TENNESSEETENNESSEE ADULT EDUCATION ADULT EDUCATION

CURRICULUM 2011CURRICULUM 2011

LEVEL 3LEVEL 3

This curriculum was written with funding of the Tennessee Department of Labor and Workforce Development and may not be reproduced in any way without written permission. ©

Basic Math OperationsLesson 1: Place Value, Addition, and Subtraction

MATH OPERATIONSMATH OPERATIONS

Why is it important to know the basic math operations?

What kind of problems are solved using basic math operations?

PercentsFractions Decimals

Algebra Geometry

WHAT ARE THE 4 BASIC MATH OPERATIONS?WHAT ARE THE 4 BASIC MATH OPERATIONS?

AdditionAddition

SubtractionSubtraction DivisionDivision

Multiplication

It doesn’t matter what kind of math problems are being It doesn’t matter what kind of math problems are being solved. These are the only Math operations used. solved. These are the only Math operations used.

DEFINITIONS: BASIC OPERATIONSDEFINITIONS: BASIC OPERATIONS

Addition (+) Adding two or more numbers together.

Subtraction (-) Finding the difference between numbers.

Multiplication (x) is repeated addition.

5 x 3 is the same as 5 + 5 + 5 or 3 sets of 5 = 15

3 x 5 is the same as 3 + 3 + 3 + 3 + 3 or 5 sets of 3 = 15

Division (divide ÷) Splitting into equal groups or parts; the result of sharing.

There are 12 chocolates, and 3 friends want to share them, how do are the chocolates divided?

4 each

SYMBOLS FOR BASIC SYMBOLS FOR BASIC OPERATIONSOPERATIONS

Multiplication: There are four ways to write a multiplication problem.

• An “ x ” - 3 x 4

• A dot - 3 • 4

• Parenthesis - (3)4 or (3)(4) or 3(4)

• Algebraic expression - 5n = (5 x n)

Division: There are three ways to write a division problem.

255

25÷ 5“÷ ”5 25Using a division bracket

The division sign

A fraction

Addition

AddSumTotal

AltogetherCombine

Increased byIn all

Multiplication

MultiplyProduct

TotalTimes TwicePer

KEY WORDS

Division

DivideEach

AverageSplit

Share

Subtraction

SubtractDifferenceCompare

Minus Less thanMore than

Decreased by

Place ValuePlace Value

This curriculum was written with funding of the Tennessee Department of Labor and Workforce Development and may not be reproduced in any way without written permission. ©

PLACE VALUEPLACE VALUE

Before any numbers can be added, subtracted, multiplied or divided, the place value of numbers must be understood.

Each place has a given value, therefore each digit has a given value.

OnesTensHundredsThousandsTen Thousands

Hundred Thousands

458721

Written: 1 2 7 , 8 5 4

WHAT IS PLACE VALUE?WHAT IS PLACE VALUE?

Place value is the basis of our entire number system.

A place value system is one in which the position of a digit in a number determines its value.

In the standard system, called base ten, each place represents ten times the value of the place to its right.

Think of this as making groups of ten of the smaller unit and combining them to make a new unit.

Think of this:

1 x 10 = 10 The tens place has ten times the value of the ones place

10 x 10 = 100 The hundreds place has 10 X the value of the tens place

100 x 10 = 1,000 The thousands place has 10 X the value of the hundreds place

1000 x 10= 10,000 The ten thousands place has 10 X the value of the thousands place

10,000 x 10 = 100,000 The hundred thousands place has 10 X the value of the ten thousands place

In the number 456, each digit has a specific value.

4 6 5

onestenshundreds

The value for each number is as follows:

400 50 6+ +

4 x 100 5 x 10 6 x 1

456

GUIDED PRACTICE: PLACE VALUEGUIDED PRACTICE: PLACE VALUE

Write the value for the underlined number below.

1. 478

2. 985

3. 225

___________

___________

___________

4. 761 ___________

GUIDED PRACTICE: PLACE VALUEGUIDED PRACTICE: PLACE VALUE

Write the value for the underlined number below.

1. 478

2. 985

3. 225

___________

___________

___________

8 ones

4. 761 _____________

9 hundreds

2 tens

7 hundreds

PLACEPLACE VALUE VALUE

A comma is used to separate the thousands place from the hundreds place.

1 2 7 8 5 4

OnesTens

Hundreds

Hundred thousands

Ten thousands

Thousands

comma

,

PLACEPLACE VALUEVALUE

When there is no digit to represent a place, a zero (0) is used as a place holder.

1 2 3 4 0 0,

ones

hundreds

hundred thousands

tens tens thousands

thousands

1 0 7 , 8 0 4

No tens digit place holder

No ten thousands digit

Zeros used as a place holder

GUIDED PRACTICE: PLACE VALUEGUIDED PRACTICE: PLACE VALUE

Write the place value for the underlined digit.

1. 16,780 ________________

2. 5078 __________________

4. 209,721 _________________

3. 156,006 _________________

Write the place value for the underlined digit.

1. 16,780 ________________

2. 5078 __________________

4. 209,721 _________________

3. 156,006 _________________1 hundred thousands

0 ten thousands

5 thousands

0 ones

ReadingReading && WritingWriting Whole Numbers

Writing whole numbers can be done by following a few rules.

1. Some words are compound and need a hyphen: twenty-one

2. Do not use AND when writing whole numbers: 1,120

one thousand one hundred one thousand one hundred twentytwenty3. Place a comma between the digit in the millions and

hundred thousands place and the thousands

and hundreds place1,000,000.

millions thousand

s

1,0 0 0,0 0 0

ADDITIONADDITION

This curriculum was written with funding of the Tennessee Department of Labor and Workforce Development and may not be reproduced in any way without written permission. ©

ones

tenshundreds

ADDITIONADDITION

When adding digits, it doesn’t matter which order the numbers are placed.

The numbers must be lined up in the correct place value column.

4 1 2 4+ 2 5

2 5+ 4 1 2 4

25 + 4124

Thousands Hundreds Tens Ones

4 1 2 4

+ 2 5

thousands

onestens

hundreds

thousands

PLACE VALUE OF NUMBERSPLACE VALUE OF NUMBERS

Each number has a value in the problem.

Thousands Hundreds Tens Ones

4 1 2 4

+ 2 5

When working the problem, the ones column is added first.

Labels must be carried to the answer

If labels are given with the numbers, add them to the answer after the problem is solved.

5 miles + 3 miles 5+ 3 8 miles

8

GUIDED PRACTICEGUIDED PRACTICE

6 3 7

1. 605 + 32 =

2. 334 + 52 =

3. 456 quarts + 233 quart =

4. 2546 + 151 =

Solve the following problems. Rewrite each problem using the column form.

6 0 5+ 3 2

2. 334 + 52 =3 3 4+ 5 2

3 8 6

3. 456 quarts + 233 quarts = 4 5 6+ 2 3 36 8 9 quarts

4. 2546 + 151 =2 5 4 6+ 1 5 12, 6 9 7

63 8

96 8

2 796

CARRYING WITH ADDITIONCARRYING WITH ADDITION

5 5 8+ 1 4 5

onestens

hundreds

•Addition starts with the digits in the ONES column

• Be sure the numbers are lined up in the correct place value column.

tens

5 5 8+ 1 4 5

8+5= 13

tensones

1

1.Add the two numbers in the ones column.

2.If the sum of the numbers in the ones column is greater (>) than 9, the number in the tens column is carried over.

3

5 5 8+ 1 4 5

hundreds

4. The next set of numbers which are in the tens

column are now added together.

3. In this case the 3 is placed in the ones column and the 1 is stacked on the 5 in the

tens column.

5 5 8+ 1 4 5

8+5=

3

1

5 5 8+ 1 4 5 3 0

1

105 + 4 + 1=

1

13

6. The digits in the hundreds column

are added together and the total is written down in the hundreds column.

5 5 8+ 1 4 5 0

1

3

1

5 + 1 + 1= 7

5 5 8+ 1 4 5 30

11

7

ANSWER: 703

GUIDED PRACTICEGUIDED PRACTICE

Use the correct steps to solve each problem. Rewrite each problem in column form.

1. 7,170 + 342 =

2. 254 + 676 =

3. 5,667 feet + 654 feet =

4. 1,678 + 435

7,512

930

Use the correct steps to solve each problem. Rewrite each problem in column form.

1. 7,170 + 342 =

2. 254 + 676 = 2 5 4 + 6 7 6

039

11

7,1 7 0 + 3 4 2

2157

1

4. 1,678 + 435

1,6 7 8 + 4 3 5

3

1

11

11

6

3. 5,667 feet + 654 feet =

3. 5,6 6 7 + 6 5 4

123

2

111

6,321 feet

2,113

KEY WORDS: KEY WORDS: IMPORTANT VOCABULARY FOR WORD PROBLEMS

Subtraction

SubtractDifferenceCompare

Minus Less thanMore than

Decreased by

Multiplication

MultiplyProduct

TotalTimes TwicePer

Division

DivideEach

AverageSplit

Share

Addition

AddSumTotal

AltogetherCombine

Increased byIn all

Addition

AddSumTotal

AltogetherCombine

Increased byIn all

Addition

Addition problems do not have the “+” symbol in written problems.

Know the key words that apply to help solve problems.

STEPS FOR SOLVING WORD PROBLEMSSTEPS FOR SOLVING WORD PROBLEMS

What is the question being asked?

What information is necessary to solve the problem?

What math operations will be needed to solve the problem?

Does the answer make sense?

Step 1:

Step 2:

Step 3:

Step 4:

Decide what information in the question is NOT necessary.

Step 5:

In the following word problems, identify the KEY WORDS used in ADDITION and write on a piece of paper

1. At rush hour, the Busy Bee Café has 4 waitresses, 1 dishwasher, 2 cooks, 2 busboys, and 1 manager.

How many people in all work at the Busy Bee Café during rush hour?

The first step to answer any word problem is The first step to answer any word problem is to find to find keykey words. words.

Key words:

How many people in all work at the Busy Bee Café during rush hour?

In all

2. Zack bought a cheesecake for $ 8.15 and a coffeecake for $6.98 and tax was $1.20.

What was the total cost?

Key word:

What was the total cost?

Total

In order to understand any word problem, it must be broken down into steps.

The problem may require a student to read and re-read the problem to understand what information in necessary to answer the question correctly.

Kathryn goes out to lunch with Mia and Fran.

Each girl orders the $5 lunch special.

Kathryn wants to treat her friends to lunch.

The tax is 9% and a 25% tip will add $3.75.

Not counting the tax and tip, how much will Kathryn have to pay?

What is the question: How much will she have to pay?

Total cost of each meals

What is the necessary information need to solve.

How many meals did she buy?

Addition Meal + Meal + Meal

or the total cost to Kathryn

What math operations will be needed to solve the problem?

$15

Total cost of each meals

What is the necessary information need to solve.

How many meals did she buy?

Addition Meal + Meal + Meal

What math operations will be needed to solve the problem?

Answer:

$5

3

5 + 5 5+

What information is not necessary to solve this problem?

The tax is 9% and a 25% tip will add $3.75.

GUIDEDGUIDED PRACTICE: ADDITIONPRACTICE: ADDITION

1. Julia teaches a GED class. She has many students that faithfully

attend her class. On the roll, there are 15 men and 13

women but only 7 men and 11 women are currently attending the GED class.

How many students are currently attending the class?

How many students are currently attending the class?

Key word/ words?

Answer?

How many

18

1 1+ 7

1 8

2. In 2010, 6,525 people participated in the Knoxville Marathon. In 2011 448 more people signed up to

participate. What was the total number of participants

in the 2011 Marathon?

2. What was the total number of participants in the 2011 Marathon?

Key word/ words? Total

Answer? 6,700 6 5 2 5+ 4 4 8

11

6 9 7 3

3. In 2010, the NCAA Men’s Basketball Tournament

had a viewing audience of 506,000. In 2011, the number viewers increased by 72,000 which was the largest viewing audience since 2005. If 2010 and 2011 viewing audience was combined together, what was the size of the viewing audience for 2011?

If 2010 and 2011 viewing audience was combined together, what was the size of the viewing audience for 2011?

Key word/ words?

Answer?

Combined together

578,000

5 0 6, 0 0 0+ 7 2, 0 0 0

000875

4. David goes to the Spartanburg Speedway and watches his favorite

NascarNascar driver, Buddy Barnes, qualify for the Cola 500.

On the first run, his car was clocked at 150 mph and on the second run his car was clocked at 149 mph. What was the sum of the two track

passes for Buddy?

299

What was the sum of the two track passes for Buddy?

1 5 0+ 1 4 9 2 99

Key Word: Sum

Answer:

5. Frank and Steven rent a condo downtown for $1221 per month.

The condo maintenance is an additional $63 per month.

What is the total cost of the condo rent?

What is the total cost of the condo rent?

$1284

1 2 2 1+ 6 3

4821

Key Word:

Answer:

Total

6 . Amanda is having surprise birthday party for Red. She invited twenty of Red’s friends. Her menu will be hamburgers, hot dogs,

chips, a birthday cake and ice cream. She spent $25 for a table cloth, $35

balloons, $12 for a centerpiece plus a $144 for groceries.

Altogether how much did Amanda spend for the table cloth and groceries?

$169

Altogether how much did Amanda spend for the table cloth and groceries?

1 4 4+ 2 5

961

Key Word: Altogether

Answer:

Subtraction

This curriculum was written with funding of the Tennessee Department of Labor and Workforce Development and may not be reproduced in any way without written permission. ©

2. Always bring down the labels.

SubtractionSubtraction

Just like addition problems:

1. Always line up numbers from right to left.

The process of finding the difference between two numbers.

1. Always line up numbers from right to left starting in the ones column.

Hundreds Tens Ones

-

6 5 9- 1 4 2

956

1 4 2

In subtraction, the larger number must be placed on top of the smaller number.

6 5 9- 1 4 2

In subtraction, start in the ones column.

6 5 9-1 4 2

ones

tenshundreds

6 5 9- 1 4 2

659-142

Remember the place value each digit.

9 – 2=

7

7

6 5 9- 1 4 2

Next, subtract the digits in the tens column.

7

5 – 4=

1

1

6 5 9- 1 4 2

7

Last, subtract the numbers in the hundreds column.

6 – 1=

6 5 9- 1 4 2

5

7 15

6 5 9- 1 4 2 71

5 1 7+1 4 2 6 5 9

6 5 9-1 4 2 5 1 7

The answer should be the largest or the top number in the problem. Does it work?

517 + 142 = 659

To check the answer- do the opposite operation.

GUIDED PRACTICEGUIDED PRACTICE

1. 1,356 – 254 =

2. 5,654 feet – 654 feet =

3. 676 – 254 =

Remember to drop the comma and label when subtracting. Add back after problem solved.

4. 678 – 135 =

5. 1 3 5 6 – 1 2 5 4

1 3 5 6- 2 5 4

5 6 5 4- 6 5 4

6 7 6- 2 5 4

5,000 feet

1 1 0 2 + 2 5 4

5 0 0 0+ 6 5 4

1. 1,356 – 254 =

2. 5,654 feet – 654 feet =

3. 676 – 254 =

Remember to drop the comma and label when subtracting. Add back after problem solved.

4 2 2 + 2 5 4

1 3 5 6 1,102

5 6 5 4

4 2 2

6 7 6

211 0

05 0 0

224

Drop the zero at the front of the number.

4. 678 – 135 =

5. 1 3 5 6 – 1 2 5 4

5 4 3+ 1 3 5

1 2 5 4 + 1 0 2

6 7 8

1 3 5 6

6 7 8- 1 3 5

What is the answer now? 102

35 4

2010

SUBTRACTIONSUBTRACTION

Subtraction Key Words to Know

Subtract Difference Compare

Minus Less than

How many more Decreased Take Away

NOTE: words that end in “er” might be key words. Example: fewer, faster

How much more

SUBTRACTIONSUBTRACTION: WORD PROBLEMS: WORD PROBLEMS

1. The speed limit is posted on the highway 55 mph. Alex is driving under the speed limit at 34 mph to avoid a ticket.

5 5 - 3 4

1

Key word: difference

What is the difference in Alex’s current speed and the posted speed limit?

2 mph

2. Bubba and his buddies were going fishing. The boys had planned a big camping trip all

winter. A bet was made on who could catch the most fish on the first day. The loser would cook supper and clean up. At the end of the day, Bubba caught 17 fish and his buddies together caught 6 fish. How many more fish did Bubba catch?

How many more fish did Bubba catch?

1 7- 0 6 11 fish

11

3. John bought a used motorcycle. The cost of the bike was $6,440. He also wanted to buy a jacket and helmet. If he had $7,860 total and

subtracted the cost of the bike, what was left to spend on the helmet and jacket?

7 8 6 0- 6 4 4 0

$1,420 0241

If he had $7,860 total and subtracted the cost of the bike, what was left to spend on the helmet and jacket?

subtractedKey Word:

Answer:

BORROWING WITH SUBTRACTION:BORROWING WITH SUBTRACTION:

To subtract, write the numbers in column form, and begin with the digits in the ones column.

Remember the: _____ ____

Start from the ones place and move left

place value

The smaller number is always subtracted from the larger number.

753 – 145= Re-write in column form

7 5 3-1 4 5

7 5 3- 1 4 5

ones

tens

hundreds

What happens when the bottom number can’t be subtracted from the top number?

7 5 3- 1 4 5

Cannot subtract 5 from 3

…need to borrow from the next column

Since the next column is the tens column, one set of ten will be borrowed.

7 5 3- 1 4 5

4 1

Now the 5 can be subtracted from 13

13 – 5=

The digit in the tens column (5) is reduced by one set of ten making it 4

7 5 3- 1 4 5

41

7 5 3- 1 4 5

13 – 5 = 8

8

Look in the tens column and see if the digits can be subtracted.

The operation can be completed.

14

The digit was reduced by 1 set of ten.

7 5 3- 1 4 5 8

Can 4 be subtracted from 4? 4 - 4= 0

7 5 3- 1 4 5

Look in the hundreds column. Can the numbers be subtracted?

Can 1 be subtracted from 7?

7 – 1 = 6

6

1 4

4 1

0

80

Check answerCheck answer

What is the opposite operation of subtraction?

AdditionAddition

7 5 3- 1 4 5

Add the answer (608) to the smallest number (145)

6 0 8+ 1 4 5 7

4 1 1

Does it work?Does it work?

356 80

GUIDEDGUIDED PRACTICE PRACTICE

1. 2 7 1 - 7 3

2. 6 5 8 - 1 4 9

3. 3 4 8 0 - 1 6

4. 3 5 0 0 - 3 5 0

1. 2 7 1 - 7 3

2. 6 5 8 - 1 4 9

3. 3 4 8 0 - 1 6

4. 3 5 0 0 - 3 5 0

891

1 6 11

5 0 9

14

7 1 14

051343 4 6

SUBTRACTION WORD PROBLEMSSUBTRACTION WORD PROBLEMS

Subtraction Key Words to Know

Subtract Difference Compare

Minus Less than

How many more Decreased Take Away

NOTE: words that end in “er” might be key words. Example: fewer, faster

How much more

Tori loves to play bingo at her grandma’s church. Tonight Tori was excited

because she won the big bingo prize of $25.

If she spent $9 on a bingo card, how much money did she have after she subtracted the cost of card?

Identify and write the key word in each problem then Identify and write the key word in each problem then solve.solve.

If she spent $9 on a bingo card, how much money did she have after she subtracted the cost of card?

2 5- 9

Key words: 1 1

$1661

Answer:

subtracted

1. In 1998, the unemployment rate was at 4%. In 2010,the unemployment rate as

13%. What was the difference in the

unemployment rate during the 12 year span?

GUIDED PRACTICE:GUIDED PRACTICE:

9%

What was the difference in the unemployment rate during the 12 year span?

1 3 - 4 9

10

0

Key word:

Answer:

difference

2 . Trudy is having a Sunday brunch for Easter with her family.

She went shopping and her total was $129.

What was the difference in the cost and her estimation?

If she serves eggs, sausage, bacon, French Toast, waffles, and orange juice, she estimated her grocery bill will be around $150.

What was the difference in the cost and estimation?

1 5 0- 1 2 9

$21

4 1

120Answer:

Key word: difference

3. Monte wants to buy a new car that costs $21,620. He is researching how much insurance will cost for the particular model. He received quotes from WeInsureAll Insurance, an online company, and the local Field and Farm Insurance Company. Both companies provided quotes for six months full coverage.

WeInsureAll quoted Monte a price of $592 and Farm Insurance Company provided a quote of $635.

Assuming the coverage is of equal quality, What is the comparison difference between the two companies?

$43 6 3 5 - 5 9 2

5 1

340

Assuming the coverage is of equal quality, What is the comparison difference between the two companies?

Key words:

Answer:

comparison difference (compare)

4. David goes to the Speedway and watches

his favorite Nascar Nascar driver, in the 00 car, Buckshot Stevens, qualify for the Ontario 200.

On the first pass, Buckshot’s car was clocked at 134 mph.

The next driver, I.B. Faster, was clocked at 182 mph. How much faster was I.B. than Buckshot?

Buckshot had a nickname of “double ought Buckshot” because he drove the “00” car.

48 mph 1 8 2- 1 3 4

7 1

840

How much faster was I.B. than Buckshot?

Key words : How much faster

Answer:

5. Frank and Wendy are planning a vacation and had two options for a week rental of a beach home.

One home rented for $1416 per week on the beach. The other rented for $1122 per week and it was located two blocks from the beach.

How much more was the beach home rental that was closest to the beach?