bundle integers and rational...

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Integers and Rational Numbers Stations, Games, and More

Common Core Resource File Thank you so much for purchasing this integers and rational numbers resource file. I created these activities to use in station rotations in my classroom. However, they can easily be used in a variety of ways. You will find activities within this file also suitable for math centers, game day, formative assessment, or summative assessment. The following resources are included in this file:

1. Stations Organization and Tips 2. Article – Station Learning 3. Brainstorm Sheet – Station Rules 4. Number System Three of a Kind and Sort 5. Numbers and Operations Math Match 6. Ordering and Operations - Decimals 7. Article – Integers in the Real World 8. Ordering and Operations - Integers 9. Article – The Absolute Truth About Absolute Value 10. Absolute Value “Go Fish!”

I use the first four stations as rotation practice at the beginning of the year. Students get to learn about stations, create expectations for their own behavior, and try out a couple of station activities. The majority of these stations focus on my Unit 6: Extending the Number System. I will use the last seven stations for these rotations, having students complete the Numbers and Operations Math Match again for review.

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**A note about printing cards double-sided** The Go Fish, Math Match, and Domino cards have backs that you can print, if you wish. They are centered to line up when printed double-sided. I have the best luck with printers that feed the paper from the top. When I have tried with large copy machines that feed paper from the side, the precision is off and thus the fronts and backs don’t line up perfectly. If you are like me, this will really drive you crazy! Try a printer that feeds from the top, don’t print the backs, or accept that the lines won’t be perfect!

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Table of Contents

Article: Station Learning .......................................... 11

Brainstorm: Station Rules ......................................... 14

Three of a Kind and Sort: Number Systems ............... 17

Math Match: Numbers and Operations ........................ 20

Ordering and Operations: Decimals ........................... 28

Article – Integers in the Real World ........................ 38

Ordering and Operations: Integers .......................... 43

Article – Absolute Value ........................................... 53

GO FISH: Absolute Value ........................................... 57

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CCSS Alignment

Activity CCSS Number System Three of a Kind and Sort

6.NS.C.5, 6.NS.C.6

Numbers and Operations Math Match

6.EE.A.2b, 6.NS.C.5, 6.NS.C.6, 6.NS.C.6a

Ordering and Operations - Decimals

6.NS.C.6, 6.NS.C.6c

Article – Integers in the Real World

6.NS.C.5, 6.NS.C.7a, 6.NS.C.7b, 6.NS.C.7d

Ordering and Operations - Integers

6.NS.C.5, 6.NS.C.7a

Article – The Absolute Truth About Absolute Value

6.NS.C.7c

Absolute Value “Go Fish!” 6.NS.C.7c

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Stations Organization and Tips

You probably have heard a lot of buzz about stations in the

classroom. I’ve gone to professional developments on math

centers. I’ve seen cute games and foldables. I always thought, “I

have so many things to teach, there’s no way I have time for this!”

My classroom was pretty old school. Warm-up problems. Check

homework. Take notes. Start tonight’s homework. Honestly, I felt

pretty successful with this system. My students always exceeded the

state requirements. So why change?

Well, the teacher evaluation system in my state has been

revamped. I found myself in a situation where I needed to

change the way I was teaching. I had to start differentiating and

I needed to work in student-directed learning. If I didn’t change

my ways, my evaluation scores were going to plummet. I don’t

know about you, but this was enough motivation to get me to try

something new. I was amazed at how incorporating stations

actually gave me a great deal of time in the classroom. I found

that organizing my classroom into seven or eight stations opened

up a world of possibilities.

My students have never spent so much time problem solving

in class. Not only that, but I hear them justifying mathematical

reasoning to their peers. It’s amazing. There’s another bonus. I

can work in more technology. I can have a video station. I can

do online benchmarking. What good are four computers in a class

of 28? Now that I have seven groups of four, I can do all of these

things that I just “didn’t have time for”. I could go on and on

about all of the perks and benefits that I discovered, but it will

be way more fun if you see it for yourself in your own classroom.

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Here are some things that I discovered.

1) Group by ability. If there is one “star student” in every

group, they are not going to bring up the level of their

group mates. Rather, they will just do the work for them.

Grouping by ability is what has afforded me the

opportunity to effectively differentiate. You can challenge

the groups that need challenged. You can truly remediate

for those who have need. It is easy to swap things out

while the groups rotate.

2) Group also by motivation. You know those kids that

kill group work by distracting everyone? Put them all

together. Maybe they won’t get anything done, but I

actually found that most of them got the picture and got

to work. I have been so surprised at what my kids will do

when the expectations are raised. How will you know who

these kids are at the beginning of the year? Trust your

gut.

3) Practice station rotations. Teach them the

expectations. Have a station where they read about station

learning. Have another where they come up with the rules

for their group. They know what is right. They will come

up with the same rules you would. Give them some other

stations where they can learn how to play your “games”.

This initial set up time is crucial.

4) Get accustomed to the noise. When you start stations,

you will need some quiet time at the end of the day.

Remind yourself that they need to talk; they need to have

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mathematical discussions to work out their thought

processes.

5) Supervise. At least the first few times that you do station

rotations, put yourself in a supervision role. This is my

favorite aspect of stations. I get to float around the room

troubleshooting, inspiring, and redirecting when necessary.

Later on you can have a teacher-led station. I’ve used this

to go over homework with students, introduce the next

topic, or challenge groups on just the right level. It is so

refreshing working with students grouped by ability level,

because you can finally give the students instruction,

remediation, and enrichment on a needs-basis.

I found two different rotation set-ups that worked well for

me. We have approximately 45-minute periods. I tried 10, 15, and

20-minute stations. I prefer 15 minutes. It was enough time to get

something done and keep the students’ focus. The number of

stations you need is determined by the greatest number of

students you have, but there is some flexibility. I really don’t want

to have more than four students per group. I feel it’s too many

and I only have four computers. I have at most 28 students per

class, so I need at least 7 groups and 7 stations. Next year, if my

classes are overloaded, I will need 8 groups. 7 or 8 activities

seem like a great deal of prep, but it is all on the front end. I

come in early and get stations set up one day, and then it is two

or three days before I need to pack them up. Organizing into

seven different stations worked well. Here’s the schedule I used to

complete seven stations:

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Day one:

15 minutes direct instruction/introduction

15 minutes 1st station

15 minutes 2nd station

Day two:

15 minutes 3rd station

15 minutes 4th station


Day three:



15 minutes wrap-up

This worked really well, but I found that making 7 stations

for every rotation was a lot of work and not always necessary.

There are some topics that the kids can pick up in less time. I

realized that I could actually have 4 stations, each set up twice.

This is the other rotation set-up that I found particularly

effective. My tables and stations set-up looked like this:

1

2

3 4 5 (1)

6 (2)

7 (3) 8 (4)

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Now, I could create four stations for a topic and have all

groups complete those stations in four rotations. There will always

be one empty station with seven groups, but this allows for eight

groups if you have more than 28 students in a class. In a smaller

class, you’ll just have more empty stations while the groups rotate

through. I’m sure you are realizing now how flexible stations

really are. Here’s the schedule I used to complete four stations:

Day one:

15 minutes direct instruction/introduction

15 minutes 1st station

15 minutes 2nd station

Day two:

15 minutes 3rd station


15 minutes wrap-up

The way that you work wrap-up time is up to you. You can

do clarification, think-pair-share, journaling, exit slips, or

administrative tasks that need completing like a homework check.

Open yourself up to trying stations in the classroom. I’m sure you

will be pleasantly surprised at what it brings to your instruction

and what your students are capable of doing.

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Article: Station Learning

This activity is designed in my classroom stations for

groups of four. However, a student could read the article individually or you could read it as a whole class. I have included a simple summarizing graphic organizer. I like to keep four copies of the article in plastic sheet protectors at the station, or you could laminate them. I laminate the directions below to keep at the station, as well.

Article Group

• Everyone in your group grabs a copy of the article.

• Take turns reading paragraphs. • Complete the summarizing graphic organizer

together. • Each person chooses the main idea from the

paragraph that they read. • Use these main ideas to write a summary of the

article. • Choose one person to write the article, but

everyone should add their input about the summary.

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Station Learning in Middle School Math

By, Kimberly Wasylyk

Any middle school student in the United States knows that mathematics

instruction is an important part of the school day. For some students, this time is

challenging and fun. However, many students in the middle grades find math class boring

and maybe even confusing. The old routine of checking homework, doing notes, writing

journals, and taking tests becomes a drag. You may wonder if there is a better way to learn

that would also be more fun. There is a new movement taking over math instruction that is

just what you're looking for. Station learning will fix what is broken in your math class.

Instead of a teacher in front of the room talking to 28 students all at once,

students are split into groups of four. These groups rotate through a series of activities,

engaging them in the topic at hand. These activities commonly have students working in

pairs, groups, independently, and with the teacher for part of the period. Students often

find themselves playing math games, matching, sorting, drawing, solving problems, and

reading with their classmates. The variety you find assures that students with many

different learning styles get the instruction they need.

There are two more major advantages to working in stations instead of the old

whole-‐class model. First, having students in small groups allows the teacher to modify

activities for different ability levels. Whether you are a struggling student or very advanced,

you can have instruction tailored to your specific needs. Second, your confidence in your

own abilities will grow as you will work independently and also with your peers. At first

this may seem impossible, but the more you practice independent learning, the better you

will be at attacking difficult problems on your own.

What does all of this mean for you? Gone are the days of sitting back and

listening to your teacher drone for 45 minutes. Instead, you will move around the

classroom and work with your peers to access the information you need in a variety of

ways. Middle school students tend to prefer this method of instruction. It breaks the period

up into smaller chunks and allows them to take advantage of the social atmosphere. This

change in instruction will assure that you learn better and have more fun in the classroom.

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Brainstorm: Station Rules


groups of four. Students always create all the same rules I do, but now they have ownership. It’s great to hear one student call another out and say, “That’s one of OUR rules!” I laminate the directions below to keep at the station, as well.

Brainstorm Group

• You need ONE copy of the brainstorming sheet per group.

• Take turns writing down things that you would see in an effective station group.

• Each group member must contribute TWO ideas. • Take turns writing down rules for your station

group. • Each group member must contribute TWO ideas.

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Station Success and Rules Brainstorm Group Members: _____________________________________

With your station group, discuss things that you think are

important to make station learning successful. Write down

eight things that you would see in an effective station group.

1. ________________________________________________

2. ________________________________________________

3. ________________________________________________

4. ________________________________________________

5. ________________________________________________

6. ________________________________________________

7. ________________________________________________

8. ________________________________________________

Next, brainstorm and record eight rules for your station

group to follow.

1. ________________________________________________

2. ________________________________________________

3. ________________________________________________

4. ________________________________________________

5. ________________________________________________

6. ________________________________________________

7. ________________________________________________

8. ________________________________________________

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Three of a Kind and Sort: Number Systems


individuals working in groups of four. However, it could be used as summative or formative assessment for any size group. The great thing about this activity is that it is completely open ended. They must create three examples for each number type then sort numbers into all possible classifications, thereby discovering things about the number system. I laminate the directions below to keep at the station.

Three of a Kind and Sort Individuals

• Everyone in your group grabs an activity sheet. • Create three examples for each problem using

what you know about expressions and equations. • You may ask other group members for help. • You may not just write down the same examples

as someone else in your group.

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Number Systems Three of a Kind and Sort Three of a Kind: List three examples of each type of number. Use your number system graphic organizer to help. 1) Natural Number ______________ ______________ ______________

2) Whole Number ______________ ______________ ______________

3) Integer ______________ ______________ ______________

4) Rational Number ______________ ______________ ______________

Sort: List all the possible classifications for each number. Circle the most descriptive name. Use your number system graphic organizer to help. 5) 2 _____________________________________________________________________

6) 14.5 _____________________________________________________________________

7) !! _____________________________________________________________________

8) 0.045 _____________________________________________________________________

9) -‐27 _____________________________________________________________________

10) 9 !! _____________________________________________________________________

11) 0 _____________________________________________________________________

12) -‐7.01 _____________________________________________________________________

13) 3. 09 _____________________________________________________________________

14) 8,952,024 _____________________________________________________________________

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Math Match: Numbers and Operations

Directions: This activity is designed as a classroom station for partners. However, a student could play individually or groups of four could play together. It works perfectly in stations as it is easily differentiated. As my students are rotating from one station to the next, I can grab the stack of cards and remove some pairs to modify the game for a lower level group. That being said, including all cards, 18 pairs, would be a definite challenge. I usually separate this into two sets. I have groups of four rotate through stations. At this station, the groups of four split into two partner pairs. When both partner pairs finish the match, they can trade and do the other half. I laminate the directions below to keep at the station. Math Memory Match Partners

• Shuffle the cards and lay them face down on your desk.

• The first player flips over two cards. • If the cards have the same meaning, keep them,

if not, turn them back over. • The next player tries to find a match. • Take turns until all the cards have been picked

up. • The person with the most cards at the end wins. • Switch decks with the other partners in your

group and start again.

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Addition Subtraction Multiplication

+ - ⋅

Division Not equal Equal

÷ ≠ =

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Math Match Math

Match Math Match

Math Match Math

Match Math Match

Math Match Math

Match Math Match

Math Match Math

Match Math Match

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Sum Difference Product

The answer in an

addition problem

The answer in a

subtraction problem

The answer in a

multiplication problem

Variable Quotient Coefficient

A letter that stands for a

number

The answer in a division

problem

A number multiplied by a variable

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Math Match

Math Match

Math Match

Math Match

Math Match

Math Match

Math Match

Math Match

Math Match

Math Match

Math Match

Math Match

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Term Factor Rational Number

A single number or a

variable

A number, grouping, or variable to

be multiplied

Any number that can be expressed as a fraction

Integers Opposites Absolute Value

Positive and negative whole

numbers and zero

Two numbers with the same absolute value, but different

signs

The distance from a

number to zero

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Math Match

Math Match

Math Match

Math Match

Math Match

Math Match

Math Match

Math Match

Math Match

Math Match

Math Match

Math Match

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Ordering and Operations: Decimals

Directions: These resources are designed as station practice

for groups of four. This ordering and operations set includes

resources for a variety of activities. Laminate the following

pages. Cut out the number pieces, spinners and number lines.

I prefer to use a paper clip for the spinners, but you can cut

out the arrow and use a paper fastener. Tape the number line

pieces together.

I have included three suggested stations. There are two

sheets for students to show their work, depending on whether

they are ordering or computing. Here are some ideas for

activities with these resources.

Number Line Practice – Students place all number slips on

the number line, using the arrows to point precisely to the

numbers’ locations. If you make four number lines, they can

practice individually and share with the group.

Ordering Practice – Choose two number slips. I like to

keep them in a small plastic container, or something reused

(for example, an empty breadcrumb tub with the label

removed). Spin the ordering spinner. The students arrange

the numbers on their paper so that the symbol fits between

them.

Operations Practice – Students choose two number slips

and spin the operations spinner. They write the problem down

and solve it on their paper.

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Ordering and Operations – Number Line Practice Individual

• Each person in your group needs a number line. • Shake up the number slips and pass them out to

everyone in your group. • Place all number slips on the number line, using the

arrows to point precisely to the numbers’ locations. • Trade places with someone in your group and check

their placements. • Discuss any you disagree about, and ask your group for

help if you need it.

Ordering and Operations - Ordering Practice Partner

• Choose two number slips. • Spin the ordering spinner. • Arrange the numbers on your paper so that the symbol

fits between them. • Put the slips back and choose two more. • Take turns until you both complete the activity sheet.

Ordering and Operations - Operations Practice Partner

• Choose two number slips. • Spin the operations spinner. • Write the problem down and solve it on your paper. • Put the slips back and choose two more. • Take turns until you both complete the activity sheet.

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Ordering Decimals You and partner will take turns. First, choose two number slips. Then, spin the spinner. Write down you two numbers in the right order with relation to the symbol on the spinner. If you get the “less than” symbol (<), make sure the number on the left is less than the number on the right. If you get the “greater than” symbol (>), make sure the number on the left is greater than the number on the right. Put the numbers back when you’re done. Each of you must repeat this 15 times. Number Symbol Number

1. _______ _____ _______

2. _______ _____ _______

3. _______ _____ _______

4. _______ _____ _______

5. _______ _____ _______

6. _______ _____ _______

7. _______ _____ _______

8. _______ _____ _______

9. _______ _____ _______

10. _______ _____ _______

11. _______ _____ _______

12. _______ _____ _______

13. _______ _____ _______

14. _______ _____ _______

15. _______ _____ _______

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Decimal Operations You and partner will take turns. First, choose two number slips. Then, spin the spinner. Write down the two numbers with your operation symbol between. If you get subtraction, be sure to put the larger number first. There is space below each problem to show your work. Put the numbers back when you’re done. Each of you must repeat this 10 times. Number Symbol Number

1. ______ ___ ______ = _______

2. ______ ___ ______ = _______

3. ______ ___ ______ = _______

4. ______ ___ ______ = _______

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5. ______ ___ ______ = _______

6. ______ ___ ______ = _______

7. ______ ___ ______ = _______

8. ______ ___ ______ = _______

9. ______ ___ ______ = _______

10. ______ ___ ______ = _______

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0.045

2.3 1.06

0.44

2.07 7.05

0.89 0.09

2.13

0.81

1.45

1.6

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4.5

1.01 0.20

0.17

8.31 3.02

0.9 9.9

2.03 1.045

0.08 0.8

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Article – Integers in the Real World

Directions: This activity is designed in my classroom stations for partners or groups. Directions are included for either activity. I like to laminate the articles as well as the simple instructions. I modify the partner activity for lower groups by reducing the number of important facts and true/false statements that they must write. You can give sentence starters for the summarizing graphic organizer to differentiate, as well.

Article Partners

• Everyone in your group grabs a copy of the article and the Partner Reading Activity Sheet.

• Take turns reading one paragraph at a time with your partner.

• Complete the partner reading activity together. Article Groups

• Everyone in your group grabs a copy of the article and the Graphic Organizer for Summarizing.

• Take turns reading one paragraph at a time with your group.

• Discuss the main ideas from each paragraph and complete your graphic organizers.

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Integers in the Real World

By Kimberly Wasylyk

Integers are the set of positive and negative whole numbers and zero. That sounds

like something straight out of your math class, and it is. However, the truth is that integers

are all over the place. Think about times in your life that you have seen negative numbers.

If you consider temperature, sports, and money, you will see that integers really are all

around us. In fact, can you think of any other examples of negative numbers?

The simplest example here is probably temperature. If you live somewhere in the

country with cold winters you are definitely familiar with negative numbers. When it gets

cold, really cold, below zero, the temperature is expressed as a negative number. The

interesting thing is that the colder it gets, the more negative the number gets. For example,

the temperature -‐10° is lower than -‐5°. It is exactly the opposite of the way positive numbers

work. With positive temperatures, 10° is five degrees warmer than 5°. However, with

negatives, -‐10° is five degrees colder than -‐5°.

Let’s look at the sports example. In football you can gain yards on a play or you can

loose yards. Whenever you gain yards, you can think of it as a positive number. If you were

at the 30-‐yard line and you gain 12 yards, you will be at the 42-‐yard line. That’s 30 + 12 =

42. Now, if you were at the 30-‐yard line and you lose 12 yards, you will move back to the

18-‐yard line. That’s 30 + (-‐12) = 18. You may be thinking to yourself that adding negative

12 is the same as subtracting positive twelve. That is exactly right!

Finally, we need to think about money and negative numbers. You probably have

never had a negative amount of money. How is that even possible? Well, when you owe

someone money, this is called debt, it is often expressed as a negative number. When you

have a bank account, you have to be very careful of this. If you overdraw you account (take

out more money than you have in the bank), your account will show a negative balance and

the bank will charge you a pretty big fee. You can see that in many ways, negative numbers

are an important part of our world.

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Graphic Organizer – Summarizing

Main Idea – Paragraph 1





Summary

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Partner Reading

Take turns reading one paragraph at a time with your partner. Write down what you think are the three most important points from the article. Compare with your partner. Add two of their points to yours that are also very important. Important Points 1. ___________________________________________________________ _____________________________________________________________ 2. ___________________________________________________________ _____________________________________________________________ 3. ___________________________________________________________ _____________________________________________________________ 4. ___________________________________________________________ _____________________________________________________________ 5. ___________________________________________________________ _____________________________________________________________ Write down five statements about this topic. Make some of them true and some of them false. Trade papers with your partner so they can determine whether your statements are true or false. Trade back and check each other’s work. Discuss any disagreements you have. True/False Statements ___ 1. ________________________________________________________ _____________________________________________________________ ___ 2. _______________________________________________________ _____________________________________________________________ ___ 3. _______________________________________________________ _____________________________________________________________ ___ 4. _______________________________________________________ _____________________________________________________________ ___ 5. _______________________________________________________ _____________________________________________________________

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Ordering and Operations: Integers

Directions: These resources are designed as station practice

for groups of four. This ordering and operations set includes

resources for a variety of activities. Laminate the following

pages. Cut out the number pieces, spinners and number lines.

I prefer to use a paper clip for the spinners, but you can cut

out the arrow and use a paper fastener. Tape the number line

pieces together.

I have included three suggested stations. There are two

sheets for students to show their work, depending on whether

they are ordering or computing. Here are some ideas for

activities with these resources.

Number Line Practice – Students place all number slips on

the number line, using the arrows to point precisely to the

numbers’ locations. If you make four number lines, they can

practice individually and share with the group.

Ordering Practice – Choose two number slips. I like to

keep them in a small plastic container, or something reused

(for example, an empty breadcrumb tub with the label

removed). Spin the ordering spinner. The students arrange

the numbers on their paper so that the symbol fits between

them.

Operations Practice – Students choose two number slips

and spin the operations spinner. They write the problem down

and solve it on their paper.

44

Ordering and Operations – Number Line Practice Individual

• Each person in your group needs a number line. • Shake up the number slips and pass them out to

everyone in your group. • Place all number slips on the number line, using the

arrows to point precisely to the numbers’ locations. • Trade places with someone in your group and check

their placements. • Discuss any you disagree about, and ask your group for

help if you need it.

Ordering and Operations - Ordering Practice Partner

• Choose two number slips. • Spin the ordering spinner. • Arrange the numbers on your paper so that the symbol

fits between them. • Put the slips back and choose two more. • Take turns until you both complete the activity sheet.

Ordering and Operations - Operations Practice Partner

• Choose two number slips. • Spin the operations spinner. • Write the problem down and solve it on your paper. • Put the slips back and choose two more. • Take turns until you both complete the activity sheet.

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Ordering Integers You and partner will take turns. First, choose two number slips. Then, spin the spinner. Write down you two numbers in the right order with relation to the symbol on the spinner. If you get the “less than” symbol (<), make sure the number on the left is less than the number on the right. If you get the “greater than” symbol (>), make sure the number on the left is greater than the number on the right. Put the numbers back when you’re done. Each of you must repeat this 15 times. Number Symbol Number

1. _______ _____ _______

2. _______ _____ _______

3. _______ _____ _______

4. _______ _____ _______

5. _______ _____ _______

6. _______ _____ _______

7. _______ _____ _______

8. _______ _____ _______

9. _______ _____ _______

10. _______ _____ _______

11. _______ _____ _______

12. _______ _____ _______

13. _______ _____ _______

14. _______ _____ _______

15. _______ _____ _______

46

Integer Operations You and partner will take turns. First, choose two number slips. Then, spin the spinner. Write down the two numbers with your operation symbol between. If you get subtraction, be sure to put the larger number first. There is space below each problem to show your work. Put the numbers back when you’re done. Each of you must repeat this 10 times. Number Symbol Number 1. ______ ___ ______ = _______

2. ______ ___ ______ = _______

3. ______ ___ ______ = _______

4. ______ ___ ______ = _______

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5. ______ ___ ______ = _______

6. ______ ___ ______ = _______

7. ______ ___ ______ = _______

8. ______ ___ ______ = _______

9. ______ ___ ______ = _______

10. ______ ___ ______ = _______

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-10

9 -9

10

7 -7

8 -8

-6

5

6

-5

49

-4

3 -3

4

1 -1

2 -2

0

53

Article – Absolute Value

Directions: This activity is designed in my classroom stations for partners or groups. Directions are included for either activity. I like to laminate the articles as well as the simple instructions. I modify the partner activity for lower groups by reducing the number of important facts and true/false statements that they must write. You can give sentence starters for the summarizing graphic organizer to differentiate, as well.

Article Partners • Everyone in your group grabs a copy of the article and the Partner Reading Activity Sheet.

• Take turns reading one paragraph at a time with your partner.

• Complete the partner reading activity together. Article Groups • Everyone in your group grabs a copy of the article and the Graphic Organizer for Summarizing.

• Take turns reading one paragraph at a time with your group.

• Discuss the main ideas from each paragraph and complete your graphic organizers.

54

The Absolute Truth About Absolute Value

By Kimberly Wasylyk

Absolute value is a concept that you come across in middle school math after you

learn about negative numbers. Before we go any further, I will tell you that this is one of the

EASIEST topics you will ever learn about in math class. The absolute value of a number is

simply its distance from zero. The important thing for you to remember is that distance is

always positive, so absolute values are always positive. Sometimes, we say this is the

magnitude of a number. There is a special symbol for absolute value. For example, if you

want to know the absolute value of 15, you write 15 .

For positive numbers, the absolute value of a number is just equal to the number

itself. In the example we just examined, the absolute value of 15 equals 15. This seems too

simple, but it is true. Remember that the absolute value of a number is its distance from

zero. How far is 15 from zero? 15! The same is true for any positive number. The absolute

value of 165 is 165. The absolute value of 3,187 is 3,187.

Now let’s consider negative numbers. It is helpful to picture a number line when you

first learn about the absolute value of negative numbers.

To find the absolute value of -‐6, take a look at the number line. How far away from zero is -‐

6? Since -‐6 is six spaces away from zero, −6 = 6. How about the absolute value of -‐19?

Since absolute value is the distance from zero, −19 = 19. So, for negative numbers, the

absolute value is always the opposite, or positive, of that number.

The last thing that you need to know about absolute values is how to compare them.

Of course, I mean with less than or greater than symbols. Here, don’t think about the

number inside the absolute value bars, think about its distance from zero. Even though 15

is larger than -‐19, since -‐19 is farther from zero than 15, −19 > 15 . As you can see,

absolute value really is easier than it seems!

55

Graphic Organizer – Summarizing






Summary

56

Partner Reading

Take turns reading one paragraph at a time with your partner. Write down what you think are the three most important points from the article. Compare with your partner. Add two of their points to yours that are also very important. Important Points 1. ___________________________________________________________ _____________________________________________________________ 2. ___________________________________________________________ _____________________________________________________________ 3. ___________________________________________________________ _____________________________________________________________ 4. ___________________________________________________________ _____________________________________________________________ 5. ___________________________________________________________ _____________________________________________________________ Write down five statements about this topic. Make some of them true and some of them false. Trade papers with your partner so they can determine whether your statements are true or false. Trade back and check each other’s work. Discuss any disagreements you have. True/False Statements ___ 1. ________________________________________________________ _____________________________________________________________ ___ 2. _______________________________________________________ _____________________________________________________________ ___ 3. _______________________________________________________ _____________________________________________________________ ___ 4. _______________________________________________________ _____________________________________________________________ ___ 5. _______________________________________________________ _____________________________________________________________

57

GO FISH: Absolute Value

58

Directions: This classic card game is designed as a classroom station for groups of four. However, students could play in pairs or in larger groups. It works perfectly in stations as it is easily differentiated. As students are rotating from one station to the next, you can grab the stack of cards and remove some pairs to modify the game for a lower level group. Print the cards double-sided and laminate the pages before cutting them out. You can also laminate the directions below to keep at the station.

GO FISH Group

• Shuffle the cards and pass out four to each player. • Lay the rest in a pile face down on your desk. • The player left of the dealer goes first. • If you have two equivalent expressions, lay them

down. • If not, ask a question like, “Does anyone have the

absolute value of 19?” • If someone has the card, they must give it to the

player who asked. Otherwise they say, “GO FISH!” • If the player picks up a match, they may lay them

down. Otherwise, it is the next player’s turn. • The game continues until all the cards are gone. • The player with the most pairs at the end wins.

59

−30 −21 24

30 21 24

0 −12 16

0 12 16

60

GO FISH GO

FISH GO FISH

GO FISH GO

FISH GO FISH

GO FISH GO

FISH GO FISH

GO FISH GO

FISH GO FISH

61

9 −19 25

9 19 25

−24 11 −22

24 11 22

62

GO FISH

GO FISH

GO FISH

GO FISH

GO FISH

GO FISH

GO FISH

GO FISH

GO FISH

GO FISH

GO FISH

GO FISH

63

23 −32 4

23 32 4

−7 8 −27

7 8 27

64

GO FISH

GO FISH

GO FISH

GO FISH

GO FISH

GO FISH

GO FISH

GO FISH

GO FISH

GO FISH

GO FISH

GO FISH

bundle integers and rational...

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