Lessons and Worksheets

WIN CAREER SOLUTIONS

Applied Mathematics

LEVEL 1

A Self-Study Course for

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2 • Applied Mathematics

INTRODUCTION

Hi! I’m EdWIN!

Hi, my name is EdWIN. I will be your guide

through Applied Mathematics. We will go

through this course together. Look for me to

pop up throughout your lessons to give you

helpful tips.

Now, don’t get nervous. I know how many

of you feel about math, especially when the word

fraction is mentioned. We will cover one topic

at a time. I will be here to give you examples to

help you along.

If the content of the lesson is something that

you understand, you should be able to work

through it at a faster pace. If the material is

difficult, read the text several times. Then, try

to work the exercises one at a time. After you

try one problem, look at the solution. You can

learn by reviewing each step that is provided in

the solution. Think about the process being

shown. Now, think positive. Negative attitudes

are not allowed!

Applied Mathematics is a course designed to

help you solve math problems. It is important

that you have basic math skills. It is also

important that you can apply them to problems

that arise on your job. The main focus of this

level of Applied Mathematics is to learn the basics.

We will start at the very beginning.

Applied Mathematics • 3

PREREQUISITE SKILLS

At Level 1 you should be able to:

• recognize whole numbers.

• count using whole numbers.

• add whole numbers.

• count by 2s, 5s, 10s, and 25s.

• read and follow basic instructions.

• define time units.


LEARNING OBJECTIVES

In this level you will:

• learn math symbols (+, -, ×, =, %, $, ¢, @, #, ˚).

• read a clock to determine time.

• read simple meters to determine measurements.

• learn whole number place values.

• read and write numbers in standard notation

and in words.

• use tenths and hundredths place values.

• count money and write units of money.

• explain the idea of a fraction and write

fractional units.


OUTLINE

LESSON 1

LESSON 2

LESSON 3

LESSON 4

LESSON 5

LESSON 6

LESSON 7

LESSON 8

LESSON 9

LESSON 10

Reviewing Skills

Recognizing Basic Math Symbols

Telling Time

Reading Simple Meters

Recognizing Whole Number Place Values

Reading and Expressing Numbers

Recognizing Place Values in Money

Counting Money

Reading and Writing Fractions

Posttest


LESSON 1

REVIEWING SKILLS

Let’s begin by taking a Pretest on the skills

that you should already know. These skills include

knowing whole numbers, counting with whole

numbers, and following basic instructions.

See if you are ready for this level by completing

the exercise. The answers will be on the pages

following the Pretest. You should be able to

complete all of the problems. If you cannot, please

seek instruction from a tutor before you begin

this course. Good luck!

Let’s review your math skills.


LESSON 1

EXERCISE – PRETEST

Instructions:

Select the answers that show the correct number.

1. Count the following objects. How many objects are in the

box

a. 5

b. 21

c. 16

d. 15

e. 4


LESSON 1


box

a. 4

b. 8

c. 18

d. 3

e. 2


box

a. 11

b. 12

c. 9

d. 8

e. 0


LESSON 1

Instructions:

Look at the pattern of whole numbers. Decide if the pattern is

counting by 1s, 2s, or 5s. Write the missing number in the space

provided.

4. 1, 2, 3, ____, 5

5. ____, 1, 2, 3

6. 25, 30, 35, 40, ____

7. 126, 127,128, ____

8. 0, 2, 4, 6, ____, 10, 12

Instructions:

Read the following passage and answer the questions that follow.

Sandy works in a factory that makes shirts. She has

trouble staying awake during the day because she

works the night shift. She makes $5.75 per hour. Sandy

and her husband live in Griffin, Georgia. Her husband

is a plumber, and they have three children.


LESSON 1

9. Where does Sandy work _________________________

10. Why can’t Sandy stay awake during the day

_____________________________________________________

11. How many children does Sandy have _____

12. Place an X on the third object counting from the left side of

the page.

^ ^ ^ ^ ^ ^

13. Circle the number that is under the middle letter.

P A Y D A Y S

5 10 15 20 25 30 35


LESSON 1

14. Count the pencils in the box. Write your answer in the space

provided.

Answer: _________ pencils

15. Place a check mark on the circle with an arrow showing

movement to the left at the top of the circle.


LESSON 1

ANSWERS TO EXERCISE

1. Answer: c. 16 objects

2. Answer: d. 3 objects

3. Answer: a. 11 objects

4. Answer: 1, 2, 3, 4, 5

5. Answer: 0, 1, 2, 3

6. Answer: 25, 30, 35, 40, 45

7. Answer: 126, 127, 128, 129

8. Answer: 0, 2, 4, 6, 8 , 10, 12

9. Answer: in a factory

10. Answer: She works the night shift.

11. Answer: 3


LESSON 1

12. Place an X on the third object counting from the left side of

the page.

✗

^ ^ ^ ^ ^ ^

13. Circle the number that is under the middle letter.

P A Y D A Y S

5 10 15 20 25 30 35

14. Answer: 5 pencils

15. Place a check mark on the circle with an arrow showing

movement to the left at the top of the circle.

✔


LESSON 2

RECOGNIZING

BASIC MATH SYMBOLS

You’re about to start Lesson 2. You must have

done well on the Pretest. This lesson is going to

teach some basic math symbols. Sometimes, we

call symbols signs. You may know some of them.

If that is the case, that’s great.

There are a lot of signs in math. People who

do a lot of math like shortcuts. Symbols are easier

and faster to write than writing words. Symbols

are used for math processes. Here are the symbols

we will look at in this lesson.

MATH SYMBOLS

+ add - subtract × multiply

÷ divide = equal % percent

$ dollar ¢ cent @at

# number/pound ° degree

SALE

25% OFF

We will go over each symbol and talk about

what it means. You will need to practice

remembering the ones you do not know. We

are going to start with symbols that mean a math

process.

What symbol do you

see


LESSON 2

Addition

Let’s begin by looking at the + (plus) sign.

This symbol means to add. If you see 4 + 5, you

should add four and five. Four books plus five

books adds to nine books.

is

I will not try to teach you to add in this

course. This lesson is about symbols. In the next

level, I will show you how to add using a

calculator. For now, I want you to know the

symbol used to show addition. When we read

4+5, we say 4 plus 5.


LESSON 2

Subtraction

Next, let’s talk about the minus sign. It looks

like this: - . This sign means to subtract. It is the

opposite of the plus or addition sign. If you have

9 - 5, you take five away from nine.

For example:

Do you see that if you have 9 books and 5 are

taken away, you have 4 left

Some people say the minus sign means take

away or less.

9 - 5

This is read as 9 minus 5. You might think:

9 take away 5

or

9 less 5


LESSON 2

Some minds like to think:

5 less than 9

Five numbers less than nine is the number four.

This process is called subtraction.

Equal

The answers to math problems are often

found after the symbol =. It means equals or is

equal to. Earlier, we had:

4 + 5

four plus five

We said when you add 4 and 5, the answer is 9.

We write this phrase like this:

4 + 5 = 9

four plus five equals nine

Some people might say the result of working a

math process follows the equals sign.


LESSON 2

Multiplication

Multiplication is really a fast way to add. We

use the symbol × to mean multiply. When you

see 3 × 4, it means the number 3 is to be

multiplied by the number 4. We often say,

3 times 4. That is because in multiplication, you

are counting the same number multiple times.

In this example, 3 × 4, you are counting a group

of 4 … 3 times.

groups of 4 - 3 times

Do you see why I said multiplying is really

counting fast Instead of making a drawing to

count, we learn the fact that 3 groups of 4 equals

12.


LESSON 2

There are many jobs where you may need to

multiply, such as carpentry, landscaping, and

decorating. Being able to multiply helps you do

some jobs faster. There are basic multiplication

facts that are taught in school. I hope you

remember them. If you have not needed to

multiply often, you may have forgotten them.

Do not worry. We will learn to multiply using a

calculator in the next level.

However, you may not always have a

calculator handy. If you know some of the facts,

but have forgotten others, you may use the table

to review.

The numbers across the top and the left side

of the chart are your guides. The problem 10 × 7

is read ten times seven. Find the 10 on the left

side of the chart and touch the 10 with a finger

on your left hand. Find the 7 at the top of the

chart and touch the 7 with a finger on your right

hand. Slide your fingers over the chart as shown

until they meet. You should see the number 70.

Ten times seven equals seventy.


LESSON 2

MULTIPLICATION TABLE

1 2 3 4 5 6 7 8 9 10

2 4 6 8 10 12 14 16 18 20

3 6 9 12 15 18 21 24 27 30

4 8 12 16 20 24 28 32 36 40

5 10 15 20 25 30 35 40 45 50

6 12 18 24 30 36 42 48 54 60

7 14 21 28 35 42 49 56 63 70

8 16 24 32 40 48 56 64 72 80

9 18 27 36 45 54 63 72 81 90

10 20 30 40 50 60 70 80 90 100

Let’s try another problem: 5 × 8. Find the 5

on the left side of the chart. Find the 8 on the

top. You should find that five times eight is forty.

If you do not know these facts, you might

want to try learning them by making a set of

cards. Write the problem on one side of a card

or paper. Write the problem and answer on the

other side. Start with 5 to 10 cards. If you start

with too many, you might get frustrated.


LESSON 2

From time to time, look at the sides of the

cards without the answer. See if you know the

answer. If you do not remember it, turn the card

over. Studying multiplication facts will help you

learn them. Practice a few at a time until you

begin to remember them. Then, try adding new

facts to your set.

This can be a hard process. You do not have

to know how to multiply to complete this course.

Knowing at least some facts will make it easier

at times.

Practice if you

want to learn multiplication facts.


LESSON 2

Division

The next symbol we will look at is the division

sign. This means the opposite of multiplication.

We said that 5 × 8 = 40. If we go backward,

40 ÷ 8 = 5. This is read as forty divided by eight

equals five. Forty can be divided into eight equal

parts. Look at the following example of division.

An office with 4 workers won the local radio station’s

morning breakfast. The station sent 12 doughnuts.

How many doughnuts can each worker have

12 doughnuts ÷ among 4 workers

Each worker gets 3 doughnuts when the 12 are

divided.

12 ÷ 4 = 3

These symbols, +, -, ×, and ÷, have

introduced the four basic math operations. Now,

let’s look at some other math symbols.


LESSON 2

Money

You probably know the dollar sign when you

see it. The dollar symbol looks like this: $. We

put it in front of dollar amounts. When we write

four dollars in symbols, we write $4.00. We

always write the $ symbol in front of the amount.

We sometimes use the cent symbol, which looks

like this: ¢. This sign goes behind the amount.

Four cents can be written as 4¢. Remember that

4 cents is part of a dollar, so it can also be written

as $.04. We will talk about how to write amounts

of money in another lesson.

You may not know the next few symbols.

They are not used as much as the others. Hang

in there, though. They’re not too difficult.

I like these symbols.


LESSON 2

Percent

Another symbol that is used to give important

information is the percent sign, %. Percents are

commonly used in the business world. They are

used to measure things like taxes and interest.

Percents are a way of describing parts of a whole.

With percents, one whole is divided into 100

parts. When referring to a percent, it means out

of 100. For instance, look at Figures A and B.

Figure A Figure B

In Figure A, all of the squares (the 100 parts

of this whole) are shaded. It means 100%. We

put the sign % after the number. When you hear

or say, 100% of something, this means all of it.

In Figure B, 50 of the squares are shaded.

This shows 50%. Notice 50 out of 100 is onehalf.


LESSON 2

Most of the time when percents are used,

visuals like Figures A and B will not be shown.

You should know what it means when you hear

different percents. For example, you might hear

that 25% of your wages are withheld for taxes.

25%

25%

If you are paid $100, then $25 will be

withheld. Your take-home pay will be $75.

Twenty-five percent of your wages goes to pay

taxes. Again, remember percent is based on 100.


LESSON 2

Other Symbols

The @ symbol is sometimes used in math

problems. To say that we have 4 items at 10¢

each, we write: 4 @ 10¢. In math, if you use the

word at, you may use this symbol. This symbol

is also used in Web addresses.

A symbol for the word number is #. It’s really

a shorthand symbol. I can write the number four,

or I can write #4. It’s a short way to write the

word number. This same symbol is sometimes

used to mean pounds. We write that the

computer weighs 15#. If the symbol is before a

number, it means number. If it follows a

number, it means pounds.

#10 number 10

10# 10 pounds


LESSON 2

The last symbol we will talk about is called

the degree symbol. It looks like a small circle.

You will see it when you read temperatures. If it

is sixty degrees outside, you could write 60°. You

may also see it when referring to angles. If you

do carpentry work, you have worked with ninety

degree angles. This is written as 90°. It is read as

ninety degrees. Though we will not study angles,

you should know the sign for degree.

Symbols have meanings. Most of them are

shorthand for words. Let’s see if you can

remember what the symbols mean by doing the

following exercise. The answers will follow. Good

luck!

I hope you can remember what all

of these math symbols mean.


LESSON 2

EXERCISE – NUMBERS AND SYMBOLS

Instructions:

Write the following words in numbers and symbols.

1. seventy-six degrees ____________________

2. number thirty-two ____________________

3. five dollars ____________________

4. forty-seven cents ____________________

5. eighty-seven percent ____________________

6. six plus four equals ten ____________________

7. twelve minus three equals nine ____________________

8. eight times seven equals fifty-six ____________________

9. ten divided by two equals five ____________________

10. five items at twelve cents each ____________________


LESSON 2

ANSWERS TO EXERCISE

1. seventy-six degrees

6. six plus four equals ten

Answer:

76˚

Answer: 6 + 4 = 10

2. number thirty-two

Answer: #32

7. twelve minus three equals

nine

Answer: 12 - 3 = 9

3. five dollars

Answer: $5.00

8. eight times seven equals

fifty-six

Answer: 8 × 7 = 56

4. forty-seven cents

Answer: 47¢ or $.47

9. ten divided by two equals

five

Answer: 10 ÷ 2 = 5

5. eighty-seven percent

Answer: 87%

10. five items at twelve cents

each

Answer: 5 @ 12¢ or

5 @ .12


LESSON 3

TELLING TIME

To begin this lesson, let’s review counting by

5s. You need this skill when reading a clock face.

Since there are 60 minutes in an hour, we will

practice counting to 60 by 5s. When we count

by fives, we are adding faster.

5

10

15

20

25

30

35

5

5 10

5 10 15

5 10 15 20

5 10 15 20 25

5 10 15 20 25 30

5 10 15 20 25 30

35


LESSON 3

40

5 10 15 20 25 30

35 40

45

5 10 15 20 25 30

35 40 45

50

5 10 15 20 25 30

35 40 45 50

55

5 10 15 20 25 30

35 40 45 50 55

60

5 10 15 20 25 30

35 40 45 50 55 60


LESSON 3

Knowing how to count by fives will help you

tell time. If you already know how to tell time,

turn to page 42. Here you will find the exercise

for Lesson 3. Make sure you can do all of these

problems. If so, move on to Lesson 4. If you do

not know how to tell time, follow me and I will

show you how.

This is a clock face.

Figure 1

Look around your home or workplace and

find a clock that has numbers on it like the one

in Figure 1. You may find more than one kind

of clock. The kind with lighted numbers as in

Figure 2 is called a digital clock.


LESSON 3

7:32

Figure 2

Digital clocks show time in the standard written

format:

hour : minutes past the hour

The time 7:32 means it is 32 minutes after 7

o’clock. What does 4:05 mean It is five minutes

after 4 o’clock. It is easier to read a digital clock

than a clock face.

Before we talk more about time, let’s review

some basic units that measure time.

Day

Hour

Minute

Second

period of light between one

night and the next; or 24

hours

one 24th part of a day; or

60 minutes

one 60th part of an hour; or

60 seconds

one 60th part of a minute


LESSON 3

If you’ve found a clock, take a look at it. It

probably has a knob so that you can move the

parts on the front. Turn this knob a few times.

The parts that move on the front are called

hands. In Figure 3, the longer hand is on the 12.

The shorter hand is on the 5.

5:00

Figure 3

The long hand is called the minute hand. The

short hand is the hour hand … the hour that it

is. In Figure 3, it is five o’clock, which is written

as 5:00.

On the hour (that is at one o’clock, 2 o’clock,

3 o’clock, and so on) the long hand always points

toward the 12. The short hand points to the

hour. Look at the following clocks to see what I

mean.

12:00 2:00 4:00 10:00

Figure 4


LESSON 3

Some clocks have a little hand that is

constantly going around the clock face. That

hand keeps track of seconds. It is called the second

hand. It will travel around the clock once in one

minute. Each time the second hand moves all

the way around the clock face, the minute hand

(long hand) will move once to show that one

minute has passed.

In the same way, the minute hand (long hand)

will move around the clock face once showing

that one hour has passed. When the minute hand

moves completely around the clock face, the

hour hand (short hand) will move to the next

hour.

As you have seen, the numbers 1 through 12

on your clock show the hour. The short hand

points to the hour. These 12 numbers are also

used to show minutes using the long hand. The

numbers are read in 5-minute increments.

1 means 5 minutes

2 means 10 minutes

3 means 15 minutes

4 means 20 minutes

5 means 25 minutes

6 means 30 minutes

7 means 35 minutes

8 means 40 minutes

9 means 45 minutes

10 means 50 minutes

11 means 55 minutes


LESSON 3

For example, look at Figure 5. When the short

hand is on the 2 and the long hand on the 3, we

say it is 15 minutes after 2. The short hand (hour

hand) tells you the hour is two o’clock. The long

hand (minute hand) is on the 3, which means

15 minutes. This clock shows 2:15. It is 15

minutes after two o’clock.

Figure 5


LESSON 3

START

START

START

CLOCKWISE

CLOCKWISE

CLOCKWISE

one minute four minutes fifteen minutes

Figure 6

Some clocks will show the minutes like those

in Figure 6. If your clock does, start counting at

12. Move in a clockwise direction. In Figure 6,

you count to where the long hand points to the

3. The long hand shows that 15 minutes have

passed since 2 o’clock. Here are 2 more examples:

20 minutes after 3 o’clock 25 minutes after 11 o’clock (11:25)

(We write this as 3:20)

Figure 7 Figure 8


LESSON 3

When the long hand in on the 6, we can say

several things that mean the same time. Look at

Figure 9. It is 30 minutes after 2 o’clock. We

usually say it is two-thirty. We write this as 2:30.

2:30

Figure 9

When the long hand passes 6 and is on 7, it

is two thirty-five (2:35). There are 60 minutes

in an hour. If it is thirty-five minutes past one

hour, then it is 25 more minutes until the next

hour.

60 - 35 = 25

Look at Figure 10. Two thirty-five is often

called twenty-five minutes before three o’clock.

Sometimes we say 25 till 3. Do you see that they

are the same times

2:35 or twenty-five till three

Figure 10


LESSON 3

Here are some examples of time:

3:00 – three o’clock 2:05 – five after two 8:45 – fifteen till nine

3:22 – twenty-two after three 10:41 – nineteen till eleven 12:00 – noon or midnight

Since there are 24 hours in a day, the hour

hand must move around the clock face twice in

one day. The morning hours are shown by a.m.

(I get up at 7:00 a.m.) The afternoon and

evening hours are shown using p.m. The 12:00

after the morning hours is called noon. The

12:00 after the evening hours is called midnight.


LESSON 3

Remember, a digital clock simply tells the

correct time.

I2:45

It is forty-five minutes after twelve or twelve

forty-five. You could say it is (60 - 45 = 15) 15

minutes until 1 o’clock.

Practice telling time by looking at a clock face

and then a digital clock. They should tell the

same time.

Now, let’s practice a little. I’m going to show

you some clocks and ask you to match the correct

time. The answers will be provided afterward.

Try your best before you look. Good luck!

Ready, set, go!


LESSON 3

EXERCISE – TELLING TIME

Instructions:

Match the clocks on the left with the correct time on the right.

Place the letter corresponding to the correct time in the blank

beside each problem number.

A. 3 o’clock

1. ___

B. 2:15

C. 6:29

2. ___

D. twenty minutes till four

3. ___

E. 8:59

F. ten after twelve

4. ___

G. seven-thirty

H. midnight

5. ___

I. fifteen after one

J. twelve minutes till ten


LESSON 3

6. ___

A. 3 o’clock

B. 2:15

7. ___

C. 6:29

D. twenty minutes till four

8. ___

E. 8:59

F. ten after twelve

9. ___

G. seven-thirty

H. midnight

10.___

I. fifteen after one

J. twelve minutes till ten


LESSON 3

ANSWERS TO EXERCISE

1. C C. 6:29

2. D D. twenty minutes till four

3. A A. 3 o’clock (3:00)

4. H H. midnight (or noon)

5. F F. ten after twelve


LESSON 3

6. G G. seven-thirty

7. J J. twelve minutes till ten

8. E E. 8:59

9. B B. 2:15

10. I I. fifteen after one

You’ve just completed Lesson 3. I hope you

did well. Now, it’s time to move on.


LESSON 4

READING SIMPLE METERS

In Lesson 3, you practiced telling time. Did

you know that you were reading a simple meter

Meters are devices used to measure things. You

could say a clock measures time. You may not

realize it, but you probably read other meters all

the time. We have to read rulers, timers, scales,

speedometers, and a number of things that

measure using numbers.

A common meter is the scale. Scales are

instruments or machines used for weighing. The

instruments must have a part that has marks to

show expected measures and a pointer. For

instance, the scales in a doctor’s office might look

something like this:

2 4 6 8 10 12 14 16 18 20

You never know when

you might need to

read a meter.

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300

Medical Scale

Figure 11


LESSON 4

The scales in your home may look like these:

100

110

120

130

140

Home Scales

Figure 12

Both types of scales have marks to show

different possible weights and a pointer. The

pointer shows the measurement of the object

being weighed. Most meters work the same way.

Thermometers are another type of meter.

They measure temperature. Some thermometers

have a pointer. Others may have a liquid that

rises to the point showing the temperature. (see

examples shown in figure 13 on the following

page)


LESSON 4

120

110

100

90

140

130

THERMOMETER

-20

-10

0

10

20

30

80

40

70 60 50

Thermometers

Figure 13

Speedometers measure the rate of movement.

Cars have this meter in the dashboard. This lets

drivers know how fast they are going.

30

50

70

90 110

miles per hour

(mph)

130

150

10

170

Speedometer

Figure 14


LESSON 4

Let’s look at another meter. The ampere meter

measures the amount of electrical current. An

ampere meter looks something like Figure 15:

10

20 30

40

0

50

Ampere Meter

Figure 15

The numbers on this meter range from 0 to

50. The pointer on this meter is pointing to the

30. This means there are 30 amperes of current

showing on this particular meter reading.

Look at the meter in Figure 16. The pointer

is halfway between 30 and 40. The halfway point

is 35. There are 35 amperes of current on this

meter reading.

10

20 30

40

0

50

Ampere Meter

Figure 16


LESSON 4

Another meter you may have seen is your

electric meter. It may look like Figure 17. Read

the number that the arrow points to. If the arrow

is between two numbers, read the lower number.

Write the numbers down from left to right. Look

at the meter in Figure 17.

Electric Meter

Figure 17

This meter reads 00807. You could use this

number to figure your electric bill.

Now, let’s see if you can read some meters on

your own. The answers will follow after the

problems. Good luck!


LESSON 4

EXERCISE – METERS

Instructions:

Look at the following meters. Write the number shown by the

meter in the space provided.

1. ____________

10

20 30

40

0

50

2. ____________

20 30

3. ____________

0

10

40

50

4. ____________

5. ____________

120

110

140

130

THERMOMETER

-20

-10

0

10

100

20

90

30

80

40

70 60 50


LESSON 4

ANSWERS TO EXERCISE

1. Answer: 25

2. Answer: 25937

3. Answer: 50

4. Answer: 02437

5. Answer: 65˚ or 65 degrees


LESSON 5

ten thousands

thousands

hundreds

tens

millions

hundred thousands

RECOGNIZING WHOLE

NUMBER PLACE VALUES

0 0 0 0 0 0 0

How are you doing Don’t be afraid of math.

Try to think of it as a game. The more you play

or practice, the better you will be at playing.

Lesson 5 is about reading whole numbers.

Whole numbers are the numbers beginning with

zero:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and so on

Digits are used to write whole numbers.

There are ten digits. They are:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

The position of a digit in a number shows its

place value. Let’s start by looking at a place value

or position chart.

Place Value Chart

ones (units)


LESSON 5

When we write a number, each digit has a

place. Look at the number 52. We line up the

ones place with the 2, and the 5 will be in the

tens place. This means there are 2 units of one

and 5 tens.

5 GROUPS OF 10 2 ONES

tens

5 2

ones (units)

Where a digit is located in a place value chart

tells the place value of that digit. Look at the

digit 9 in the following numbers:

Hang in there. Place

value is very important.

935

91

9

The value of the digit is nine. The place value

varies. In 935, the 9 means 9 hundreds. In 91,

the 9 means 9 tens. In the number 9, the 9 means

9 ones.


LESSON 5

Think about 435.

hundreds

tens

4 3 5

ones (units)

There are 4 groups of hundreds, 3 groups of

tens, and 5 ones. Together these digits placed in

this order make the number 435.

Let’s look at another number: 11,380

ten thousands

thousands

hundreds

tens

1 1 3 8 0

ones (units)

11380 ,

ones

tens

hundreds

thousands

ten thousands

Always think about the place value chart, and

you will not go wrong!

In the following exercise, try to find place

values on your own. As always, the answers will

follow the practice problems.


LESSON 5

EXERCISE – PLACE VALUES

Instructions:

1. 2

Use the place value chart as needed. Write the place value of the

digit in each problem.

millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones (units)

2 is in __________ place

2. 25

millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones (units)

2 is in __________ place

3. 327

millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones (units)

3 is in __________ place


LESSON 5

4. 1,527

5. 123,345

millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones (units)

millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones (units)

1 is in __________ place

5 is in __________ place

1 is in __________ place

2 is in __________ place

4 is in __________ place


LESSON 5

ANSWERS TO EXERCISE

1. 2

Answer:

2

ones (units)

2 is in ones place.

2. 25

Answer:

tens

2 5

ones (units)

2 is in tens place.

3. 327

Answer:

hundreds

tens

3 2 7

ones (units)

3 is in hundreds place.


LESSON 5

4. 1,527

Answer:

thousands

hundreds

tens

1 5 2 7

ones (units)

1 is in thousands place.

5 is in hundreds place.

5. 123,345

Answer:

ten thousands

thousands

hundreds

tens

hundred thousands

1 2 3 3 4 5

ones (units)

1 is in hundred thousands

place.

2 is in ten thousands place.

4 is in tens place.


LESSON 6

READING AND

EXPRESSING NUMBERS

I hope you won’t find Lesson 6 too difficult.

We did not talk about all place values in Lesson

5. We could have the place value chart show

numbers greater than millions. After millions

place, there are billions, trillions, and so forth.

We will not go into the entire number system

in this course. I just want you to understand

that the place value chart keeps moving to the

left as numbers get bigger.

ten thousands

thousands

hundreds

tens

millions

hundred thousands

0 0 0 0 0 0 0

ones (units)

In this lesson, you’re going to write whole

numbers in words.

Check out the

commas.

Some place value charts look like this:

0 _ 0 _ 0 _ , 0 _ 0 _ 0 _ , _ 0 _ 0 _ 0 , _ 0 _ 0 _ 0

billions

millions

thousands

ones


LESSON 6

Do you see the commas in the previous chart

Commas are written from right to left after every

third number. This helps the reader see place

values. In the number 9592136, you will have a

comma before the 1 and the 5. Always count

back three numbers from ones place.

9,592,136

start here

1 3 2 1 3 2

1 count

Where would you put commas in this

number

14035068

You should place one between the 5 and 0.

Another one goes between 4 and 0. Did you get

it right 14,035,068

These commas show sets of numbers. Look

at the place value chart again.

0 _ 0 _ 0 _ , 0 _ 0 _ 0 _ , _ 0 _ 0 _ 0 , _ 0 _ 0 _ 0

ones

billions

millions

thousands

Do you see a set of billions a set of millions

thousands and ones These sets are important

in reading numbers.


LESSON 6

You read numbers according to values on the

chart. Think about the number 5,468. You can

place the digits on the chart as shown beginning

on the right side above ones.

_ _ _ , _ _ _ , _ _ _ 5 , _ 4 _ 6 _ 8

ones

billions

millions

thousands

We write this number in words as: five

thousand, four hundred sixty-eight. The 5 falls

in the set of thousands, and so we say or

write … five thousand. The comma behind the

five shows a move to the next set of three.

thousands

hundreds

tens

5 4 6 8

ones (units)

The 4 is in the hundreds place, and we say or

write four hundred. The tens place is always

written with numbers counting by tens: ten,

twenty, thirty, forty, fifty, sixty, seventy, eighty,

or ninety. In this case, we have six in the tens

place, so we say or write sixty. The ones place is

written just like we talk: one, two, three, four,

five, six, seven, eight, or nine. In this number,

we have eight (ones).


LESSON 6

Let’s practice writing another number in

words. Think about the number 11,035,018.

First, we place the digits on the place value chart.

_ 1 _ 1 _ , _ 0 _ 3 _ 5 , 0 _ 1 _ 8_

ones

millions

thousands

The first two digits fall in the set of millions,

so we write eleven million. The comma tells us

to move to the next set, which is thousands. We

would write thirty-five thousand. There is

another comma, so we move to the set of ones

and write eighteen. The number 11,035,018

would be written in words as eleven million,

thirty-five thousand, eighteen.

Hope you win this one!

PLACE #1

VALUE

AWARD


LESSON 6

hundred billions

ten billions

Let’s look again at a place value chart.

billions

hundred millions

ten millions

millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones (units)

The values are marked in blocks of three. The

first block has ones, tens, hundreds. Each can

be written using ones as shown below.

100 ones

10 ones

ones

This next block of three repeats this pattern

with ones replaced by thousands.

100 thousands

10 thousands

thousands

100 ones

10 ones

ones


LESSON 6

The next set of three values shows millions.

100 millions

10 millions

100 millions thousands

100 thousands

10 thousands

thousands

100 ones

10 ones

ones

hundred billions

Though we did not talk about billions in our

lesson on place values, we have used them in

this lesson. You can see the chart continues.

ten billions

billions

hundred millions

ten millions

millions

hundred thousands

ten thousands

thousands

hundreds

tens

ones (units)

Numbers go on forever. I will stop with

billions. What I need you to see are the sets of

three. These are important to reading and

writing numbers.


LESSON 6

Notice I used a hyphen earlier to connect

sixty-eight. We use a hyphen to connect the

rightmost two digits of each set of numbers

between:

21 – 29

31 – 39

41 – 49

51 – 59

61 – 69

71 – 79

81 – 89

91 – 99

This is not easy to see at first. Let’s write

another number to see what I mean.

26,732

We write this as twenty-six thousand, seven

hundred thirty-two.

rightmost

hundred millions

ten millions

millions

hundred thousands

2 6 7 3 2

rightmost

ten thousands

thousands

hundreds

tens

rightmost

ones (units)

The digits 2 and 6 are the rightmost in the

set showing thousands, so we write twenty-six

thousand. The digits 3 and 2 are rightmost in

the set showing ones. We write seven hundred

thirty-two.


It is not correct to say or write the word and

between numbers.

LESSON 6

Examples of writing numbers with words:

ones place

2 — two

5 — five

tens place

10 — ten

11 — eleven

12 — twelve

*15 — fifteen

20 — twenty

21 — twenty-one

47 — forty-seven

65 — sixty-five

*Note: The teens are written as thirteen, fourteen, fifteen, sixteen,

seventeen, eighteen, nineteen.

hundreds place

*123 — one hundred twenty-three

291 — two hundred ninety-one

504 — five hundred four

*Note: You do not use “and” between the numbers.

thousands place

4,689 — four thousand, six hundred eighty-nine

9,999 — nine thousand, nine hundred ninety-nine

ten thousands place

54,535 — fifty-four thousand, five hundred thirty-five

Did you notice the hyphens More

importantly, do you see the place values You

should try some on your own. As always, the

answers will follow.


LESSON 6

EXERCISE – WRITING NUMBERS

Instructions:

Fill in the blanks with the correct words for each number.

1. 29,450

twenty-nine_______________, four hundred fifty

2. 2,600

two ____________, six _____________

3. 3,495,200,000

three__________________,

four hundred ninety-five______________,

two hundred______________

4. 23,009

twenty-three_______________, nine

5. 15,068

_____________ thousand, _____________ _____________


LESSON 6

Instructions:Write the numbers for the following words.

6. fifty-four

_______________

7. six thousand, fifty-six

_______________

8. eight million, five hundred thousand, four

_______________

Instructions:

Look at the following words and numbers. Decide what’s wrong

in each pair.

9. 543,268 five hundred forty three thousand two hundred

sixty eight

_________________________________________________

_________________________________________________

10. 800,000 eighty thousand

________________________________________________________


LESSON 6

ANSWERS TO EXERCISE

1. Answer: twenty-nine thousand, four hundred fifty

2. Answer: two thousand, six hundred

3. Answer: three billion,

four hundred ninety-five million,

two hundred thousand

4. Answer: twenty-three thousand, nine

5. Answer: fifteen thousand, sixty-eight

6. Answer: 54

7. Answer: 6,056

8. Answer: 8,500,004

9. Answer: no comma after thousand

hyphens are missing in forty-three and sixty-eight

10. Answer: eighty should be eight hundred


LESSON 7

RECOGNIZING PLACE

VALUES IN MONEY

Lesson 7 also uses place value. As I said, the

place value chart keeps adding places to the left

as numbers get bigger.

Now, let’s think about that for a minute. As

we add places to the left, we can show numbers

getting larger. What if I add a place value to the

right of the ones place Will I show numbers

smaller than one The answer is yes. However, I

have to have a way to show where the ones place

is located. We use a dot called a decimal point. A

decimal point is placed after the number that is

in the ones place. The decimal point makes it

possible to show place values less than one.

I want to know all about money.


LESSON 7

5 ones can be written as:

5

5.

5.0

5.00

All of these numbers mean 5 ones.

millions

There are often reasons to show these place

values. Money is an example where we need to

be able to show amounts less than one. We write

amounts of money using two places to the right

of the decimal point. Therefore, let’s talk about

these two place values.

hundred thousands

ten thousands

thousands

hundreds

tens

ones (units)

0 0 0 0 0 0 5 . 0 0

decimal point

tenths

hundredths


LESSON 7

I want to keep this lesson as simple as possible.

I do not plan to explain decimals. At this level,

you should know that decimals or numbers to

the right of a decimal point show amounts less

than one. The place value just to the right of the

decimal point shows tenths and the next place

shows hundredths. Be careful as you study tenths

and hundredths because their names are so close

to tens and hundreds. Remember they are on

the other side of the decimal point. The th on

the end of the words will help remind you that

tenths and hundredths are parts of one whole.

Money is often shown using tenths and

hundredths. One dollar and twenty-five cents

is written as $1.25. We read the decimal point

as the word and. We say one dollar and twentyfive

cents.

1 . 2 5

ones (units)

decimal point

tenths

hundredths

This means there is one dollar. Notice it is in

the ones place. The twenty-five cents is the

amount of money less than one dollar. The 2 is

in the tenths place and the 5 is in the hundredths

place.


LESSON 7

Ten dollars and seventy-five cents is written

as $10.75. Do you see how the numbers to the

left of the decimal point follow the place value

chart

tens

ones (units)

1 0 . 7 5

decimal point

tenths

hundredths

There is 1 ten and no ones. The seventy-five

cents is the part less than one dollar.

Let’s move on to Lesson 8 and talk more

about money.


LESSON 8

COUNTING MONEY

Lesson 8 is about counting money. We’re

going to practice counting money and see

different ways to write it. You may already know

how to count money. If you do, you may move

on to the practice problems at the end of this

lesson. It is a good idea, even if you know how

to count money, to do these problems for review.

Usually, it’s not as easy to write units of money

as it is to count them.

Money comes in several forms. Let’s take a

look at some of them:

penny nickel dime quarter

$.01 $.05 $.10 $.25

one-dollar bill

five-dollar bill

$1.00 $5.00

ten-dollar bill

twenty-dollar bill

$10.00 $20.00


LESSON 8

Remember, the symbol $ means dollars. It

means money is being shown. There are 100

pennies in one dollar. We usually show the

number of pennies or cents using the hundredths

place value. Do you remember the hundredths

place from the last lesson

$.08 8 cents

$.02 2 cents

The amount, $.10, shows ten pennies or ten

cents. Notice the decimal point. Two places to

the right of it shows hundredths. This means

we have 10 out of 100 pennies (or one dollar).

We write 50 cents or 50 pennies as $.50.

Sometimes a zero is placed in the ones place:

$0.50

This means the same amount as $.50.

Remember …

$ dollars

¢ cents


LESSON 8

We can also write this amount as 50¢ using a

different symbol that shows money. The symbol

¢ means cents. Earlier I wrote $.05 under the

picture of the nickel. We read this as five cents

even though we write a dollar sign in front of it.

The placement of the 05 to the right of the

decimal shows that a nickel is part of a dollar. In

the same way, we can write $.25 for 25 cents.

Can you read these amounts

$.01 = 1 cent (1¢ or 1 penny)

$.05 = 5 cents (5¢ or 1 nickel)

$.10 = 10 cents (10¢ or 1 dime)

$.25 = 25 cents (25¢ or 1 quarter)

$1.00 = 1 dollar

$5.00 = 5 dollars

$10.00 = 10 dollars


LESSON 8

Pennies are counted by ones. If we have 4

pennies, we have 4 cents. Nickels are counted

by fives since a nickel means the same as 5

pennies. (5, 10, 15, 20, 25, 30, 35, 40, …)

If I have two nickels,

I count by fives — 5,10 — I have 10 cents.

If I have 4 dimes,

I count by tens — 10, 20, 30, 40 — I have 40

cents.

If I have 3 quarters, I count by 25s.

25, 50, 75 — I have 75¢


LESSON 8

If I have 4 quarters, I have $1.00. This means

that every time I have four quarters, I will have

$1.00.

Let’s practice counting money together. You

must know how much each coin is worth. If

you do not, review page 75.

When counting money, start with the coins

that have the greatest value.

quarter dime nickel penny

We have one quarter. It is worth 25¢. Then,

we have a dime. It is worth 10¢. Next, we have

a nickel worth 5¢. Last, we have 1¢.

Add:

• one quarter 25¢

• one dime 10¢

• one nickel 5¢

• one penny + 1¢

41¢

We have $.41 or 41 cents.


LESSON 8

Let’s look at another example.

25¢ + 25¢ + 1¢

We have $.51 or 51 cents.

one-dollar bill

five-dollar bill

ten-dollar bill

twenty-dollar bill

Paper money seems easier to count for some

people. It has the amount written on each bill.

As with coins, always start counting with the

bill of greatest value. This can make it easier to

count. If you have 20s, count by 20s. If you

have 10s, count by 10s. If you have 5s, count by

5s.

Let’s practice counting some bills.


LESSON 8

START

COUNTING2

TOTAL

$20 = $20

$20 + $20 = $40

$40 + $10 = $50

$50 + $5 = $55

$55 + $1 = $56

$56 + $1 = $57

You should count $57.00. Notice the bills of greatest value were counted

first.


LESSON 8

START

COUNTING2

TOTAL

$50 = $50

$50 + $50 = $100

$100 + $50 = $150

$150 + $20 = $170

$170 + $5 = $175

$175 + $5 = $180

continued


LESSON 8

TOTAL

$180 + $5 = $185

$185 + $1 = $186

$186 + $1 = $187

You should get $187. Notice again, the bills of greatest value were counted

first.


LESSON 8

Try this one on your own. The answer is on

the following pages.


LESSON 8

TOTAL

$20 = $20

$20 + $20 = $40

$40 + $20 = $60

$60 + $20 = $80

$80 + $20 = $100

$100 + $20 = $120

continued


LESSON 8

TOTAL

$120 + $5 = $125

$125 + $.25 = $125.25

$125.25 + $.25 = $125.50

$125.50 + $.25 = $125.75

$125.75 + $.25 = $126.00

You should count $126.


LESSON 8

Let’s practice counting one more time. The

value of each bill or coin is shown being added

together – largest amount to smallest.

20 + 20 + 5 + 1 + 1 + .25 + .10 + .10 + .01 + .01 = $47.47

Now, you should practice on your own. As

always, answers will be provided after you do

the work. Good luck!


LESSON 8

EXERCISE – COUNTING MONEY

Instructions:

Write the amount of money as numbers.

1. fifty-six cents __________

2. twenty-seven dollars __________

3. four hundred eighty dollars __________

4. sixty-eight dollars and forty-two cents __________

5. one penny __________

Instructions:

Count the following money. Write the total beside the drawing.

6.

____________

7. _____________


LESSON 8

8.

_ ____________

9.

____ _________

10.

_____________


LESSON 8

ANSWERS TO EXERCISE

1. Answer: $.56 or 56¢

2. Answer: $27.00 or $27

3. Answer: $480.00 or $480

4. Answer: $68.42

5. Answer: $.01 or 1¢

6. Answer: $35.41

7. Answer: $.32 or 32¢

8. Answer: $120.02

9. Answer: $1.22

(Did you count the quarters first … then dimes This

can make it easier.)

10. Answer: $17.00 or $17


LESSON 9

READING AND

WRITING FRACTIONS

You are almost finished with this workbook.

You only have one more lesson to do after this

one. You should be proud of your progress!

This lesson is about fractions. Fractions are

pieces of larger things. For instance, if you have

a piece of pie, you have a fraction of the pie.

Let’s take a look at some pictures that should

help you see this clearer.

This is one whole

sandwich. Soon there

will be one half left.

This is a whole circle. We can draw a line

through the center of the circle. When we do,

we have divided the circle in half (written 1 2 ).


LESSON 9

The circle is in two pieces. We have made

fractions, parts of a whole. To show a fraction,

we have shaded one of the two pieces. The

fraction is written:

1

2

This means one out of two parts.

The top number is the shaded part (called

the numerator). The bottom number is the total

number of pieces (the denominator).

Let’s look at another circle:

We have divided this circle into four pieces –

showing it as fourths.


LESSON 9

3

4

If we shade 3 of the 4 pieces, we have shaded

of the circle.

Now, think about the lesson on money. When

we talked about money, we said that every time

you had 4 quarters, you would have one dollar.

Four quarters makes one whole dollar. This

means that one quarter is 1 4

of a dollar.

(Sometimes when we write the fraction 1 4 , we

say one quarter of something.)

is the

same

as

So,

is 1 of one dollar 4 25¢

25¢ 25¢

25¢


LESSON 9

What part of a dollar is two quarters or fifty

cents

Fifty cents $.50 is half of a dollar.

25¢

50¢

25¢

Make sure that when you read fractions you

read the top number first. Then, read the bottom

number as half, third, fourth, fifth, and so on.

For example, 3 4

is read three-fourths.

The bottom number of a fraction shows how

many equal pieces make up the whole. The top

number shows how many pieces you are talking

about. The larger the number on the bottom,

the smaller the parts compared to the whole.

Think about that for a minute. Do you see the

parts getting smaller as the bottom number gets

bigger For example:

1

4

1

8

1

16

1

32

Which was larger, 1 4 or 1 Look at the

16

pictures. You can see 1 4 is larger than 1

16 . When

the top number is the same, the larger the

bottom number, the smaller the fraction.


LESSON 9

If the bottom number doesn’t change and the

top number gets larger, then you have more parts

of the whole. For example:

1

8

2

8

3

8

What is more, 1 8 or 3 The top number

8

means more parts. Three parts are more than

4

8

one part. Therefore, 3 8 is more than 1 8 .

What if the number on the top and the

bottom of the fraction are the same Then, you

have a whole, or 1.

4

4

3

3

8

8

A ruler is often marked off in inches. Each

inch is divided into halves, fourths, eighths, and

sixteenths of an inch.

1

2

1

4

1

8

1

16

1 1

We will not practice using fractions to

measure distance. You should see that fractions

are found in everyday activities, like using a ruler

to measure distance.


LESSON 9

EXERCISE – FRACTION OF A WHOLE

Instructions:

What part of each figure is shaded

1. 2.

________

________

3. 4.

________

________

5. 6.

________

_______


LESSON 9

7. Write 2 in words.

3

_______________

8. Write seven-eighths using numbers.

_______________

9. Three quarters is what fraction of a dollar

_______________

10. Draw a circle and shade 5 6 of it.


LESSON 9

ANSWERS TO EXERCISE

1. 2.

Answer:

1

6

Answer:

1

4

3. 4.

Answer:

2

9

Answer:

5

6

5. 6.

Answer:

5

8

Answer:

5

16


LESSON 9

7. Write 2 3

in words.

Answer:

two-thirds

8. Write seven-eighths using numbers.

Answer:

7

8

9. Three quarters is what fraction of a dollar

Answer:

3

4

of a dollar ($.75)

10. Draw a circle and shade 5 6

of it.

Answer:

You should have drawn 6 parts the same size. You

should have shaded any 5 of the 6 parts.


LESSON 10

You have made it to the end of this level. I

am proud of you. I hope that you learned

something and think that the review was good

for you. Let’s see exactly how much you

remember. The last lesson is a Posttest. You

should be able to do all of the problems. As

always, the answers will follow the questions. If

you cannot do a problem, you should review

the lesson with those problems. Good luck!

Don’t peek!


POSTTEST

EXERCISE – POSTTEST

Instructions:

Select the letter that shows the time or measurement on each clock

or meter.

1. __________

a. 4:03

b. 3:04

c. 3:20

d. 4:15

2. __________

a. 6:40

b. 8:30

c. 8:06

d. 6:20

3. __________

a. 20 till 5:00

b. 40 till 5:00

c. 20 after 8:00

d. 20 till 8:00


POSTTEST

4. __________

a. 20 amperes

10

20 30

40

b. 20 1 2 amperes

0

50

c. 30 amperes

d. 25 amperes

5. __________

a. 00584

b. 00564

c. 11684

d. 11695

6. __________

a. 35˚

b. 41˚

c. 32˚

d. 29˚

120

110

100

90

140

130

THERMOMETER

-20

-10

0

10

20

30

80

40

70 60 50


POSTTEST

Instructions:

Count the money. Then, select the letter showing the correct

amount.

7.

a. $30.40

b. $60.45

c. $50.45

d. $50.40

8.

a. $6.25

b. $15.45

c. $6.65

d. $15.65


POSTTEST

9.

a. $18.00

b. $22.00

c. $30.00

d. $17.00

Instructions:

Look at the number: 5,382. Select the letter that shows the place

value of the digit.

10. 5

a. thousands

b. hundreds

c. tens

d. ones

11. 2

a. thousands

b. hundreds

c. tens

d. ones


POSTTEST

Instructions:

Select the letter that best completes or answers each problem.

12. Three-tenths is written as:

a.

b.

10

3

3

10

c. 310

d. 103

13. Select the circle that shows 9

10 .

a. c.

b. d.


POSTTEST

14. What fraction of this box is shaded __________

a.

b.

c.

d.

3

4

3

8

4

3

8

3

15. The symbol ˚ following a number means:

a. circle

b. number

c. pounds

d. degrees

16. Look at $123.25. The 25 means:

a. 25 dollars

b. 2 tens and five ones

c. 25 quarters

d. a part of one dollar


POSTTEST

17. Select the two numbers that mean the same amount.

a. 0.2 and 2.0

b. 7.0 and 7.00

c. 5.6 and 6.5

d. 0.0 and 0.1

18. The number 12,450 is written as:

a. twelve thousand, four hundred fifty

b. twelve ten thousand, four hundred fifty

c. twelve million, four thousand, fifty

d. one hundred two thousand, forty-five hundred

19. Choose the statement about percent that is true. (Think

about the pictures of percent that you studied.)

a. 10% is more than half of something

b. 50% is all of something

c. 50% is less than half of something

d. 100% is all of something

20. If you see 20# paper, it means:

a. 20 pieces of paper

b. 20 pound weight paper

c. number 20 paper

d. 20 percent paper


POSTTEST

ANSWERS TO EXERCISE

1. Answer: c. 3:20

2. Answer: b. 8:30

3. Answer: a. 20 till 5:00

4. Answer: d. 25 amperes

5. Answer: a. 00584

6. Answer: c. 32˚

7. Answer: d. $50.40

8. Answer: b. $15.45

9. Answer: b. $22.00

10. Answer: a. thousands


POSTTEST

11. Answer: d. ones

12. Answer: b. 3

10

13. Answer: b.

14. Answer: b. 3 8

15. Answer: d. degrees

16. Answer: d. a part of one dollar

17. Answer: b. 7.0 and 7.00

18. Answer: a. twelve thousand, four hundred fifty

19. Answer: d. 100% is all of something

20. Answer: b. 20 pound weight paper


YOUR SCORE

The following chart will provide you with scoring information. Count the

number of correct answers on your Posttest. Find that number in the left

column. The number in the right column is your score. Repeat the exercises

that you missed and, if needed, go back to the lesson that talks about those

topics.

NUMBER OF

CORRECT ANSWERS

SCORE

20 100%

19 95%

18 90%

17 85%

16 80%

15 75%

14 70%

13 65%

below 13 review entire level


SUMMARY

Well, how did you do on the Posttest If you

scored 90% or higher, you are ready for Level 2.

Don’t be discouraged if you scored below 90%.

There are a lot of skills to learn. Practice, practice,

practice! You can do it!

Remember, learning basic math skills will

help you in the workplace and throughout your

life.

You should be proud of your progress!


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