
different geometry problems that they will face in life and on the EOG. The state uses
the EOG to rank students and to determine which students are capable of moving to
the next grade. Do you think the state is correct in believing that memorizing
formulas is part of being a good math student or should the state provide the formulas
on the test? (Explain - and don't say provide just because you don't feel like
memorizing formulas!)

Objective (s) Numbers: 2.01; 2.02

Outcomes: The student will be able to estimate and measure length, perimeter, area, angles, weight, and
mass of two- and three-dimensional figures using appropriate tools and solve problems
involving perimeter/circumference and area of plane figures.

Materials: Textbook pages 538-541

Anticipatory Set: Today we learn to find volumes of cylinders.

During the Lesson

Presentation of Information:
Integration of Other Subjects: Writing (opinion)
Reading (vocabulary, problem solving, analyzing expectation)
Integration of Reading: Reading for information and interpretation.
Integration of Technology: Computer, Projector, PowerPoint, Internet

Modeling: Volume is the number of cubic units needed to fill a space. It is particularly easy to do
with rectangular and triangular prisms. Simply find the area of the base times the
third dimension Height (H). This formula will work with any prism.

Differentiation: 504 modifications ET and RA. Additional student and teacher modeling will help to
guide all students to reach expected outcomes.

Guided Practice: Model finding the area of triangular prisms. (6 x 4 x 5) (8 x 3 x 6)

Model finding the area of rectangular prisms. (5 x 7 x 3) (3 x 3 x 3)
Model finding the area of cylinders. (R=5 H=10) (D=9 H=6)....r*r*π*h

After the Lesson

Independent Practice Text page 540-541 {1-22}

AIG: {9-23, 26}
Assign workbook page 10.9

Closure / Assessment: Finding the volume of cones isn't really harder than finding the volume of a cylinder,
you just have to use a different formula. The formula for finding the volume of a cone
is π*d*d*h÷12. Why do you think that finding the volume of cylinders is considered a
sixth grade objective while finding the volume of cones is saved for higher math?

Reflection:

Integration with School-wide Focus: Improve mathematics computation and problem solving.
 Math Objectives
1.04d, 2.01, 2.02, 3.02
The student will be able to judge the reasonableness of solutions;
estimate and measure length, perimeter, area, angles, weight, and
mass of two- and three-dimensional figures using appropriate tools
and solve problems involving perimeter/circumference and area of
plane
l fi
figures. The
Th student willill be able
bl to solve problems
bl involving
perimeter/circumference and area of plane figures, identify the
radius, diameter, chord, center, and circumference of a circle and
determine the relationships among them.
Instructor: _______________ Time Frame: 80 minutes
Subject: Math Grade 6 Date: _______________
Perimeter, Area, and Volume Chapter Review
Essential Question: What steps do you think have been the most helpful in preparing yourself for the
examination on a set of skills? (decision making)

Objective (s) Numbers: 1.04d, 2.01, 2.02, 3.02

Outcomes: The student will be able to judge the reasonableness of solutions; estimate and
measure length, perimeter, area, angles, weight, and mass of two- and three-
dimensional figures using appropriate tools and solve problems involving
perimeter/circumference and area of plane figures. The student will be able to solve
problems involving perimeter/circumference and area of plane figures, identify the
radius, diameter, chord, center, and circumference of a circle and determine the
relationships among them.

Materials: Textbook pages 546-549; Test Form B

Anticipatory Set: Today we will review the skills that we have been studying during this unit. We will
practice test taking skills and remediate those skills about which we don't feel as
comfortable as others.

During the Lesson

Presentation of Information:
Integration of Other Subjects:
Reading (vocabulary, problem solving, analyzing expectation)
Integration of Reading: Reading for information and interpretation.
Integration of Technology: Computer, Projector, PowerPoint, Internet

Modeling: Discuss the value of careful review, the process that should occur when errors are
made and the importance of reviewing material that students are less comfortable
with.

Differentiation: 504 modifications ET and RA. Additional student and teacher modeling will help to
guide all students to reach expected outcomes.

Guided Practice: Discuss Instructions for the review on pages 546-549. Have the students review the
Headings and address and questions or requests for immediate remediation.

After the Lesson

Independent Practice Text page 546-549 {1-25}
AIG: {1-25}
Assign Test Form B

Closure / Assessment: Have co-operative learning groups review and discuss their answers before turning
their papers in for correction by the teacher.

Reflection:

Integration with School-wide Focus: Improve mathematics computation and problem solving.
Name Date Class

CHAPTER Chapter Test

10 Form B
Find the perimeter of each figure. 6. 9m
1. 10 m
15 in.
15 m
27 in.

7. How does the area of a square

2. change when the side length is
11 in.
doubled?

30 in. 8 in.
15 in. 8. The length and width of a rectangle
11 in. are each multiplied by 6. Find how
15 in. the perimeter and area of the
rectangle change.

Find the area of each figure.

3.
15 cm Name two radii and find the
circumference and area for each
circle. Use 3.14 for ␲ and round to
12 cm the nearest hundredth.
9.

4. O
A C
8 yd 9 cm
B
11 yd

Find the area of each polygon. 10.

5. M
L N
16 cm
7 in. 3 in.
7 in.
3 in.

Copyright © by Holt, Rinehart and Winston.

All rights reserved.
87 Holt Middle School Math Course 1
Name Date Class

CHAPTER Chapter Test

10 Form B, continued
11. Identify the number of faces, edges, Find the volume of each prism.
and vertices.
15.

5 cm 13 cm
12 cm

12. Tell whether the figure is a 16.

polyhedron and name the solid. 9 cm

8.5 cm
7 cm

Find the surface area of each figure. Find the volume V of each cylinder to
Use 3.14 for ␲. the nearest cubic unit. Use 3.14 for ␲.
13. 17. 10 in.
7 cm
12 in.
10 cm
8 cm

18. 8 yd
14.
9m

18 yd
10 m 10 m

Copyright © by Holt, Rinehart and Winston.

All rights reserved.
88 Holt Middle School Math Course 1
Instructor: _______________ Time Frame: 80 minutes
Subject: Math Grade 6 Date: _______________
Perimeter, Area, and Volume Assessment
Essential Question: Did you implement the action plan from yesterday's Essential Question? (Explain)

Objective (s) Numbers: 1.04d, 2.01, 2.02, 3.02

Outcomes: The student will be able to judge the reasonableness of solutions; estimate and
measure length, perimeter, area, angles, weight, and mass of two- and three-
dimensional figures using appropriate tools and solve problems involving
perimeter/circumference and area of plane figures. The student will be able to solve
problems involving perimeter/circumference and area of plane figures, identify the
radius, diameter, chord, center, and circumference of a circle and determine the
relationships among them.
Materials: Cumulative Assessment (Form B)
Anticipatory Set: Today we will assess our mastery of Perimeter, Area, and Volume.

During the Lesson

Presentation of Information:
Integration of Other Subjects: Writing (evaluation)
Reading (vocabulary, problem solving, analyzing expectation)
Integration of Reading: Reading for information and interpretation.
Integration of Technology: Computer, Projector, PowerPoint, Internet

Modeling: Review the Practice Test, answer questions and model answers.

Differentiation: 504 modifications ET and RA. Additional student and teacher modeling will help to
guide all students to reach expected outcomes.

Guided Practice: Discuss the Instructions.

After the Lesson

Independent Practice Assign Cumulative Review Test Form B

Closure / Assessment: Write a paragraph evaluation of your expected performance on this test. What did
you do well on? What did you have trouble with? How did you prepare for this test
and what would you like to do differently for the next exam?
Choose a Journal entry to share with your class.
Reflection:

Integration with School-wide Focus: Improve mathematics computation and problem solving.
Name Date Class

CHAPTER Cumulative Test

10 Form B
Select the best answer. 8. Add ⴚ19 ⴙ 21.
1. What is the perimeter of a rectangle F ⴚ2 H ⴚ40
having length 9 cm and width 6 cm? G2 J 40
A 15 cm C 24 cm
B 30 cm D 54 cm 9. Which of the following is the best
deal?
2. Which expression has the greatest A 3 lb for $7.60 C 5 lb for $12.70
value? B 4 lb for $10.00 D 6 lb for $15.30
1 1
F 30% of 200 H 7ᎏ2ᎏ • 3ᎏ5ᎏ
10. What is the perimeter of a square
2 2 with an area of 169 cm2?
G5 ⴙ9ⴚ2 J ᎏ3ᎏ of 70
F 13 cm H 52 cm
3. Find the difference 90 ⴚ 37.23. G 26 cm J 84.5 cm
A 67.23 C 52.77
11. Yancy has a board 25 feet long. He
B 57.77 D 32.23 1
wants to cut it into 4ᎏ2ᎏ -foot lengths.
3 1
4. Which ratio is equivalent to ᎏ ᎏ? Into how many 4ᎏ2ᎏ -foot lengths can
20
F 5 to 100 H 140 to 21 he cut it?
G 100 to 5 J 21 to 140 A 2 C 5
B 4 D 6
5. In which quadrant on a coordinate
plane is the point (ⴚ3, 4) located? 12. What is the circumference of a circle
A I C III with a radius of 7.5 cm? Use 3.14
for ␲.
B II D IV
F 23.55 cm H 47.1 cm
1 G 176.625 cm J 94.2 cm
6. Solve 6z ⴝ ᎏ9ᎏ.
F z ⴝ 54 H z ⴝ 30 13. Divide 19.24 by 2.6.
1
G z ⴝ 15 J z ⴝ ᎏ5ᎏ
4 A 50.024 C 500.24
B 7.4 D 74
7. Which phrase matches the algebraic
x
expression ᎏ5ᎏ?
A the product of x and 5
B the sum of x and 5
C the quotient of x and 5
D five less than x

Copyright © by Holt, Rinehart and Winston.

All rights reserved.
239 Holt Middle School Math Course 1
Name Date Class

CHAPTER Cumulative Test

10 Form B, continued
14. Identify the figure shown. Carter’s Lunch Counter Specials
Chili $3.95
Garden Salad $4.75
Vegetable Soup $2.25
Turkey Sandwich $4.95

18. How much more does the garden

salad cost than the vegetable soup?
F triangular pyramid
F $2.25 H $3.00
G triangular prism
G $2.50 J $7.00
H rectangular prism
J rectangular pyramid 19. What is the prime factorization of 96?
1 A 24 ⴛ 3 C 25 ⴛ 3
15. Len bought 1ᎏ4ᎏ pounds of pecans.
B 2 ⴛ 48 D 2 ⴛ 34
1
Lisa bought 1ᎏ2ᎏ pounds of pecans.
How many more pounds did Lisa buy? 20. What is the GCF of 54 and 72?
3 3 F 1 H 9
A 2ᎏ4ᎏ lb C ᎏ4ᎏ lb
G6 J 18
1
B 2 lb D ᎏ4ᎏ lb
21. There are 126 students in Jennifer’s
senior class. One-third of the students
16. Adrian is training for a 5K race. She
live over 8 miles from school. How
ran 5.5 miles the first week, 7.25 miles
many students live over 8 miles from
the second week and 10 miles the
school?
third week. On the average, how
many miles did she run per week? A 16 C 48
Round to the nearest hundredth. B 42 D 63
F 22.75 mi H 7.58 mi
22. Which expression illustrates the
G 8.00 mi J 7.25 mi
Associative Property?
17. Batteries are packed 12 packages to F 24 ⴛ 2 ⴝ 2 ⴛ 24
a box. A box of batteries costs $51.00. G (53 ⴙ 17) ⴙ 10 ⴝ 53 ⴙ (17 ⴙ 10)
How much do 7 packages cost? H 12 ⴙ 13 ⴙ 18 ⴙ 37 ⴝ 80
A $4.25 C $29.75 J 9 ⴛ (20 ⴙ 6) ⴝ (9 ⴛ 20) ⴙ (9 ⴛ 6)
B $7.29 D $87.43
23. Express 5.37 ⴛ 105 in standard form.
A 5,370,000 C 53,700
B 537,000 D 5,370

Copyright © by Holt, Rinehart and Winston.

All rights reserved.
240 Holt Middle School Math Course 1
Name Date Class

CHAPTER Cumulative Test

10 Form B, continued
24. Which pair of angles is 28. The measures of two angles in a
supplementary? triangle are 45 and 55 degrees. What
F 45°, 45° H 90°, 180° is the measure of the third angle?
G 120°, 60° J 30°, 70° F 80 degrees H 100 degrees
G 90 degrees J 110 degrees
Use the diagram for question 25.
29. What is the area of a rectangle if its
length is 15 cm and its width is 13 cm?
L M A 28 cm C 56 cm2
N
O B 56 cm D 195 cm2

30. What is the area of a circle with a

diameter of 6 cm? Use 3.14 for ␲.
P
Q F 18.84 cm2 H 76.43 cm2
G 28.26 cm2 J 113.04 cm2

25. Which two lines meet at a right 31. In one field, a farmer finds crop circle
angle? with a diameter of 110 feet. How
៭៮៬ and PQ
៭៮៬ ៭៮៬ and PL ៭៮៬ many square feet does the crop
A LN C NO
circle cover? Use 3.14 for ␲.
៭៮៬ and NO
B QM ៭៮៬ ៭៮៬ and MQ
D PQ ៭៮៬
A 172.7 ft2 C 9,498.5 ft2
26. Which statement is false? B 345.4 ft2 D 37,994 ft2
F Every square is a parallelogram.
32. Which number has the least value?
G Every parallelogram is a square.
F 12.2 H 12.5
H Some rectangles are squares.
H 12.25 J 12.52
J All squares are rectangles.
33. Which set of integers is ordered from
27. A triangle with angles measuring 95°, least to greatest?
45°, and 40° is what type of triangle?
A ⴚ18, ⴚ15, ⴚ4, 0
A acute C equilateral
B ⴚ19, ⴚ23, ⴚ26, ⴚ30
B obtuse D isosceles
C 10, ⴚ2, ⴚ15, ⴚ12
D 12, ⴚ4, ⴚ7, 12

Copyright © by Holt, Rinehart and Winston.

All rights reserved.
241 Holt Middle School Math Course 1
Name Date Class

CHAPTER Cumulative Test

10 Form B, continued
34. Bart had $377 in his savings Use the rate schedule for questions
account. He attempted to withdraw 40 and 41.
$390 from an ATM machine. How
much money would he need to Electric Rate Schedule
deposit in his savings account to First 2,000 kWh $0.053 per kWh
cover his withdrawal? Over 2,000 kWh $0.04 per kWh
F ⴚ$13 H $767
G $13 J $780 40. To the nearest penny, what is the
charge for using 1,195 kWh of
35. Solve d ⴙ 3.5 ⴝ 9.8. electricity?
A d ⴝ 2.8 C d ⴝ 13.3 F $63.34 H $47.80
B d ⴝ 6.3 D d ⴝ 34.3 G $60.80 J $35.10

36. Simplify 48 ⴜ 4 ⴙ 6 ⴛ 7 ⴚ 5. 41. Delsin runs a small used bookstore.

Last month his store used 8,000 kWh
F 5 H 49
of electricity. What was his bill?
G 20 J 121
A $375 C $320
37. Tony is 185 cm tall. He is 12 cm B $346 D $240
taller than Catherine. How tall is
Catherine? 42. What is seventy thousand three
hundred five and twelve hundredths
A 197 cm C 150 cm
in numerals?
B 173 cm D 15 cm
F 7,030,512 H 70,305.012
G 70,315 J 70,305.12
38. What is the value of 34?
F 9 H 27
43. How many liters are equal to
G 12 J 81 8,000 kL?
A 8 C 800,000
39. Which value is a solution of the
B 800 D 8,000,000
equation 4y ⴝ 124?
A 6 C 31
44. Which number is prime?
B 20 D 496
F 27 H 51
G 47 J 81

Copyright © by Holt, Rinehart and Winston.

All rights reserved.
242 Holt Middle School Math Course 1
Name ________________________________ Name ________________________________
Perimeter, Area, and Volume Assessment Perimeter, Area, and Volume Assessment

1 A B C D 24 F G H J 1 A B C D 24 F G H J
2 F G H J 25 A B C D 2 F G H J 25 A B C D
3 A B C D 26 F G H J 3 A B C D 26 F G H J
4 F G H J 27 A B C D 4 F G H J 27 A B C D
5 A B C D 28 F G H J 5 A B C D 28 F G H J
6 F G H J 29 A B C D 6 F G H J 29 A B C D
7 A B C D 30 F G H J 7 A B C D 30 F G H J
8 F G H J 31 A B C D 8 F G H J 31 A B C D
9 A B C D 32 F G H J 9 A B C D 32 F G H J
10 F G H J 33 A B C D 10 F G H J 33 A B C D
11 A B C D 34 F G H J 11 A B C D 34 F G H J
12 F G H J 35 A B C D 12 F G H J 35 A B C D
13 A B C D 36 F G H J 13 A B C D 36 F G H J
14 F G H J 37 A B C D 14 F G H J 37 A B C D
15 A B C D 38 F G H J 15 A B C D 38 F G H J
16 F G H J 39 A B C D 16 F G H J 39 A B C D
17 A B C D 40 F G H J 17 A B C D 40 F G H J
18 F G H J 41 A B C D 18 F G H J 41 A B C D
19 A B C D 42 F G H J 19 A B C D 42 F G H J
20 F G H J 43 A B C D 20 F G H J 43 A B C D
21 A B C D 44 F G H J 21 A B C D 44 F G H J
22 F G H J 22 F G H J
23 A B C D 23 A B C D
 Perimeter, Area, and Volume Assessment

1 A B C D 24 F G H J Chapter 10 Assessment
2 F G H J 25 A B C D 8 100%
3 A B C D 26 F G H J 7 88%
4 F G H J 27 A B C D 6 75%
5 A B C D 28 F G H J 5 63%
6 F G H J 29 A B C D 4 50%
7 A B C D 30 F G H J 3 38%
8 F G H J 31 A B C D 2 25%
9 A B C D 32 F G H J 1 13%
10 F G H J 33 A B C D 0 0%
11 A B C D 34 F G H J
12 F G H J 35 A B C D
13 A B C D 36 F G H J
14 F G H J 37 A B C D
15 A B C D 38 F G H J
16 F G H J 39 A B C D
17 A B C D 40 F G H J
18 F G H J 41 A B C D
19 A B C D 42 F G H J
20 F G H J 43 A B C D
21 A B C D 44 F G H J
22 F G H J
23 A B C D