Classroom: Teacher’s Guide

Middle School Math

Classroom: Teacher’s Guide

Middle School Math

The Port of Long Beach 925 Harbor Plaza Long Beach, CA 90802 (562) 590-4121 www.polb.com © 2008 Port of Long Beach

Classroom: Teacher’s Guide

Middle School Math Contents Preface About Classroom Introduction Lesson One

v vii ix 1

Proportions in the Port of Long Beach Terminal Objective Key Words Lesson Closure

Lesson Two

1 2 3 9

11

Distance, Rate and Time Terminal Objective Lesson Key Words Closure Worksheet Worksheet Answers

11 12 12 17 19 21

Lesson Three

23

Scale Factors Terminal Objective Lesson Key Words Closure Worksheet

23 24 24 30 31

Lesson Four

33

Volume of Prisms

Terminal Objective

33

Lesson Key Words Closure

34 34 43

Lesson Five

45

Dimensional Analysis at the Port of Long Beach Terminal Objective Lesson Key Words Closure Worksheet Worksheet Answers Handout Handout Answers

45 46 46 52 53 55 57 59

Lesson Six

61

Money Conversion Terminal Objective Lesson Key Words Closure Worksheet Worksheet Answers

61 62 62 66 67 69

contents

| iii

Preface The Port of Long Beach is an industry-leading, environmentally friendly global seaport. Every year about $100 billion worth of

cargo passes across the Port of Long Beach’s docks. Imported cargo arrives at the Port bound for store shelves, factories and other destinations locally and across the United States; and exports

leave, bound for foreign ports and international consumers. These goods include everything from electronics and machinery to food, cars and petroleum products.

As a key international trade hub, the Port of Long Beach supports

nearly 1.5 million jobs across Southern California and the nation, and these jobs – as engineers, environmental scientists, freight

forwarders, crane operators and logistics specialists, just to name a few – require a highly skilled workforce.

Port of Long Beach: Classroom aims to make students aware of the Port of Long Beach and to prepare them for port career opportunities. These lessons combine real-world Port of Long Beach situations with content from the California state-approved curriculum.

The result is an engaging and interactive series of lessons that fully conform to the state content standards while getting

students excited about the major global seaport right in their own backyards.

If you want more information about any of the information in these lessons, please visit our Web site at www.polb.com. Let’s get started!

preface

|v

About Port of Long Beach: Classroom Middle School Math Teacher’s Guide

These math lessons were developed in partnership with the Long

Beach Unified School District. The teacher’s guide should be used in conjunction with the PowerPoint presentations to provide

an interactive and visual representation of the content. These

lessons are fully aligned to the California State Curriculum and are intended to complement the teacher’s own lesson plans.

The lessons are divided into several parts, which should be completed in order.

Terminal Objective: The overall lesson objective Content Standard Reference: The California Content Standard to which the lesson teaches



Materials: Materials required for the lesson

Time Required: The estimated number of 1-hour classes needed to complete the lesson.

Introduction of Lesson: Pre-lesson preparation Anticipatory Set: Information or activities that prepare students for the upcoming lesson

Student Objective: What the students will get out of the lesson

about Port of Long Beach

| vii

Purpose: Description of real-life applications of the content and why the skills are important for students



Procedure: The body of the lesson

Input: Information needed to understand the lesson, such as definitions or formulas

Modeling: A description of how to use the formulas or complete the problems

Check for Understanding: Practice problems and activities to check for student learning

Guided Practice: An opportunity for students to apply their skills to new problems

Closure: A summary of the lesson, which may include homework or additional activities

viii | about Port of Long Beach

Introduction: Port of Long Beach

In order to understand the math lessons that follow, you will

need to become familiar with the Port of Long Beach, particularly with some of the special terminology used in goods movement and international trade. This section and the accompanying

PowerPoint presentation (Port of Long Beach Basics.ppt) provide background information to facilitate student learning. About the Port of Long Beach The Port of Long Beach is the second busiest seaport in the United States and a major gateway for U.S.-Asian trade. Every year

about $100 billion worth of cargo passes across the Port of Long

Beach’s docks. Imported cargo arrives at the Port bound for store shelves, factories and other destinations locally and across the United States; and exports leave, bound for foreign ports and international consumers.

The Port of Long Beach is a full-service seaport. Everything from electronics and machinery to food, cars and petroleum products

are shipped through the Port. The Port generates roughly 30,000 jobs in Long Beach, or about 1 in 8 jobs. Types of Cargo Cargo coming through the Port of Long Beach is divided into four categories:

Introduction

| ix

1. Containerized cargo 2. Dry bulk cargo

3. Liquid bulk cargo

4. Break bulk cargo and roll-on, roll-off cargo Containerized cargo is cargo that comes in containers. These containers hold just about anything…iPods, tennis shoes, furniture, you name it.

Containers come in two sizes. The smaller ones are twenty-foot containers.

The larger containers are forty-foot containers. Most of the containers you see on the road are 40-foot containers.

A 20-foot container can hold 320 19-inch LCD televisions.

8.6 ft

holds 320 LCD TVs 20 ft

x | introduction

8 ft

A 40-foot container holds 640 of these LCD televisions. 40 ft 8 ft

holds 640 LCD TVs

8.6 ft

The number of containers a ship can hold is measured in TEUs, or a 20-foot-equivalent. One TEU is one 20-foot container. A fortyfoot container is 2 TEUs. Large ships carry about 8,000 TEUs. 1 TEU = 1 Twenty Foot Equivalent Unit = 1 20-foot container

2 TEUs = 2 Twenty Foot Equivalent Units = 1 40-foot container

8.6 ft 8 ft 20 ft

40 ft 8 ft

8.6 ft

Tell your neighbor:

1. What does TEU stand for? Answer: Twenty-Foot Equivalent Unit 2. What size are the containers you normally see on the back of semi trucks? Answer: 2 TEUs. They are 40 feet long.

Introduction

| xi

Dry bulk cargo is dry stuff that does not come in containers. It is measured by weight or volume. Some examples are salt, cement, gravel, sand and grain. Tell your neighbor:

1. What is dry bulk? Answer: Dry stuff that does not come in containers.

2. Give an example. Answer: salt, cement, gravel, sand, etc. Liquid bulk cargo is wet stuff that does not come in containers. It is measured by weight or volume. Some examples are oil, gasoline, and chemicals. Tell your neighbor:

3. What is liquid bulk? Answer: Wet stuff that does not come in containers.

4. Give an example. Answer: oil, gasoline, chemicals. Break bulk cargo is comprised of large or heavy items moved on

pallets, bundles or rolls. Some examples are steel, lumber, paper on rolls, machinery and food products.

Roll On-Roll Off cargo is comprised of items that are driven on and off the ship. Examples are cars, trucks, buses and

construction vehicles. Roll on-roll off cargo is often called ro-ro cargo, pronounced just as it looks – row, row. Tell your neighbor:

1. What is break bulk? Answer: large or heavy items moved on pallets, bundles or rolls.

2. Give an example of ro-ro cargo. Answer: cars, trucks, buses and construction vehicles.

xii | introduction

Create this table in your notes and fill it in to summarize the lesson:

Type of Cargo

Description

Example

Containerized

In containers

Shoes, computers, etc.

Dry bulk

Dry material

Salt, etc.

Liquid bulk

Liquid material

Oil, etc.

Break bulk, ro-ro

Large or rolling

Wood, etc.

Introduction

| xiii

Proportions in the Port of Long Beach Lesson 1

Proportions in the Port of Long Beach

Lesson one Terminal Objective Students will solve Port of Long Beach

word problems by writing a proportion and using the cross product property to write an equation and solve it.

Content Standard Reference: Grade 6 Number Sense 6.1.3: Use proportions to solve problems. Use crossmultiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. Materials 1. Proportions PowerPoint 2. Popsicle stick Time Required 1 class

Proportions in the Port of Long Beach

|1

Proportions in the Port of Long Beach Lesson 1

Introduction of Lesson Anticipatory Set: Keyword 1. Proportion – two equal ratios

Students should know how to determine whether two ratios form a proportion and how to solve a proportion in two ways: using the equal fraction approach or crossproducts. Recall #1: Do these two ratios form a proportion? 2 = 3 Tell you neighbor yes or no. 8



12

Answer: Yes Recall #2: Tell your neighbor the cross product property. Explain how it can be used in the first problem. Answer: 2 × 12 = 3 × 8, so this must be a proportion. Recall #3: Equal fraction approach: Solve this proportion by thinking of them as two different fractions: 2

3

=

8

x

Answer: x= 12 (multiply the denominator by 4 to get 12) Recall #4: Crossproducts: Solve this proportion using cross products to write an equation and solve it. Solution:

2 6

=

x 15

6 x = 30 x =5

Student Objective:

Students will solve word problems involving the Port of Long Beach that use proportions.

Purpose:

Proportions are used in measurement, cooking, and enlarging and reducing photos. They are also used in the Port of Long Beach to calculate quantity

2 | Proportions in the Port of Long Beach

Proportions in the Port of Long Beach Lesson 1

Introduction of Lesson cont’d changes, like changes in cargo container sizes. Explain any other real-life use of proportions that come to mind.

Lesson Input

A proportion is two equal ratios. Today all of the numbers in the ratios will include a unit or label, such as “feet” or “shoes.” Each proportion will have four numbers, each with a label. Students can use an equal fraction approach to determine if the ratios are equal or use cross-products.

Modeling

Show the four numbers, each with a label in this situation. Also show students that the ratios are equal. A twenty-foot container holds 15,000 shoes. A forty-foot container holds 30,000 shoes.

1 TEU 2 TEUs = 15,000 shoes 30,000 shoes Check for Understanding What is the definition of a proportion? Answer: A proportion is two equal ratios. How many numbers will be in the proportion? Answer: 4. Each of the numbers will have a _____ . Answer: unit or label.

Guided Practice

Is this a proportion?

1 cargo hold 6 cargo holds = 10,000 tons 60,000 tons

Proportions in the Port of Long Beach

|3

Proportions in the Port of Long Beach Lesson 1

Lesson cont’d The teacher will pull a Popsicle stick to pick a random person to answer. Answer: Yes, multiply both the holds and the tons by 6 or the cross-products are equal.

Input

Write a proportion to represent a situation. There are four steps: 1. Read the situation. Identify the four numbers and their labels. 2. Write two fraction bars and the equal sign. 3. Write the labels in the proportion so they match either vertically or horizontally. 4. Fill in the matching numbers. There must be a relationship both vertically and horizontally.

Modeling

Model the four steps to write a proportion for this situation: A crane operator unloads one container in two minutes. The operator can unload 10 containers in 20 minutes. 1. Step 1 is to identify the units. In this case, the units are containers and minutes. 2. Step 2 is to write one unit on top of the other: cont' r 1 10 = min 2 20 3. Step 3 is to write two fraction bars and the equal sign: cont' r = min 4. Step 4 is to fill in the numbers so each ratio has a meaning: cont' r 1 10 = min 2 20

4 | Proportions in the Port of Long Beach

Proportions in the Port of Long Beach Lesson 1

Lesson cont’d Check for Understanding

Show two new proportions for the same problem. Partners discuss if the new proportions make sense. After one minute, select a student at random to say the answer. 1. Does this proportion make sense? min 2 20 = cont' r 1 10 Answer: Yes. 2. Does this proportion make sense? cont' r 1 2 = min 10 20 Answer: No, this proportion shows that it takes 10 minutes to unload one container

Guided Practice

Write a proportion for this situation: One shipping container is 8 feet tall, so 5 containers are 40 feet tall. Answer: cont'r 1 5

ft

Input

8

=

40

Write a proportion to represent a word problem with one number missing. Students will follow the same steps, but a variable will need to be used to represent the missing number.

Modeling

Write a proportion to represent this problem: The Morton Salt Company can package 20 50pound bags of salt in a minute. How many bags can it package in an hour? Follow the four steps. Answer: bags 20 = x min

1

60

or

20 bags = x bags

1min 60 min

Proportions in the Port of Long Beach

|5

Proportions in the Port of Long Beach Lesson 1

Lesson cont’d Check for Understanding

1. How do you know which numbers go with each label? Answer: The proportion has to match the situation you were given, both horizontally and vertically. 2. Does it matter if I put bags on the top or bottom? Answer: No.

Guided Practice

Write a proportion only for this word problem. Do not answer the “how many bags?” question: One bag sells for $5. How many bags would you get for $75? Answer:

bag

1

$

5

=

x 75

or

1 bag x bags

=

$5 $ 75

Input

Solve a proportion by using an equal fractions approach. There are four steps: 1. Write the proportion for the problem. 2. Determine the factor you need to multiply by. 3. Multiply to find the missing number. 4. Rewrite the answer so it answers the question.

Modeling

Use the Morton Salt Company example: The Morton Salt Company can package 20 50-pound bags of salt in a minute. How many bags can it package in an hour? 1.

6 | Proportions in the Port of Long Beach

20 bags x bags = 1 min 60 min

Proportions in the Port of Long Beach Lesson 1

Lesson cont’d 2. 1 min x 60 = 60 min 3. 20 bags x 60 = 120 bags 4. 120 bags are packaged in an hour.

Check for Understanding

When is the equal fraction approach appropriate? Answer: One of the numerators or denominators must be a factor of the other. Here, 1 goes into 60: 20 bags x bags = 1 min 60 min

Guided Practice

Solve the Morton Salt proportion you wrote earlier: 1 bag sells for $5. How many bags would you get for $75? 1. 1 bag $5

=

x bags $75

2. $5 x 15 = $75 3. 1 bag x 15 = 15 bags 4. I would get 15 bags for $75.

Input

Solve a proportion by using cross-products to write the equation and solving it. 1. Write the proportion for the problem. 2. Use cross-products property to write equation. 3. Divide both sides by the coefficient. 4. Rewrite answer so it answers the question.

Proportions in the Port of Long Beach

|7

Proportions in the Port of Long Beach Lesson 1

Lesson cont’d Modeling

The Morton Salt Company receives two shipments each year totaling 120,000 tons of salt. How much salt would it receive in a year if it receives three shipments? 1. 2 shipments

120,000 tons

=

3 shipments x tons

2. 2x = 120,000 • 3 3. 2x = 120,000 • 3 2 2 x = 180,000 4. It would receive 180,000 tons of salt.

Check for Understanding

Why was cross-multiplying a better way to solve the last proportion? Answer: Because 2 does not go into 3, or 2 is not a factor of 3.

Guided Practice

Write and solve a proportion to solve this problem: A crane operator unloads 30 containers in 60 minutes. How many containers are unloaded in 90 minutes? 1. 3 0 cont' r = x cont' r 6 0 min

90 min

2. 60 x = 30 • 90 3. 60 x = 2700 60 60 x = 45 4. 45 containers are unloaded in 90 minutes.

8 | Proportions in the Port of Long Beach

Proportions in the Port of Long Beach Lesson 1

Closure Have students exchange notes with their partner and look for any differences. Students should add to their notes if they see something they would like to include. Lastly, they should write the summary on the bottom of their notes.

Proportions in the Port of Long Beach

|9

Lesson two Terminal Objective

Content Standard Reference:

Given a word problem involving distance,

Grade 6 Algebra and Functions 2.3: Solve problems involving rates, average speed, distance, and time.

students will be able to apply the formula d = rt to find missing information.

Materials 1. Distance, Rate and Time PowerPoint Time Required 2 classes

Distance, Rate and Time

| 11

Distance, Rate and Time Lesson 2

Distance, Rate and Time

Distance, Rate and Time Lesson 2

Introduction of Lesson Anticipatory Set:

You are shipping a container with about 30,000 tennis shoes from Hong Kong to Long Beach. Keywords 1. Rate – speed 2. Nautical mile - about 1.15 miles or 1.852 km.

When are your shoes going to arrive in Long Beach? As long as you know distance and rate of speed for the boat, you can figure out when the shoes are expected to arrive.

Student Objective:

Students will learn how to apply the distance formula to find distance traveled, time traveled, or rate (speed).

Purpose:

Calculating distance, rate and time is important for moving cargo into and out of the Port of Long Beach.

Lesson Input

Keyword 1. Knot  - 1 nautical mile per hour.

State the distance formula: d = r*t Define and provide examples for: • Distance (miles, kilometers, inches, feet, meters …) • Rate (mph, kmph, feet per second, meters per minute, knot) • Time (minutes, hours, days, seconds, years, weeks)

Check for Understanding

• What does r stand for? Answer: Rate. Units? Answer: mph, kmph, feet per second, meters per minute • What does d stand for? Answer: Distance. Units? Answer: miles, kilometers, inches, feet, meters

12 | Distance, Rate and Time

Lesson cont’d

Distance, Rate and Time Lesson 2

• What does t stand for? Answer: Time. Units? Answer: minutes, hours, days, seconds, years, weeks • What is the distance formula? Answer: d=r*t

Input

First, students will learn how to find distance using the distance formula.

Modeling

If you are traveling for 3 hours at 65 mph, how far will you have gone? 1. Write down the formula. d=rxt 2. W  hat are you trying to find AND what do you know? D= ?? r = 65 mph t = 3 hours 3. Substitute known variables and solve. d = 3 hours x 65 mph d = 195 miles

Check for Understanding

If you are traveling for 4 hours at 55 mph, how far will you have gone? • What is the rate? r=55 • What is the time? t=4 • How would you apply distance formula? D=r*t D=55*4 D=220 miles

Distance, Rate and Time

| 13

Lesson cont’d Distance, Rate and Time Lesson 2

Guided Practice

If you are traveling for 2 hours to get to your job at the Port of Long Beach at a rate of 35 mph, how far did you travel? d=r•t d = 35 miles/hour • 2 hours d = 70 miles

Modeling

The Glory Sanye, a cargo ship, is traveling from Long Beach to Quigdoa Port in China’s Jiaozhou Gulf. If it travels for approximately 15 days at a rate of 480 miles per day, how far is the Gloria Sanye traveling? d = r• t d = 480 miles/day • 15 days d = 7,200 miles

Guided Practice

Now, the Glory Sanye is traveling from the Quigdoa Port to Dubai in the United Arab Emirates. Now empty, it travels 520 miles per day for 7 days. How far is Quigdoa Port from Dubai? d=r•t d = 520 • 7 d = 3,640 miles

Input

Distance is measured at sea and in aviation (air) by nautical miles. A nautical mile is historically equal to 1° latitude. It is about 1.15 miles or 1.852 km. A nautical mile is abbreviated as nm. A knot equals 1 nautical mile per hour.

Check for Understanding

Students will use nautical miles and knots to solve the next set of problems.

14 | Distance, Rate and Time

Lesson cont’d

Distance, Rate and Time Lesson 2

• What is the abbreviation for nautical mile? nm • How many miles is 1 nautical mile? 1.15 miles • Who uses nautical miles? Ships and airplanes • What is a knot? 1 nautical mile per hour

Modeling

The MSC Texas, a cargo ship, is traveling from Hong Kong to Long Beach. It is full of containers, about 8,200 TEUs (1 TEU = Twenty-Foot Equivalent Unit, or a 20-foot-long container). MSC Texas will take about 600 hours (about 25 days) to travel 13,200 nautical miles. How fast is the MSC Texas traveling? d=r•t 13200 nm = r • 600 hours 22 nm/hour or 22 knots = r

Check for Understanding

The MSC Texas is traveling back to Hong Kong but only a third of the containers are full. It will take the MSC Texas about 15 days to travel 12,500 kilometers to Hong Kong. How fast is the MSC Texas traveling on the return trip? • What is the distance? 12,500 km • What is the time? 15 days • How would you find the rate? Substitute distance and time and solve for r

Guided Practice

The MSC Texas is traveling back to Hong Kong but only half of the containers are full. It will take the MSC Texas about 550 hours (about 23 days) to travel 13,200 nm. How fast is the MSC Texas traveling on its return trip?

Distance, Rate and Time

| 15

Lesson cont’d Distance, Rate and Time Lesson 2

d = rt 13200 nm = r • 550 hours 24 nm/hour or 24 knots = r

Input

Now students will find time using the same formula.

Modeling

You are traveling to Sacramento, CA from Los Angeles, about 375 miles by train. If the train travels an average speed of 30 mph, how long will it take to reach Sacramento? d=r•t 375 miles = 30 miles/hour • t 12.5 = t About 12 ½ hours

Check for Understanding

The new speed trains that the State of California is looking to buy can travel 100 mph. How long would the trip from Los Angeles to Sacramento, about 375 miles, take in the new trains? • What is the rate? 100 mph • What is the distance? 375 miles • How would you find the time? 375=100*t

Guided Practice

In 2000, trains could only travel 10 mph down Alameda street to get to the train transfer point from the Port of Long Beach. If the distance is 20 miles, how long did it take a train to travel down Alameda Street? d=r•t 20 miles = 10 miles/hour • t 2 hours = t

16 | Distance, Rate and Time

Lesson cont’d

Distance, Rate and Time Lesson 2

Now trains can travel 40 mph down the new 20mile Alameda Corridor, an expanded rail route. How long will it take trains to travel the Alameda Corridor? D=r•t 20 miles = 40 miles/hour • t .5 hour = t or about ½ hour

Closure Have students summarize in their notes the steps for using the distance formula to find: • distance • rate • time Have students complete the worksheet for homework.

Distance, Rate and Time

| 17

Worksheet

Distance, Rate and Time Lesson 2

Lesson two

Distance, Rate and Time Worksheet Solve 1. You are shipping a 40-foot container full of athletic

shoes, about 30,000 shoes, to Long Beach from Shanghai

China, approximately 11,500 nautical miles. The Hyundai

Independence cargo ship can travel 23 nm/hour, or 23 knots.

How many hours will it take to get the shoes to Long Beach? 2. A car carrier is traveling 442 miles from Tokyo to the Port of

Long Beach with new Toyotas. The ship will travel at a rate of 22 knots. How long will it take for the ship to reach the Port?

3. The new Toyota cars will be sent to New York by train, about

2,850 miles. The train will travel an average speed of 50 miles per hour. How long will it take to reach New York?

4. An electronics store is shipping new LCD televisions from

Taiwan to Long Beach, about 11,040 nautical miles. The MSC

Texas cargo ship can make the trip from Taiwan to Long Beach in 460 hours, about 19 days. How fast will the MSC Texas be traveling?

Distance, Rate and Time

| 19

Worksheet Solutions

Distance, Rate and Time Lesson 2

Lesson two

Distance, Rate and Time Worksheet Solutions 1. You are shipping a 40-foot container full of athletic

shoes, about 30,000 shoes, to Long Beach from Shanghai

China, approximately 11,500 nautical miles. The Hyundai

Independence cargo ship can travel 23 nm/hour, or 23 knots.

How many hours will it take to get the shoes to Long Beach? d = rt

11,500 nm = 23 nm/hour • t 23 nm/hour

23 nm/hour

500 hours = t

2. A car carrier is traveling 442 nautical miles from Tokyo to the Port of Long Beach with new Toyotas. The ship will travel at a rate of





22 knots. How long will it take the ship to reach the Port? d = rt

442 nm = 22 nm/hour • t 20.1 hr = t

3. The new Toyota cars will be sent to New York by train, about

2,850 miles. The train will travel an average speed of 50 miles



per hour. How long will it take to reach New York? d = rt

Distance, Rate and Time

| 21

Distance, Rate and Time Lesson 2





2850 miles

57 hours = t

= 50 miles/hour • t

4. An electronics store is shipping new LCD televisions from

Taiwan to Long Beach, about 11,040 nautical miles. The MSC

Texas cargo ship can make the trip from Taiwan to Long Beach in 460 hours, about 19 days. How fast will the MSC Texas be



traveling? d = rt

11,040 nm = r • 460 hour 460 hour

460 hour

24 nm/hour = r or 24 knots = r

22 | Distance, Rate and Time

Scale Factors

Terminal Objective Given the volume of a prism in which the

dimensions have been multiplied by a scale factor, students will be able to accurately

determine the new volume without using a formula.

Content Standard Reference: Grade 7 Measurement & Geometry 2.3 Compute the length of the perimeter, the surface area of the faces, and the volume of a threedimensional object built from rectangular solids. Understand that when the lengths of all dimensions are multiplied by a scale factor, the surface area is multiplied by the square of the scale factor and the volume is multiplied by the cube of the scale factor. Materials 1. Centimeter cubes 2. Box 3. Scale Factors PowerPoint Time Required 1 class

scale factors

| 23

Scale Factors Lesson 3

Lesson three

Introduction of Lesson Anticipatory Set:

Students will be asked to find the volume of a triangular prism and rectangular prism.

Student Objective:

Scale Factors Lesson 3

Given a prism with its dimensions multiplied by a scale factor, you will find the new volume without using a formula.

Purpose:

• Architects and engineers need to know the effect of scale factors on volume when they make scale models of buildings. • Shippers who come through the Port of Long Beach may need to know the effect of scale factors on volume when they load cargo ships.

Lesson Keyword 1. Scale  factor - A number that multiplies a quantity.

Input

Describe a scale factor. A scale factor is a number that multiplies a quantity.

Modeling

Fill a box with centimeter cubes and show the students what a scale factor is. Ask students to predict the number of cubes that would be needed if the dimensions of the box were doubled. Use the cubes to find the volume of the new box.

24 | scale factors

Lesson cont’d Check for Understanding

Ask the students to write a description of a scale factor in their own words. Students will share their descriptions with their partner and the teacher will randomly call on members of each pair to share with the class.

Input

Scale Factors Lesson 3

Students will use a table to explore the effects of scale factors on rectangular prisms.

Modeling

We know that the volume of a 40 foot container is 2,752 ft3. What do you suppose would happen to the volume if we multiplied the length, width and height by a scale factor of 2? Or by a scale factor of 3? Or by a scale factor of 4? Complete the table when multiplying the dimensions by a scale factor of 2.

hx2 lx2 wx2

Original x2 x3 x4 x5

Length Width Height

Volume

40 80

2,752 ft3 22,016 ft3

8 16

8.6 17.2

Volume compared to original Same 23 or 8 times larger

scale factors

| 25

Lesson cont’d

Scale Factors Lesson 3

Now, multiply the original dimensions by a scale factor of 3 and complete the table. Length

Width Height Volume Volume compared to original

Original x2

40 80

8 16

8.6 17.2

2,752 ft3 22,016 ft 3

Same

x3

120

24

25.8

74,304 ft3

33 or 27 times

x4 x5

23 or 8 times larger

Let’s complete the entire table. Length

Width Height Volume Volume compared to original

Original x2

40 80

8 16

8.6 17.2

2,752 ft3 22,016 ft3

Same

x3

120

24

25.8

74,304 ft3

x4

160

32

34.4

176,128 ft3

33 or 27 times

x5

200

40

43

344,000 53 or 125 ft3 times larger

Check for Understanding

23 or 8 times larger

43 or 64 times larger

Display five true/false questions. Students will answer by giving a “thumbs up” if the statement is true and a “thumbs down” if the statement is false. 1. Whenever the length, width, and height are multiplied by a scale factor of 2, the original volume is multiplied by 23.

26 | scale factors

Answer: True

Lesson cont’d 2. Whenever the length, width, and height are multiplied by a scale factor of 3, the original volume is multiplied by 34. Answer: False

Scale Factors Lesson 3

3. Whenever the length, width, and height are multiplied by a scale factor of 23, the original volume is multiplied by 232. Answer: False.

4. Whenever the length, width, and height are multiplied by a scale factor of 54, the original volume is multiplied by 543. Answer: True.

5. Whenever the length, width, and height are multiplied by a scale factor of x, the original volume is multiplied by x3. Answer: True.

Input Students will use a table to explore the effects of scale factors on triangular prisms.

5f

4f

5f

14f

6f

scale factors

| 27

Lesson cont’d Modeling

Show how to complete the table when multiplying the dimensions by a scale factor of 2.

Scale Factors Lesson 3

Base Height Height Volume Volume of the of the of the compared triangle triangle prism to original

Original x2

6 12

4 8

14 28

168 ft3 1,344 ft3

x3 x4 x5

Same

23 or 8 times larger

Show how to complete the table when multiplying the dimensions by a scale factor of 2, 3, 4 and 5. Base Height Height Volume Volume of the of the of the compared triangle triangle prism to original

Original x2

6 12

4 8

14 28

168 ft3 1,344 ft3

x3

18

12

42

x4

24

16

56

x5

30

20

70

4,536 ft3 33 or 27 times larger 10,752 43 or 64 ft3 times larger 21,000 53 or 125 ft3 times larger

Check for Understanding

Same

23 or 8 times larger

Display five true/false questions. Students will answer by giving a “thumbs up” if the statement is true and a “thumbs down” if the statement is false.

28 | scale factors

Lesson cont’d 1. The volume of a triangular prism is 100m3. If the dimensions are multiplied by a scale factor of 2, the new volume will be 800m3. Answer: True.

Scale Factors Lesson 3

2. The volume of a triangular prism is 310 ft3. If the dimensions are multiplied by a scale factor of 2, the new volume will be 620 ft3. Answer: False. 3. The volume of a rectangular prism is 10 km3. If the dimensions are multiplied by a scale factor of 4, the new volume will be 270 km3. Answer: False 4. Th  e volume of a rectangular prism is 21 yd3. If the dimensions are multiplied by a scale factor of 3, the new volume will be 567 yd3. Answer: True 5. The volume of a rectangular prism is 50 m3. If the dimensions are multiplied by a scale factor of x, the new volume will be 50x3 m3. Answer: True

Guided Practice

Display the following problems: 1. Suppose the volume of a rectangular prism is 40 ft3. Find the new volume, if the dimensions are multiplied by a scale factor of 3. Answer: 1,080 ft3

scale factors

| 29

Lesson cont’d 2. Suppose the dimensions of a triangular prism are multiplied by a scale factor of 2 and the new volume is 432 cm3. What was the original volume? Answer: 54 cm3

Scale Factors Lesson 3

3. Suppose the original volume of a triangular prism is 120 m3 and the new volume is 3,240 m3. What scale factor were the dimensions multiplied by? Answer: 3 Partners will be asked to check each other’s work.

Closure Students will be asked to write a brief explanation of what would happen to the volume of a triangular prism if the dimensions were multiplied by a scale factor. Students will share their responses with their partner and several students will be selected to share with the class.

30 | scale factors

Worksheet

Lesson three

Scale Factors Scale Factors Lesson 3

Solve Using scale factors for rectangular prisms. Base Height Height Volume Volume of the of the of the compared triangle triangle prism to original

Original x2 x3 x4 x5

40

8

8.6

2,752 ft3

Same

Using scale factors for triangular prisms. Base Height Height Volume Volume of the of the of the compared triangle triangle prism to original

Original x2 x3 x4 x5

6

4

14

168 ft3

Same

scale factors

| 31

Volume of Prisms Terminal Objective

Given a set of prisms with their

dimensions labeled, students will be able

to use the formula for volume to accurately calculate the volume of each one.

Content Standard Reference: Measurement and Geometry 6.1.3: Know and use the formulas for the volume of triangular prisms and cylinders (area of base x height); compare these formulas and explain the similarity between them and the formula for the volume of a rectangular solid. 7.2.1: Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the surface area and volume of basic three-dimensional figures, including rectangles, parallelograms, trapezoids, squares, triangles, circles, prisms, and cylinders. Materials 1. Volume of Prisms PowerPoint Presentation 2. Three bowls of different sizes 3. Centimeter cubes 4. Three boxes of different sizes Time Required 1 class

volume of prisms

| 33

Volume of Prisms Lesson 4

Lesson four

Introduction of Lesson Anticipatory Set:

Have students suppose they had a bag of their favorite candy, but they were only allowed to take the amount that fits into one of three displayed bowls of different sizes. Ask students which bowl they would take and why.

Volume of Prisms Lesson 4

Keyword 1. Volume  – the number of cubic units needed to fill a three-dimensional figure

Student Objective:

Given a rectangular or triangular prism, students will be able to find its volume.

Purpose:

Companies that export products overseas need to know how many items can fit inside a container.

Lesson Input

Define volume: the number of cubic units needed to fill a three-dimensional figure

Modeling

Fill three different boxes with centimeter cubes and count the number of cubes each box holds. Point out that the number of cubes required to fill each box represents the volume. Define the volume of a three-dimensional figure.

Check for Understanding

Display examples representing surface area, area, and volume. Ask students to hold up the number of fingers that matches the number of the correct description. Which of the following is a description of volume?

34 | volume of prisms

Lesson cont’d 1. The amount of wrapping paper used to wrap a box 2. The amount of tile used on a floor 3. The number of dice needed to fill a box Answer: 3, the number of dice needed to fill a box

Input

Volume of Prisms Lesson 4

Give the formula for the volume of a rectangular prism. v=l × w × h or v=lwh where l is the length, w is the width, and h is the height.

h l

w

Give the formula for the volume of a prism or cylinder. v=b × h or v=bh where B is the area of the base and h is the height.

h

h h

B

B B volume of prisms

| 35

Lesson cont’d Modeling

Display the formula for a rectangular prism. Use a box to describe the different dimensions of a rectangular prism. Display the formula V=Bh for prisms and cylinders and use a box, a soda can and an object shaped like a triangular prism, such as a slice of cheese, to describe B and h.

Check for Understanding Volume of Prisms Lesson 4

Ask students to form groups of two. Each pair will be assigned a letter, A or B. Partner A will name one of the following: rectangular prism, triangular prism, or cylinder. Partner B will describe the formula required to calculate the volume of the named object. Partner A will name all three objects. Then the students will switch roles.

Input

Find the volume of a rectangular prism using the formula V=lwh.

Modeling

The teacher will model how to use the formula V=lwh to find the volume of a rectangular prism using a cargo container as an example.

8.6 ft 20 ft 8 ft

36 | volume of prisms

Lesson cont’d Step 1: Use the formula for the volume of a rectangular prism V=lwh. Step 2: Identify l, w, and h l = 20 ft w = 8 ft h = 8.6 ft

Volume of Prisms Lesson 4

Step 3: Substitute 20 for l, 8 for w, and 8.6 for h. V= (20) (8) (8.6) Step 4: Simplify V= 1,376 ft3

Check for Understanding

Ask students to describe to their partner how to use the formula V=lwh to find the volume of a rectangular prism. Partner A will describe how to find the volume of prism A and Partner B will describe how to find the volume of prism B. Randomly call on members of each pair to share with the class.

Prism A 12 cm

4 cm 2 cm

volume of prisms

| 37

Lesson cont’d

5yd

Prism B

3yd 9yd

Volume of Prisms Lesson 4

Guided Practice

Students will be given three problems one at a time and will be asked to find the volume of each. Ask students for answers and write each given answer on the board (correct or incorrect without giving any cues as to which answer is correct.) Point to each answer and ask students to raise their hand if they had the same answer. If necessary, model how to find the volume of a rectangular prism using the given problem. Repeat the process above with the remaining two problems. Question 1: Find the volume of this 40-foot cargo container.

8.6 ft 8 ft

40 ft

38 | volume of prisms

Lesson cont’d Answer: Step 1: Use the formula for the volume of a rectangular prism, V=lwh. Step 2: Identify l, w, and h l = 40 ft w = 8 ft h = 8.6 ft

Volume of Prisms Lesson 4

Step 3: Substitute 40 for l , 8 for w, and 8.6 for h. V= (40) (8) (8.6) Step 4: Simplify. V= 2,752 ft3 Question 2: Find the volume of the rectangular prism formed by four containers.

17.2 ft

40 ft

16 ft

volume of prisms

| 39

Lesson cont’d Answer: Step 1: Use the formula for the volume of a rectangular prism, V=lwh. Step 2: Identify l, w, and h l = 40 ft w = 16 ft h = 17.2 ft

Volume of Prisms Lesson 4

Step 3: Substitute 40 for l, 16 for w, and 17.2 for h. V= (40) (16) (17.2) Step 4: Simplify. V= 11,008 ft3

Question 3: Find the volume of the rectangular prism formed by nine containers.

25.8 ft

40 ft

40 | volume of prisms

24 ft

Lesson cont’d Answer: Step 1: Use the formula for the volume of a rectangular prism, V=lwh. Step 2: Identify l, w, and h l = 40 ft w = 24 ft h = 25.8 ft

Volume of Prisms Lesson 4

Step 3: Substitute 40 for l, 24 for w, and 25.8 for h. V= (40) (24) (25.8) Step 4: Simplify. V= 24,768 ft3

Input

Find the volume of a triangular prism.

Modeling

Model how to use the formula V = bh to find the volume of a triangular prism.

h

h h

B

B B

volume of prisms

| 41

Lesson cont’d Check for Understanding

Ask students to describe to their partner how to use the formula V = bh to find the volume of a triangular prism. Partner A will describe how to find the volume of prism A and Partner B will describe how to find the volume of prism B. The teacher will randomly call on members of each pair to share with the class.

Volume of Prisms Lesson 4

Prism A

6cm

Prism B

10cm 18cm 8cm

13ft

13ft

9ft

36ft

8ft

Guided Practice

Students will be given three figures one at a time and will be asked to find the volume of each. Ask for answers and write each given answer on the board (correct or incorrect without giving any cues as to which answer is correct.) Point to each answer and ask students to raise their hand if they had the same answer. If necessary, model how to find the volume of a triangular prism using the given problem. Repeat the process above with the remaining two problems. Display a set of four prisms and ask students to find the volume of each one. Partners will be asked to check each other’s work.

42 | volume of prisms

Closure

Volume of Prisms Lesson 4

Students will be asked to write a brief explanation of how to find the volume of a triangular prism. Students will share their responses with their partner and several students will be selected to share with the class.

volume of prisms

| 43

Dimensional Analysis at the Port of Long Beach

Lesson five Students will be able to use dimensional

analysis to convert units used at the Port of Long Beach.

Grade 7 Measurement and Geometry 7.1.3: Use measures expressed as rates and measures expressed as person-days to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer Materials 1. Dimensional Analysis PowerPoint 2. Whiteboard Time Required 1 class

Dimensional Analysis at the Port of Long Beach

| 45

Dimensional Analysis at the Port of Long Beach Lesson 5

Content Standard Reference:

Terminal Objective

Introduction of Lesson Anticipatory Set:

Ask students where they have seen containers in the city of Long Beach. They may have seen them on campus where they are used to store earthquake supplies or on the back of a truck driving along the freeway.

Student Objective:

Students will be able to use dimensional analysis to convert units used at the Port of Long Beach.

Purpose:

Dimensional Analysis at the Port of Long Beach Lesson 5

Dimensional analysis is useful to convert units that are not common.

Lesson Keyword 1. Dimensional  analysis using unit analysis to help make conversions from one unit to another.

Input

Dimensional anaylsis is using unit analysis to help make conversions from one unit to another. Review the five steps for dimensional analysis.

Modeling

1. Read the situation. Identify the original units. 2. Write the original units as a fraction. 3. Decide what is the conversion factor for the new unit. 4. Be sure to set up the problem so the original units will divide out. 5. Simplify the expression and divide out the common units.

Check for Understanding

Have students work with a partner to make sure they have the five steps written correctly in their notes.

46 | Dimensional Analysis at the Port of Long Beach

Lesson cont’d Input

Review converting simple units using dimensional analysis.

Modeling

Example 1: 5 feet = ? inches 1. What information is given? 5 feet 2. Write all information as fractions. Number of yards = 5/1

Dimensional Analysis at the Port of Long Beach Lesson 5

3. What units do you want? inches What conversion rate can be used? 1 foot = 12 inches 4. S  et up the expression so the original units divide out. 5 feet 12 inches 1 × 1 foot = 60 inches 5. Simplify

Check for Understanding

How do you write a fraction of one for the conversion factor? Answer: 1/1

Modeling

Example 2: 5 feet = ? meters 1. What information is given? 5 feet 2. Write all information as fractions. Number of meters = 5/1

Dimensional Analysis at the Port of Long Beach

| 47

Lesson cont’d 3. What units do you want? meters 4. What conversion rate can be used? 1 foot = 0.3 meters 5 feet .3 meters 1 × 1 foot

= 1.5 meters

Dimensional Analysis at the Port of Long Beach Lesson 5

Guided Practice

A ship from China is measured in meters but the Port of Long Beach berths are measured in linear feet. The ship is 300 meters long. How many linear feet are needed at the Port of Long Beach pier? Conversion Factor: One meter is approximately 3.3 feet Have students put their expressions on white boards. On the count of three, check the expressions. 300 meters 1 ×

3.3 feet 1 meter

Solve the expression. 300 meters 3.3 feet 1 × 1 meter

= 990 feet

300 × 3.3 = 990 feet

Input

Select a student randomly to explain the expression.

Guided Practice

The Neptune Amber, a cargo ship, is 231 meters long. Is the expression below correct to change the length to feet?

48 | Dimensional Analysis at the Port of Long Beach

Lesson cont’d 231 meters 1 meters 1 × 3.3 feet Tell your partner if the expression is correct or not. Explain what is wrong if it is not correct. Answer: No - It is not correct. Students should identify that the original units did not divide out, so the reciprocal of the conversion factor should be used.

Input

Dimensional Analysis at the Port of Long Beach Lesson 5

Oil is sold in barrels. One barrel of oil is 42 gallons. How many barrels are in a tanker truck that holds 11,000 gallons of oil? 1 barrel=42 gallons

Modeling

Have students set up the expression to convert the units to barrels.

Check for Understanding

Have students put the expressions on their white boards. On the count of three, check to see if the expressions are correct. 11,000 gallons 1

x

1 barrel 42 gallons

Dimensional Analysis at the Port of Long Beach

| 49

Lesson cont’d Guided Practice

Write the expression to find out how many barrels of oil are on an oil tanker that holds 1.3 million gallons of oil. 1,300,000 gallons 1

x

1 barrel 42 gallons

Input

Cargo containers are measured in TEUs, or twentyfoot equivalent units.

Dimensional Analysis at the Port of Long Beach Lesson 5

1 TEU = 1 Twenty-foot Equivalent Unit

Modeling

Review the different sizes of cargo containers from the introductory lesson, including an explanation of 1 TEU (20-foot container) and 2 TEUs (40-footcontainer).

Check for Understanding

Tell your neighbor: 1. What does TEU stand for? Answer: Twenty-foot Equivalent Unit 2. What size are the containers you normally see on the back of semi trucks? Answer: 2 TEUs. They are 40 feet long.

Input

Let’s convert 50 forty-foot containers to TEUs.

Modeling

How many TEUs are in 50 forty-foot containers?

50 forty-foot x 2 TEUs = 100 TEUs 1 1 forty-foot 50 × 2 = 100 TEUs

50 | Dimensional Analysis at the Port of Long Beach

Lesson cont’d Input

Convert a 45-foot container to TEUs.

Modeling

How many TEUs are in a 45-foot container? 45 ft x 1 TEU =2.25 TEU 1 20 ft

45 9 = = 2.25 TEU 20 4

Input

Dimensional Analysis at the Port of Long Beach Lesson 5

Convert a 20-foot container to meters. One meter is approximately 3.3 feet.

Modeling

20 ft x 1 m =6 m 1 3.3 ft

Input

A train has 50 cars that hold forty-foot containers. How many TEUs are on the train? (1 forty-foot container = 2 TEUs)

Modeling 50 forty-foot x 2 TEUs = 100 TEUs 1 1 forty-foot 50 × 2 = 100 TEUs

Guided Practice

A train has 100 cars that hold forty-foot containers. How many TEUs are on the train? 100 forty-foot . 2 TEUs = 200 TEUs 1 1 forty-foot 100 × 2 = 200 TEUs

Dimensional Analysis at the Port of Long Beach

| 51

Lesson cont’d Guided Practice

The Hanjin Amsterdam cargo ship holds 5,618 TEUs. How many forty-foot containers are on the ship? 5,618 TEUs . 1 forty-foot 1 2 TEUs

= 2,809 forty-foots

Dimensional Analysis at the Port of Long Beach Lesson 5

Closure Fill in the Blank: The most important thing to remember when using dimensional analysis is if you want to eliminate unit from the numerator, you need to put the same unit in the ________ of the conversion fraction. Answer: Denominator Have students complete the Dimensional Analysis and Dockage Charges worksheets.

52 | Dimensional Analysis at the Port of Long Beach

Worksheet

Lesson five

Dimensional Analysis Worksheet Directions Use dimensional analysis to convert the following units. Use the Dimensional Analysis at the Port of Long Beach Lesson 5

conversion chart to find the conversion factors. Conversion Chart

1 foot is approximately 0.3 meters 1 meter is approximately 3.3 feet 1 barrel of oil = 42 gallons of oil

1 twenty- foot container = 1 TEU 1 forty-foot container = 2 TEUs

1. 350 feet = ______ meters

2. 600 feet = _______ meters

3. 400 meters = ______ feet

4. 520 meters = ______ feet

5. 60 barrels = ______ gallons of oil

6. 550 barrels = ______ gallons of oil

7. 840 gallons of oil = ______ barrels

8. 210 gallons of oil = _______ barrels

9. 500 forty-ft containers = _____ TEUs

10. 500 forty-five ft containers = _____ TEUs

11. 250 TEUs = ______ forty-ft containers

12. 600 TEUs = ______ forty-ft containers

Dimensional Analysis at the Port of Long Beach

| 53

Worksheet Solutions

Lesson five

Dimensional Analysis Worksheet Answers Use dimensional analysis to convert the following units. Use the Dimensional Analysis at the Port of Long Beach Lesson 5

conversion chart to find the conversion factors. Conversion Chart

1 foot is approximately 0.3 meters 1 meter is approximately 3.3 feet 1 barrel of oil = 42 gallons of oil

1 twenty- foot container = 1 TEU 1 forty-foot container = 2 TEUs

1. 350 feet = 105 meters

2. 600 feet = 180 meters

3. 400 meters = 1320feet

4. 520 meters = 1716 feet

5. 60 barrels = 2520 gallons of oil

6. 550 barrels = 23,100 gallons of oil

7. 840 gallons of oil = 20 barrels

8. 210 gallons of oil = 5 barrels

9. 500 forty-ft containers = 1000 TEUs

10. 500 forty-five ft containers = 1125 TEUs

11. 250 TEUs = 125 forty-ft containers

12. 600 TEUs = 300 forty-ft containers

Dimensional Analysis at the Port of Long Beach

| 55

Dockage Charges Handout

Lesson five

Directions

ship in feet and meters.

Ship

Dimensional Analysis at the Port of Long Beach Lesson 5

The Port of Long Beach berths are measured in linear feet, so all ship lengths must be calculated in feet to determine at which berth a ship can dock. The Port also charges dockage fees based on the length of the ship in meters. Therefore all ship lengths must be calculated in meters and feet. Use dimensional analysis to complete the chart to give the length of each

Chart A

Complete the following chart using dimensional analysis. Length in Meters

Hanjin Amsterdam Neptune Amber Zim Atlantic

279

15.

231

Length in Feet

13.

14.

823 feet

Dockage Charges

Use the information in Chart A to determine the dockage charge for each ship. Length Range in Meters

24-hour Charge per Day

226 – 240

$3899

256- 270

$5066

210 – 225

$3371

241 – 255

$4463

271 – 285 Ship

$6379

24-hour Charge per day

Hanjin Amsterdam

16.

17.

Neptune Amber

18.

19.

Zim Atlantic

20.

Five Day Charge

21.

Dimensional Analysis at the Port of Long Beach

| 57

Dockage Charges Answers

Lesson five

Directions Chart A Length in Meters

Hanjin Amsterdam Neptune Amber Zim Atlantic

279

15.

231

Length in Feet

13.

920.7

14.

246.9

Dimensional Analysis at the Port of Long Beach Lesson 5

Ship

Complete the following chart using dimensional analysis.

762.3

823 feet

Dockage Charges

Use the information in Chart A to determine the dockage charge for each ship. Length Range in Meters

24-hour Charge per Day

226 – 240

$3899

256- 270

$5066

210 – 225

$3371

241 – 255

$4463

271 – 285 Ship

$6379

24-hour Charge per day

Hanjin Amsterdam

16.

$6379

17.

Neptune Amber

18.

$3899

19.

Zim Atlantic

20.

$4463

21.

Five Day Charge $31,895

$19,495

$22315

Dimensional Analysis at the Port of Long Beach

| 59

Money Conversion

Lesson six Use dimensional analysis to convert money from US dollars to foreign currency or foreign currency to US dollars.

Content Standard Reference: Grade 7 Measurement and Geometry 7.1.3 – Use measures expressed as rates and measures expressed as person-days to solve problems; check the units of the solutions; and use dimensional analysis to check the reasonableness of the answer. Materials 1. Money Conversion PowerPoint 2. Money Conversion Worksheet 3. White board

Money Conversion Lesson 6

Terminal Objective

Time Required 1 class

money conversion

| 61

Introduction of Lesson Anticipatory Set:

Ask students: How many dimes are in a ten dollar bill? They are converting dollars to dimes.

Student Objective:

Students will be able to use dimensional analysis to convert money from US dollars to a foreign currency and foreign currency to US dollars.

Purpose:

When students travel to other countries, they must use the currency of that country. The Port of Long Beach is a major international seaport. It is important for Port employees to understand how to convert foreign currencies.

Lesson Keyword 1. Dimensional  analysis using unit analysis to help make conversions from one unit to another.

Input

Dimensional analysis is using unit analysis to help make conversions from one unit to another. Review the five steps for dimensional analysis.

Modeling

Money Conversion Lesson 6

1. Read the situation. Identify the original units. 2. Write the original units as a fraction. 3. Decide what is the conversion factor for the new unit. 4. Be sure to set up the problem so the original units will divide out. 5. Simplify the expression and divide out the common units.

Check for Understanding

Have students work with a partner to make sure they have the five steps written correctly in their notes.

62 | money conversion

Lesson cont’d Input

Use dimensional analysis to convert the units for this situation: I have ten dollars. How many dimes are in ten dollars?

Modeling

Step 1. What are the original units? dollars Step 2. Write as a fraction. 10 dollars 1 Step 3. Write the multiplication sign and fraction bar. 10 dollars . 1 Step 4. What is the conversion factor? 1 dollar = 10 dimes Step 5. S  implify the expression and divide out the common units. = 100 dimes

Money Conversion Lesson 6

10 dollars . 10 dimes 1 1 dollar

Input

Tell students: Let’s pretend you are traveling to Great Britain. You have a food bill for 10 pounds. How many U.S. dollars would that be?

Modeling

The conversion rate is 1 pound = 2.04 dollars. Set up the expression using the five steps.

Check for Understanding

Have students put their expressions on white boards. On the count of three, check the expressions.

money conversion

| 63

Lesson cont’d Answer: 10 pounds . 2.04 dollars 1 1 pound

= 20.4 dollars

Input

A ship from China is coming to the Port of Long Beach. The captain of the ship has 2,500 yuan. How many US dollars does he have?

Modeling

The conversion rate is 1 yuan = 0.1321 dollars Set up the expression using the five steps.

Check for Understanding

Have students put their expressions on white boards. On the count of three, check the expressions. 2,500 yuan . 1321 dollars 1 1 yuan

= 300.25 dollars

Have students work with a partner or in their group. Explain how to change foreign currency to U.S. dollars. Call on one group to explain the process.

Money Conversion Lesson 6

Answer: Write an expression using dimensional analysis to eliminate the original units.

Input

Now let’s change U.S. dollars to foreign currency. Ten dollars is how many euros? Look at the conversion chart on the Money Conversion Worksheet. A Country

B Money

Britain

Pound

Mexico

Peso

France

64 | money conversion

Euro

C D One dollar in Foreign Currency Foreign currency in one dollar $1 = 0.49 pound

1 pound = $2.04

$1 = 10.78 pesos

1 peso = $0.09

$1 = 0.73 euro

1 euro = $1.38

Lesson cont’d Modeling

See Money Conversion Worksheet for the chart. Students should decide which column they will use to find the conversion factor. The original unit is dollars so they will be using column C.

Check for Understanding Have students use • one finger for A • two fingers for B • three fingers for C • four fingers for D A Country

B Money

Britain

Pound

Mexico

Peso

France

Euro

C D One dollar in Foreign Currency Foreign currency in one dollar $1 = 0.49 pound

1 pound = $2.04

$1 = 10.78 pesos

1 peso = $0.09

$1 = 0.73 euro

1 euro = $1.38

Question: Convert ten dollars to euros. One dollar = 0.73 Euros Write the expression:

Money Conversion Lesson 6

10 dollars . .73 euros 1 1 dollars Answer:

10 dollars 0.73 euros • = 7.30 euros 1 1 dollar

Input

Students work alone for five minutes doing the problems independently. Then students will work in small groups to compare their answers. Select two groups to share out how they set up the problems.

money conversion

| 65

Lesson cont’d Guided Practice

Use the chart to try these two examples. Question 1: One hundred dollars to pounds. Answer: 100 dollars 1

•

.49 pounds 1 dollars

= 49.00 pounds

Question 2: Convert one hundred pesos to dollars. Answer:

100 • 1

.09 1

= 9 dollars

Closure Tell students to discuss the steps used to convert money with their group. Students should give the five steps to dimensional analysis.

Money Conversion Lesson 6

Input

Have students complete the Money Conversion Worksheet.

Check for Understanding

Students will work alone on the worksheet. Once most students have finished the first five problems, have them compare answers with members of their group or their partner. Select one student from each group to explain how to work the first five problems. Students should complete the rest of the worksheet for homework.

66 | money conversion

Money Conversion Worksheet

Lesson six

Directions Use the conversion chart to complete the problems. Be careful to use the correct column. Country

Money

Britain

Pound

Mexico

Pesos

10.78

0.09

Yen

121.82

0.008

China Japan

Euro

Yuan

Foreign Currency in One US Dollar

0.73

1.38

0.49

7.57

2.04

0.13

1. 5 dollars = _______ pounds

6. 5000 yen = ______ dollars

2.

10 dollars = ______ euros

7. 650 Yuan = ______ dollars

3. 50 dollars = ______ pesos

8. 850 euros = ______ dollars

4. 150 dollars = _______ Yuan

9. 700 pounds = ______ dollars

5. 1000 dollars = _______ yens

10. 500 pesos = ______ dollars

Money Conversion Lesson 6

France

One US Dollar in Foreign Currency

The Port of Long Beach charges ships for the time they are at the berth being loaded and unloaded. The length of the vessel determines the daily charge. A ship that is 200 meters long must pay $2882 per day. 11. If the ship is from China, how many Yuan would the company pay for each day? 12. If the ship is from France, how many euros would the company pay for each day? money conversion

| 67

Money Conversion Worksheet Answers

Lesson six

Answers Answers:

1. 2.45 pounds 2. 7.30 euros 3. 539 pesos

4. 1,135.5 Yuan

5. 121,820 yens 6. 40 dollars

7. 84.50 dollars 8. 1,173 dollars

9. 1,428 dollars 10. 45 dollars

11. 21,816.74 Yuan

Money Conversion Lesson 6

12. 2,103.86 euros

money conversion

| 69