fractions, decimals, &...

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Appendix

Fractions, Decimals, & Algebra

Supplementary 5th grade Math Curriculum

for Students with Special Needs

Courtney Franz

University of La Verne

2

Table of Contents Fractions: Equivalent Fractions Teacher Summary Sheet…………………………………………..............4

Equivalent Fraction Worksheets ………………………………………………………….…...5-7

Hershey Bar worksheet……………………………………………………………………....…..8

Simplest Form Teacher Summary Sheet……………………………………………….………...9

Simplest Form worksheet………………………………………………………………….…....10

Reducing Fractions……………………………………………………………………….……..11

Double Bubble GCF……………………………………………………………………….……12

Red Light/Green Light Template………………………………………………………….…….13

Fraction Dominoes……………………………………………………………………….……...14

Mixed Numbers Teacher Summary Sheet…………………………………………………....15-16

Parts of a mixed number…………………………………………………………………….…...17

Converting Improper Fractions…………………………………………………………….…….18

Converting Mixed Numbers……………………………………………………………….…….19

Mixed Number Review…………………………………………………………………….…….20

Writing Fractions Directions……………………………………………………………….….....21

Denominator Poem…………………………………………………………………………...22-23

Numerator Poem……………………………………………………………………………...24-25

Adding & Subtracting Fractions Teacher Summary Sheet…………………………………..….26

Adding Fractions (common denominator)……………………………………………….…..27-28

Fraction Mad Minute…………………………………………………………………….…..29-30

Subtracting Fractions…………………………………………………………………….…..31-32

Adding Unlike Fractions………………………………………………………………….….33-39

Subtracting Unlike Fractions…………………………………………………………….….…..40

Multiplying Fractions (whole numbers)…………………………………………………......41-42

Fraction Frenzy Spinning Game………………………………………………………..………43

Multiplying Fractions (by a fraction)…………………………………………………….….….44

Fraction Card Game…………………………………………………………………………….45

Fraction Pretzel Recipe ……………………………………………………………………..46-47

Multiplying Fractions (mixed numbers)………………………………………………….....48-49

Dividing Fractions…………………………………………………………………………..50-52

Fraction Bingo……………………………………………………………………………….53-59

Decimals Decimal Bingo………………………………………………………………………………..60-65

Decimal Place Value Chart…………………………………………………………………...…..66

Decimals………………………………………………………………………………………67-69

Fractions & Decimals…………………………………………………………………….………70

Identifying Place Value…………………………………………………………………….…….71

Decimal Dice……………………………………………………………………………………..72

Decimal Money worksheet……………………………………………………………….………73

Comparing Decimals……………………………………………………………………….....74-76

Ordering Decimals……………………………………………………………………….……….77

Decimal Chant……………………………………………………………………………………78

Adding & Subtracting Decimals……………………………………………………….……..79-80

Decimal Guide Sheet……………………………………………………………………………..81

Multiplying Decimals (by a whole number)……………………………………………..…...82-84

Multiplying Decimals (by a decimal)………………………………………………………...85-93

Decimal Division (by a whole number…………………………………………………………..94

Decimal Division (by a decimal)……………………………………………………………….95-96

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Algebra Algebra Expressions……………………………………………………………………………97-98

Solving Equations……………………………………………………………………………..99-100

Symbols as Variables…………………………………………………………………………..…101

Order of Operations…………………………………………………………………………..…..102

Order of Operations Treasure Hunt………………………………………………………….103-104

Order of Operations Spinners………………………………………………………………..105-108

Mnemonic Mania…………………………………………………………………………………109

The Mystery Number Song…………………………………………………………………..110-111

Keeping it True (algebra song)……………………………………………………………….112-113

Addition Properties…………………………………………………………………………...114-116

Solving Equations worksheet (addition)………………………………………………………......117

Multiplication Properties……………………………………………………………………..118-120

Distributive Property………………………………………………………………………………121

Distributive Dice Game…………………………………………………………………….....122-123

Positive & Negative Numbers……………………………………………………………………..124

Integer Art………………………………………………………………………………………….125

Solving Equations worksheet (multiplication & division)…………………………………………126

The Property Song………………………………………………………………………………….127

Human Number Line…………………………………………………………………………..128-132

Adding Integers………………………………………………………………………………..133-135

Subtracting Integers………………………………………………………………………………..136

Adding & Subtracting Integers (mixed review)……………………………………………………137

Format for Mnemonic Mania………………………………………………………………………138

Addition Properties Tree Map……………………………………………………………………...139

Multiplication Properties Tree Map………………………………………………………………...140

Power Point Presentations Equivalent Fractions……………………………………………………………………………141-145

Mixed Numbers and Fractions………………………………………………………………….146-150

Multiplying Fractions…………………………………………………………………………...151-156

Dividing Fractions………………………………………………………………………………157-160

Decimals & You………………………………………………………………………………...161-166

Adding & Subtracting Decimals………………………………………………………………...167-172

Multiplying & Dividing Decimals………………………………………………………………172-177

Algebra – Solving Equations……………………………………………………………………178-184

Integers………………………………………………………………………………………….185-194

Adding Integers…………………………………………………………………………………195-199

Integer Jeopardy………………………………………………………………………………...200-206

Additional Resources Fraction Circles & Dominoes..……………………………………………………………….….207-220

Fraction Strips………………………………………………………………………………….……..221

Fraction Pizza………………………………………………………………………………….……...222

Fraction worksheets (division & word problems)……………………………………………......223-224

Cube Template………………………………………………………………………………….……..225

Tens & Hundreds Grid…………………………………………………………………………….…..226

Decimal Games……………………………………………………………………………………227-232

Decimal worksheets (division & multiplication)………………………………………………….233-235

Order of Operations activities……………………………………………………………………..236-240

Integer activities…………………………………………………………………………………...241-245

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Key Concept #1: Equivalent Fractions Teacher summary sheet

Vocabulary : *Equivalent fraction – are fractions that name the same number or amount (T.E. p. 143)

Review vocabulary: *Numerator *Denominator

Students should be able to create their own definition for the word following teacher explanation.

The students & teacher can generate an original classroom definition of the concept. ● Two ways to make equivalent fractions 1.) By multiplying the numerator & the denominator by the same number. Examples #1 : to make an equivalent fraction for 1/3 multiply the fraction by any number. 1 x 2 = 2 3 x 2 = 6 1/3 = 2/6 2.) By dividing the numerator & the denominator by the same number. Example #2 : to make an equivalent fraction for 3/15 divide the fraction by a common factor. 3 ÷ 3 = 1 15 ÷ 3 = 5 3/15 = 1/5 Student Activities & Practice Opportunities:

Student Practice: ● Equivalent Fraction W.S ● Harcourt Intervention pg. 95; skill 16 ● Student Text pg. 145

Equivalent Fraction Frenzy *Students are to demonstrate their understanding of equivalent fractions by either using multiplication or division to make 2 or more equivalent fractions for a teacher given fraction.

Extension Activity - Students can create a matching game making their own equivalent fractions flash cards.

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Name: ______________________________ Date:___________________

Equivalent Fractions

Equivalent fractions are_______________________________________________

__________________________________________________________________

Match the letters of the equivalent fractions:

A. 2/3

1/3 1/3 1/3

B. 2/5

1/5 1/5 1/5 1/5 1/5

C. 1/3

1/3 1/3 1/3

D. 8/12

1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12 1/12

E. 4/10

1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10

F. 2/6

1/6 1/6 1/6 1/6 1/6 1/6

Answers:

Letter _____ & _____ are equal. ( ― = ― )

Letter _____ & _____ are equal. ( ― = ― )

Letter _____ & _____ are equal. ( ― = ― )

6

Write an equivalent fraction:

4.) 2 5.) 3 3 6.) 1

— x ― = ― ― x ― = ― ― x ― = ―—

7 2 4 2

7.) 6 8.) 2 9.) 4

— = —— — = —— — = ——

12 5 5

10.) 1 11.) 4 12.) 8

― = —— ― = —— ― = ——

6 12 1

7

Problem Solving:

1.) John and Brandon are going to share a pepperoni pizza on Monday. Brandon

wants to eat 2/5 of the pizza leaving John with 3/5. Will John and Brandon have an

equal amount of the pizza? If not, who gets more?

Brandon’s share

1/5 1/5 1/5 1/5 1/5

John’s share

1/5 1/5 1/5 1/5 1/5

Answer:

2.) Caitlyn and Sara are best friends and like to share their jewelry. They have 3

rings, 4 bracelets, and 3 necklaces a total of 10 pieces. If Sara wears 6/10 of the

jewelry and leaves 4/10 for Caitlyn, who gets to wear more jewelry?

Caitlyn

Sara

Answer:

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Hershey Fraction Bars

_________

_________

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Key Concept #2: Simplest Form Teacher summary sheet

Vocabulary:

● Simplest Form – A fraction is in simplest form when the numerator & denominator

have only 1 as their common factor (T.E. p. 146).

●Greatest Common Factor (GCF)– is the greatest factor that two or more numbers have

in common (T.E. p. 147).

●Review Vocabulary:

Equivalent fractions

Divisor

Students should be able to demonstrate an understanding of simplest form.

Reduce fractions to simplest form through division of the GCF.

Simplest Form through Division:

1.) Divide the numerator & denominator by the same number until the only

common divisor is one.

*Example #1: to reduce 3/12 to simplest form:

1.) Find the GCF of 3 and 12

3: 1, 3

12: 1, 2, 3, 4, 6 3 is the GCF for the two factors

2.) To reduce the fraction 3/12, simply divide the numerator & denominator by

the GCF (3).

3÷3 = 1

― ―

12÷3 = 4 The fraction 3/12 has been reduced to ¼.

Student Activities & Practice Opportunities:

Student Practice

●Double Bubble GCF Activity

● Simplest Form Instruction W.S

● Student Text pg. 148

Student Activities

● Red Light Green Light

* Given a circle of red & green paper and a popsicle stick students will make a red & green answer

paddle.

* The teacher will give the class a fraction that must be reduced. By using the colored paddles, the students will tell the student volunteer if they can stop (red paddle) or must keep going (green paddle) to reduce the fraction to simplest form.

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Name: ____________________ Date:______________

Simplest Form

To get a fraction into its simplest form I must:

First_________________________________________________________

Next _________________________________________________________

Last _________________________________________________________

Write each fraction in simplest form:

1.) 2 ÷ 2.) 9 ÷ 3.) 15 ÷

― ― = ― ― ― = ― ― ― = ― 12 ÷ 30 ÷ 75 ÷

GCF is ___ GCF is ___ GCF is ___

4.) 12 5.) 14 6.) 10

― ― ―

15 16 14

7.) 18 8.) 20 9.) 48

― ― ―

24 200 54

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Reducing Fractions to Simplest Form

5 1

― = ―

10 2

4 1

― = ―

12

7

― = ―

14 2

6

― = ―

9

8

― = ―

16

5

― = ―

15

3

― = ―

12

4

― = ―

6

2

― = ―

6

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Double Bubble GCF

Students can use the Double Bubble to find the common factors of a

fraction

Factors of ___ Factors of ___

Common Factors

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Red Light / Green Light Template

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How to Play Fraction Dominoes www.enchantedlearning.com

Starting: Put the dominoes face down on the table and mix them up.

Each player takes 6 dominos; for a game with more than 3 players, each player should

draw 3 dominos.

The remaining dominoes are left on the table (these are the "sleeping" dominoes).

Don't let the other players see your dominos.

The youngest player goes first (or you can go in alphabetical or reverse alphabetical

order). In traditional dominoes, the person with the highest double starts.

Playing: The first player places one of their dominoes (right-side up) on the table.

The second player tries to put a domino on the table that matches one side

of what's already there. If a player cannot go, the player picks a domino

from the pile and skips that turn.

The chain of the played dominoes develops randomly, and can look a lot

like a snake.

Continue taking turns putting dominoes on the board (or picking one from the pile if

you cannot go) until someone wins. In regular dominoes, the best strategy is to get rid

of doubles first.

Winning: The winner is the first person to get rid of all of their dominoes. But if no one can go

out, then the person with the fewest dominos left is the winner.

http://www.enchantedlearning.com/

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Key Concept #3: Mixed Number Teacher summary sheet

Vocabulary: ●Mixed number – is a made up of a whole number and a fraction (T.E.p.150).

●Improper fraction – is when the numerator is greater than the denominator

Review Vocabulary: ●Simplest Form

●Equivalent Fraction

●Numerator

●Denominator

Students should be able to convert a mixed number into an improper fraction.

Students should be able to convert an improper fraction into a mixed number.

*How to change a mixed number into an improper fractions*

1.) Multiply the denominator and the whole number

Example: 1

5 ― 5 x 4 = 20

4

2.) Add the numerator to the product

20 + 1 = 21

3.) The answer (21) becomes the new numerator and the original denominator (4) stays the same.

21

―

4

So… 21

― is the improper fraction

4

*How to change an improper fraction into a mixed number*

1.) Divide the denominator into the numerator:

Example: change 21 into a mixed number

―

8

2 (whole number)

(denominator) 8 21

-16

5 (remainder)

2.) ●The 2 becomes the new whole number ● The remainder is the new numerator

●The divisor is the new denominator

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Student Activities & Practice Opportunities:

Student Practice

● Labeling parts of a mixed number before and after conversion

●Student Text pg. 151

● Show what you know worksheet

Student Instruction Manuel

Students are to demonstrate their procedural understanding of converting mixed numbers

to fraction and fractions into mixed numbers by writing an each direction for each

process. The students should use a minimum of one original example for each process.

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Parts of a Mixed Number

Name the three parts of a mixed number:

*Whole Number *Numerator *Denominator

3

7 5

Name the parts of a mixed number when converting into an

improper fraction:

2 (____________)

(__________)8 21

-16

5 (___________)

Example: Convert 3 2/5 to an improper fraction

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Multiply the whole number by the fraction’s denominator

Example:

Add that to the numerator

Example

Then write the result on top of the denominator

Example:

Example: Convert 11/4 to a mixed number:

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Divide the numerator by the denominator.

Example:

Write down the whole number answer

Example:

Then write down any remainder above the denominator.

Example:

Name:_____________________ Date:___________________

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Show What You Know

*Mixed Numbers*

Explain the three steps it takes to change a mixed number into an improper fraction

using 3

3 ―

6

Step 1 : ____________________________________________________________

Show your work:

Step 2: ____________________________________________________________

Show your work:

Step 3: ____________________________________________________________

Show your work & the final answer:

Write each mixed number as an improper fraction:

1.) 3 2.) 7 3.) 1

2 ― = ― 5 ― = ― 2 ― = ―

4 9 8

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Follow the Right Steps in Fractions

You are on the fast track to understanding fractions. Now it is your

turn to teach someone else how to change mixed numbers to improper

fractions and fractions to mixed numbers.

Step 1: You are to write all of the steps it takes in order to change a

mixed number into an improper fraction using an example from your

class work.

Step 2: You are to write all of the steps it takes to change an

improper fraction into a mixed number using an example from your

class work.

Step 3: You must check your work & have a partner check your work to

make sure you have all of the steps you need!

Use one square for each direction and your examples…Good Luck!

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My Dog, Denominator

I was only,

A tiny,

Third-grader...

Got a new dog,

Denominator...

A good pup,

She was,

Truth be told,

But things she did,

Got to get old...

She'd hide under things,

Don't ask me why,

Hide under stuff,

Regardless of size...

Yes, being below,

Her favorite thing,

"Denominator on bottom!"

I heard her sing...

Under the bed,

When I came home,

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I called her,

She barked,

"Leave me alone!"

I tried, and tried,

To pull her out,

Pulled her long tail,

Yanked her short snout!!!

One day I came home,

What did I see,

She'd braided her fur,

Into Three hundred Three!

Now she was happy,

Not a drop sad,

Being below,

Made my dog glad,

"Oh Denominator,

You're so silly like that,"

I laughed,

And told her,

To put on a hat,

To hide the number,

303,

She whimpered and cried,

Looked up at me,

Sad puppy eyes,

Poor puppie's pout,

"Denominator on bottom!!!"

Is what she did shout!

http://mathstory.com/Poems/Mathpoemspage.html


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My Dog, Numerator

Numerator!

Numerator!

Down from there!

You'll drive me crazy!

Dog, ya hear!!!

I have a dog named, Numerator,

Not equal, less,

Or any greater,

Than dogs, Addition,

Or Take away,

He likes the top,

That's what he'd say...

I came home one day,

Where could he be?

Out for a run,

A swim in the sea???

I searched and searched,

My eyes were red,

I looked in the mirror,

He was asleep on my head!!!

Numerator's always on top of things,

Bunk-beds, slides,

See-saws, swings...

Late last night,

Heard a scared, woooooof,

Numerator, was balanced,

Up on the roof!!

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I was scared so stiff,

Horrified with horror,

If Numerator slipped,

He'd see no tomorra'

A ladder, I grabbed,

Climbed to the top,

Screamed, "Get down!"

But he didn't stop...

Numerator began dancing,

A-one, two, a-three,

Soon we were dancing,

Numerator and me...

All fears were gone,

We waltzed the roof...

If I had a camera,

The pictures would be proof...

After hours of Tango,

Of salsa,

And swing,

We fell to the ground,

With a big, big, big Ding!!!

I looked at Numerator,

"This has to stop!"

But Numerator gave a lick

―I just like the top‖. a lick, like the top!!!"



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Key Concept #4: Adding & Subtracting Fractions Teacher summary sheet

Review Vocabulary:

*Numerator

*Denominator

Students should be able to add and subtract fractions with common denominators

Students should be able to add and subtract fractions with unlike denominators

Student Activities & Practice Opportunities

Student Practice

● Word problem practice

● Addition & Subtraction fraction worksheet with common denominators

● Addition worksheet - fractions with unlike denominators

● Subtraction worksheet – fractions with unlike denominators

● Fraction Mad Minute ● Fraction Spinning Game

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Adding Fractions with Common Denominators When adding fractions with common denominators, all you have to do is add the two

numerators.

Example: 1 2 (1 + 2) = 3

— + — = —

4 4 4

* The denominator stays exactly the same!!!

1 Whole

1/4 1/4 1/4 1/4

+

1/4 1/4 1/4 1/4

Example: 3 2

— + — =

7 7

Example: 1 6

— + — =

10 10

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Adding Fractions

(Common denominators)

1.) 5 3

10 10

2.) 2 5

8 8

3.) 1 2

5 5

4.) 7 4

12 12

Problem Solving:

Michael and Mrs. Brown are sharing a giant chocolate chip cookie and promised to

give the leftovers to Mrs. Franz. There are 8 equal pieces of the cookie. If Michael

has 3/8 of the cookie and Mrs. Brown have 2/8 of the cookie, how many pieces are

left over to share with Mrs. Franz?

Michael: 3/8

1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8

+

Mrs. Brown: 2/8

1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8

So… 3 2

8 8

1/10 1/10 1/10 1/10 1/10

1/10 1/10 1/10 1/10 1/10

1/8 1/8 1/8 1/8

1/8 1/8 1/8 1/8

1/5 1/5 1/5 1/5 1/5

1/12 1/12 1/12 1/12 1/12 1/12

1/12 1/12 1/12 1/12 1/12 1/12

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Fraction Mad Minute Directions

Students are in teams of three and are given one minute to answer as

many fraction addition problems as possible.

Player #1 – is the player answering as many math problems as possible.

Player 1 must also say the answer in a fraction form.

Player #2 – is the score keeper and is responsible for keeping track of

how many problems player 1 correctly answered.

Player #3 – is responsible for setting up two or three flash cards at a

time for player 1 to calculate.

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Fraction Flash Cards – Common Denominators

4

— 12

7

—

12

6

—

12

9

—

12

2

—

12

1

—

12

3

—

12

6

—

12

5

—

12

1

—

12

12

—

12

9

—

12

10

—

12

11

—

12

7

—

12

3

—

12

1

—

12

2

—

12

5

—

12

4

—

12

31

Subtracting Fractions

(Common Denominator)

When adding fractions with common denominators, all you have to do is

subtract the two numerators.

Example: 5 2 (5 -2) = 3

— - — = —

7 7 7

* The denominator stays exactly the same!!!

1/7 1/7 1/7 1/7 1/7 1/7 1/7

You are left with 3

—

7

Example: 3 1 (3 - 1) = 2

— - — = —

4 4 4 Don’t forget that the

denominator does not

change, it stays the same!

¼ ¼ ¼ ¼

32

Subtracting Like Fractions

1.) 9 4

-

12 12 12

2.) 6 1

-

8 8

3.) 8 7

- —

9 9

4.) 2 1

-

4 4

Problem Solving:

James is getting ready to share his cupcakes with Mr. McGovern’s class.

He brought a total of 15 cupcakes for his class enough for everyone.

During Recess Mr. McGovern ate 11/15 of the cupcakes, Ms. Liz at 5/15

of the cupcakes. How many cupcakes are left for James’ class?

11 5

— - — = 15 15

1/12 1/12 1/12 1/12 1/12 1/12

1/12 1/12 1/12 1/12 1/12 1/12

1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8

1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9

¼ ¼ ¼ ¼

1/15 1/15 1/15 1/15 1/15 1/15 1/15 1/15 1/15 1/15 1/15 1/15 1/15 1/15 1/15

33

Adding Unlike Fractions

When adding fractions with different denominators, you must find a

common denominator.

Method #1 – Hands on approach

Add ½ + ¼ - This is a problem because

they do not have the same

denominators.

So…start with placing ½ bar & a ¼ bar under the 1-whole bar

1 Whole

1/2 1/4

Looks good…now let’s find the

fraction bar that fits exactly

under the 1/2 & 1/4 fraction

bars…that would be the 1/4 bars.

It looks like it took 3 fourths to fit under the 1/2 & 1/4 bars. This means that:

½ + ¼ = ¾ That makes sense since the least

common multiple of 2 and 4 is .4

1/4 1/4 1/4

34


Let’s try some more!

1 1 — + — 2 3 …Don’t forget your fraction bars!

I Whole

1/2 1/3

1/6 1/6 1/6 1/6 1/6

So…

1 1 5 — + — = —

2 3 6

Add: 1 3 — + —

2 8

I whole

1/2 1/8 1/8 1/8

1/8 1/8 1/8 1/8 1/8 1/8 1/8

1 3 7 — + — = —

2 8 8

35

Adding Fractions

Practice Time:

Use Fraction Bars to find the sum:

1.) 1/2 + 1/5 =

1/2 1/5

2.) 2/3 + 1/6

1/3 1/3 1/6

3.) 1/2 + 2/5

1/2 1/5 1/5

4.) 2/4 + 3/8

1/3 1/3 1/8 1/8 1/8

36


Using Least Common Multiple (LCM)

Least Common Multiple (LCM) is the smallest multiple (number) that

two numbers have in common.

Ex: If I am trying to find the least common multiples of 3 & 5 I would

list the multiples until I found a match.

3: 3, 6, 9, 12, 15, 18

5: 5, 10, 15, 20

15 is the least common multiple for 3 & 5! You want to make sure

that you pick the smallest

number that is common

or else you will have more

work to do

Here is how we add unlike fractions using LCM Step 1: First find the least common multiple for the denominator

½ + ¼

Let’s find the multiples of 2 & 4

2: 2, 4, 6, 8, 10

4: 4, 8, 12, 16 4 is the LCM…don’t be tricked because 8 & 12 are also

common multiples, but you want the smallest number that is the same.

37

Step 2: Now that you have the LCM (4) here is what to do

next: The goal is to get both fractions with the denominator

of 4

½ + ¼ since 4 is already the denominator for 1/4 you

can leave that fraction alone…it does not have

to change.

*We must change 1/2 so it has a denominator of 4

So… multiply the numerator (top) and the denominator (bottom) by the

same number. 1 x 2 = 2

— — The new fraction is 2/4

2 x 2 = 4 Multiply 2 to get the

denominator 4

Step 3: Now that both denominators are the same, you can

add the two fractions.

2 1 3

— + — = — 4 4 4

38


1.

1 3

— + — =

4 2

3 1

— + — =

4 6

1 7

— + — =

5 10

5 1

— + — =

8 4

5 2

— + — =

6 12

7 1

— + — =

9 18

1 3

— + — =

12 4

2 1

— + — =

5 15

39

Name _____________________________

Date ___________________ (Answer ID # 0989186)

Add Fractions

Find the sum.

1. 5

7

+

1

2

=

2. 2

3

+

1

2

=

3. 4

9

+

2

3

=

4. 7

8

+

1

2

=

5. 3

4

+

1

12

=

6. 1

5

+

2

3

=

7. 1

2

+

4

10

=

8. 7

9

+

1

3

=

9. 2

8

+

1

2

=

10. 3

4

+

1

2

=

11. 5

6

+

2

3

=

12. 2

3

+

3

4

=

13. 4

5

+

2

3

=

14. 1

2

+

1

4

=

15. 1

4

+

7

12

=

16. 5

8

+

1

2

=

www.edhelper.com

http://www.edhelper.com/

40

Subtracting Unlike Fractions

1.) 7/8 – 1/4 =

1 whole

1/8 1/8 1/8 1/8 1/8 1/8 1/8

1/4 ?

2.) 4/5 – 3/10 =

1 whole

3.) 3/6 – 1/2 =

1 whole

1/6 1/6 1/6 1/6

1/2 ?

1/5 1/5 1/5 1/5

1/

10

1/

10

1/

10 ?

41

Multiplying a Fraction

and a Whole Number

One method to successfully multiply a whole number & a fraction is to

draw a picture.

Example:

If Stephanie wanted to make cookies for school and she needed 3/4

cup of sugar and she wanted to make 3 batches she would have to

multiply the whole number 3 and the fraction 3/4.

3 x 3/4… is really 3 groups of 3/4:

So… 3/4 + 3/4 + 3/4 = 9/4

Your Turn

John needs 1/2 cup of flour to make donuts with his mom. He plans to

make 4 batches. What would the problem look like?

Sam wanted to make some pumpkin pies for Thanksgiving. He needed

1/3 teaspoon of vanilla for each pie and he wanted to make 5 pies.

What would that look like?

42


and a Whole Number

1.) 2.) 3.)

1/2 X 6 = 3 2/3 x 9 = 1/4 x 12 =

4.) 5.)

1/4 x 8 = 1/3 x 15 =

43

Fraction Frenzy Spinning Game

Materials:

Each student needs 1 fraction circle

Pencil

1 paper clip

Crayons/markers

Directions:

1.) Students work independently to color and select a

different fraction for each piece of the fraction circle.

2.) Next, students select a partner and each will spin the

paperclip on their fraction circles.

3.) Whatever fractions the paperclips land on, the students

must multiply the two fractions. Each student in the group

attempts the same problem and then they check their

answers.

4.) Students must be careful with their work, because

whichever pair has the most correct answers and shows their

work WINS!!!

44


By a Fraction

Multiplying fractions can be easy…just be careful with your

multiplication facts!

1.) 1 3 (1 x 3) 3 You are not done until you

— x — = _____ = — check & simplify your answer!!!

2 4 ( 2 x 4) 8

2.) 2 3 3.) 3 1 4.) 2 6

— x — = — x — = — x — =

4 5 5 2 7 8

5.) 7 5 6.) 2 3 7.) 5 1

— x — = — x — = — x — =

9 6 3 4 9 4

8.) 3 2 9.) 1 4 10.) 3 6

— x — = — x — = — x — =

5 4 2 5 5 7

45

Fraction Card Game

Below are steps to a card game that can be used to help you multiply and divide

fractions.

It works best in small groups (no more than four).

Directions:

1. Get into groups of 2-4.

2. Get a deck of playing cards and take out all of the face cards.

3. Deal each player four cards.

4. Use your cards to make different fractions for one another (choose one card to

be

the numerator and another to be the denominator).

5. Call on someone in your group. This person will multiply or divide his/her

fraction by yours. If he/she is not correct, you get the two fraction cards of

his/her.

6. Continue taking turns among the group so that everyone has a chance to play.

7. Whoever ends up with the most cards at the end of the time period given, or

whoever gets ALL of the cards, wins

http://ellerbruch.nmu.edu/classes/cs255f03/CS255students/ahebein/P13/Hebein

Final.html

http://ellerbruch.nmu.edu/classes/cs255f03/CS255students/ahebein/P13/HebeinFinal.html

http://ellerbruch.nmu.edu/classes/cs255f03/CS255students/ahebein/P13/HebeinFinal.html

46

Fraction Pretzels

Ingredients:

* two thirds + two thirds = ? cups warm water

* 1 tablespoon sugar

*1 package active dry yeast

* 1 tablespoon vegetable oil

* 2 cups all purpose flour

* one and one fourth cups whole wheat flour

* 1 teaspoon salt

* 1 teaspoon vegetable oil

* 1 egg

* 2 teaspoons water

* 2 teaspoons course salt

(extra flour for kneading)

Steps

1. Make sure the oven is on 450°f.

2. Take the cooking sheets and spray it with the vegetable oil spray.

3. Put the water in a big mixing bowl, and make sure the temperature is between

105°- 115°f.

4. Add the sugar to the bowl. Stir it until the sugar dissolves.

5. Sprinkle the yeast over the water and sugar mixture. Don't stir the yeast!!!

Let it sit for about 5 minutes until it looks foamy!!!

6. Add the tablespoon of oil to the water.

7. In one of the middle sized mixing bowls, put together the all purpose flour,

whole wheat flour, and salt.

8. Add the flour combination to the liquid ingredients small amounts. Stir well

after each addition until the mixture becomes a dough.

9. Softly sprinkle about 2 tablespoons of flour on a cutting board or a flat

surface. place the dough on the powdered surface and knead it for about 8-10

minutes. Fold the dough in and out while kneading it. When your done kneading,

roll the dough into a ball.

10. Use a pastry brush to brush the vegetable oil on the dough.

47

11. Place the ball of oiled dough in the bowl.

12. Cover the bowl with a kitchen towel in a warm place for about a hour.

13. After the dough is risen like a bubble, punch it down in the bowl by folding it

on the sides and center and pressing it down.

14. Put the dough on a cutting bard and use a paring knife to divide the dough in

to 12 equal parts.

15. Roll the dough into 12 inch strips. Cut them into 6 inch strips. Shape 18

dough strips into numbers. Use the last 6 strips for dashes for the fractions. Put

the Fraction strips on a cookie sheet.

16. In a small mixing bowl, mix the egg with the 1 teaspoon of water. Then, beat

well with a fork.

17. Lightly brush the egg mixture on the pretzels. Sprinkle a little salt on the

pretzels

18. Bake the pretzels for 15-20 minutes or until they're a golden brown color.

Take oven mitts to remove the cookie sheets from the oven.

19. Allow the pretzels to cool for 10 minutes before removing them. Then, ENJOY!

http://library.thinkquest.org/J002328F/recipes.htm

http://library.thinkquest.org/J002328F/recipes.htm

48

Multiplying a Fraction and

Mixed Numbers

Example: Solve ¾ x 1½ One way to solve this problem is to…use paper & pencil

Remember…you must change the mixed number into an improper

fraction.

1½ =

(2 x 1 = 2)

Now add the numerator to the product : (2 + 1 = 3)

3

Now you can put the fraction back together again : —

2

Now you can solve the problem:

3 3 ( 3 x 3) 9 1

— X — = ______ = — or 1 —

4 2 (4 x 2) 8 8

Practice: Solve:

1.) 3 1 2.) 2 1

— x 2 — = 1 — x — =

5 2 9 3

3.) 1 1 3.) 1 3

2 — x — = 1 — x — =

5 3 4 5

49

Name _____________________________

Date ___________________ (Answer ID # 0720980)

Multiply Fractions

Multiply. Write your answer as a mixed number in simplest form.

1.

2

6

× 2

3

5

=

2.

7 ×

1

2

=

3.

6

7

× 3 =

4.

1

11

× 3

5

8

=

5.

1

3

8

×

8

12

=

6.

2

4

5

×

10

12

=

7.

6

12

× 9 =

8.

2

1

3

× 1

2

6

=

www.edhelper.com


50

Dividing Whole Numbers

by Fractions

Solve: 2 ÷ 1 /5 =

1 whole 1 whole

1/5 ? ? ? ? ? ? ? ? ?

Solve : 2 ÷ 1 / 3 =

1 whole 1 whole

1/3 1/3 1/3 1/3 1/3 1/3

Solve: 1 ÷ 1 / 6 =

1 whole

1/6 ? ? ? ? ?

Solve : 1 ÷ 2 / 8 =

1 whole

1/8 1/8

51

Dividing Fractions

Solve: 8/8 ÷ 2/8 =

1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8

1/8 1/8 ?

Solve: 2/3 ÷ 1/6 =

1/3 1/3

1/6

Solve: 3/4 ÷ 1/8 =

1/4 1/4 1/4

1/8

Solve : 4/6 ÷ 2/6 =

1/6 1/6 1/6 1/6

1/6 1/6 ?

52

Dividing Fractions

Another way to divide fractions is to use reciprocal multiplication

A reciprocal is :

______________________________________________

Write the reciprocal for the following fractions:

1.) 2 2.) 4 3.) 6 4.) 1 — = — — = — — = — — = —

3 5 9 2

Use reciprocal multiplication to set up the problem…you don’t have to

solve it, just set it up!

1.) 3 1 4 2 2.) 2 1 3.) 7 3

― ÷ ― = ― x ― ― ÷ ― = ― x ― ― ÷ ― =

4 2 3 1 5 10 9 5

Divide. Write your answer in SIMPLEST FORM!

1.) 3 1 2.) 3 1 3.) 5 1

― ÷ ― = ― ÷ ― = ― ÷ ― =

5 5 4 8 6 3

4.) 3 1 5.) 1 2 6.) 5 3

― ÷ ― = ― ÷ ― = ― ÷ ― =

8 2 6 3 8

53

Fraction Bingo Card #1

B I N G O

Three -fifths

7/9

2/3

One-

Eighth

11/12

1/2

7/12

Free

Space

3/7

One-

Ninth

Two-

Thirds

2 ¼

Two and

four-fifths

7/8

One and one

third

1/9

7/12

Six and seven-

eighths

5/9

Two-thirds

54


B I N G O

Two -fifths

6/9

2/9

One-

seventh

1/12

1/8

9/12

Free

Space

3/5

Three-

Ninths

Two and

one-fourth

7 ¼

Two and

seven-fifths

8/8

One and two

third

2/9

4/12

Five and

seven-eighths

5/6

Two and one-

sixth

55


B I N G O

3/7

1 1/9

2/3

Seven-

eighths

One-fourth

1/9

One-

Twelfth

Free

Space

1 ½

2/7

Five-

ninths

8 ¼

Two and

three-fifths

7/7

One and

three fifths

11/12

3/12

Five and

seven-eighths

2/9

One half

56


B I N G O

One half

1 1/4

7 1/3

Seven and

two-eighths

One-sixth

3/9

Seven-

twelfths

Free

Space

Six and seven-

eighths

3/7

Five-

sixteenths

13 ¼

Two and

three-eights

One whole

One and

three fourths

4/12

2/9

12 ½

3/11

One third

57

Fraction Bingo Answer Cards

One half

1 1/4

7 1/3

Seven and two-

eighths

One-sixth

3/9

Seven-

twelfths

5/9

Six and seven-

eighths

3/7

Five-

sixteenths

13 ¼

Two and three-

eights

One whole

One and three

fourths

4/12

2/9

12 ½

3/11

One third

3/7

1 1/9

2/3

Seven-

eighths

One-fourth

1/9

One-

twelfth

3/4

1 ½

2/7

five-

ninths

8 ¼

Two and three-

fifths

7/7

One and three

fifths

58

11/12

3/12

Five and seven-

eighths

2/9

One half

Two -fifths

6/9

2/9

One-

seventh

1/12

1/8

9/12

1/2

3/5

three-

ninths

Two and one-

fourth

7 ¼

Two and seven-

fifths

8/8

One and two

third

2/9

4/12

Five and seven-

eighths

5/6

Two and one-

sixth

Three -fifths

7/9

2/3

One-

Eighth

11/12

1/2

7/12

1/9

3/7

One-

ninth

Two-

thirds

2 ¼

Two and four-

fifths

7/8

One and one

third

59

1/9

7/12

Six and seven-

eighths

5/9

Two-thirds

60

Decimal Bingo Card #1

B I N G O

One tenths

0.03

1.259

Two and

four tenths

0.12

Seven and

sixteen

hundredths

12.1

Free

Space

0.367

One hundred

and ten

thousandths

2.475

Seven tenths

0.128

1.9

Nine

hundredths

5.486

0.008

Six and seven

thousandths

3.4

0.56

61


B I N G O

One

hundredth

12.45

2.56

Two and one

tenths

0.23

Six and

twelve

hundredths

1.25

Free

Space

0.782

three

thousandths

6.145

Six tenths

0.289

3.14

Two

hundredths

8.459

0.05

three and two

thousandths

0.005

0.9

62


B I N G O

One

hundredth

0.786

0.3

six and one

tenths

0.861

Twenty-

three

hundredths

.121

Free

Space

0.79

Two

hundred and

eleven

thousandths

1.259

Five tenths

0.45

1.76

Four

hundredths

7.15

0.05

Two and three

thousandths

0.96

0.003

63


B I N G O

Five tenths

0.356

2.4

Six and one

tenths

2.45

One and

fifteen

hundredths

0.009

Free

Space

0.1

One hundred

and two

thousandths

1.269

Four tenths

0.08

3.7

Seven

hundredths

2.85

0.007

Three and two

thousandths

1.06

0.79

64

Decimal Bingo Answer Cards

Five tenths

0.356

2.4

Six and one

tenths

2.45

One and

fifteen

hundredths

0.009

0.2

0.1

One hundred

and two

thousandths

1.269

Four tenths

0.08

3.7

Seven

hundredths

2.85

0.007

Three and two

thousandths

1.06

0.79

One hundredth

0.786

0.3

Six and one

tenths

0.861

Twenty-three

hundredths

.121

1.23

0.79

Two hundred

and eleven

thousandths

1.259

Five tenths

0.45

1.76

Four

hundredths

7.15

0.05

Two and three

thousandths

0.96

0.003

65

One hundredth

12.45

2.56

Two and

one tenths

0.23

Six and twelve

hundredths

1.25

3.6

0.782

Three

thousandths

6.145

Six tenths

0.289

3.14

Two

hundredths

8.459

0.05

Three and two

thousandths

0.005

0.9

One tenth

0.03

1.259

Two and

four tenths

0.12

Seven and

sixteen

hundredths

12.1

1.6

0.367

One hundred

and ten

thousandths

2.475

Seven

tenths

0.128

1.9

Nine

hundredths

5.486

0.008

Six and seven

thousandths

3.4

0.56

66

Place Value Chart

Millions

Hundred

Thousand

Ten

Thousand

Thousand

Hundred

Tens

Ones

Tenths

Hundredths

Thousandths

67

Decimals

Getting to know your decimals through place value:

1 2 4 . 1 7 8

______ _____ ____ decimal ___ ____ ____ Point

(and)

1.) Using a place value chart, what would 1.24 look like?

2.) Twenty seven hundredths

3.)Three and seven hundred fifty-six thousandths

4.) Five hundred thirteen thousandths

Ones Tenths Hundredths thousandths




68

It is important to know that 1 number after the decimal point means

that it is a tenth because it is 1 out of 10 equal parts.

This represents .7 ____________

______________ ______________

_______________ _____________

69

Two numbers after the decimal point is a hundredth because it is out

of 100 equal parts. Hundredths are written 2 places after the decimal.

This represents .50 ______________

because 50 of the 100

pieces are shaded in.

______________ ______________

Review:

____________ ______________

70

Fractions & Decimals Write the fraction & decimal for the shaded part.

Fraction: _______ Fraction: _______

Decimal : _______ Decimal : _______

Fraction: _______ Fraction: _______

Decimal : _______ Decimal : _______

Fraction:________ Fraction:_______

Decimal: ________ Decimal:_______

71

Identifying Place Value

Write the value for the underlined digit:

1.) 2.034 2.) 14.75 3.) 5. 791

__________ __________ _________

4.) 214.5 5.) 6.845 6.) 0.109

__________ __________ _________

7.) 0.45 8.) 9.3 9.) 52.107

____________ __________ __________

Match the numbers:

10.) Three and seven tenths ___ a.) 0.534

11.) 5.12 ___ b.) 0.23

12.) 3+0.7+0.05+0.006__ c.) 3.7

13.) Twenty-three hundredths___ d.) 3.756

14.) 0.5+0.03+0.004__ e.)Five and twelve hundredths

72

Decimal Dice

Materials:

1 cube template / student

Glue stick

Objective:

The object of the game is to have students work in either individually

or in pairs to get more practice with adding, subtracting, and/or

multiplying decimals.

How it works?

●Decimal Dice is very easy to use. All you need is a cube template with

a variety of decimals ranging from easy to challenging.

●For each problem the students are to roll the dice twice and

whichever decimal it lands on, that is the first part of the problem.

●The student gets the other number to complete the problem after

he/she rolls the second time.

●Encourage students to increase the amount of rolls in order to

increase the difficulty of the problem

●Students should be reminded that in order to successfully answer the

problem, they must correctly line up the decimals and check their work!

73

Decimals & Money Write as a decimal:

1.) Three dollars and one penny 2.) Seven dollars 3.) Forty-six cents

_________ _________ _________

4.) Thirty-five dollars and 5.) Two dollars & 6.) Two quarters

twenty-five cents six dimes

_________ _________ _________

7.) 4 dimes and 7 pennies 8.) 3 quarters 9.) 86 pennies

_________ _________ _________

10.) 13 dollars and 1 quarter 11.) 5 dimes and 2 pennies 12.) 90 dimes

_________ _________ _________

74

Comparing Decimals

Don’t forget the vocabulary:

●Greater than >

●Less than <

●Equal =

When comparing decimals make sure that the numbers line up

on the left. This will help you better see which number is

bigger.

Ex: Which is bigger 3.24 and 3.248 ?

Step 1 : Use the table to help identify which number is bigger

3.24

3.245

All of the numbers are exactly

the same except in the thousandths place.

So… 3.240

3.245 0 < 5

So…this means that 3.24 is < than 3.245


3

2 4 0

3 2 4 5

When there is not a

number, put in a zero

to make it easier to

compare.

75

Comparing Decimals

Practice:

Using the table as a guide, compare each set of numbers.

Write <, >, or = in the

1.) 5.43 5.432

2.) 0.28 0.208

3.) 9.39 9.90




76

4.) 10.3 1.898

5.) 0.746 0.746

6.) 3.602 3.082

7.) 6.7 6.701





77

Ordering Decimals

Using a number line put the decimals in order from smallest to largest

1.) Which length is bigger? 0.528 or 0.534

0.52 0.53 0.54

2.) Compare 0.72 & 0.7

0.7 0.75 0.8

3.) Compare 8.69 & 8.85

8.5 8.6 8.7 8.8 8.9 9.0

78

Decimal Chant

Sang to a marching tune.

“Attention!”

“Yes Ma’am/Sir!”

When you’re ADDING and SUBTRACTING decimals,

You’ve gotta:

Line up the Soldiers,

Fill in the Blank,

Put a Decimal Point,

At the Bottom of the Tank!

http://www.songsforteaching.com/math/decimals/musiclearn-addingandsubtractingdecimals.php



79

Adding & Subtracting

Decimals Vocabulary Review:

Hundredth Tenth Thousandth

1.) I am the first number after the decimal and I am equal to 1/10.

Who am I? ______________

2.) I am the place value that is three places after the decimal point,

equal to 1/1,000. What is my name? ____________

3.) I am the second number after the decimal and I am equal to 1/100.

What place value am I? ______________

Adding Decimals

1.) 1 ● 5 8 2.) 0 ● 2 3 5

+ 4 ● 5 3 + 1 ● 0 9

● ●

3.) 1 4 ● 0 1 4.) 5 ● 5 1 5.) 9 3 ● 0 7 8

+ 2 0 ● 7 8 0 ● 2 5 0 6 ● 1 3

Make sure that

your decimals

are lined up!

80

Subtracting Decimals

1.) 1 ● 2 3 2.) 0 ● 5 0 3.) 4 ● 0 7

- 0 ● 1 4 - 0 ● 4 3 - 0 ● 2 3

4.) 3 ● 1 5 5.) 2 2 ● 0 8 6.) 0 ● 2 9

- 1 ● 0 6 - 1 0 ● 0 2 0 ● 0 8

7.) 14 . 089 8.) 12 . 357 9.) 0.025

- 1 2 . 037 - 8 . 156 - 0.0 1 4

10.) Mark and his mom are going to the mall. Mark went to Game Stop

and bought a new game for $ 24.75. He paid with $40.00. How much

change will Mark get back?

11.) Corey and James are sharing a bag of Doritos. The bag costs 2.75

and James has 1.27. How much is left for Corey to pay for the chips?

Think about how to set

up the problem…do

you add or subtract?

When in doubt,

Line it out!

81

Decimals Guide Sheet

Use this as a guide when adding & subtracting decimals to make sure

everything is lined up!

82

Multiplying Decimals

As with all decimals, it is important to pay attention to place

value when multiplying!

Here is what multiplying 2 x 0.53 looks like:

0.53 is shaded in two times using 2 different colors:

When you count all of the squares, you get 106.

So…2 x 0.53 = 1.06

Let’s try : 2 x 0.12

If I count all of the squares I get 0.24

So…2 x 0.12 = 0.24

83


by a Whole Number

Let’s try some more:

1.) 3 x 0.6 =

2.) 5 x 0.5 =

3.) 4 x 0.12 =

Shade 0.6, 6

times. Using

different

colors might

help!

84

4.) 3 x 0.03 =

5.) 3 x 0.3 =

6.) 3 x 0.4 =

85

Multiplying a Decimal

By a Decimal

When multiplying a decimal by a decimal, start with making a

model

Example : 0.5 x 0.2

The 5 rows represents 0.5 The two red rows represents 0.2

the green represents

the answer: 0.10

*So… 0.5 x 0.2 = 0.10

86

1.) 0.5 x 0.7 = 0.35 because there are 35 squares that overlap.

2.) 0.3 x 0.3 =

3.) 0.8 x 0.4 =

Think…

how many

squares

overlap?

87


By a Decimal Write a multiplication sentence for each model

1.) ____ x _____ = 2.) _____ x _____ =

3.) ____ x _____ = 4.) ______ x ______ =

88

Color in the model to multiply the decimals:

5.) 0.6 x 0.4 = 6.) 0.2 x 0.7 = 7.) 0.3 x 0.5 =

8.) 0.1 x 0.8 = 9.) 0.8 x 0.3 = 10.) 0.5 x 0.6 =

11.) 0.1 x 0.5 = 12.) .09 x 0.2 = 13.) .04 x .08 =

89


By a Decimal You can also multiply a decimal by a decimal by placing the

decimal point…Here’s how to do it!

Ex: 0.5 x 0.7

Step 1 – Set up the multiplication problem

0.5

X 0.7

Step 2 – Multiply (just like normal, you can ignore the decimal

until step 3).

0.5

X 0.7

035

Step 3 – Count how many numbers are after the decimal for

each number.

0.5 0.5 0.7

X 0.7

035 1 place after 1 place after the decimal + the decimal = 2 places after the decimal

Count 2 places to put the decimal

So… 0.5

X 0.7

0.35 When adding the decimal always start

on the right at the end of the number

90


Solve:

1.) 1.23 2.) 0.5 3.) 0.78 4.) 1.23

x 3 x 0.2 x 5 x 0.06

5.) 2.98 6.) 0.37 7.)1.8 8.) 29

X 0.7 x 0. 64 x 0.2 x 0.7

9.) 11 10.) 0.83 11.) 0.43 12.) 13

X 0.3 x 2 x 5 x 0.2

13.) Josh wanted to make his mom some cookies. He went to

the market and bought 3 rolls of cookie dough. Each roll cost

$3.27. How much money did Josh spend at the store?

14.) John went to Vons to buy Flamin’ Hot Cheetos. He wanted

to buy 2 bags. Each bag cost $1.78. How much money will John

spend?

91


Solve:

1.) 23.1 2.) 7.51 3.) 13.7

x 2.3 x 1.01 x 1.2

5.) 203.1 6.) 1.24 7.) 72.5

X 12.4 x 1.5 x 2.2

9.) 38.12 10.) 19.8 11.) 126.1

X 4.6 x 2.6 x 4

12.) Jason wants to buy a new X-Box 360 for himself and his

best friend. Each X-Box 360 costs $368.97. How much

money will Jason have to spend to get what he wants?

Show your Work!

Watch your

multiplication…&

don’t forget the

decimal!

92

Decimal Division

Decimal Division using a model:

Example: 0.24 ÷ 6

Step 1: Step 2:

Start by shading 0.24 Cut out the squares

Squares and arrange them in 6

Equal groups

Practice:

1.) 0.25 ÷ 5 = _____ Now, take the 25 colored squares and

put them into equal groups.

93

2.) 0.08 ÷ 2 =

3.) 0.12 ÷ 4 =

4.) 0.18 ÷ 6 =

94

Decimal Division

Example: 3 4.2

When dividing decimals using paper & pencil:

Step 1: Put the decimal point directly above where the answer

goes.

3 4.2

Step 2: Divide as normal

1.4

3 4.2

1.) 8 5.6 2.) 2 3.2 3.) 4 .36 4.) 2 1.2

5.) 7 22.4 6.) 7 47.6 7.) 3 2.22 8.) 3 2.7

9.) 9 7.2 10.) 7 3.43 11.) 7 4.97 12.) 6 4.8

95

Decimal Division Use the models to find the quotient:

1.) 1.5 ÷ 0.5 =

2.) 1.4 ÷ 0.7 =

96

Decimal Division

Solve: 1.4 ÷ 0.7 2

1.) 0 . 7 1 . 4 7. 14. 7. 14.

2.) 0.2 2.6 3.) 0.5 1.15 4.) 0.16 2.6 5.)0.2 2.12

5.) 0.7 8.05 6.) 0.7 5.32 7.) 0.7 5.32 8.) 0.7 5.25

9.) 2.1 71.4 10.) 3.4 0.34 11.) 0.7 3.22 12.) 0.4 0.64

13.) 0.12 0.75 14.) 0.07 1.33 15.) 0.05 1.75 16.) 0.4 .60

17.) Suzy has 3.5 pounds of chocolate and wants to share it with her

friends. How many 0.5 pound servings does she have?

Don’t forget to

move the

decimals!!!

97

Algebra Expressions Vocabulary:

Solution Expression Variable

1.) A __________ is a math sentence that has numbers, an

operation sign ( +, -, x ÷), and sometimes variables (x, y, n,

etc). It does not have an equal sign.

2.) A __________ is a letter that stands for a number.

3.) A __________ is the answer to an equation.

How to write an expression:

Key words to know:

Addition words: more, sum, plus, added, increased, gave,

joined

Subtraction words: less, minus, loss, difference, spent,

left, ate

Multiplication words: product, each,

Division Words: quotient

Practice: Set up the problem & solve it:

1.) Brandon had 11 video games. He got 3 more for his

birthday.

11 + 3 = 14 (add)

98

2.) Mrs. Franz baked 15 cupcakes. Her husband ate 6 of them.

_____ - ____ = (subtract)

3.) 11 cars were racing. 6 more cars joined the race.

_____ ______ =

Think about what

sign goes here

4.) There were 25 books on the shelf. 6 of the books fell off.

_______ _______ =

5.) Sally went to the beach and collected 19 shells. She gave

12 to her sister.

________ ________ =

6.) Michael had 31 pens. He gave 15 to Alex.

_______ _________ =

7.) Jimmy had $27.00. He spent $11.75 at the mall.

________ ________ =

99

Solving Equations

When solving equations with variables you must:

Find the number of the variable that makes the number

sentence true.

The equation must be balanced and equal the same

amount. variable

Example: 5 + x = 12

Method # 1: use Mental Math to find the answer…think

5 + what number equals 12?

1.) n – 17 = 8 2.) n + 8 = 14 3.) 10 + n = 32

4.) x + 12 = 20 5.) 14 + z = 32 6.) n – 10 = 10

7.) 23 + a = 30 8.) n – 15 = 5 9.) 60 – n = 2

10.) 16 + n = 40 11.) 7 + z = 16 12.) 42 – n = 26

You want to find the

value for x.

When the numbers are the same

on both sides of the equal

sign…you have a balanced

equation.

100

Method # 2: Do the Math:

Whatever the sign is, do the opposite with the numbers

on both sides of the equal sign.

You want to get the variable all by itself

5 + x = 12

-5 -5

0 = 7

5 + x = 12

-5 = -5 x = 7

x = 7

Your work by replacing x for the answer 7 in the equation:

5 + 7 = 12

1.) 29 – b = 22 2.) 46 + n = 59 3.) x – 16= 9

4.) 25 + y = 40 5.) 80 – x = 69 6.) 6 + n = 32

7.) n – 2 = 9 8.) 8 + x = 15 9.) 29 – y = 7

10.) a + 35 = 48 11.) 10 + b = 32 12.) x + 9 = 26

Opposite of addition (+)

is subtraction (-)

101

Using Symbols for Variables

Each symbol represents one number. Find the value of each

symbol.

*Symbol Key*

= 6 = 2 = 5 = 4 = 8 = 3 = 1

1.) + 3 = 9 2.) 10 + = 18 3.) 6 = + 3

___ + 3 = 9

4.) - 3 =2 5.) 12 - = 8 6.) 4 + = 5

7.) + = 8.) + = 12 9.) 9 = -

Letters are just the

placeholders. You

can also use

symbols or pictures.

102

Order of Operation

Order of Operations is needed when you have an expression

that has more than one operation:

6 + 3 – 7 =

(Two operations)

Rules for Order of Operation:

1. Do everything inside of the parentheses first

2. Next, multiply and divide from left to right

3. Last, add and subtract from left to right

Example: solve 5 x (3 + 9) =

12 (do everything in the parentheses first)

5 x 12 = 60

______________________________________________

Practice:

1.) 32 – (7 x 3) = 2.) 30 ÷ (8 + 7) = 3.) 20 x 4 – 2 =

4.) (6 ÷ 3) x 4 + 8 = 5.) (3 x 25) + (2 x 45) = 4.) 8+ (3 x 2) =

5.) (18 - 6) x 4 + 6 = 6.) 3 x (45 ÷ 5) = 7.) (12 x 2) - 20 =

Don’t forget

to follow the

steps!

103

Order of Operations Treasure Hunt

http://www.uen.org/Lessonplan/preview.cgi?LPid=21529

Summary:

The purpose of this activity is to give students the opportunity to use order of operations equations in a fun, engaging

environment. During this activity, students will have the opportunity to work collaboratively as they create a treasure

map and clues that are based on order of operation equations of their own design.

Materials: ●Construction paper

Crayons

―Treasure‖

Order of Operations Compass

Treasure Chest

Treasure Map

Lined paper

Pencils

Background For Teachers:

As I tried this activity in my classroom, I found that students wanted to use a lot of numbers for each problem. The

students need to start with simple problems that deal with addition or subtraction and then work their way towards

more difficult problems that include parentheses, multiplication, and division. I would limit the amount of numbers for

each problem to less than 6 numbers for the more difficult problems.

Instructional Procedures: Invitation to Learn

This invitation to learn is simple. Ask the students what they would do if they found hidden treasure. What would they

buy, where would they go, or who would they help? Have them write their answers in their math journals. Discuss

their answers as a class.

Instructional Procedures

1. Before starting this activity, draw a simple map of your room on the board. Label important features such as the door, windows, teacher‟s desk, and whiteboards. Then hide something in your room (it could be anything) and come up with a series of clues or steps that the students need to follow in order to find the object. These clues should focus on students doing things a certain number of times, such as “take 4 steps towards the front of the room” or “spin around 2 times and face the windows.” Write the clues on the board next to the map but instead of writing “Take 5 paces north” write “Take (4 x 3) + 2 – 9 paces north”. For your first three clues, come up with order of operations problems that tell how many times the students need to do something. On the rest of your clues, leave a blank space where the order of operations should go. The class will work in groups of 4 to create their own order of operation problems that equal the number in each clue.

2. Begin this activity by placing the treasure chest in front of the class. Ask the students, “Does anyone know what this is?” Allow the students to answer and then ask, “Who can tell me what a treasure box is?” or “What do you find inside of a treasure chest?”

3. Continue the class discussion by asking, “Where do you find a treasure chest? Are they easy to find?” Allow the class to continue answering and then ask, if it hasn't already been brought up, “What do you usually need in order to find a treasure chest? That‟s right. You need a treasure map.” Hold up the treasure map so that your students can see it.

4. Then ask, “Do you need anything else besides a treasure map? What kind of tools and clues would make finding the treasure chest easier?”

5. Then explain, “Today we are going to go on a quick treasure hunt. However, instead of using the treasure map in my hands, we are going to use the map I have drawn on the board.” Pointing at the map and clues on the board say, “This is a map of our classroom. I have hidden “treasure” somewhere in our room and we need to use the map and clues in order to find it.”

6. Divide your class into groups of 4 and assign each group member one of the following roles: Map Maker, Interpreter, Guide and Captain. Give them a few minutes to decide a team name.


http://www.uen.org/Lessonplan/downloadFile.cgi?file=21529-2-27818-Order_of_Operations_Compass.pdf&filename=Order_of_Operations_Compass.pdf

104

7. Point at the board and say, “The treasure is hidden somewhere in our room. Let‟s look at our first clue to see if it can help us.” Read the first clue to the class and then ask, “How is this clue different from regular clues?” Help the students understand that the order of operation problems need to be solved before we can do what the clue tells us.

8. Take this time to review the class mnemonic that you have developed and to pass out a piece of lined paper and the order of operations compass.

9. Have the students solve the order of operation problem as a group and then choose one student from the class to follow and do what the clues say to do as the class solves them.

10. Repeat this process for the next two clues. 11. For your next clue say, “Notice that the next clue does not have an order of operations problem or number

listed. For the next few clues, I am going to give you the number and you are going to have to create your own order of operation problem that equals that number.”

12. Start the students out with simple problems that deal with addition and subtraction. Give the students time to work on their problems and then have them trade problems with a different group.

13. Repeat this same process with the rest of your clues until the student finds your hidden “treasure”. Allow the students to use multiplication and division to make the clues more difficult.

14. Once you feel that the students are capable of writing order of operation problems, they can start on their own treasure maps and clues.

15. As students are deciding where to hide their treasure, the students should choose places that are not in classrooms or in locations that will disturb other teachers or students. (If you decide to do this activity in your school, talk to your school administrator and inform him/her what is going to be happening.)

16. Say, “I am going to give you 5 minutes to decide where you would like to hide your treasure. Captains make sure that your group is back on time. Once you have decided, come back to the classroom. As you come back into the classroom, the Guides will get two pieces of lined paper, one for your treasure map and the other for your clues.”

17. When all of the students have found their spots, the next step is to develop their clues and maps. Begin this process by saying, “Now that you have found your spots, we now need to come up with clues that will lead us to the treasure. Interpreters are going to write the clues on one piece and Map Makers are going to draw a rough draft of the treasure map on the other.”

18. “Your clues should be simple but fun. You can hop, skip, walk backwards, pace, and even army crawl towards the treasure. For example, as you go towards the treasure you could have a group „Hop 5 times down the hall‟.”

19. “As the Interpreter is writing down your clues, the Map Maker needs to be drawing your treasure map. Make sure you label important places on the maps such as rooms, stairs, or playground equipment.”

20. “Captains, you are responsible for taking care of your group. When you get done with your clues and treasure map, come back to the classroom. As you come into the classroom, Guides need to get a piece of tan construction paper to draw your map on.”

21. When all of the students are back in the classroom and working on their maps, say, “Let‟s take a few minutes and talk about your clues. Remember that we are going to be developing order of operations problems for each clue. This will make each clue more difficult and fun to follow.”

22. Then say, “Everybody look at your first clue. As a group, I want you to come up with an order of operations problem for your first clue. Remember to use your order of operation compasses and our classroom mnemonic to make sure that each problem is solved correctly. Raise your hands when you have created your first problem and I will come and check it.”

23. Once you have checked the first clue say, “You are now going to create order of operation problems for each of your clues.” Have the students turn their papers in when they are done.

24. Once the order of operation problems have been checked, pass them back to each group. The group will then write the clues on the back of their treasure maps.

25. When the students are finished with their maps and clues, have the group follow their own clues and map one more time. As the students are trying it out, give the students “treasure” that they can hide.

26. The final part of this activity will be to trade the maps and clues with other groups. The students will need to have a piece of lined paper to solve the equations as they look for the treasure. The students will only get to keep the treasure if they show the other group their work and answers for each clue.

27. End this activity by having the students reflect on the following questions in their math journals. Write the following questions on the board. “What did you learn from this activity?” “What was the most difficult part of this activity?” “What was the most enjoyable part of this activity” “Did this activity help you understand order of

operation problems? How?” http://www.uen.org/Lessonplan/preview.cgi?LPid=21529


105

Order of Operation Spinners

Materials:

* 1 set of spinners for each student

* Paper

*Pencil

* Order of Operation worksheet

Object:

Each student is given a minimum of 2 spinners (1 spinner is called

the operation spinner and tells the student the operations used in

each problem). The other spinners contain a variety of numbers.

The students can work in pairs or individually and take turns

spinning each of the spinners.

o Ex: player 1 must go in order of the spinners, starting with

spinner 1 (number), spinner 2 (operation), back to spinner 1

(number), etc. until the student has a minimum of 3 numbers

and 2 operations.

The students then fill in their numbers & operations on the

worksheet with parentheses.

Challenge: Increase the numbers and operations the student must

complete.

106


Number Spinner (medium)

Operation Spinner (medium)

7 5

8 2

3 4

9 6

5

3

4

1 6

X

+ -

X

107


Number Spinner (challenge)

Operation Spinner (challenge)

18 9

45 12

25 36

14 7

5

3

4

1 6

÷

+ -

x

108

Order of Operation Spinners Worksheet

operation sign

1.) ( __ __ ) ___ = 2.) ___ ____ ____ =

3.) __ ( __ __ ) = 4.) __ __ ( __ __) =

5.) ( __ __) ( __ __ ) = 6.) __ ( __ __ ) =

7.) __ __ ( __ __) = 8.) ( __ __ ) __ =

9.) ( __ __) ( __ __ ) = 10.) ___ ___ =

11.) __ __ ( __ __) = 12.) ( __ __ ) __ =

109

Mnemonic Mania Materials:

PMDAS worksheet & Overhead

Pencil

Paper

Objective:

Students are given the opportunity to create their own

mnemonic phrase/saying to remember the order of

operations.

It is important for the teacher to explain what a

mnemonic devise is and how it is helpful.

Several examples should be given such as Please Excuse

My Dear Aunt Sally.

The students should use their PMDAS worksheet in

order to create their phrase/saying.

The students should be given the opportunity to share

their mnemonic phrase/saying to the rest of the class.

110

The Mystery Number (value of variables)

http://www.harcourtschool.com/jingles/jingles_all/35mystery_number.html

If you don't know all the numbers

When you write an expression,

A letter can stand for the missing information.

The variable-it's the mystery number.

Nine dogs in the waiting room at the vet's.

You know some information: (Nine!)

But in through the door come some cats. (Meow!)

How many cats? That's the variable-c for cats.

So how can you write the number of pets

In the waiting room now?

It's nine plus c,

Because you don't know the value of c-

How many cats?

Chorus

c is the unknown, unknown;

It's the missing information, the variable.

It's the mystery number.


When you write an expression,

A letter can stand for the missing information-

The variable! It's the variable!

But if you know the values of the other numbers,

You can find the value of the variable.

Use a letter to stand for it in your equation,

And then do the math to find the information.

Dr. Boggs has eighteen treats. (Sit, Rover!)

He gives the treats to some dogs. (Woof!)

Each dog gets two treats, with none left over.

You know some information:

Eighteen treats, two treats each.

But how many dogs?

http://www.harcourtschool.com/jingles/jingles_all/35mystery_number.html

111

That's the variable, d for dogs.

You can do the math and it works out fine.

18 divided by 2 equals d,

So how many dogs get treats? (Nine.)

Chorus

d is the unknown, unknown;




When you write an equation,

A letter can stand for the missing information-

The variable!

It's the unknown, unknown,



The variable!

Mystery number.

It's the variable!

112

Keeping It True (algebra)

http://www.harcourtschool.com/jingles/jingles_all/3keeping_it_true.html

Hi! I'm your new mathematical pal.

My name is Al Gebra, but you can call me Al.

One math idea I can offer to you

Is how to make sure an equation stays true.

(Hey, Al, what's an equation?)

It's another name for a number sentence.

It states that two amounts are equal.

Draw a little line and another little line;

That's an equal sign.

(Yeah, I knew that.)

The amounts on both sides of the sign that you drew

Have to have exactly the same value,

Or else your equation can never, can never be true.

Three equals three. Three plus six equals nine.

These equations are true-they balance just fine.

Four equals five. Four times three equals eight.

These equations are false-the two sides do not equate.

(What do you have to do to keep the equation true?)

If one side gets changed,

Then the other side does too.

Add, subtract, multiply, or divide;

If you do it over here,

You've got to do the same thing on the other side.

Keeping it even, keeping it true.

If the left gets five added, the right gets five, too.

(Give me five!)

That will keep the equation true.

Chorus

Keeping it equal, keeping it true-

All we want to do is keep the equation true.


113

Keeping it even, keeping it fair-

If you do it over here,

You've got to do it over there.

Subtract three, subtract three-

If we take some from you, we have to take it from me.

If it's out of balance, that's unfair,

If you take from here, you've got to take from there.

Out of balance, that's not right.

If you do it on the left,

Then you've got to do it on the right.

(Mom! Now he has more than me!)

Add four, add four-

You don't add less, and you don't add more.

If you multiply one side times ten,

Do it over there, and you're equal again.

Repeat chorus. (2 times)

Keeping it true, uh huh, keeping it true.

You know I'm keeping it true.



114

Addition Properties Directions:

1st Cut out the properties and match them to their definition.

2nd Cut out the examples and match them with their

properties.

3rd Write your own example for each property.

Associative Property:

Commutative Property:

Zero Property:

115

Addition Properties

This property says you can group addends (the numbers in the

problem) differently without changing the value of the sum (+).

This property says that you can add zero to any number without

changing the value of the number.

This property says you can add the numbers in any order without

changing the answer.

223 + 0 =223 (which property am I?)

(3+1) + 6 = 3 + (1 + 6) (which property am I?)

4 + 10 = 10 + 4 (which property am I?)

116

Addition Properties Name the Properties:

Associative Zero Property Commutative

Property Property

1.) (5+6)+3 = 5+(6+3) 2.) 145+0 = 145 3.) 5.25+10 = 10+5.25

_____________ ____________ _____________

4.) 50+(2+3) = (50+2)+3 6.) (3+1)+6=3+(1+6) 5.) 427+0=427

_______________ ____________ ____________

6.) 1.5+(8.2+6)=(1.5+8.2)+6 7.) 12+4 = 4+12 8.) 486+0=486

_________________ ____________ ___________

Find the value of x and name the property:

9.) 3 + 12 = x + 3 10.) 0 + x = 49 11.) (15+3) +2 = 15+(2+x)

_____________ _____________ _______________

12.) 7 + 18 = x + 7 13.) 4.7+x = 2+4.7 14.) 10+(x+3)=3+(5+10)

_____________ _____________ ______________

117

Name _____________________________

Date ___________________ (Answer ID # 0219852)

Solving Equations

Write an equation for each problem. Then solve the equation.

1. 35 plus a number is 38.

2. 99 minus a number is 54.

3. The difference between a number and 9 is

15.

4. A number plus 21 is 104.

5. A number divided by 5 is 11.

6. A number multiplied by 8 is 96.

7. 10 divided by a number is 5.

8. Two times a number is 18.

9. The difference between a number and 32 is

12.

10. 12 divided by a number is 4.

11. 96 minus a number is 81.

12. Three times a number is 30.

13. A number divided by 6 is 9.

14. A number plus 8 is 59.

15. 77 plus a number is 136.

16. A number multiplied by 11 is 77.

17. The difference between 39 and a number

is 7.

18. A number minus 26 is 67.

www.edhelper.com


118

Multiplication Properties: Vocabulary:

Directions:

1st Cut out the properties and match them to their definition.

2nd Cut out the examples and match them with their

properties.

3rd Write your own example for each property.

Distributive Property:

Property of 1

Zero Property

Associative Property

Commutative Property

119

This property allows you to break apart numbers to make them easier to

multiply. You can also use this property to find the value of expressions with

variables.

This property says you can multiply numbers in any order and the answer is

always the same.

This property allows you to group numbers differently and the answer is

always the same.

When one of the factors is a 1, the answer always is the same as the other

number in the equation.

When one factor is a 0, the answer is always 0.

71 x 1 = 71 18 x 3 = 3 x 18

4 x (2 x 5) = (4 x 2) x 5 6 x (n + 5) if n = 10

13 x 0 = 0

120

Multiplication Properties

Match the properties:

1.) 17 x 23 = 23 x 17 ● ● Distributive Property

2.) n x 1 =240 ● ● Zero Property

3.) (n x 14) x 8 = 9 x (14 x 8) ● ● Commutative Property

4.) 340 x a = 0 ● ● Associative Property

5.) 8 x ( m + 6) if m=10 ● ● Property of 1

Solve:

1.) 16 x p = 16 2.) 5 x (a x 13) = (5 x 4) x 13

P =_______ a = __________

3.) 65 x 0 = g 4.) 28 x 6 = 6 x f

g = _______ f =________

5.) 17 x d = 23 x 17 6.) (4 x 2) x 5 = 4 x (b x 5)

d = ________ b = ________

7.) 285 x y = 285 8.) 8 x 2 = 2 x k

Y = ________ k:________

121

Distributive Property

The _____________ _____________ allows you to break a

multiplication problem with variables into smaller pieces.

Example: 6 x ( y + 8) if y=10

= (6 x 10) + (6 x 8)

= 60 + 48

= 108

______________________________________________

Solve using the Distributive Property:

1.) 7 x (8 + n) if n = 30 2.) 4 x (n + 6) if n=20

= (7 x 8) + (7x __ ) = (__x__) + (__x__)

= ___ +___ = ___ +___

= ___ = ___

3.) 9 x (5 + n) if n=20 3.) 3 x (n + 7) if n=30

4.) 5 x (45 - n) if n=20 5.) 7 x (2 + n) if n=50

6.) 8 x (60 - n) if n=30 7.) 6 x (4 + n) if n=60

Multiply everything in the

parentheses by the outside

number

122

Distributive Dice Game Materials:

Distributive Dice worksheet

Cube template

Glue

Paper/pencil

How to Play:

Students are given the worksheet with a variety of

problems that require the student to use the distributive

property.

The students are to construct their cube and write a

variety of numbers on each side.

For each problem, the students roll their cube and fill in

the value of the variable on the worksheet.

The students then solve the problem.

123

Distributive Dice Game

1.) 9 x (y + 8) if y =___ 2.) .) 9 x (y + 8) if y =___

3.) 10 x (h + 4) if h = ___ 4.) (25 - z) x 9 if z = ____

5.) 5 x (b + 16) if b = ___ 6.) 7 x (h + 13) if h =___

7.) 3 x (y + 10) if y =___ 8.) (42 - z) x 9 if z = ____

9.) 4 x (h + 22) if h =___ 10.) 6 x (4 + j) if j =___

11.) 2 x (m + 5) if m =___ 12.) 7 x (k + 2) if k =___

13.) 6 x (60 - a) if a =___ 14.) 3 x (75 - f) if f =___

124

Positive & Negative Numbers

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7

Negative #’s Positive #’s

Negative numbers are always to the ______ of the zero.

Positive numbers are always to the _______ of the zero.

Absolute Value is the distance of a number from ______.

Numbers that are opposites are the same distance from

_______ on a number line.

______________________________________________

Write the opposite of each number:

1.) -54 ____ 2.) +36 ____ 3.) – 89 ____ 4.) 14 ___

5.) -2 ____ 6.) +289 ___ 7.) +68 ____ 8.) –52___

Name each integer’s absolute value:

1.) +36 2.) -230 3.) -2 4.) 27 5.) -396

____ ____ ____ ____ ____

Remember…absolute

value is written as

with the number in

between

You can write a

positive integer two

ways: +3 or 3.

Negative integers

are written as -3

For every positive number,

there is an opposite,

negative number.

125

Integer Art

Materials

Construction paper

Markers, crayons, colored pencils

Number line example

Instructions:

Students are to demonstrate their understanding of

positive & negative numbers through illustration.

Provide an example of a number line with positive &

negative numbers.

Provide the students with examples of completed

projects.

126

Name _____________________________

Date ___________________ (Answer ID # 0821342)

Algebra

Solve each equation.

1. t ÷ 4 = 8

2. 26 = 13c

3. 90 = 18b

4. 117 ÷ a = 13

5. 187 ÷ q = 17

6.

12 =

z

2

7. 90 = 5p

8. 3x = 27

9. 42 = 14e

10. 12s = 132

11. 16v = 240

12. 19 = 114 ÷ u

13. h ÷ 17 = 7

14. 100 = 10n

15.

16 =

w

7

16. 32 ÷ g = 4

17. 19j = 114

18. d

15

= 14

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127

THE PROPERTY SONG

WORDS BY: JOHN A. CARTER

TUNE: "THIS OLD MAN"

This property, the Commutative Property,

Tells us that we are free

To change the order of a sum,

Also in a multiplication.

This property, the Associative Property,

Tells us that you and me

Can change the grouping when we multiply,

Do it when you add, it'll make you look sly,

This property, the Identity,

Tells us that so obviously

Anything times one will not change,

Anything add zero will still remain.

This property, the Inverse Property,

Tells us that which we can see

Multiply by the reciprocal to always obtain one,

Add the opposite to anything to always leave none.

This property, the Distributive Property,

Talks to us about a quantity

Which contains a sum and is being multiplied.

Take the product with each term inside.

http://rogertaylor.com/clientuploads/documents/references/Mathsongsing-a-

long.pdf

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128

Human Number Line (Positive & Negative numbers)

Materials: A variety of positive & negative numbers (including zero) for the students to

hold.

Long piece of yarn (to be the number line).

Objective: The students will demonstrate an understanding of positive & negative

numbers on a number line.

The students will be able to compare positive & negative numbers.

>

<

=

129

0

+1

+2

+3

+4

+5

130

+6

+7

+8

+9

+10

+11

131

-1

-2

-3

-4

-5

-6

132

-7

-8

-9

-10

-11

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Adding Integers Adding Integers using counters:

= positive numbers (+) = negative numbers (-)

Example: +6 + -3 =

The answer is what

you are left with.

+ 6 + -3 = +3 _____________________________________________________

Practice – Use counters to find the sum:

1.) + 7 + - 2 = 2.) +3 + -2 =

3.) -5 + +2 = 4.) -1 + -8 =

5.) – 7 + +10 = 6.) -8 + +8 =

7.) +9 + -12 = 8.) -2 + -10 =

+ -

+ + +

- - -

_

+ + +

Positive number &

a negative number

cancel each other

out

134

Student Counters (Positive & Negative numbers)

+ + + + + + + +

+ + + + + + + +

+ + + + + + + +

- - - - - - - -

- - - - - - - -

- - - - - - - -

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Adding Integers (Using a number line)

Example: +8 + -5 = (start)

+8 -5

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

So… + 8 + -5 = +3

Use the number line to find the sum:

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

1.) -5 + 2 = 2.) -1 + -8 = 3.) -2 + -10 =

4.) -7 + 10 = 5.) +9 + -12 6.) 0 + -8 =

7.) +9 + -10 = 8.) +4 + - 4 = 9.) +1 + -6 =

10.) +10 + -10 = 11.) -5 + 0 = 12.) +3 + -7 =

When using a

number

line…Always

start at zero

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Subtracting Integers Subtracting Integers using counters:

= positive numbers (+) = negative numbers (-)

Example: -5 - +3

Add both the positive number

& its opposite. ( +3 and -3)

Take away 3 of the positive circles

*The number of circles left over is your answer

So… -5 + +3 = -8

Solve using counters:

1.) -2 - +2 = 2.) -8 - +6 = 3.) -3 - +6 = 4.) -11 - +5 =

5.) -8 - +1 = 6.) -7 - +6 = 7.) -1 - +9 8.) -5 - +7 =

9.) -3 - +11 = 10.) -10 - +4 = 11.) -3 - +11 = 12.) -9 - +3 =

+ -

- - - - -

+ + +

- - -

137

Adding & Subtracting Integers

(Mixed review)

Solve:

1.) -6 + -4 = 2.) +9 + -5 = 3.) -5 + -5 =

4.)-8 - +5 = 5.) -2 + 3 = 6.) -7 - +4 =

7.) +12 - +7 = 8.) +11 + 9 = 9.) -6 + -7 =

10.) +2 - +10 = 11.) -12 + 5 = 12.) +8 + -6 =

13.) +11 + -11 = 14.) -20 + 15 = 15.) -10 - +4 =

16.) +13 - +8 = 17.) -9 - +15 = 18.) +21 - +14 =

19.) An elevator at the Sears Tower is on the 15th floor. It

drops 7 floors. What floor is the elevator on?

20.) At the beginning of the day the temperature was 67 .

The temperature increased 17 . What was the temperature at

the end of the day?

138

Format for Mnemonic Mania

P M D A S

Parentheses ( ) Multiply (x) Divide (÷) Add (+) Subtract (-)

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Directions: Write the definition of each addition property & give an

example for each.

Addition Properties

Associative Zero Property Commutative

Property Property

140

Directions: Give an example of each multiplication property

Multiplication Properties

Associative Zero Property Commutative Property of Distributive

Property Property One Property

fractions, decimals, &...

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