Lesson Plans - Chapter 10 - Perimeter, Area and Volume

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

Showed understanding, cited examples and communicated effectively enough to enable

others to understand.

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

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

Word

Definition

Example

area

base

center

circle

circumference

cone

cylinder

diameter

edge

face

net

perimeter

polyhedron

prism

pyramid

radius

surface area

vertex

volume

The amount of surface that an object covers.

(measured in square units).

L x W

Name ______________

Matching

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

Perimeter, Area, and Volume – Matching

________1) area

________2) base

________3) center

________4) circle

________5) circumference

________6) cone

________7) cylinder

________8) diameter

________9) edge

________10) face

________11) net

________12) perimeter

________13) pi

________14) polyhedron

________15) prism

________16) pyramid

________17) radius

________18) surface area

________19) vertex

________20) volume

A. the middle of a circle.

the point that is equidistant to all the points in a circle.

B. the number of cubic units needed to fill the space of a solid.

(measured in cubes)

C. the ratio that compares the circumference and diameter of any

circle.

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

from a given point.

F. a polyhedron with two congruent and parallel bases.

(made of bases and rectangles)

G. the sum of the areas of all of the surfaces of a solid figure.

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

the other endpoint on the circle.

J. a chord that passes through the center of a circle.

K. a 3 dimensional object, or solid figure, with flat surfaces

L. a point at which three or more edges of a polyhedron meet.

M. the measure of the distance around a figure.

N. the flat surface of any polyhedron.

O. a polyhedron with a single polygon shaped base.

(made of a base and triangles)

P. formed when two faces of a solid figure share a side.

Q. a solid that has a single circle for a base and a single triangle

that comes to a point.

R. a solid that has two congruent circles as bases and a single

rectangle to connect them.

S. the amount of surface that an object covers.

(measured in square units)

T. the measure of the distance around a circle.

(perimeter of a circle)

Name ______________

Matching

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

---------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

Math Objectives

2.02

The student will be able to solve problems

involving perimeter/circumference and area of

plane figures.

t d t t h t d t

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

id ll t d t t h t d t

e a

s u en s o reac expec e ou comes.

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.

8 Holt Middle School Math Course 1

Find the perimeter of each figure.

1. 2.

3. 4.

Find the perimeter P of each rectangle.

5. 6. 7.

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?

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?

20 yd

10 yd

7 in.

6 in.

8 in.

17 ft

20 ft

9 mi

12 mi

3 yd

6 yd

14 ft

10 ft

12 ft

8 ft

9 ft

3 m

7 m

5 m

2 m

4 m

8 m

4 cm

6 cm

7 cm

3 in.

1 in.

5 in.

2 in.

Name Date Class

Practice A

Finding Perimeter

10-1

LESSON

9 Holt Middle School Math Course 1

Find the perimeter of each figure.

1. 2.

3. 4.

Find the perimeter P of each rectangle.

5. 6. 7.

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?

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?

22 yd

59 yd

7 in.

13 in.

11 in.

1.7 ft

2.8 ft

19 mi

32 mi

16 yd

24 yd

1.2 ft

1.6 ft

9.4 ft

8.3 ft

14 ft

38 m

15 m

18 m

41 m

12 m

17 m

26 cm

37 cm

48 cm

23 in.

16 in.

15 in.

11 in.

Name Date Class

Practice B

Finding Perimeter

10-1

LESSON

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 and three dimensional figures using

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: _______________

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.

17 Holt Middle School Math Course 1

Estimate the area of each figure.

1. 2.

3. 4.

Find the area of each rectangle.

5. 6.

7. 8.

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?

3 ft

4 ft

3 mi

5 mi

2 in.

7 in.

4 yd

6 yd

ⴝ 1 yd

ⴝ 1 m

ⴝ 1 in

ⴝ 1 ft

Name Date Class

Practice A

Estimating and Finding Area

10-2

LESSON

18 Holt Middle School Math Course 1

Estimate the area of each figure.

1. 2.

Find the area of each rectangle.

3. 4.

Find the area of each parallelogram.

5. 6.

Find the area of each triangle.

7. 8.

4 ft

3.5 ft

4 yd

25 yd

16 ft

18 ft

2.1 in.

5 in.

8 mi

12 mi

7 yd

9 yd

ⴝ 1 m

ⴝ 1 ft

Name Date Class

Practice B

Estimating and Finding Area

10-2

LESSON

9. A section of a stained-glass window

is shaped like a parallelogram. Its

base is 6.5 inches, and its height is

4 inches. How much glass is needed

to cover the section completely?

10. Your rectangular yard is 10 feet wide

and 26 feet long. How many square

feet of grass do you need to plant if

you want to cover the entire yard?

and

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 solve problems involving

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

and

Additional

student

and

teacher

modeling

will

help

504

modifications

and

Additional

student

and

teacher

modeling

will

help

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.

27 Holt Middle School Math Course 1

Find the area of each polygon.

1. 2.

3. 4.

5. 6.

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?

6 mi

1 mi

5 mi

4 yd

2 yd

3 m

2 m

4 ft

2 ft

1 ft

3 cm

2 cm

1 cm

2 in.

1 in.

Name Date Class

Practice A

Break into Simpler Parts

10-3

LESSON

28 Holt Middle School Math Course 1

Name Date Class

Practice B

Break into Simpler Parts

10-3

LESSON

Find the area of each polygon.

1. 2.

3. 4.

5. 6.

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?

6 m 6 m

6 m

2.5 mi

1 mi 1 mi

4 yd

2 yd

3 ft

4.5 ft

2 ft

4 cm

12 cm

8 cm

9 in.

3 in.

2 in.

and

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 solve problems involving

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

lane figures, identify the radius, diameter, chord,

center and circumference of a circle and

center

and

circumference

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.

dditional 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.

Freely reproducible for “non profit” educational purposes – visit http://www.math6.org/legal.htm

for more details concerning “non profit”.

Activity Sheet

10.5 Circles

Write a defining sentence for each of the following words.

Circle

Center

Radius

Radii

Chord

Diameter

Circumference

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

Radius = D ÷ 2

Pi ≈ 3.14 or

Circumference = D * π

Circumference = π * 2R

A = π * R * R

A = π R

Activity Sheet

10.5 Circles

Write a defining sentence for each of the following words.

Circle

Center

Radius

Radii

Chord

Diameter

Circumference

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

Radius = D ÷ 2

Pi ≈ 3.14 or

Circumference = D * π

Circumference = π * 2R

A = π * R * R

A = π R

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

appropriate

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

and

Additional

student

and

teacher

modeling

will

help

504

modifications

and

Additional

student

and

teacher

modeling

will

help

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.

65 Holt Middle School Math Course 1

Find the surface area S of each net.

1. 2.

3. 4.

Find the surface area S of each prism.

5. 6.

1 ft

3 ft

1 ft

ⴝ 2 in.

ⴝ 1 m

ⴝ 1 yd

ⴝ 1 in

ⴝ 1 ft

Name Date Class

Practice A

Surface Area

10-7

LESSON

66 Holt Middle School Math Course 1

Find the surface area S of each prism.

1. 2.

Find the surface area S of each pyramid.

3. 4.

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

5. 6.

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?

4 in.

9 in.

7 cm

6 cm

16 m

6 m

12 m

9 m

10 ft

8 ft

3 ft

ⴝ 10 in.

Name Date Class

Practice B

Surface Area

10-7

LESSON

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

appropriate

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.

and

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 solve problems involving

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.

b l i l i

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

l fi Th d ill b bl l bl i l i

ane

gures.

e stu ent w

ill

e a

e to so ve pro

ems nvo v ng

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.

87 Holt Middle School Math Course 1

Name Date Class

Find the perimeter of each figure.

Find the area of each figure.

Find the area of each polygon.

7. How does the area of a square

change when the side length is

doubled?

8. The length and width of a rectangle

are each multiplied by 6. Find how

the perimeter and area of the

rectangle change.

Name two radii and find the

circumference and area for each

circle. Use 3.14 for ␲ and round to

the nearest hundredth.

10.

16 cm

9 cm

10 m

15 m

9 m

3 in.

7 in.

3 in.7 in.

11 yd

8 yd

12 cm

15 cm

15 in.

30 in. 8 in.

11 in.

27 in.

15 in.

Chapter Test

Form B

CHAPTER

11. Identify the number of faces, edges,

and vertices.

12. Tell whether the figure is a

polyhedron and name the solid.

Find the surface area of each figure.

Use 3.14 for ␲.

13.

14.

Find the volume of each prism.

15.

16.

Find the volume V of each cylinder to

the nearest cubic unit. Use 3.14 for ␲.

17.

18.

18 yd

8 yd

10 in.

12 in.

7 cm

8.5 cm

9 cm

12 cm

13 cm

5 cm

10 m

9 m

7 cm

8 cm

10 cm

88 Holt Middle School Math Course 1

Name Date Class

Chapter Test

Form B, continued

CHAPTER

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.

239 Holt Middle School Math Course 1

Name Date Class

Select the best answer.

1. What is the perimeter of a rectangle

having length 9 cm and width 6 cm?

A 15 cm C 24 cm

30 cm D 54 cm

2. Which expression has the greatest

value?

30% of 200 H 7

ᎏ

• 3

ᎏ

G 5

ⴙ 9 ⴚ 2 J

ᎏ

of 70

3. Find the difference 90 ⴚ 37.23.

A 67.23 52.77

B 57.77 D 32.23

4. Which ratio is equivalent to

ᎏ

F 5 to 100 H 140 to 21

G 100 to 5 21 to 140

5. In which quadrant on a coordinate

plane is the point (ⴚ3, 4) located?

A I C III

II D IV

6. Solve 6z ⴝ

ᎏ

F z ⴝ 54 H z ⴝ 30

G z ⴝ 15 z ⴝ

ᎏ

7. Which phrase matches the algebraic

expression

ᎏ

A the product of x and 5

B the sum of x and 5

the quotient of x and 5

D five less than x

8. Add ⴚ19 ⴙ 21.

F ⴚ2 H ⴚ40

2 J 40

9. Which of the following is the best

deal?

A 3 lb for $7.60 C 5 lb for $12.70

4 lb for $10.00 D 6 lb for $15.30

10. What is the perimeter of a square

with an area of 169 cm

F 13 cm 52 cm

G 26 cm J 84.5 cm

11. Yancy has a board 25 feet long. He

wants to cut it into 4

ᎏ

-foot lengths.

Into how many 4

ᎏ

-foot lengths can

he cut it?

A 25

B 4 D 6

12. What is the circumference of a circle

with a radius of 7.5 cm? Use 3.14

for ␲.

F 23.55 cm 47.1 cm

G 176.625 cm J 94.2 cm

13. Divide 19.24 by 2.6.

A 50.024 C 500.24

7.4 D 74

Cumulative Test

Form B

CHAPTER

14. Identify the figure shown.

triangular pyramid

G triangular prism

H rectangular prism

J rectangular pyramid

15. Len bought 1

ᎏ

pounds of pecans.

Lisa bought 1

ᎏ

pounds of pecans.

How many more pounds did Lisa buy?

A 2

ᎏ

lb C

ᎏ

B 2 lb

ᎏ

16. Adrian is training for a 5K race. She

ran 5.5 miles the first week, 7.25 miles

the second week and 10 miles the

third week. On the average, how

many miles did she run per week?

Round to the nearest hundredth.

F 22.75 mi 7.58 mi

G 8.00 mi J 7.25 mi

17. Batteries are packed 12 packages to

a box. A box of batteries costs $51.00.

How much do 7 packages cost?

A $4.25 $29.75

B $7.29 D $87.43

18. How much more does the garden

salad cost than the vegetable soup?

F $2.25 H $3.00

$2.50 J $7.00

19. What is the prime factorization of 96?

A 2

ⴛ 32

ⴛ 3

B 2 ⴛ 48 D 2 ⴛ 3

20. What is the GCF of 54 and 72?

F 1 H 9

G 618

21. There are 126 students in Jennifer’s

senior class. One-third of the students

live over 8 miles from school. How

many students live over 8 miles from

school?

A 16 C 48

42 D 63

22. Which expression illustrates the

Associative Property?

F 24 ⴛ 2 ⴝ 2 ⴛ 24

(53 ⴙ 17) ⴙ 10 ⴝ 53 ⴙ (17 ⴙ 10)

H 12 ⴙ 13 ⴙ 18 ⴙ 37 ⴝ 80

J 9 ⴛ (20 ⴙ 6) ⴝ (9 ⴛ 20) ⴙ (9 ⴛ 6)

23. Express 5.37 ⴛ 10

in standard form.

A 5,370,000 C 53,700

537,000 D 5,370

240 Holt Middle School Math Course 1

Name Date Class

Cumulative Test

Form B, continued

CHAPTER

Carter’s Lunch Counter Specials

Chili $3.95

Garden Salad $4.75

Vegetable Soup $2.25

Turkey Sandwich $4.95

241 Holt Middle School Math Course 1

Name Date Class

24. Which pair of angles is

supplementary?

F 45°, 45° H 90°, 180°

120°, 60° J 30°, 70°

Use the diagram for question 25.

25. Which two lines meet at a right

angle?

៭

៮

៬

and PQ

៭

៮

៬

C NO

៭

៮

៬

and PL

៭

៮

៬

B QM

៭

៮

៬

and NO

៭

៮

៬

D PQ

៭

៮

៬

and MQ

៭

៮

៬

26. Which statement is false?

F Every square is a parallelogram.

Every parallelogram is a square.

H Some rectangles are squares.

J All squares are rectangles.

27. A triangle with angles measuring 95°,

45°, and 40° is what type of triangle?

A acute C equilateral

obtuse D isosceles

28. The measures of two angles in a

triangle are 45 and 55 degrees. What

is the measure of the third angle?

80 degrees H 100 degrees

G 90 degrees J 110 degrees

29. What is the area of a rectangle if its

length is 15 cm and its width is 13 cm?

A 28 cm C 56 cm

B 56 cm 195 cm

30. What is the area of a circle with a

diameter of 6 cm? Use 3.14 for ␲.

F 18.84 cm

H 76.43 cm

28.26 cm

J 113.04 cm

31. In one field, a farmer finds crop circle

with a diameter of 110 feet. How

many square feet does the crop

circle cover? Use 3.14 for ␲.

A 172.7 ft

9,498.5 ft

B 345.4 ft

D 37,994 ft

32. Which number has the least value?

12.2 H 12.5

H 12.25 J 12.52

33. Which set of integers is ordered from

least to greatest?

ⴚ18, ⴚ15, ⴚ4, 0

B ⴚ19, ⴚ23, ⴚ26, ⴚ30

C 10, ⴚ2, ⴚ15, ⴚ12

D 12, ⴚ4, ⴚ7, 12

Cumulative Test

Form B, continued

CHAPTER

34. Bart had $377 in his savings

account. He attempted to withdraw

$390 from an ATM machine. How

much money would he need to

deposit in his savings account to

cover his withdrawal?

F ⴚ$13 H $767

$13 J $780

35. Solve d ⴙ 3.5 ⴝ 9.8.

A d ⴝ 2.8 C d ⴝ 13.3

d ⴝ 6.3 D d ⴝ 34.3

36. Simplify 48 ⴜ 4 ⴙ 6 ⴛ 7 ⴚ 5.

F 549

G 20 J 121

37. Tony is 185 cm tall. He is 12 cm

taller than Catherine. How tall is

Catherine?

A 197 cm C 150 cm

173 cm D 15 cm

38. What is the value of 3

F 9 H 27

G 12 81

39. Which value is a solution of the

equation 4y ⴝ 124?

A 631

B 20 D 496

Use the rate schedule for questions

40 and 41.

40. To the nearest penny, what is the

charge for using 1,195 kWh of

electricity?

$63.34 H $47.80

G $60.80 J $35.10

41. Delsin runs a small used bookstore.

Last month his store used 8,000 kWh

of electricity. What was his bill?

A $375 C $320

$346 D $240

42. What is seventy thousand three

hundred five and twelve hundredths

in numerals?

F 7,030,512 H 70,305.012

G 70,315 70,305.12

43. How many liters are equal to

8,000 kL?

A 8 C 800,000

B 800 8,000,000

44. Which number is prime?

F 27 H 51

47 J 81

242 Holt Middle School Math Course 1

Name Date Class

Cumulative Test

Form B, continued

CHAPTER

Electric Rate Schedule

First 2,000 kWh $0.053 per kWh

Over 2,000 kWh $0.04 per kWh

Name ________________________________ Name ________________________________

Perimeter, Area, and Volume Assessmen Perimeter, Area, and Volume Assessment

ABCD 24 FGHJ

2FGHJ 25ABCD 2FGHJ 25ABCD

3ABCD 26FGHJ 3ABCD 26FGHJ

4FGHJ 27ABCD 4FGHJ 27ABCD

5ABCD 28FGHJ 5ABCD 28FGHJ

6FGHJ

ABCD 6 FGHJ

ABCD

7ABCD

FGHJ 7 ABCD

FGHJ

8FGHJ

ABCD 8 FGHJ

ABCD

9ABCD 32FGHJ 9ABCD 32FGHJ

FGHJ 33ABCD

ABCD 34 FGHJ

ABC

D 34 FGHJ

FGHJ 35ABCD

ABCD 36 FGHJ

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

75%

100%

88%

63%

50%

38%

25%

13%

Perimeter, Area, and Volume Assessment

ABCD 24 FGHJ

Chapter 10 Assessment

2FGHJ 25ABCD

3ABCD 26FGHJ

4FGHJ 27ABCD

5ABCD 28FGHJ

6FGHJ

ABCD

7ABCD

FGHJ

8FGHJ

ABCD

9ABCD 32FGHJ

FGHJ 33ABCD

ABCD 34 FGHJ

FGHJ 35ABCD

ABCD 36 FGHJ

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