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Lesson 9�8 747

Advance PreparationFor Part 1, make models of the open boxes on Activity Sheet 8 to illustrate where to fold and where to tape the patterns for Boxes A and B. Have students save the boxes for use in Project 9.

Teacher’s Reference Manual, Grades 4–6 pp. 187–189, 222–225

Key Concepts and Skills• Use formulas (l ∗ w ∗ h or B ∗ h) to

calculate the volumes of rectangular prisms. [Measurement and Reference Frames Goal 2]

• Define the base and height of a rectangular prism. [Geometry Goal 2]

• Explore the properties of rectangular prisms. [Geometry Goal 2]

• Write number sentences with variables to model volume problems.  [Patterns, Functions, and Algebra Goal 2]

Key ActivitiesStudents discuss the difference between volume and area. They define base and height for a rectangular prism and develop a formula for the volume of a rectangular prism. Students use a formula to find volumes and to model a rectangular prism with a given volume.

Ongoing Assessment: Informing Instruction See page 751.

Key Vocabularyvolume � cubic unit � rectangular prism �

face � base (of a rectangular prism) � height (of a rectangular prism) � Associative Property of Multiplication

MaterialsMath Journal 2, pp. 321, 322, and Activity Sheet 8 Student Reference Book, pp. 195–197Study Link 9�7scissors � transparent tape � 36 centimeter cubes � slate

Math Boxes 9�8Math Journal 2, p. 323 Students practice and maintain skillsthrough Math Box problems.

Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 3. [Number and Numeration Goal 5]

Study Link 9�8Math Masters, p. 279 Students practice and maintain skillsthrough Study Link activities.

READINESS

Analyzing Prism Nets for CubesMath Masters, pp. 280 and 429Students investigate solid geometry concepts using cube diagrams.

ENRICHMENTFinding the Volume of One Stick-On NoteMath Masters, p. 281per partnership: one stick-on note, pad of unused stick-on notes, centimeter cubeStudents compare the volume of a single stick-on note to the volume of a centimeter cube.

EXTRA PRACTICE 5-Minute Math5-Minute Math™, pp. 52 and 214Students calculate the volumes of prisms.

Teaching the Lesson Ongoing Learning & Practice Differentiation Options

Volume ofRectangular Prisms

Objective To provide experiences with using a formula for the volume of rectangular prisms.f

�������

Common Core State Standards

747_EMCS_T_TLG2_G5_U09_L08_576914.indd 747 3/23/11 2:48 PM

Metric Units

1 liter (L) = 1,000 milliliters (mL)

1 milliliter = 1 _ 1,000 liter

1 liter = 1,000 cubic centimeters

1 milliliter = 1 cubic centimeter

U.S. Customary Units

1 gallon (gal) = 4 quarts (qt)1 gallon = 2 half-gallons1 half-gallon = 2 quarts1 quart = 2 pints (pt)1 pint = 2 cups (c)1 cup = 8 fluid ounces (fl oz)1 pint = 16 fluid ounces1 quart = 32 fluid ounces1 half-gallon = 64 fluid ounces1 gallon = 128 fluid ounces

Measurement

Volume and Capacity

VolumeThe volume of a solid object such as a brick or a ball is a measure of how much space the object takes up. The volume of a container such as a freezer is a measure of how much the container will hold.

Volume is measured in cubic units, such as cubic inches (in.3), cubic feet (ft3), and cubic centimeters (cm3). It is easy to find the volume of an object that is shaped like a cube or other rectangular prism. For example, picture a container in the shape of a 10-centimeter cube (that is, a cube that is 10 cm by 10 cm by 10 cm). It can be filled with exactly 1,000 centimeter cubes. Therefore, the volume of a 10-centimeter cube is 1,000 cubic centimeters (1,000 cm3).

To find the volume of a rectangular prism, all you need to know are the length and width of its base and its height. The length, width, and height are called the dimensions of the prism.

You can also find the volume of another solid, such as a triangular prism, pyramid, cone, or sphere, by measuring its dimensions. It is even possible to find the volume of an irregular object such as a rock or your own body.

CapacityWe often measure things that can be poured into or out of containers such as liquids, grains, salt, and so on. The volume of a container that is filled with a liquid or a solid that can be poured is often called its capacity.

Capacity is usually measured in units such as gallons, quarts, pints, cups, fluid ounces, liters, and milliliters.

The tables at the right compare different units of capacity. These units of capacity are not cubic units, but liters and milliliters are easily converted to cubic units:

1 milliter = 1 cm3 1 liter = 1,000 cm3

length width

height

1 cm3 1,000 cm3

The dimensions of a rectangular prism

182_214_EMCS_S_SRB_G5_MEA_576515.indd 195 3/8/11 5:00 PM

Student Reference Book, p. 195

Student Page

748 Unit 9 Coordinates, Area, Volume, and Capacity

Getting Started

1 Teaching the Lesson

▶ Math Message Follow-Up WHOLE-CLASSDISCUSSION

(Student Reference Book, p. 195)

Ask students to pose their questions for the class. Use the questions and responses to discuss the difference between area and volume. To support English language learners, write the key ideas on the board. Emphasize the following points:

� Shapes that are 2-dimensional are flat. The surfaces they enclose take up a certain amount of area, but they do not have any thickness, so they do not take up any space.

� Shapes that are 3-dimensional have length, width, and thickness, so they enclose a certain amount of space.

� The amount of surface inside a 2-dimensional shape is the area of the shape. Area is measured in square units, such as square inches, square feet, square centimeters, and so on.

� The amount of space enclosed by a 3-dimensional shape is the volume of the shape. Volume is measured in cubic units, such as cubic inches, cubic feet, cubic centimeters, and so on.

� The symbol used to indicate square units is the abbreviation of the unit name with a superscript 2, for example, in2, ft2, cm2, m2, and so on. For cubic units, the symbol is the abbreviation of the unit name with a superscript 3, for example, in3, ft3, cm3, m3, and so on. To support English language learners, discuss the meanings of the word volume. Students might have heard the word used in contexts involving sound level or a book. Emphasize that volume is also used in the mathematical context involving 3-dimensional shapes.

ELL

Mental Math and Reflexes Students practice rounding numbers. Have them write their answers on their slates. Suggestions:

Round 654 to the nearest hundred. 700 Round 4,654.97 to the nearest whole number. 4,655 Round 67.072 to the nearest tenth. 67.1 Round 3.452 to the nearest hundredth. 3.45 Round 67% of 100 to the nearest ten. 70 Round 8.006 to the nearest tenth. 8.0

Math MessageWrite 2 questions that can be answered by reading Student Reference Book, page 195.

Study Link 9�7 Follow-Up Ask volunteers to present the area formulas for a triangle and for a parallelogram and the number models they used to solve the Study Link Problems.

Project Note

For more practice finding the volume of rectangular prisms, see Project 9: Adding Volumes of Solid Figures.

Mathematical PracticesSMP1, SMP2, SMP3, SMP4, SMP5, SMP6, SMP7, SMP8Content Standards5.NBT.4, 5.NBT.7, 5.MD.3a, 5.MD.3b, 5.MD.4, 5.MD.5a, 5.MD.5b

748-752_EMCS_T_TLG2_G5_U09_L08_576914.indd 748 3/14/12 9:16 AM

Rectangular PrismsLESSON

9 �8

Date Time

A rectangular prism is a geometric solid enclosed by six flat surfaces formed by rectangles. If each of the six rectangles is also a square, then the prism is a cube. The flat surfaces are called faces of the prism.

Bricks, paperback books, and most boxes are rectangular prisms. Dice and sugar cubes are examples of cubes.

Below are three different views of the same rectangular prism.

base

height

63 12

base

height

63

12

base6

312

height

1. Study the figures above. Write your own definitions for base and height.

Base of a rectangular prism:

Height of a rectangular prism:

Examine the patterns on Activity Sheet 6. These patterns will be used to construct open boxes—boxes that have no tops. Try to figure out how many centimeter cubes are needed to fill each box to the top. Do not cut out the patterns yet.

2. I think that centimeter cubes are needed to fill Box A to the top.

3. I think that centimeter cubes are needed to fill Box B to the top.

Sample answer: Any face of the

Sample answer: The shortest prism; usually the face the prism sits on

distance between the base and the opposite face

Answers vary.

292-332_EMCS_S_G5_MJ2_U09_576434.indd 321 2/22/11 5:18 PM

Math Journal 2, p. 321

Student Page

Links to the Future

Adjusting the Activity

Lesson 9�8 749

▶ Defining Base and Height WHOLE-CLASSDISCUSSION

for Rectangular Prisms(Math Journal 2, p. 321)

As a class, read the introduction on journal page 321. Have students study the figures and then write their own definitions for the base and height of a rectangular prism. Ask volunteers to share their definitions with the class. Use their responses to reinforce the following points:

� A rectangular prism is formed by six flat surfaces, or faces, that are rectangles. To support English language learners, compare the common meaning and the mathematical meaning of the word face.

� Any of the six faces of the prism can be a base, but the face that the prism “sits on” is often chosen as a base.

� The height (for a given base) is the shortest distance between the base and the opposite face.

The names and properties of prisms will be revisited in more detail in Unit 11.

There are two types of prisms, right and oblique. (See below.)When the faces of a prism are all rectangles, it is a right rectangular prism. When the faces are not all rectangles, it is an oblique rectangular prism. Oblique prisms are not considered in Fifth Grade Everyday Mathematics.

Right rectangular prism Oblique rectangular prism

Have students identify objects in the classroom that have the shape of rectangular prisms.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

▶ Developing a Formula

WHOLE-CLASS ACTIVITY

for Volume (Math Journal 2, pp. 321, 322, and Activity Sheet 8; Student Reference Book, pp. 196 and 197)

Algebraic Thinking Give 24 centimeter cubes to each student. Ask students to tear out Activity Sheet 8 from the back of their journals and follow the directions on journal page 321 to answer Problems 2 and 3.

ELL

ELL

PROBLEMBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEMBLEBLLELBLLLLBLEBLEBLEBLEBLEBLEBLEBLEEEMMMMMMMMMMMOOOOOOOOOOBBBBBBLBLBLBLBLBLBLLLLPROPROPROPROPROPROPROPROPROPROPRPPRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROOROROROOOPPPPPPP MMMMMMMMMMMMMMMMMMMMMEEEEEEEEEEEEEEELELEELEEEEEEEELLLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRPROBLEMSOLVING

BBBBBBBBBBBBBBBBBBBB EEELEMMMMMMMMOOOOOOOOOBBLBBLBLBLBBBOOOOROROROROROROROROROO LELELELEEEEEELEEMMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGLLLLLLLLLLLLLVINVINVINVINNNVINVINNNVINVINVINVINVINVV GGGGGGGGGGGOLOOOLOOOLOLOO VINVINVVLLLLLLLLVINVINVINVINNVINVINVINVINVINVIVINVINGGGGGGGGGGGOOOLOLOLOLOLOLOLOO VVVVLLLLLLLLLLVVVVVVVVVOOSOSOOSOSOSOSOSOSOSOOSOSOSOSOSOOOOOSOSOSOSOSOSOSOOSOSOSOSOOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVLLLLLLLVVVVVVVVLLLVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIIIISOLVING

NOTE You may want to remind students that to be a prism, a polyhedron must have at least one pair of parallel and congruent faces, which can be called bases. Rectangular prisms have 3 pairs of parallel congruent faces. Therefore, when calculating the volume of a rectangular prism, any face can be chosen as the base.

748-752_EMCS_T_TLG2_G5_U09_L08_576914.indd 749 3/23/11 2:49 PM

Volume of Rectangular PrismsLESSON

9 � 8

Date Time

Write the formulas for the volume of a rectangular prism.

B is the area of the base (l ∗ w ).

h is the height from that base.

V is the volume of the prism.

Find the volume of each rectangular prism below.

1. 2.

V = V = (unit) (unit)

3. 4.

V = V =

(unit) (unit)

5. 6.

V = V =

(unit) (unit)

base

height

80 in3

343 cm3

90 ft3

192 in3

50 cm3

72 cm34 in.

4 in.

5 in.

3 cm4 cm

6 cm

7 cm

7 cm

7 cm8 in.

6 in.

4 in.

3 ft6 ft

5 ft

4 cm

2.5 cm

5 cm

V = B ∗ h or V = l ∗ w ∗ h

292-332_EMCS_S_MJ2_G5_U09_576434.indd 322 3/22/11 12:42 PM

Math Journal 2, p. 322

Student Page

750 Unit 9 Coordinates, Area, Volume, and Capacity

When students have completed the problems, display your prepared models as guides for folding and taping the boxes. Direct students to do the following:

1. Cut out the pattern for Box A, fold it on the dashed lines, and tape it to make an open box.

2. Cover the bottom of Box A with one layer of centimeter cubes. Ask: How many cubes are in this layer? 8

3. Put a second layer of cubes on top of the first layer. Ask: How many cubes are in the box now? 16

4. Put a third layer on top of the second layer. Ask: How many cubes are in the box now? 24 What is the volume of the box? 24 cm3

5. Cut out the pattern for Box B, fold it on the dashed lines, and tape it to make an open box.

6. Cover the bottom of Box B with one layer of cubes. Ask: How many cubes are in this layer? 9

Ask students to answer the following questions without putting any more cubes in the box:

● How many layers of cubes are needed to fill the box? 5

● How many centimeter cubes in all are needed to fill the box? 45 How did you find the answer? Sample answer: By multiplying the number of cubes in 1 layer by the number of layers.

● What is the volume of the box? 45 cm3

Point out that the number of cubes in one layer is the same as the number of square centimeters in the base (l ∗ w), and that the number of layers is the same as the height in centimeters of the box. Ask students how this information might be used in a formula to find the volume of the box. Multiply the area of the base by the height of the box.

This formula is written as V = B ∗ h, where V represents the volume, B represents the area of the base, and h represents the height from that base. Ask students to write this formula at the top of journal page 322. Have students refer to pages 196 and 197 of the Student Reference Book as needed.

NOTE Traditionally, linear measures are represented in formulas by lowercase letters, and 2- and 3-dimensional measures are represented by uppercase letters. For example, b is used to represent the length of the base of a rectangle, and B is used to represent the area of the base of a prism.

748-752_EMCS_T_TLG2_G5_U09_L08_576914.indd 750 3/23/11 2:49 PM

Measurement

The area of the Pacific Ocean is about 64 million square miles. The average depth of that ocean is about 2.5 miles. So, the volume of the Pacific Ocean is about 64 million mi 2 ∗ 2.5 mi, or 160 million cubic miles.

For a right rectangular prism with side lengths l, w, and h units, the volume V can be found using the formula

V = l ∗ w ∗ h.

Note

Volume of a Geometric Solid

You can think of the volume of a geometric solid as the total number of whole unit cubes and fractions of unit cubes needed to fill the interior of the solid without any gaps or overlaps.

Prisms and CylindersIn a prism or cylinder, the cubes can be arranged in layers that each contain the same number of cubes or fractions of cubes.

The height of a prism or cylinder is the shortest distance between its bases. The volume of a prism or cylinder is the product of the area of the base (the number of cubes in one layer) multiplied by its height (the number of layers).

Pyramids and ConesThe height of a pyramid or cone is the shortest distance between its base and the vertex opposite its base.

If a prism and a pyramid have the same size base and height, then the volume of the pyramid is one-third the volume of the prism. If a cylinder and a cone have the same size base and height, then the volume of the cone is one-third the volume of the cylinder.

Find the volume of the prism.

8 cubes in 1 layer 3 layers

3 layers with 8 cubes in each layer makes a total of 24 cubes.

Volume = 24 cubic units

base base

height height

heig

ht

base

heig

ht

base

base

base

sam

e he

ight

same base area

sam

e he

ight

same base area

182_214_EMCS_S_SRB_G5_MEA_576515.indd 196 4/4/11 5:01 PM

Student Reference Book, p. 196

Student Page

Check your answers on page 440.

Volume of a Rectangular or Triangular Prism

Measurement

Volume of a Prism Area of a Rectangle Area of a Triangle

V = B ∗ h A = b ∗ h A = 1 _ 2 ∗ (b ∗ h)V is the volume, B is the area A is the area, b is the length A is the area, b is the length of the base, h is the height of of the base, h is the height of of the base, h is the height of the prism. the rectangle. the triangle.

Find the volume of the rectangular prism.

Step 1: Find the area of the base (B). Use the formula A = b ∗ h. • length of the rectangular base (b) = 8 cm • height of the rectangular base (h) = 5 cm • area of base (B) = 8 cm ∗ 5 cm = 40 cm2

Step 2: Multiply the area of the base by the height of the rectangular prism. Use the formula V = B ∗ h. • area of base (B) = 40 cm2

• height of prism (h) = 6 cm • volume (V) = 40 cm2 ∗ 6 cm = 240 cm3

The volume of the rectangular prism is 240 cm3.

Find the volume of each prism. Include the unit in each answer.

1. 2. 3.

Find the volume of the triangular prism.

Step 1: Find the area of the base (B). Use the formula A = 1 _ 2 (b ∗ h). • length of the triangular base (b) = 5 in. • height of the triangular base (h) = 4 in. • area of base (B) = 1 _ 2 ∗ (5 in. ∗ 4 in.) = 10 in.2

Step 2: Multiply the area of the base by the height of the triangular prism. Use the formula V = B ∗ h. • area of base (B) = 10 in.2

• height of prism (h) = 6 in. • volume (V) = 10 in.2 ∗ 6 in. = 60 in.3

The volume of the triangular prism is 60 in.3.

5 in.6 in.

4 in.

6 cm

5 cm8 cm

2 yd

7 yd

3 yd10 cm

10 cm

10 cm

8 ft

6 ft12

ft

182_214_EMCS_S_SRB_G5_MEA_576515.indd 197 3/8/11 5:00 PM

Student Reference Book, p. 197

Student Page

Lesson 9�8 750A

▶ Another Formula for Volume

WHOLE-CLASS ACTIVITY

of a Rectangular Prism (Student Reference Book, pp. 196 and 197)

Ask students to review pages 196 and 197 of the Student Reference Book. Give each student 12 more centimeter cubes so each student has 36 cubes.

NOTE If you do not have 36 centimeter cubes per student, ask students to build the rectangular prisms in partnerships.

Ask students to use the centimeter cubes to do the following:

1. Build a rectangular prism with a base that is 4 cubes long and 3 cubes wide, and that is 1 cube high.

Ask: Describe a way you could determine the volume of the rectangular prism. Sample answer: Multiply 4 ∗ 3 ∗ 1 to obtain 12 cm3. What do the 4, 3, and 1 represent in the prism? The length, width, and height

2. Build a second 4-by-3-by-1 rectangular prism. Place it on top of the original rectangular prism.

Ask: How could you determine the volume of the new rectangular prism? Sample answers: Multiply 4 ∗ 3 ∗ 2 to obtain 24 cm3; multiply 12 ∗ 2 to get 24 cm3.

3. Build a third 4-by-3-by-1 layer. Place it on top of the existing rectangular prism. Ask students to write a number model using three factors to find the volume of the new prism. 4 ∗ 3 ∗ 3 = 36 cm3

Now ask the following question: Suppose you know the number of cubes in the length, width, and height of a rectangular prism. How could this information be used to write another formula for finding the volume of a rectangular prism? Multiply: length ∗ width ∗ height (l ∗ w ∗ h); V = l ∗ w ∗ h.

Have students write this formula at the top of journal page 322, next to the first formula they derived for finding the volume of a rectangular prism. Discuss why both formulas will result in the same volume.

Conclude by asking students to explain how they could use the new formula to find the volume of a cube. Sample answers: Replace each side-length letter in the formula with the length of a side of the cube. You could rewrite the formula as V = s3, where s is the length of a side of the cube.

748-752_EMCS_T_TLG2_G5_U09_L08_576914.indd 750A 4/7/11 9:30 AM

750B Unit 9 Coordinates, Area, Volume, and Capacity

▶ Building a Rectangular PARTNER ACTIVITY

Prism with a Given VolumeAlgebraic Thinking Ask students to use centimeter cubes to build the shape of a rectangular prism with a volume of 24 cm3.

Ask: What are the possible areas for the base (B) and the length of the height (h) from that base? B = 24 cm2, h = 1 cm; B = 12 cm2, h = 2 cm; B = 8 cm2, h = 3 cm; B = 6 cm2, h = 4 cm; B = 4 cm2, h = 6 cm; B = 3 cm2, h = 8 cm; B = 2 cm2, h = 12 cm; B = 1 cm2, h = 24 cm

Ask students to use the cubes to make a rectangular prism that has a length of 3 cm, a width of 2 cm (base of 6 cm2), and a height of 4 cm. Explain that the volume can be found as follows:

V = (l ∗ w) ∗ h = (3 ∗ 2) ∗ 4

Now ask students to carefully rotate their rectangular prism so that it now has a length of 4 cm, a width of 2 cm (base of 8 cm2), and a height of 3 cm. Explain that the volume can be found as follows:

V = (l ∗ w) ∗ h = 3 ∗ (2 ∗ 4)

Ask: What do the two rectangular prisms have in common? Sample answer: The dimensions of the prisms have the same three measures, and each has a volume of 24 cm3.

Guide students to conclude that if the measures of the three dimensions of two rectangular prisms are the same, the volumes are the same. Then point out that this is an illustration of the Associative Property of Multiplication, which means that changing the grouping of factors does not change the product.

So, (3 º 2) º 4 = 3 º (2 º 4)

6 º 4 = 3 º 824 = 24

Have students repeat this activity by comparing the volumes of two rectangular prisms that have dimensions of 2 cm, 3 cm, and 5 cm, but different bases.

▶ Finding the Volumes of

INDEPENDENT ACTIVITY

Rectangular Prisms(Math Journal 2, p. 322)

Algebraic Thinking Have students complete journal page 322 by calculating the volume of six rectangular prisms from the given dimensions.

748-752_EMCS_T_TLG2_G5_U09_L08_576914.indd 750B 3/23/11 2:49 PM

Math Boxes LESSON

9 � 8

Date Time

5. Use the graph to answer the questions.

a. Which day had the greatest attendance? Friday

b. What was the total attendance for the five-day period? 90

1. Solve.

a. b.

c. d.

3. Find the least common denominator for the fraction pairs.

a. 2 _ 7 and 1 _ 3 21 b. 5 _ 8 and 4 _ 16 16

c. 3 _ 8 and 4 _ 12

d. 2 _ 5 and 2 _ 3 15

e. 4 _ 16 and 6 _ 12 48

f. 5 _ 15 and 2 _ 8 120

4. Elena received the following scores on math tests: 80, 85, 76, 70, 87, 80, 90,80, and 90.

Find the following landmarks:

maximum: 90 minimum: 70 range: 20 mode: 80 mean: 82

2. Complete the “What’s My Rule?” table, and state the rule.

254.04

523.81Rule

÷30

in out

240 8

600 20

12

50

2,100 70 1,200 40

3601,500

�

42.82128.07

– 85.25

12.8818.95

– 6.07215.29

+ 38.75

306.85+ 216.96

M Tu W Th FDay of the Week

Movie Theater Attendance

05

1015202530

Num

ber o

f Tic

kets

Sol

d

34–36

65 119

124

231 232

24

292-332_EMCS_S_G5_MJ2_U09_576434.indd 323 2/22/11 5:18 PM

Math Journal 2, p. 323

Student Page

STUDY LINK

9�8 Volumes of Cube Structures

195–197

Name Date Time

The structures below are made up of centimeter cubes.

1.

Area of base = cm2

Volume of first layer = cm3

Volume of entire cube structure = cm3

3.

Area of base = cm2

Volume of first layer = cm3

Volume of entire cube structure = cm327

99

45

1515

2.

Area of base = cm2

Volume of first layer = cm3

Volume of entire cube structure = cm3

4.

Area of base = cm2

Volume of first layer = cm3

Volume of entire cube structure = cm356

1414

16

88

1st layer

1st layer

1st layer

1st layer

2nd layer

Practice

5. 3 _ 5 ∗ 1 _ 8 = 6. 3,840 / 4 =

7. 960 ∗ 4 = 8. 4 _ 5 ∗ 5 _ 6 = 3,840960

4 _ 6 , or

2

_ 3

3 _ 40

254-293_497_EMCS_B_MM_G5_U09_576973.indd 279 2/22/11 6:06 PM

Math Masters, p. 279

Study Link Master

Lesson 9�8 751

Ongoing Assessment: Informing InstructionWatch for students who are not correctly matching the given dimensions to the formula variables. Have them make and complete a table for the problems on journal page 322, such as the following:

2 Ongoing Learning & Practice

▶ Math Boxes 9�8

INDEPENDENT ACTIVITY

(Math Journal 2, p. 323)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 9-10. The skills in Problems 2 and 5 preview Unit 10 content.

Writing/Reasoning Have students write a response to the following: Explain the strategy you used to solve Problem 1c and explain your reasoning. Answers vary.

Ongoing Assessment:Recognizing Student Achievement

Math Boxes Problem 3 �

Use Math Boxes, Problem 3 to assess students’ abilities to find common denominators. Students are making adequate progress if they correctly identify the least common denominators. [Number and Numeration Goal 5]

▶ Study Link 9�8

INDEPENDENT ACTIVITY

(Math Masters, p. 279)

Home Connection Students find the volume of cube structures.

Problem V B h

1 80 in3 4 ∗ 4 5

2 72 cm3 4 ∗ 3 6

3 343 cm3 7 ∗ 7 7

4 192 in3 8 ∗ 6 4

5 90 ft3 6 ∗ 3 5

6 50 cm3 2.5 ∗ 4 5

748-752_EMCS_T_TLG2_G5_U09_L08_576914.indd 751 10/14/11 2:13 PM

What is the volume of one stick-on note? In other words, how much space is taken up by a single stick-on note? How does the volume of a stick-on note compare to the volume of a centimeter cube?

1. An unused pad of stick-on notes is an example of what shape?

2. Estimate the volume of one stick-on note.

3. Calculate the volume of one stick-on note. Volume =

Record your strategy.

4. Use a formula to calculate the volume of one centimeter cube. Volume =

Write the number sentence for this calculation.

5. Explain how the volume of one stick-on note compares with the volume of one centimeter cube.

Name Date Time

LESSON

9�8 Comparing Volume

1 cm3

Answers vary.

Rectangular prism

Sample answer: About 0.75 cm3

Volume = (1 cm ∗ 1 cm) ∗ 1 cm = 1 cm3

Answers vary.y

254-293_497_EMCS_B_MM_G5_U09_576973.indd 281 2/23/11 4:20 PM

Math Masters, p. 281

Teaching Master

Name Date Time

LESSON

9�8 Unfolding Prisms

No

No

Yes

If you could unfold a prism so that its faces are laid out as a set attached at their edges, you would have a flat diagram for the shape. Imagine unfolding a cube. There are many different ways that you could make diagrams, depending on how you unfold the cube.

Which of the following are diagrams that could be folded to make a cube? Write yes or no in the blank next to each diagram.

1.

2.

3.

4.

Yes

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Math Masters, p. 280

Teaching Master

752 Unit 9 Coordinates, Area, Volume, and Capacity

3 Differentiation Options

READINESS PARTNER ACTIVITY

▶ Analyzing Prism Nets 5–15 Min

for Cubes(Math Masters, pp. 280 and 429)

To stimulate students’ ability to visualize, name, and describe geometric solids, have students look at diagrams to determine which shapes can and cannot be folded into

cubes. Read and discuss the introduction as a group. As students choose which of the diagrams can be folded into a cube, provide inch grid paper so students may check their work.

Discuss students’ solutions.

ENRICHMENT PARTNER ACTIVITY

▶ Finding the Volume of 5–15 Min

One Stick-On Note(Math Masters, p. 281)

To apply students’ understanding of how to find the volume of a rectangular prism, have partners compare the volume of a single stick-on note and that of a centimeter

cube. Give each partnership one stick-on note, one unused pad of stick-on notes, and one centimeter cube. Ask students to estimate how the volume of the single stick-on note compares with the volume of the cube.

Have students record their strategies and solutions on Math Masters, page 281. When partners have completed the page, ask them to present their solutions.

NOTE One approach to finding the volume of a single stick-on note would be to measure the dimensions and find the volume of the unused pad of stick-on notes. A single stick-on note would represent a fraction of the pad.

EXTRA PRACTICE

SMALL-GROUP ACTIVITY

▶ 5-Minute Math 5–15 Min

To offer students more experience with calculating the volumes of prisms, see 5-Minute Math, pages 52 and 214.

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