Adult Literacy Fundamental Mathematics: Book One

Wendy Tagami, Liz Girard, BC Open Textbook Project, BCcampus, and British Columbia Ministry of Advanced Education and Labour Market Development

To the extent possible under law, Wendy Tagami, Liz Girard, BC Open Textbook Project, BCcampus, and British Columbia Ministry of Advanced Education and Labour Market Development has waived all copyright and related or neighboring rights to Adult Literacy Fundamental Mathematics: Book One, except where otherwise noted.

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Unit 1

Number Sense

Topic A: Emotions and Learning

Emotions, or what we feel about something, play a big part in how we learn. If we are calm, we learn well. If we are afraid or stressed, we do not learn as well. Many people are afraid of math. They fear making a mistake. “Math anxiety” is the fear of math.

People who suffer from math anxiety may get headaches, sick stomachs, cold hands or they may just sweat a lot or just feel scared.

Do you suffer from math anxiety?

Read the list below and put a check mark (√) beside the ones you feel.

Are your palms moist?

Is your stomach fluttering?

Do you feel like you can’t think clearly?

Do you feel like you would rather do anything else than learning math?

Are you breathing faster than normal?

Is your heart pounding?

Do you feel cold?

Add any other things you are feeling.

Math Anxiety

“Math anxiety” or the fear of math is a learned habit. If it is learned, it can be unlearned. Most math anxiety comes from bad memories while learning math. It may be from doing badly on a test or asking a question then being made fun of. These bad memories can make learning math hard.

Everyone can learn math. There is no special talent for math. There are some people who are better at math than others, but even these people had to learn to be good at math.

How to Deal with Math Anxiety

Anyone can feel anxiety that will slow down learning. The key to learning is to be the “boss” of your anxiety.

One way to be the “boss” is to relax. Try this breathing exercise.

Start by breathing in slowly to the count of four. It may help to close your eyes and count. Now hold your breath for four counts and then let your breath out slowly to the count of four. The counting is silent and should follow this pattern: “breathe in, two, three four; hold, two, three, four; breathe out, two, three, four; wait, two, three four.” With practice, the number of counts can be increased. This is an easy and good way to relax.

Now try this exercise quietly and repeat it five times slowly.

Each time you feel anxious about learning, use the breathing exercise to help calm yourself. Ask yourself if what you tried worked. Do you feel calmer?

Remember learning to deal with your math anxiety may take some time. It took you a long time to learn “math anxiety”, so it will take some time to overcome it.

Topic B: Counting

To learn to read, you first need to learn the letters of the alphabet. Once you know the alphabet, you put the letters together to make words, then sentences, then paragraphs and then stories.

Those letters become the “tools” used to write everything.

The same is true for math. In math we use digits. The digits are:

0123456789

Digits are named after our fingers. Our fingers are also called digits. The mathematics term comes from the days of counting on our fingers. We have ten fingers and there are ten digits. We use the letters of the alphabet to make up words, and we use digits to make up numbers. There are two ways to write numbers. You can write them as numerals. You can write them using word names.

Numeral

WordName

0

zero

1

one

2

two

3

three

4

four

5

five

6

six

7

seven

8

eight

9

nine

Counting is matching the number name to the things being counted. You see a bowl of apples on the table. You want to know how many apples are in the bowl. You answer that question by saying “There are one, two, three, four apples.” You are giving the number names “one”, “two”, “three,” and “four” to the apples. The last number you say is the total number of apples.

ExerciseOneCount the number of shapes in each picture. Then write the

numeral and the word name. Check your work using the answer key at the end of the exercise.

Numeral:3 Word name: three
Example:

Numeral: Word Name:
Numeral: Word Name:
a)b)

Numeral: Word Name
c)

Numeral: Word Name:
d)

Exercise One – Answer Key
Numeral: Word Name:
Numeral: Word Name:
e)f)

Numeral:Word Name:
Numeral: Word Name:
g)h)

Numeral: Word Name:
i)

a)

2, two

b)

6, six

c)

8, eight

d)

9, nine

e)

1, one

f)

5, five

g)

7, seven

h)

4, four

i)

0, zero

Need More Practice?

Ask your instructor for the dominoes to do this page. Take the dominoes zero-zero to five- five. Flip them over so you cannot see the dots. Pick a domino and flip it over. Draw the number of dots then count the number of dots. Write the numeral and word name. Have your instructor check these for you.

Example:

● ●

●●

●●

Numeral: 6 Word Name: six

a) b)

Numeral: Numeral:

Word Name: Word Name:

c) d)

Numeral: Numeral:

Word Name: Word Name:

e) f)

Numeral: Numeral:

Word Name: Word Name:

Exercise Two

Here are the numerals from one to ten.

1

2

3

4

5

6

7

8

9

10

Practice writing them below.

Now practice writing the numerals from one to ten in the following. Try to do them without looking. Check your work using the answer key at the end of the exercise.

a)

1

3

5

7

9

b)

2

4

6

8

10

c)

1

4

7

d)

3

6

9

e)

1

4

7

f)

1

5

9

g)

1

6

h)

5

i)

Answers to Exercise Two

a)

2

4

6

8

10

b)

1

3

5

7

9

c)

2

3

5

6

8

9

10

d)

1

2

4

5

7

8

10

e)

2

3

5

6

8

9

10

23467810
f)

g)

2

3

4

5

7

8

9

10

1234678910
h)

i)

1

2

3

4

5

6

7

8

9

10

Topic B: Self-Test Mark /18 Aim 15/18

Count the number of things in each picture, then write the numeral and the

word name. 8 marks

- ●●● ●● ●
b)

Numeral:Numeral:

Word Name: Word Name:

● ●● ●● ●● ●
●●●● ● ●● ● ●
c)d)

Numeral:Numeral:

Word Name: Word Name:

- Write the numerals from one to 10. 10 marks

Topic B: Self-Test – Answer KeyA:a)0, zerob) 6, sixc) 8, eightd) 9, nineB:

1

2

3

4

5

6

7

8

9

10

Emotions Check

How are you feeling? Are your palms moist? How is your breathing?

Take control. Be the boss. If you are feeling anxious, practice your breathing exercise.

Remember: breathe in slowly to the count of four, hold it for the count of four and breathe out slowly to the count of four.

Topic C: Place Value

As you know, we count much higher than ten in our world. Each place in a number has a value.

The ones place tells how many ones there are.

3 means 3 ones

0 means 0 ones

9 means 9 ones

9 is the largest amount that we can express (write or say) with one digit.

The tens place shows how many tens there are. The ones place must have a digit in it before there can be a digit in the tens place.

Every ten is tenones.

=

43 means 4 tens and 3 ones

20 means 2 tens and 0 ones. The zero holds the ones place.

99 means 9 tens and 9 ones. 99 is the largest amount that we can express (write or say) using only two digits.

Exercise OneFill in the blanks to make each sentence true. Draw a

picture for questions c, f, h and j like the examples. Check your work using the answer key at the end of the exercise. Ask your instructor to check your sketches.

Example: 49 means 4tens and 9ones

- 37 means tens and ones.

- 65 means tens and ones.

- 56 means tens and ones.

(Draw your picture below.)

- 87 means tens and ones.

- 33 means tens and ones.

- 60 means tens and ones.

(Draw your picture below.)

- 70 means tens and ones.

- 44 means tens and ones.

(Draw your picture below.)

- 98 means tens and ones.

- 75 means tens and ones.

(Draw your picture below.)

Exercise One – Answer Key

a)

3 tens, 7 ones

b)

6 tens, 5 ones

c)

5 tens, 6 ones

d)

8 tens, 7 ones

e)

3 tens, 3 ones

f)

6 tens, 0 ones

g)

7 tens, 0 ones

h)

4 tens, 4 ones

i)

9 tens, 8 ones

j)

7 tens, 5 ones

The place to the left of the tens place is the hundreds place. It shows how many hundreds there are. A number written using three whole digits has a hundreds place, a tens place, and a ones place.

Every hundred is ten tens – every hundred is the same as one hundred ones.

100100100

425 means 4 hundreds, 2 tens, and 5 ones.

354 means 3 hundreds, 5 tens, and 4 ones.

ExerciseTwoFill in the blanks to make each sentence true. Draw a picture

for questions c, e, and h, like the examples. Check your work using the answer key at the end of the exercise. Ask your instructor to check your sketches.

- 190 = 1hundreds, 9tens, 0ones

- 555 = hundreds, tens, ones

- 309 = hundreds, tens, ones

(Draw your picture below.)

- 499 = hundreds, tens, ones

- 480 = hundreds, tens, ones

(Draw your picture below.)

- 999 = hundreds, tens, ones

- 657 = hundreds, tens, ones

- 125 = hundreds, tens, ones

(Draw your picture below.)

i)212 = hundreds, tens, ones

b)

5 hundreds, 5 tens, 5 ones

c)

3 hundreds, 0 tens, 9 ones

d)

4 hundreds, 9 tens, 9 ones

e)

4 hundreds, 8 tens, 0 ones

f)

9 hundreds, 9 tens, 9 ones

g)

6 hundreds, 5 tens, 7 ones

h)

1 hundred, 2 tens, 5 ones

i)

2 hundreds, 1 ten, 2 ones

Answers to Exercise Two
ExerciseThreeCount the hundreds, tens, and ones shown in the drawings.

The pictures will help you understand the quantity of a number. Then write the numeral. The first one is done for you. Check your work using the answer key at the end of the exercise.

a)

2hundreds 0tens 3ones = 203

b)

hundredstensones =

c)

hundredstensones =

d)

hundredstensones =

e)

hundredstensones =

Answers to Exercise Threeb)4 hundreds, 3 tens, 1 one, 431d)3 hundreds, 1 ten, 6 ones, 316c)1 hundred, 8 tens, 0 ones, 180e)2 hundreds, 0 tens, 3 ones, 203

Need more practice?

Ask your instructor for some play money. Using the one, ten and hundred dollar bills practice trading ten of one type of bill for one of the next value.

Example:

ABE Bucks$1One
ABE Bucks$1One

ABE Bucks$1One
ABE Bucks$1One

ABE Bucks$1One
ABE Bucks$1One
ABE Bucks$10Ten
equals

ABE Bucks$1One
ABE Bucks$1One

ABE Bucks$1One
ABE Bucks$1One

ExerciseFourWrite the place value name (ones, tens, hundreds) for each

underlined digit. Check your work using the answer key at the end of the exercise.

a)

622

hundreds

b)

468

tens

c)

920

d)

920

e)

648

f)

426

g)

534

h)

555

i)

451

j)

901

k)

226

l)

486

c)

ones

d)

hundreds

e)

tens

f)

ones

g)

hundreds

h)

tens

i)

tens

j)

ones

k)

hundreds

l)

ones

Answers to Exercise Four
ExerciseFiveUnderline the digit for the place value named. Check your work

using the answer key at the end of the exercise.

a)

hundreds

416

b)

tens

368

c)

tens

364

d)

hundreds

456

e)

ones

206

f)

ones

634

g)

hundreds

742

h)

hundred

543

i)

tens

221

j)

ones

100

k)

ones

169

l)

tens

684

a)

4

b)

6

c)

6

d)

4

e)

6

f)

4

g)

7

h)

5

i)

2

j)

0

k)

9

l)

8

Answers to Exercise Five
EmotionsCheck

How are you feeling? Are your palms moist? How is your breathing? Take control. Be the boss. If you are feeling anxious, practice your breathing exercise.

Remember: breathe in slowly to the count of four, hold it for the count of four and breathe out slowly to the count of four.

Reading and Writing Numerals

You know that the digits are 0 1 2 3 4 5 6 7 8 9 and that digits are arranged in different places so we can count larger amounts than our ten fingers!

When we use digits we call what we write the numeral.

328 is a numeral 46 is a numeral 3 is a numeral

We use numerals to represent numbers.

If we think about language instead of mathematics it will be clearer.

Letters are used to make words. We respond to the meaning of words.

Digits are the “letters” of math. Numerals are the “words” of math. Numbers are the “meaning” of math.

Now you know the place value of digits up to three places. Next you will learn to read and write numerals and number words. Some of the words to read and spell may be new to you.

The numerals from 1 to 12 have special words. These are

0

zero

7

seven

1

one

8

eight

2

two

9

nine

3

three

10

ten

4

four

11

eleven

5

five

12

twelve

6

six

The number names for numerals from 13 to 19 are made up of two parts. The first part tells us how many units. The second part (“teen”) tells us there is also 1ten.

13

thirteen

three units and 1 ten

14

fourteen

four units and 1 ten

15

fifteen

five units and 1 ten

16

sixteen

six units and 1 ten

17

seventeen

seven units and 1 ten

18

eighteen

eight units and 1 ten

19

nineteen

nine units and 1 ten

ExerciseSixWrite the word name for each number. Try not to look at the

list. Check your work using the answer key at the end of the exercise.

a)

8

b)

16

c)

7

d)

15

e)

5

f)

11

g)

9

h)

18

i)

6

j)

17

k)

4

l)

14

m)

12

n)

13

o)

19

p)

3

Answers to ExerciseSix

a) eight

b)

sixteen

c) seven

d) fifteen

e)

five

f) eleven

g) nine

h)

eighteen

i) six

j) seventeen

k)

four

l) fourteen

m) twelve

n)

thirteen

o) nineteen

p) three

The word names for the numbers 20 to 90 are also made up of two parts. The first part tells us how many groups of tens. The second part (“ty”) tells us we are counting groups of tens and not something else. The “-ty” may have come from a shortening of the word “ten”.

20

twenty

two tens

30

thirty

three tens

40

forty

four tens

50

fifty

five tens

60

sixty

six tens

70

seventy

seven tens

80

eighty

eight tens

90

ninety

nine tens

The names for the numbers between groups of tens also follow a pattern. The first number tells us how many tens. The second number tells us how many ones.

TensOnes

Tens Ones

Tens Ones

20

twenty

30

thirty

40

forty

21

twenty-one

31

thirty-one

41

forty-one

22

twenty-two

32

thirty-two

42

forty-two

23

twenty-three

33

thirty-three

43

forty-three

24

twenty-four

34

thirty-four

44

forty-four

25

twenty-five

35

thirty-five

45

forty-five

26

twenty-six

36

thirty-six

46

forty-six

27

twenty-seven

37

thirty-seven

47

forty-seven

28

twenty-eight

38

thirty-eight

48

forty-eight

29

twenty-nine

39

thirty-nine

49

forty-nine

The written names for numbers that have tens and ones are written with a hyphen (-) between them. This pattern with the hyphen continues up to ninety-nine (99).

ExerciseSevenWrite the word names for these numbers. Check your work

using the answer key at the end of the exercise.

a) 24 twenty-fourb) 35 thirty-five

c) 83d) 46

e) 59f)20

g) 71h) 94

i)62j)53

Answers to Exercise Sevenc)eighty-threef)twentyi)sixty-twod)g)j)forty-sixseventy-one fifty-threee)h)fifty-nineninety-four

ExerciseEightWithout looking back, write the word names for these

numbers.Check your work using the answer key at the end of the exercise.

a)

44

forty-four

b)

97

c)

71

d)

86

e)

53

f)

25

g)

15

h)

38

30

Book 1

Answers to Exercise Eightb) ninety-sevene) fifty-threeh) thirty-eightc) seventy-onef) twenty-fived) eighty-sixg) fifteen

ExerciseNineWrite the numerals for these word names. Check your work

using the answer key at the end of the exercise.

a) ninety-nine 99b) sixty-seven 67

c) eighty-oned) eighteen

e) twenty-sixf)thirteen

g) thirtyh) forty-three

i)sixteenj)twenty

Answers to ExerciseNine

c) 81

d) 18

e) 26

f) 13 i)16

g) 30

j) 20

h) 43

When we write hundreds in words, we need two words. The first word tells us howmany

hundreds. The second word tells us we are counting hundreds.

200twohundred

You now know how to write numbers in words up to 999.

Fundamental Mathematics31

367 is made of

3 hundreds

6 tens

7 ones

Each is written:

three hundred

sixty

seven

Put the parts together:

three hundredsixty-seven

Remember:

hyphen (-) between the tens and units no hyphen anywhere else

no “s” on the hundred

504 is made of5 hundreds0 tens4 onesEach is written:five hundredfourPut the parts together:five hundred four
no „and” between the hundreds place and the tens place Here is another example. Watch out for the empty space!

Here is another example. Watch out for the empty space!

890 is made of

8 hundreds

9 tens

0 ones

Each is written:

eight hundred

ninety

Put the parts together:

eight hundredninety

Here is another example. Watch out for the empty spaces!

100 is made of

1 hundreds

0 tens

0 ones

Each is written:

one hundred

Put the parts together:

onehundred

Remember: empty spaces are not written in words.

ExerciseTenWrite the word names for these numerals. Check your work

using the answer key at the end of the exercise.

a)

623 is made of

Each is written:

Put the parts together:

b)

364 is made of

Each is written:

Put the parts together:

c)

213 is made of

Each is written:

Put the parts together:

d)

405 is made of

Each is written:

Put the parts together:

e)

820 is made of

Each is written:

Put the parts together:

f)704

g) 470

h) 993

i)100

j)972

Answers to Exercise Ten

a)

623 is made of

6hundreds

2tens

3ones

Each is written:

sixhundred

twenty

three

Put the parts together:

six hundredtwenty-three

b)

364 is made of

3hundreds

6tens

4ones

Each is written:

threehundred

sixty

four

Put the parts together:

three hundredsixty-four

c)

213 is made of

2hundreds

1ten

3ones

Each is written:

twohundred

thirteen

Put the parts together:

two hundredthirteen

d)

405 is made of

4hundreds

0tens

5ones

Each is written:

fourhundred

five

Put the parts together:

four hundredfive

e)

820 is made of

8hundreds

2tens

0ones

Each is written:

eighthundred

twenty

Put the parts together:

eight hundredtwenty

f)

seven hundred four

g) four hundred seventy

h)

nine hundred ninety-three

i)one hundred

j)

nine hundred seventy-two

Topic C: Self-Test Mark /17 Aim 14/17

Write the place value for the underlined digit.6 marks

a)

765

b)

903

c)

479

d)

185

e)

732

f)

397

- Write the word names for these numerals. 6 marks

a) 79

b) 492

c) 378

d) 820

e) 405

f) 583

Write the numerals for these word names.5 marks

- five hundred forty-seven

- three hundred eighty

- two hundred seventy-five

- four hundred sixteen

- nine hundred twenty-three

Answers to Topic C Self-testA.a) tensb) tensd) onese) onesc) hundredsf) hundredsB.a) seventy-ninec) three hundred seventy-eighte) four hundred fiveb) four hundred ninety-twod) eight hundred twentyf) five hundred eighty-threeC.a) 547d) 416b) 380e) 923c) 275

Topic D: Ordering Numerals

We arrange numerals in order from smallest to largest. Sorting numbered papers such as order forms, arranging items by the date and comparing prices are some of the ways you use this skill.

Look at two numerals and tell which one is larger. How do you do this?

Exercise OneDraw a box around the larger numeral in each pair.

48
a)43b)2721c)6463

d)2435e)9289f)7281

Answers to Exercise Oneb)27c)64d)35e)92f)81

To compare numerals, look at the place with the largest value.

ExampleA:Compare 63 and 59

Look at the tens place.

63 has a 6 in the tens place. 59 has a 5 in the tens place.

63 is larger than 59.

ExampleB:Compare 496 and 476.

Look at the hundreds – both have 4’s. Look at the tens place.

496 has a 9 in the tens place. 476 has a 7 in the tens place.

496 is larger than 476.

Note: Numerals with one digit are always less than numerals with two digits. Numerals with two digits are always less than numerals with three digits, and so on.

9 is less than 15

87 is less than 107

999 is less than 1 001

ExerciseTwoDraw a box around the larger numeral in each pair. Check your

work using the answer key at the end of the exercise.

46
a)36b)58059c)8767

d)716116e)429449f)289283

g)229329h)230210i)51159

Answers to Exercise Two
j)836935k)3637l)461468

b)

580

c)

87

d)

716

e) 449

f)

289

g)

329

h)

230

i) 159

j)

935

k)

37

l)

468

ExerciseThreeDraw a box around the larger numeral in each pair. Check your

work using the answer key at the end of the exercise.

151
a)148b)129132c)3437

d)325236e)11813f)489423

g)471422h)316322i)876319

b) 132

c) 37

d)

325

e) 118

f) 489

g) 471

h)

322

i) 876

Exercise Three – Answer Key
Now use the same ideas to arrange more than two numerals in order.

For example, to arrange 6, 616, 1, 66, 666, 61, and 16 in order from smallest to

largest, use the following method:

First, sort the numerals with the same number of digits into groups.

6, 166, 16, 61and616, 666

The group of one digit numerals contains 6 and 1. As 1 is smaller than 6, the list starts with 1, then 6.

The group of two-digit numerals contains 66, 61, and 16. Use your skills in ordering numerals to see that 16 is smallest, then 61, and 66 is the largest of this group. The list now reads, 1, 6, 16, 61, 66.

Finally, look at the three-digit numerals, 616 and 666. As 616 is smaller than 666, it will come first. The list now reads: 1, 6, 16, 61, 66, 616, 666.

ExerciseFourArrange these numbers in order from smallest to largest.

Check your work using the answer key at the end of the exercise.

a) 323323323333222

b) 447474477447477

c) 123135152125

d) 472427452475

Answers to Exercise Foura)2, 3, 32, 33, 322, 323, 332c)123, 125, 135, 152b)7, 44, 47, 74, 77, 474, 744d)427, 452, 472, 475

Greater Than, Less Than, Equals

The sign < means “is less than” (smaller than). The sign > means “is greater than” (bigger than).

The greater than and less than signs always point to the smaller number. That is, the point or the tip of the sign is close to the small number.

- < 12means 5 is less than 12

- > 3means 6 is greater than 3

The sign = means “equals” and is used when two amounts are the same.

ExerciseFiveWrite <, >, or = in each blank as needed. Check your work

using the answer key at the end of the exercise.

a)

c)

3 <5

12 9

b)

d)

8 >7

28 28

e)

48 84

f)

376 376

g)

520 530

h)

582 521

i)

674 296

j)

214 251

k)

879 900

l)

784 784

Answers to ExerciseFive

c)

>

d)

=

e)

<

f) =

g)

<

h)

>

i)

>

j) <

k)

<

l)

=

Topic D: Self-Test Mark /12 Aim 10/12

Box the larger number of each pair.6 marks

a)

978

789

b)

566

556

c)

120

142

d)

701

710

e)

430

403

f)

879

987

- Arrange these numerals in order from smallest to largest. 2 marks

a) 7575447547747574775

b) 1823742982437994112

Write >, <. or = in each blank to make a true statement.4 marks

a) 678 768b) 102 100

Answers to Topic D Self-Test
c) 463 846d) 101 101

A. a)

978

b) 566

c) 142

d)

710

e) 430

f) 987

B. a)

<

b) >

c) <

d) =

C. a)

47,

75, 475, 574, 747,

754,

775

b)

18,

37, 112, 237, 429,

824,

994

Topic E: Rounding Numbers

We use numbers a lot in our everyday lives. List some of the ways you use numbers.

You may have written money, shopping, time, and counting as part of your answer.

Think about time. Let’s say it takes eight minutes to walk to the bus. If someone asks you how long it takes, you will probably say, “About ten minutes.”

If you buy a sweater that cost $29, you may say, “Oh, it was around thirty dollars.”

How far is it from Vancouver to Prince George? The map says 796 km, but we would probably say, “About 800 kilometres.”

You have just read examples of roundingnumbers.

We round numbers for many reasons:

We may not know the exact number.

The exact number may not be important for what we are doing.

We may need a quick way to figure something out.

When you are rounding numbers, use zeros to hold the places at the end of the number. Work through the following examples and exercises carefully. Rounding is animportant skill.

Rounding to the Nearest Ten

A number rounded to the nearest ten will have a zero in the ones place. The number will end with 0, 10, 20, 30, 40, 50, 60, 70, 80, or 90.

When rounding to the nearest 10, we are looking for the closest group of 10.

Example:20, 23 and 30.

20 23 30

Is 23 closer to 20 or 30? It is closest to 20.

Which gives a better estimate of 23…..2 tens or 3 tens. 2tens

If we round 23 to the nearest ten, the result would be 20.

Remember: The rounded number has a zero in the ones place.

Example:40, 46 and 50

40 46 50

Is 46 closer to 40 or 50? it is closest to 50.

Which gives a better estimate of 46……4 tens or 5 tens? 5tens

If we round 46 to the nearest ten, the result would be 50.

Example:60, 65 and 70

60 65 70

Is 65 closer to 60 or 70? It is closer to 70.

Which gives a better estimate of 65…… 6 tens or 7 tens? 7tens

When we have a number which ends in 5, we always round up to the next ten. If we round 65 to the nearest 10, the result would be 70.

Example: Round 32 to the nearest 10.

32 is between 3 tens and 4 tens.

32 is closest to 3 tens. Rounded number is 30 .

Exercise OneRound each number to the nearest 10. Check your work using

the answer key at the end of the exercise.

- 47 is between tens and tens.

47 is closest to tens. Rounded number is .

- 81 is between tens and tens.

81 is closest to tens. Rounded number is .

- 14 is between tens and tens.

14 is closest to tens. Rounded number is .

- 26 is between tens and tens.

26 is closest to tens. Rounded number is .

- 98 is between tens and tens.

98 is closest to tens. Rounded number is .

- 57 is between tens and tens.

57 is closest to tens. Rounded number is .

- 73 is between tens and tens.

73 is closest to tens. Rounded number is .

- 2 is between tens and tens.

2 is closest to tens. Rounded number is .

- 39 is between tens and tens.

39 is closest to tens. Rounded number is .

- 65 is between tens and tens.

65 is closest to tens. Rounded number is .

- 18 is between tens and tens.

18 is closest to tens. Rounded number is .

Fundamental Mathematics47

Answers to Exercise One

a)

4 tens, 5 tens

5 ten

50

b)

8 tens, 9 tens

8 tens

80

c)

1 ten, 2 tens

1 ten

10

d)

tens, 3 tens

tens

30

e)

tens, 10 tens

tens

100

f)

tens, 6 tens

tens

60

g)

7 tens, 8 tens

7 tens

70

h)

0 tens, 1 ten

0 tens

0

i)

tens, 4 tens

tens

40

j)

tens, 7 tens

tens

70

k)

ten, 2 tens

tens

20

Now look at a shorter method to round to the nearest ten.

When rounding to the nearest ten, do this:

Step 1: Underline the tens digit.

83

Step 2: Look at the digit following in the ones place.

83

Step 3: If the digit in the ones place is less than 5,

write a 0 in the ones place. leave the tens digit as it is.

42rounds to 40 (42 is nearer to 40 than to 50)

14rounds to 10

83rounds to 80

Step 4: If the digit in the ones place is 5 or more,

write a 0 in the ones place.

add one more ten to the tens place.

36rounds to 40 (36 is nearer to 40 than to 30)

25rounds to 30

98rounds to 100 (one more ten than nine tens is ten tens)

Note: If you are rounding to the nearest ten, single digits are rounded like this: 0, 1, 2, 3, 4 all round to 0.

5, 6, 7, 8, 9 all round to 10.

When you round a number, use the sign that means “approximately equal”

ExerciseTwoRound each number to the nearest ten. Check your work using

the answer key at the end of the exercise.

a)

22

20

b)

86

90

c)

31

d)

96

e)

84

f)

55

g)

8

h)

2

i)

63

j)

49

k)

25

l)

71

m)

38

n)

51

o)

88

c)

30

d)

100

e)

80

f)

60

g)

10

h)

0

i)

60

j)

50

k)

30

l)

70

m)

40

n)

50

o)

90

Answers to Exercise Two
Numbers of any size can be rounded to the nearest ten using the method you have just learned.

238 240883 880297 300

Answers to Exercise Three
ExerciseThreeRound each number to the nearest ten. Check your work using

the answer key at the end of the exercise.

a)

424

b)

867

c)

499

d)

132

e)

278

f)

617

g)

208

h)

851

i)

124

j)

576

k)

315

l)

742

m)

397

n)

952

o)

639

a)

420

b)

870

c) 500

d)

130

e)

280

f) 620

g)

210

h)

850

i) 120

j)

580

k)

320

l) 740

m)

400

n)

950

o) 640

ExerciseFourFor each problem, round the numbers to the nearest ten.

Check your work using the answer key at the end of the exercise.

Example: Mei Ling has just moved into a new apartment. She bought the following items. Round each amount to the nearest ten.

Item

Towels

Cost

$14

Rounded to nearestten

$10

Dishes

$32

$30

Saucepan

$43

$40

Microwave

$109

$110

Carving Knife

$18

$20

- Akkul walked 12 kilometres on Monday, 26 kilometres on Tuesday and 6 kilometres on Wednesday. Round each number to the nearest ten.

Day

Number

RoundedNumber

Monday

12

Tuesday

26

Wednesday

6

- Werner is a keen bird watcher. On Monday, he saw 57 birds, on Tuesday he saw 124 birds, on Wednesday he saw 31 birds and on Thursday he saw 75 birds. Round each number to the nearest ten.

Day

Number

RoundedNumber

Monday

Tuesday

Wednesday

Thursday

- Jamir drove 678 kilometres. 493 kilometres, 387 kilometres and 914 kilometres in one week. Round each mileage to the nearest ten.

Day

Kilometres

RoundedNumber

#1

#2

#3

#4

- Koho Industries canned 281 cans of salmon last week and 392 cans of salmon this week. They plan to can 438 cans of salmon next. Round each number of cans to the nearest ten.

Week

Cans

RoundedNumber

Last week

This week

Next week

- During one week at the movie theatre there were 423 people on Monday, 328 people of Tuesday, 148 people on Wednesday and 523 people on Thursday. Round each number to the nearest ten.

Day

People

RoundedNumber

Monday

Tuesday

Wednesday

Thursday

Answers to ExerciseFour

a) 10, 30, 10

b) 60, 120, 30, 80

c)680, 490, 390, 910

d) 280, 390, 440

e)420, 330, 150, 520

Topic E: Self-Test Mark /12 Aim 10/12

Round your answer to the nearest ten.8 marks

a)

47

b)

123

c)

4

d)

945

e)

329

f)

481

g)

865

h)

916

- Round each number to the nearest ten. 4 marks

- Mary scored 78, 91, 79, 67 and 102 on her arithmetic test. Round her scores to the nearest ten.

Score

Rounded Score

Answers to Topic E Self-TestA.a) 50b)d) 950e)g) 870h)120330920c) 0f) 480B.a) 80, 90, 80, 70, 100

Topic F: More Counting

Practice your counting by filling in the counting chart. Have your instructor check your chart when you are done.

0

1

2

3

4

5

6

7

8

9

10

If you had a pile of pennies or loonies, you would count by ones in order to find out how much money you have.

Use your counting chart and start at 1. Write down every second number.

0

1

3

5

The numbers above are called odd numbers.

Use your counting chart and starting at 0. Write down every second number.

0

2

4

6

The numbers above are called the even numbers. If you had a pile of toonies, you could count by two’s to find out how much money you have.

Use your counting chart and start at 0. Count five and write down that number.

0

5

10

If you had a pile of nickels or five dollar bills and wanted to know how much money you have, you would count be 5’s.

Use your counting chart and starting at 0. Count ten and write down that number.

0

10

20

If you had a pile of dimes or ten dollar bills and wanted to know how much money you have, you would count by 10’s.

Exercise OneCount how much money you have. Check your work using the

answer key at the end of the exercise.

Example:

5 10 15

Howmanynickels? 3

How much money do you have? 15 cents

a)

How many twonies do you have?

How much money do you have? dollars

b)

How many dimes do you have?

How much money do you have? cents

c)

How many nickels to you have?

How much money do you have? cents

d)

How many dimes do you have?

How much money do you have? cents

e)

How many nickels to you have?

How much money do you have? cents

f)

How many twonies do you have?

How much money do you have? dollars

g)

How much money do you have? cents

h)

How much money do you have? dollars

i)

How much money do you have? cents

Answers to Exercise One

a)

4 twonies, $8

b)

7 dimes, 70 cents

c)

9 nickels, 45 cents

d)

4 dimes, 40 cents

e)

10 nickels, 50 cents

f)

3 twonies, $26

g)

90 cents

h)

$36

i)

70 cents

Topic F: Self-Test Mark /16 Aim 13/16

Write the first 10 odd numbers starting with 1.5 marks

- Write the first 10 even numbers starting at 2. 5 marks

How much money do you have?6 marks (2 marks each)

i)

How much money do you have? cents

ii)

How much money do you have? dollars

iii)

How much money do you have? cents

Answers to Topic F Self-Test A. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19B. 2,4,6,8,10,12,14,16,18, 20C. i) 75 centsii) 38 dollars iii) 80 cents

Emotions Check

How are you feeling? Are your palms moist? How is your breathing? Take control. Be the boss. If you are feeling anxious, practice your breathing exercise.

Remember: breathe in slowly to the count of four, hold it for the count of four and breathe out slowly to the count of four.

Unit 1 Review – Number Sense

You will now practice all the skills you learned in Unit 1. Check your work using the answer key at the end of the review.

Count the number of things in each picture. Write the number and word name.

Numeral:Word Name:
a)

- Numeral: Word Name:
Numeral:Word Name:
c)

d)e)

Numeral:Numeral:

Word Name:Word Name:

- Fill in the blanks to make each sentence true. Draw a picture for questions b and e.

- 46 means tens and ones.

- 25 means tens and ones.

Draw your picture below.

c)

means tens and ones

- 138 = hundreds, tens, ones.

- 231 = hundreds, tens, ones.

Draw your picture below.

f)

hundredstensones =

Write the place value name (ones, tens, hundreds) for each underlined digit.

a)

821

b)

294

c)

638

d)

417

e)

346

f)

573

Underline the digit for the place value named.

a)

hundreds

164

b)

tens

892

c)

tens

250

d)

hundreds

371

e)

ones

485

f)

ones

743

- Write the word names for the numbers.

a) 73 b) 14

c) 5 d) 39

e) 52 f)496

g) 803 h) 640

Write the numerals for these word names.

- forty-seven b) nineteen

c) sixty-fived) thirty-eight

e) twenty-four f)five hundred thirty-five

g) three hundred sixty h) two hundred four

Arrange these numbers in order from smallest to largest.

a)2583223282345534

b)15527635208452335

Write <, >, or = in each blank as needed.

a)

37 52

b)

4 0

c)

349 394

d)

67 67

e)

86 68

f)

732 751

- Round each number to the nearest ten.

a) 37 b) 344 c) 68

d) 25

e) 51

f)876

How much money do you have?

a)

How much money do you have? cents

70Book 1

b)

How much money do you have? dollars

c)

How much money do you have? cents

Word Problems

- Hussein’s fruit stand sold 114 watermelons, 287 honeydew melons and 345 cantaloupes. Round each number to the nearest ten.

Melon

Number

Rounded Number

Watermelons

Honeydew Melons

Cantaloupes

- Yi-Min drove her delivery van 106 kilometres on Saturday, 187 kilometres on Sunday and 285 kilometres on Monday. Round each number to the nearest ten.

Kilometres

Number

Rounded Number

Saturday

Sunday

Monday

Answers to Unit 1 Review A.

a) 9, nineb) 7, sevenc) 6, sixd) 8, eighte) 5, five

B.

a) 4 tens, 6 onesb) 2 tens, 5 onesc) 63, 6 tens, 3 ones

d) 1 hundred, 3 tens, 8 onese) 2 hundreds, 3 tens, 1 one

f) 3 hundreds, 2 tens 5 ones, 325

C.

a) hundredsb) tensc) onesd) hundreds

e) tensf) ones

D.

a) 164b) 892c) 250d) 371e) 485f) 743

E.

a) seventy-three b) fourteenc) fived) thirty-nine

e) fifty-twof) four hundred ninety-sixg) six hundred forty

F.

a) 47b) 19c) 65d) 38e) 24f) 535

g) 360h) 204

G.

a) 23, 32, 258, 282, 345, 534b) 27, 155, 208, 335, 452, 635

H.

a) <

b) >

c) <

d) =

e) >

f) <

I.

a) 40

b) 340

c) 70

d) 30

e) 50

f) 880

J.

a) 70 cents

b) 26 dollars

c) 90 cents

K. a)

b)

MelonNumberRounded NumberWatermelons114110Honeydew Melons287290Cantaloupes345350
DayKilometresRounded NumberSaturday106110Sunday187190Monday285290

CONGRATULATIONS!!Now you have finished Unit 1.TEST TIME!Ask your instructor for the Practice Test for this unit.Once you’ve done the practice test, you need to do the unit 1 test.Again, ask your instructor for this.Good luck!

2

Unit 2

Addition

Topic A: Addition

Addition puts amounts together. The answer of addition is called the sum or the total.

The plus sign + means to add.

+
=

3
+
2
=
5
says “three plus two equals five”

or “three and two is five”

The sum is 5.

You can count on your fingers to get the answers to addition questions, but counting takes too long.

Addition facts are a tool that you use to do adding questions.

Exercise One

Check out your addition facts by doing this exercise as

quickly as possible without counting on your fingers. The highest total or sum (what the numbers add up to) for these number facts is 9. Check your work using the answer key at the end of the exercise. Then, make a list of any addition facts you do not know or which are slow – practice them.

a)
2

+ 4

b)
3

+ 1

c)
1

+ 2

d)
7

+ 0

6

4

e)
0

f)
1

g)
5

h)
3

+ 4

+ 4

+ 2

+ 3

i)
2

j)
6

k)
4

l)
3

+ 0

+ 3

+ 4

+ 0

Answers to Exercise One

m)
5

n)
1

o)
0

p)
8

+ 3

+ 6

+ 5

+ 1

q)
2

r)
1

s)
1

t)
2

+ 6

+ 0

+ 5

+ 2

u)
3

v)
2

w)
5

x)
1

+ 2

+ 1

+ 4

+ 7

y)
9

z)
5

aa)

0

bb)

4

+ 0

+ 1

+ 3

+ 1

a)

6

b)

4

c)

3

d)

7

e)

4

f)

5

g)

7

h)

6

i)

2

j)

9

k)

8

l)

3

m)

8

n)

7

o)

5

p)

9

q)

8

r)

1

s)

6

t)

4

u)

5

v)

3

w)

9

x)

8

y)

9

z)

6

aa)

3

bb)

5

ExerciseTwo

Check out your addition facts by doing this exercise as

quickly as possible without counting on your fingers. The highest total or sum (what the numbers add up to) for these number facts is 9. Check your work using the answer key at the end of the exercise. Then, make a list of any addition facts you do not know or which are slow – practice them.

a)
4

+ 5

b)
1

+ 8

c)
8

+ 0

d)
4

+ 3

9

9

e)
0

f)
2

g)
7

h)
0

+ 0

+ 3

+ 1

+ 9

i)
4

j)
0

k)
0

l)
1

+ 2

+ 2

+ 7

+ 1

m)
2

n)
0

o)
6

p)
0

+ 7

+ 1

+ 2

+ 6

q)
1

r)
3

s)
2

t)
0

+ 3

+ 5

+ 5

+ 8

u)
3

v)
4

w)
3

x)
5

+ 4

+ 0

+ 6

+ 0

y)
6

z)
6

aa)

7

bb)

0

+ 1

+ 0

+2

+ 3

a)

9

b)

9

c)

8

d)

7

e)

0

f)

5

g)

8

h)

9

i)

6

j)

2

k)

7

l)

2

m)

9

n)

1

o)

8

p)

6

q)

4

r)

8

s)

7

t)

8

u)

7

v)

4

w)

9

x)

5

y)

7

z)

6

aa)

9

bb)

3

Answers to Exercise Two
ExerciseThree

Check out your addition facts by doing this exercise as

quickly as possible without counting on your fingers. The highest total or sum (what the numbers add up to) for these number facts is 9. Check your work using the answer key at the end of the exercise. Then, make a list of any addition facts you do not know or which are slow – practice them.

a)
3

+ 6

b)
4

+ 5

c)
4

+ 1

d)
9

+ 0

9

9

e)
2

f)
3

g)
0

h)
5

+ 2

+ 4

+ 6

+ 2

i)
4

j)
1

k)
2

l)
0

+ 0

+ 8

+ 3

+ 5

m)
0

n)
1

o)
4

p)
6

+ 0

+ 2

+ 3

+ 1

q)
6

r)
3

s)
2

t)
0

+ 2

+ 2

+ 7

+ 7

u)
5

v)
1

w)
5

x)
3

+ 4

+ 7

+ 3

+ 3

y)
1

z)
2

aa)

0

bb)

1

+ 4

+ 4

+ 4

+ 3

cc)

1

dd)

0

ee)

8

ff)

3

+ 6

+ 8

+ 1

+ 5

gg)

3

hh)

6

ii)
3

jj)

7

+ 0

+ 3

+ 1

+ 1

kk)

2

ll)

4

mm)

2

nn)

3

+ 6

+ 4

+ 5

+ 4

a)

9

b)

9

c)

5

d)

9

e)

4

f)

7

g)

6

h)

7

i)

4

j)

9

k)

5

l)

5

m)

0

n)

3

o)

7

p)

7

q)

8

r)

5

s)

9

t)

7

u)

9

v)

8

w)

8

x)

6

y)

5

z)

6

aa)

4

bb)

4

cc)

7

dd)

8

ee)

9

ff)

8

gg)

3

hh)

9

ii)

4

Answers to Exercise Threejj) 8kk) 8ll) 8mm) 7nn) 7
ExerciseFour

Check out your addition facts by doing this exercise as

quickly as possible without counting on your fingers. The highest total or sum (what the numbers add up to) for these number facts is 12. Check your work using the answer key at the end of the exercise. Then, make a list of any addition facts you do not know or which are slow – practice them.

a)
6

+ 5

b)
8

+ 2

c)
5

+ 3

d)
5

+ 7

11

10

e)
3

f)
2

g)
7

h)
3

+ 4

+ 6

+ 3

+ 9

Answers to Exercise Four

i)
9

j)
8

k)
4

l)
1

+ 3

+ 1

+ 5

+ 9

m)
2

n)
3

o)
6

p)
5

+ 7

+ 5

+ 6

+ 6

q)
4

r)
5

s)
8

t)
5

+ 6

+ 8

+ 4

+ 2

u)
3

v)
2

w)
2

x)
7

+ 7

+ 8

+ 9

+ 1

a)

11

b)

10

c)

8

d)

12

e)

7

f)

8

g)

10

h)

12

i)

12

j)

9

k)

9

l)

10

m)

9

n)

8

o)

12

p)

11

q)

10

r)

11

s)

12

t)

7

u)

10

v)

10

w)

11

x)

8

ExerciseFive

Check out your addition facts by doing this exercise as

quickly as possible without counting. The highest total or sum

(what the numbers add up to) for these number facts is 12. Check your work using the answer key at the end of the exercise. Then, make a list of any addition facts you do not know or which are slow – practice them.

a)
9

b)
6

c)
4

d)
2

+ 2

+ 4

+ 7

+ 5

e)
8

f)
7

g)
6

h)
5

+ 3

+ 4

+ 3

+ 5

i)
9

j)
7

k)
4

l)
6

+ 1

+ 5

+ 8

+ 2

m)
7

n)
1

o)
3

p)
5

+ 2

+ 7

+ 6

+ 4

q)
4

r)
7

s)
9

t)
4

+ 7

+ 6

+ 2

+ 8

u)
6

v)
3

w)
8

x)
4

+ 6

+ 6

+ 2

+ 5

Answers to ExerciseFive

a)

11

b)

10

c)

11

d)

7

e)

11

f)

11

g)

9

h)

10

i)

10

j)

12

k)

12

l)

8

m)

9

n)

8

o)

9

p)

9

q)

11

r)

13

s)

11

t)

12

u)

12

v)

9

w)

10

x)

9

ExerciseSix

Check out your addition facts by doing this exercise as

quickly as possible without counting. The highest total or sum

(what the numbers add up to) for these number facts is 12. Check your work using the answer key at the end of the exercise. Then, make a list of any addition facts you do not know or which are slow – practice them.

a)
3

b)
5

c)
4

d)
4

+ 9

+ 3

+ 6

+ 3

e)
6

f)
2

g)
9

h)
7

+ 5

+ 8

+ 1

+ 5

i)
3

j)
5

k)
6

l)
2

+ 8

+ 2

+ 6

+ 9

m)
4

n)
3

o)
3

p)
5

+ 6

+ 9

+ 7

+ 7

q)
8

r)
8

s)
1

t)
6

+ 3

+ 4

+ 9

+ 2

u)
2

v)
5

w)
9

x)
2

+ 9

+ 6

+ 3

+ 6

y)
3

z)
6

aa)

6

bb)

7

+ 5

+ 4

+ 5

+ 3

cc)

3

dd)

6

ee)

7

ff)

5

+ 4

+ 3

+ 4

+ 5

a)

12

b)

8

c)

10

d)

7

e)

11

f)

10

g)

10

h)

12

i)

11

j)

7

k)

12

l)

11

m)

10

n)

12

o)

10

p)

12

q)

11

r)

12

s)

10

t)

8

u)

11

v)

11

w)

12

x)

8

y)

8

z)

10

aa)

11

bb)

10

cc)

7

dd)

9

ee)

11

ff)

10

Answers to Exercise Six
Need more practice?Practice your addition facts using a set of dice. Roll the dice and add the amounts on the dice.

ExerciseSeven

Check out your addition facts by doing this exercise as

quickly as possible without counting. The highest total or sum

(what the numbers add up to) for these number facts is 20. Check your work using the answer key at the end of the exercise. Then, make a list of any addition facts you do not know or which are slow – practice them.

a)
7

+ 6

b)
5

+ 9

c)
10

+ 3

d)
5

+ 7

13

14

e)
7

f)
10

g)
8

h)
6

+ 9

+ 9

+ 7

+ 4

i)
5

j)
8

k)
8

l)
10

+ 10

+ 9

+ 2

+ 6

m)
7

n)
6

o)
6

p)
10

+ 4

+ 10

+ 7

+ 4

Answers to Exercise Seven

q)
9

r)
2

s)
9

t)
5

+ 8

+ 10

+ 7

+ 8

u)
10

v)
5

w)
8

x)
4

+ 2

+ 6

+ 5

+ 10

y)
9

z)
8

aa)

9

bb)

9

+ 6

+ 4

+ 10

+ 4

a)

13

b)

14

c)

13

d)

12

e)

16

f)

19

g)

15

h)

10

i)

15

j)

17

k)

10

l)

16

m)

11

n)

16

o)

13

p)

14

q)

17

r)

12

s)

16

t)

13

u)

12

v)

11

w)

13

x)

14

y)

15

z)

12

aa)

19

bb)

13

ExerciseEight

Check out your addition facts by doing this exercise as

quickly as possible without counting. The highest total or sum (what the numbers add up to) for these number facts is 20. The highest total or sum (what the numbers add up to) for these number facts is 20. Then, make a list of any addition facts you do not know or which are slow – practice them.

a)
10

b)
7

c)
10

d)
7

+ 1

+ 7

+ 8

+ 8

e)
4

f)
1

g)
4

h)
3

+ 6

+ 10

+ 7

+ 10

i)
0

j)
3

k)
10

l)
6

+ 7

+ 9

+ 7

+ 4

m)
0

n)
6

o)
9

p)
10

+ 10

+ 9

+ 9

+ 5

q)
4

r)
2

s)
10

t)
6

+ 8

+ 9

+ 10

+ 6

Answers to Exercise Eight

u)
9

v)
7

w)
9

x)
8

+ 3

+ 4

+ 1

+ 8

y)
7

a)
9

aa)

8

bb)

9

+ 10

+ 2

+ 6

+ 5

a)

11

b)

14

c)

18

d)

15

e)

10

f)

11

g)

11

h)

13

i)

7

f)

12

k)

17

l)

10

m)

10

n)

15

o)

18

p)

15

q)

12

r)

11

s)

20

t)

12

u)

12

v)

11

w)

10

x)

16

y)

17

z)

11

aa)

14

bb)

14

ExerciseNine

Check out your addition facts by doing this exercise as quickly as

possible without counting. The highest total or sum (what the numbers add up to) for these number facts is 20. Then, make a list of any addition facts you do not know or which are slow – practice them.

a)
4

b)
7

c)
5

d)
3

+ 9

+ 2

+ 5

+ 6

e)
6

f)
8

g)
6

h)
6

+ 10

+ 5

+ 9

+ 6

i)
3

j)
9

k)
2

l)
5

+ 7

+ 3

+ 8

+10

m)
5

n)
10

o)
8

p)
2

+ 5

+ 3

+ 8

+ 10

q)
7

r)
10

s)
5

t)
1

+ 9

+ 8

+ 8

+ 10

u)
7

v)
10

w)
7

x)
6

+ 6

+ 10

+ 7

+ 5

y)
5

z)
9

aa)

10

bb)

8

+ 7

+ 9

+ 0

+ 2

a)

13

b)

9

c)

10

d)

9

e)

16

f)

13

g)

15

h)

12

i)

10

j)

12

k)

10

l)

15

m)

10

n)

13

o)

16

p)

12

q)

16

r)

18

s)

13

t)

11

u)

13

v)

20

w)

14

x)

11

y)

12

z)

18

aa)

10

bb)

10

Answers to Exercise Nine
ExerciseTen

Check out your addition facts by doing this exercise as

quickly as possible without counting. The highest totalor

sum (what the numbers add up to) for these number facts is

20. Then, make a list of any addition facts you do not know or which are slow – practice them.

a)
7

b)
10

c)
8

d)
2

+ 10

+ 4

+ 7

+ 9

e)
4

f)
3

g)
7

h)
3

+ 6

+ 10

+ 4

+ 8

i)
8

j)
7

k)
5

l)
9

+ 3

+ 8

+ 9

+ 5

m)
8

n)
10

o)
4

o)
8

+ 6

+ 9

+ 7

+ 9

q)
7

r)
9

s)
1

t)
6

+ 5

+ 10

+ 9

+ 7

u)
9

v)
6

w)
6

x)
7

+ 4

+ 1

+ 0

+ 2

y)
3

z)
0

aa)

6

bb)

5

+ 4

+ 8

+ 4

+ 8

cc)

2

dd)

7

ee)

0

ff)

9

+ 5

+ 6

+ 3

+ 7

h)

11

i)

11

j)

15

k)

14

l)

14

m)

14

n)

19

o)

11

p)

17

q)

12

r)

19

s)

10

t)

13

u)

13

v)

7

w)

6

x)

9

y)

7

z)

8

aa)

10

bb)

13

cc)

7

dd)

13

ee)

3

ff)

16

Answers to Exercise Tena) 17b) 14c) 15d) 11e) 10f) 13g) 11
ExerciseEleven

Check out your addition facts by doing this exercise as

quickly as possible without counting. The highest total or sum

(what the numbers add up to) for these number facts is 20. Check your work using the answer key at the end of the exercise. Then, make a list of any addition facts you do not know or which are slow – practice them.

a)
7

b)
4

c)
3

d)
4

+ 2

+ 4

+ 5

+ 6

e)
8

f)
9

g)
1

h)
0

+ 1

+ 6

+ 3

+ 2

i)
4

j)
9

k)
4

l)
8

+ 9

+ 2

+ 1

+ 8

m)
1

n)
7

o)
2

p)
9

+ 5

+ 3

+ 2

+ 5

q)
6

r)
6

s)
3

t)
4

+ 1

+ 0

+ 2

+ 8

u)
5

v)
3

w)
9

x)
3

+ 5

+ 6

+ 8

+ 9

y)
2

z)
1

aa)

2

bb)

6

+ 3

+ 9

+ 8

+ 6

cc)

5

dd)

6

ee)

4

ff)

1

+ 4

+ 8

+ 5

+ 7

gg)

5

hh)

4

ii)
3

jj)

7

+ 6

+ 0

+ 5

+ 2

Answers to Exercise Eleven

a)

9

b)

8

c)

8

d)

10

e)

9

f)

15

g)

4

h)

2

i)

13

j)

11

k)

5

l)

16

m)

6

n)

10

o)

4

p)

14

q)

7

r)

6

s)

5

t)

12

u)

10

v)

9

w)

17

x)

12

y)

5

z)

10

aa)

10

bb)

12

cc)

9

dd)

14

ee)

9

ff)

8

gg)

11

hh)

4

ii)

8

jj)

9

Need some extra practice?Find a partner and play the following card game. You will use a regular deck of cards Take out the jacks, queens and kings. Shuffle the cards and deal them out. Do not look at your cards. Leave them in a pile in from of you. Each player flips over a card. Take turns adding the numbers on the cards. If the person whose turn it is gets the right answer that person gets to keep the cards. If the person whose turn it is gets the wrong answer the other player gets the cards. The person who collects all the cards is the winner. You could also set a time limit and the person with the most cards when time is up is the winner.

ExerciseTwelve

Here are some extra questions if you need more practice.

The highest total or sum (what the numbers add up to) for these number facts is 20. Check your work using the answer key at the end of the exercise.

a)
6

+ 7

b)
8

+ 3

c)
4

+ 2

d)
8

+ 7

13

11

e)
1

f)
6

g)
5

h)
2

+ 2

+ 4

+ 8

+ 5

i)
7

j)
0

k)
9

l)
7

+ 6

+ 3

+ 7

+ 2

m)
4

n)
3

o)
4

p)
8

+ 4

+ 5

+ 6

+ 1

q)
9

r)
1

s)
0

t)
4

+ 6

+ 3

+ 2

+ 9

u)
9

v)
4

w)
8

x)
1

+ 2

+ 1

+ 8

+ 5

y)
7

z)
2

aa)

9

bb)

6

+ 3

+ 2

+ 5

+ 1

cc)

6

dd)

3

ee)

4

ff)

5

+ 0

+ 2

+ 8

+ 5

gg)

3

hh)

9

ii)
3

jj)

2

+ 6

+ 8

+ 9

+ 3

kk)

1

ll)

2

mm)

6

nn)

5

+ 9

+ 8

+ 6

+ 4

oo)

6

pp)

4

qq)

1

rr)

5

+ 8

+ 5

+ 7

+ 6

Answers to Exercise Twelve

a) 13

b)

11

c)

6

d)

15

e)

3

f)

10

g)

13

h) 7

i)

13

j)

3

k)

16

l)

9

m)

8

n)

8

o) 10

p)

9

q)

15

r)

4

s)

2

t)

13

u)

11

v)
5

w)

16

x)

6

y)

10

z)

4

aa)

14

bb)

7

cc) 6

dd)

5

ee)

12

ff)

10

gg)

9

hh)

17

ii)

12

jj)

5

kk)

10

ll)

10

mm) 12

nn)

9

oo)

14

pp)

9

qq)

8

rr)

11

Adding Across

So far you have only been adding numbers when they are up and down or vertical.

Example:
4

+ 5

9

Another way to add numbers is across or horizontally. Example:

4 + 5 = 9

In math, sometimes you will need to work from left to right.

ExerciseThirteen

Practice adding across or horizontally. The highest totalor

sum (what the numbers add up to) for these number facts is 20. Check your work using the answer key at the end of the exercise.

a)
10 + 0 =
b)
2 + 2 =

c)

5

+

3

=

d)

1

+

1 =

e)

8

+

4

=

f)

7

+

1 =

g)

0

+

4

=

h)

6

+

3 =

i)

3

+

2

=

j)

1

+

10 =

k)

9

+

3

=

l)

4

+

9 =

m)

3

+

7

=

n)

4

+

8 =

o)
8 + 0 =
p)
6 + 4 =

q)
4 + 1 =
r)
7 + 2 =

Answers to Exercise Thirteen
s)
10 + 10 =
t)
6 + 5 =

a)

10

b)

4

c)

8

d)

2

e)

12

f)

8

g)
4

h)

9

i)

5

j)

11

k)

12

l)

13

m)

10

n)
12

o)

8

p)

10

q)

5

r)

9

s)

20

t)

11

ExerciseFourteen

Practice adding across or horizontally. The highest

total or sum (what the numbers add up to) for these number facts is 20. Check your work using the answer key at the end of the exercise.

a)
5 + 10 =
b)
0 + 0 =

c)
3 + 8 =
d)
8 + 3 =

e)
9 + 5 =
f)
6 + 2 =

g)
9 + 0 =
h)
2 + 9 =

i)
4 + 7 =
j)
8 + 2 =

k)
3 + 6 =
l)
9 + 4 =

m)
0 + 2 =
n)
5 + 2 =

o)
1 + 3 =
p)
4 + 2 =

q)
10 + 3 =
r)
5 + 4 =

s)
8 + 5 =
t)
6 + 6 =

Answers to ExerciseFourteen

a)

15

b)

0

c)

11

d)

11

e)

14

f)

8

g)
9

h)

11

i)

11

j)

10

k)

9

l)

13

m)

2

n)
7

o)

4

p)

6

q)

13

r)

9

s)

13

t)

12

ExerciseFifteen

Practice adding across or horizontally. The highest

total or sum (what the numbers add up to) for these number facts is 20. Check your work using the answer key at the end of the exercise.

a)
9 + 6 =
b)
8 + 9 =

c)
9 + 9 =
d)
2 + 3 =

e)
7 + 3 =
f)
10 + 8 =

g)
9 + 7 =
h)
8 + 8 =

i)
8 + 10 =
j)
3 + 9 =

k)
9 + 2 =
l)
4 + 4 =

m)
6 + 8 =
n)
2 + 7 =

o)
5 + 7 =
p)
3 + 3 =

q)
7 + 0 =
r)
5 + 8 =

s)
10 + 8 =
t)
9 + 8 =

Answers to ExerciseFifteen

a)

15

b)

17

c)

18

d)

5

e)

10

f)

18

g)
16

h)

16

i)

18

j)

12

k)

11

l)

8

m)

14

n)
9

o)

12

p)

6

q)

7

r)

13

s)

18

t)

17

Word Problems

Learning addition facts is very important. Once you know them all, you can use them to solve word problems.

Words such as more than, plus, added to, sum, total, have altogether and in all tell you to add the numbers together. Look for these words when reading word problems and underline them before trying to solve a problem. Circle the information that is given.

2 pages.
9 pages.
Example: Before lunch Jane read 2 pages. After lunch she read 9 pages. How many pages did she read in all?

Before lunch Jane read read in all?

After lunch she read

How many pages did she

You have circled 2 pages and 9 pages. This is the information you will use to find the answer.

You have underlined “in all”. These words tell you to add.

2 pages

+ 9 pages 11 pages

Jane read 11 pages in all.

Exercise One

Solve each of the following word problems. Be sure to

underline the words that tell you to add. Circle
the information that is given. Have your instructor check your underlining
and
circling.

- Sven bought 7 cans of juice on Monday. He bought 9 cans of juice on Wednesday. How many cans of juice did he buy altogether?

- During the hockey game, Ewan took 8 shots from the blue line and 4 shots from in front of the net. How many shots did he take in all?

- Marlene noticed that there were 4 people in her math class. The next day 6 more people were in her math class. What is the total number of people in Marlene’s math class?

- The Blue Jays played two baseball games in a row. They got 10 runs in the first game and 7 runs in the second game. How many runs did they score altogether?

- Jaswinder had 9 apples in her grocery cart. She added 5 more different apples. How many apples did she have in total?

- Answers to Exercise One
Enlai and his dad were fishing. Enlai caught 3 fish. His father caught 5 fish. How many fish did they have in total?

a)
16 cans

b)

12 shots

c)

10 people

d)
17 runs

e)

14 apples

f)

8 fish

Topic A: Self-Test

Mark

/22
Aim
19/22

Find the sums. Be sure to check your answers.
12 marks

a)
9

b)
5

c)
4

+ 6

+ 8

+ 2

d)
7

e)
3

f)
1

+ 6

+ 5

+ 9

g)
2

h)
6

i)
8

+ 3

+ 4

+ 1

j)
9

k)
7

l)
5

+ 8

+ 4

+ 6

- Find the sums. Be sure to check your answers.
4
marks

a)

6 + 7 =

b)

3 + 8

=

c)

4 + 6 =

d)

8 + 5

=

Solve each of the following word problems.

6 marks Be sure to include the unit of measure in your answer.
(2 marks each)

circle
Besureto
information and
underline what is beingasked.

- Paco worked 5 hours on Monday and 9 hours on Tuesday.
How many hours did Paco work in total?

- In the park, Ming-Mai counted 6 robins in the morning. In the afternoon, she counted 8 more robins. How many robins in all did Ming-Mai count?

- Omari bought 3 bananas on Monday. He bought 5 bananas on Tuesday. How many bananas did he buy altogether?

Answers to Topic A Self-TestA.C.a) 14 hoursb) 14 robinsc) 8 bananas

a)

15

b)

13

c)

6

d)

13

e)
8

f)
10

g)
5

h)

10

i)

9

j)

17

k)

11

l)
11

B.

a)

13

b)

11

c)

10

d)

13

Topic B: Addition of Three or More Numbers

To add three or more numbers together, use the following steps.

Step1:

Add the first two numbers together.

Step2:

Add that sum to the next number.

Step3:

Add that sum to the next number (if needed).

Example A:
6

1

+ 3

Step 1: Add the first two numbers together.

6

+ 1

7

Step 2: Add that sum to the next number.

7

+3

10

The sumof

6

1

+ 3

10

Example B:
4

5

+ 7

Step 1: Add the first two numbers together.

4

+ 5

9

Step 2: Add that sum to the third number.

9

+ 7

16

The sum of

4

5

+ 7

16

ExampleC:

1

3

4

+ 5

Step 1: Add the first two numbers together.

1

+ 3

4

Step 2: Add that sum to the third number.

4

+ 4

8

Step 3: Add that sum to the fourth number.

8

+ 5

13

The sum of

1

3

4

+ 5

13

Exercise One

Find the sums. Check your work using the answer key at the end of the exercise.

a)
1

2

b)
6

3

c)
7

1

d)
3

6

+ 5

+ 2

+ 6

+ 5

e)
8

1

f)
5

4

g)
1

5

h)
7

2

+ 4

+ 8

+ 7

+ 5

i)
1

8

j)
4

5

k)
2

2

l)
6

3

+ 3

+ 9

+ 8

+ 5

m)
7

2

n)
3

2

o)
6

2

p)
4

4

+ 5

+ 5

+ 5

+ 5

q)
3

3

r)
7

1

s)
1

7

t)
2

4

+ 9

+ 9

+ 5

+ 5

u)
7

2

v)
3

5

w)
1

4

x)
5

3

+ 8

+ 7

+ 8

+ 8

Answers to ExerciseOne

a)

8

b)

11

c)

14

d)

14

e)

13

f)

17

g)

13

h)

14

i)

12

j)

18

k)

12

l)

14

m)

14

n)

10

o)

13

p)

13

q)

15

r)

17

s)

13

t)

11

u)

17

v)

15

w)

13

x)

16

ExerciseTwo

Find the sums. Check your work using the answer key at the end

of the exercise.

a)
3

5

b)
2

6

c)
4

1

d)
5

4

+ 7

+ 8

+ 9

+ 2

e)
3

6

f)
2

5

g)
6

3

h)
3

5

+ 4

+ 4

+ 2

+ 3

i)
3

4

j)
4

5

k)
6

3

l)
5

2

+ 7

+ 9

+ 2

+ 9

m)
4

5

n)
5

2

o)
2

3

p)
1

5

+ 7

+ 8

+ 8

+ 6

q)
4

3

r)
2

6

s)
4

5

t)
5

2

+ 5

+ 5

+ 3

+ 4

u)
3

4

v)
7

1

w)
2

1

x)
3

6

+ 7

+ 5

+ 9

+ 3

Answers to ExerciseTwo

a)

15

b)

16

c)

14

d)

11

e)

13

f)

11

g)

11

h)

11

i)

14

j)

18

k)

11

l)

16

m)

16

n)

15

o)

13

p)

12

q)

12

r)

13

s)

12

t)

11

u)

14

v)

13

w)

12

x)

12

ExerciseThree

Find the sums. Check your work using the answer key at the

end of the exercise.

a)
3

2

b)
2

1

c)
4

3

d)
1

2

+ 8

+ 4

+ 1

+ 8

e)
3

2

f)
5

1

g)
7

2

h)
4

2

+ 2

+ 2

+ 8

+ 6

i)
7

2

j)
6

1

k)
2

7

l)
3

4

+ 7

+ 1

+ 6

+ 2

Answers to Exercise Three

m)
3

4

n)
7

1

o)
2

6

p)
3

1

+ 1

+ 9

+ 4

+ 2

q)
5

1

r)
4

2

s)
3

4

t)
8

1

+ 3

+ 6

+ 6

+ 7

u)
2

5

v)
6

3

w)
2

7

x)
6

3

+ 8

+ 1

+ 5

+ 4

a)

13

b)

7

c)

8

d)

11

e)

7

f)

8

g)

17

h)

12

i)

16

j)

8

k)

15

l)

9

m)

8

n)

17

o)

12

p)

6

q)

9

r)

12

s)

13

t)

16

u)

15

v)

10

w)

14

x)

13

ExerciseFour

Find the sums. Check your work using the answer key at the end

of the exercise.

a)
1

3

b)
2

3

c)
4

3

d)
3

1

4

4

2

5

+ 5

+ 6

+ 8

+ 6

e)
2

2

f)
3

3

g)
2

1

h)
1

2

3

1

2

4

+ 2

+ 2

+ 4

+ 6

i)
2

4

j)
3

2

k)
2

1

l)
3

1

1

3

4

4

+ 6

+ 3

+ 0

+ 1

m)
3

2

n)
3

5

o)
6

1

p)
4

3

3

1

2

2

+ 2

+ 6

+ 9

+ 1

q)
1

4

r)
4

2

s)
3

4

t)
2

4

3

1

2

3

+ 5

+ 9

+ 7

+ 6

u)
2

3

v)
1

3

w)
4

4

x)
6

2

3

5

1

1

+ 5

+ 7

+ 8

+ 7

Answers to ExerciseFour

a)

13

b)

15

c)

17

d)

15

e)

9

f)

9

g)

9

h)

13

i)

13

j)

11

k)

7

l)

9

m)

10

n)

15

o)

18

p)

10

q)

13

r)

16

s)

16

t)

15

u)

13

v)

16

w)

17

x)

16

ExerciseFive

Find the sums. Check your work using the answer key at the end

of the exercise.

a)
1

3

b)
5

3

c)
7

1

d)
2

3

4

1

1

4

+ 8

+ 4

+ 9

+ 9

e)
1

2

f)
2

3

g)
4

1

h)
1

3

6

2

4

5

+ 9

+ 3

+ 6

+ 8

i)
2

1

j)
3

1

k)
2

2

l)
3

2

5

2

5

4

+ 7

+ 9

+ 8

+ 7

m)
4

1

n)
2

4

o)
1

5

p)
3

3

1

3

2

1

+ 2

+ 6

+ 1

+ 2

q)
1

4

r)
2

1

s)
3

1

t)
2

3

3

5

6

4

+ 6

+ 3

+ 5

+ 6

u)
2

1

v)
2

3

w)
3

1

x)
1

0

4

2

3

5

+ 8

+ 6

+ 2

+ 4

Answers to ExerciseFive

a)

16

b)

13

c)

18

d)

18

e)

18

f)

10

g)

15

h)

17

i)

15

j)

15

k)

17

l)

16

m)

8

n)

15

o)

9

p)

9

q)

14

r)

11

s)

15

t)

15

u)

15

v)

13

w)

9

x)

10

ExerciseSix

Find the sums. Check your work using the answer key at the end

of the exercise.

a)
2

1

b)
4

2

c)
1

3

d)
1

2

5

2

4

6

+ 0

+ 5

+ 3

+ 4

e)
3

4

f)
2

4

g)
2

3

h)
4

3

2

4

5

1

+ 6

+ 5

+ 1

+ 5

i)
4

1

j)
3

2

k)
1

3

l)
4

2

2

5

1

3

+ 1

+ 7

+ 3

+ 7

m)
1

3

n)
2

1

o)
3

2

p)
4

1

7

3

1

1

+ 1

+ 1

+ 1

+ 2

q)
3

0

r)
2

1

s)
1

0

t)
2

3

3

1

4

4

+ 1

+ 3

+ 3

+ 7

u)
2

1

v)
4

3

w)
4

1

x)
2

4

5

2

5

2

+ 6

+ 2

+ 6

+ 5

Answers to ExerciseSix

a)

8

b)

13

c)

11

d)

13

e)

15

f)

15

g)

11

h)

13

i)

8

j)

17

k)

8

l)

16

m)

12

n)

7

o)

7

p)

8

q)

7

r)

7

s)

8

t)

16

u)

14

v)

11

w)

16

x)

13

Perimeter

Did you spot the fact that each answer in the word problems before had a unit of measure? A unit of measure just tells you what you measured. Units of measure can be pages, fish, cans, kilometres, meters, centimetres, litres, millilitres, grams or kilograms. When you answer a word problem, you must include the unit of measure in your answer.

Try the following questions. Be sure to include the unit of measure in your answer.

Perimeter means distance around. To find the perimeter of a shape, find the lengths of the sides and add them together.

Example:

3 metres

Vegetable Garden
2 metres
2 metres

3 metres

Rectangle

To find the perimeter, add the lengths of the sides of the rectangle. Perimeter = 3 + 2 + 3 + 2

Perimeter = 10 meters

Example:

4 centimetres

5 centimetres
3centimetres

Triangle

To find the perimeter, add the lengths of the sides of the triangle. Perimeter = 4 + 3 + 5 Perimeter = 12 centimetres

Exercise One

Find the perimeter of each figure. Be sure to include

the units of measure in your answer. Check your work using the answer key at the end of the exercise.

- Find the perimeter of the swimming pool.

3 metres

Pool
4 metres
4 metres

3 metres

Rectangle

- Find the perimeter of the garden.

6 metresGarden
3 metres

4 metres

Triangle

- Find the perimeter of the greenhouse.

3 metres

Greenhouse
3 metres
3 metres

3 metres

Square

- Find the perimeter of the sign.

2 metres

Sign
3metres
3
metres

2 metres Rectangle

Answers to Exercise Onea)14 metresb)13 metresc)12 metresd)10 metres

Topic B: Self-Test

Mark

/18
Aim
15/18

Find the sums. Be sure to check your answers.
12 marks

a)
4

6

b)
3

6

c)
7

2

+ 2

+ 9

+ 8

f)
2

1

g)
3

5

h)
4

6

+ 4

+ 8

+ 7

i)
3

1

j)
4

2

k)
5

3

5

3

1

+ 2

+ 7

+ 8

l)
3

5

m)
1

5

n)
2

1

1

4

6

+ 3

+ 6

+ 5

Solve each of the following word problems.

6 marks Be sure to include the unit of measure in your answer.
(2 marks each) Be sure to circle information and underline what is being asked.

- It took the cleanup crew 4 hours on Monday, 3 hours on Tuesday and 9 hours on Wednesday to clean the factory after each day’s work. How many hours in total did it take to clean the factory?

- Nella wants to put a fence around her garden. The garden measures 5 metres, 3 metres and 1 metre. How much fence does she need?

- Find the perimeter of the garden.

4 metres

Garden
2 metres
2 metres

4

4 metres

Answers to Topic B Self-TestA.a)16 hoursb)9 metresc)12 metres

a)

12

b)

18

c)

17

d) 7

e)
16

f)

17

g)

B.

11

h)

16

i)

17

j)
12

k) 16

l)

14

Topic C: Addition of Larger Numbers

Use these steps to complete each addition question.

Step 1: Add the ones to the ones.

Step 2: Add the tens to the tens.

Step 3: Add the hundreds to the hundreds.

Example A:
23

+ 56

Step 1: Add the ones to the ones. 3 ones + 6 ones = 9 ones 23

+ 56

9

Write the answer in line with the ones in the question.

Step 2: Add the tens. 2 tens + 5 tens = 7 tens

23

+ 56

79

The sum of 23 + 56 = 79

Example B:
372

+ 415

Step 1: Add the ones. 2 ones + 5 ones = 7 ones

372

+ 415

7

Step 2: Add the tens. 7 tens + 1 ten = 8 tens

372

+ 415

87

Step 3: Add the hundreds. 3 hundreds + 4 hundreds = 7 hundreds

372

+ 415

787

Exercise One

Find the sums. Check your work using the answer key at the end

of the exercise.

a)
54

b)
20

c)
58

d)
62

+ 32

+ 69

+ 21

+ 13

e)
73

f)
44

g)
10

h)
36

+ 14

+ 54

+ 75

+ 22

i)
10

j)
16

k)
40

l)
37

+ 36

+ 23

+ 50

+ 32

m)
14

n)
23

o)
41

p)
40

+ 50

+ 16

+ 38

+ 11

q)
28

r)
21

s)
72

t)
31

+ 70

+ 56

+ 12

+ 14

u)
47

v)
34

w)
63

x)
31

+ 12

+ 65

+ 34

+ 45

Answers to ExerciseOne

a)

86

b)

89

c)

79

d)

75

e)

87

f)

98

g)

85

h)

58

i)

46

j)

39

k)

90

l)

69

m)

64

n)

39

o)

79

p)

51

q)

98

r)

77

s)

84

t)

45

u)

59

v)

99

w)

97

x)

76

ExerciseTwo

Find the sums. Check your work using the answer key at the end

of the exercise.

a)
47

b)
65

c)
78

d)
84

+ 51

+ 24

+ 21

+ 12

e)
73

f)
64

g)
25

h)
51

+ 22

+ 13

+ 64

+ 38

i)
26

j)
40

k)
76

l)
86

+ 43

+ 57

+ 23

+ 13

m)
28

n)
35

o)
27

p)
19

+ 71

+ 62

+ 12

+ 40

q)
41

r)
53

s)
61

t)
52

+ 43

+ 32

+ 22

+ 21

u)
23

v)
32

w)
13

x)
46

+ 64

+ 43

+ 65

+ 42

Answers to ExerciseTwo

a)

98

b)

89

c)

99

d)

96

e)

95

f)

77

g)

89

h)

89

i)

69

j)

97

k)

99

l)

99

m)

99

n)

97

o)

39

p)

59

q)

84

r)

85

s)

83

t)

73

u)

87

v)

75

w)

78

x)

88

ExerciseThree

Find the sums. Check your work using the answer key at the

end of the exercise.

a)
32

b)
23

c)
61

d)
83

+ 64

+ 54

+ 22

+ 11

e)
32

f)
63

g)
75

h)
46

+ 45

+ 33

+ 24

+ 12

i)
44

j)
25

k)
41

l)
54

+ 35

+ 42

+ 38

+ 45

m)
25

n)
35

o)
32

p)
22

+ 32

+ 42

+ 44

+ 14

q)
57

r)
42

s)
34

t)
25

+ 21

+ 54

+ 23

+ 42

u)
13

v)
60

w)
34

x)
77

+ 41

+ 25

+ 62

+ 21

Answers to ExerciseThree

a)

96

b)

77

c)

83

d)

94

e)

77

f)

96

g)

99

h)

58

i)

79

j)

67

k)

79

l)

99

m)

57

n)

77

o)

76

p)

36

q)

78

r)

96

s)

57

t)

67

u)

54

v)

85

w)

96

x)

98

ExerciseFour

Find the sums. Check your work using the answer key at the

end of the exercise.

a)
286

b)
649

c)
156

+ 513

+ 250

+ 542

d)
503

e)
273

f)
27

+ 361

+ 620

+ 961

g)
852

h)
300

i)
364

+ 36

+ 50

+ 523

j)
568

k)
432

l)
621

+ 210

+ 325

+ 214

m)
312

n)
135

o)
231

+ 541

+ 420

+ 354

p)
532

q)
537

r)
145

+ 141

+ 21

+ 441

s)
235

t)
723

u)
521

+ 214

+ 113

+ 344

v)
624

w)
524

x)
463

+ 174

+ 221

+ 425

Answers to ExerciseFour

a)

799

b)

899

c)

698

d)

864

e)

893

f)

988

g)

888

h)

350

i)

887

j)

778

k)

757

l)

835

m)

853

n)

555

o)

585

p)

673

q)

558

r)

586

s)

449

t)

836

u)

865

v)

798

w)

745

x)

888

ExerciseFive

Find the sums. Check your work using the answer key at the

end of the exercise.

a)
172

b)
314

c)
431

+ 401

+ 553

+ 317

d)
213

e)
163

f)
412

+ 384

+ 224

+ 531

g)
731

h)
314

i)
253

+ 142

+ 524

+ 401

j)
243

k)
653

l)
576

+ 425

+ 434

+ 303

m)
732

n)
251

o)
605

+ 210

+ 734

+ 143

p)
715

q)
254

r)
351

+ 223

+ 125

+ 645

s)
754

t)
425

u)
465

+ 231

+ 143

+ 233

v)
501

w)
335

x)
561

+ 368

+ 403

+ 234

Answers to ExerciseFive

a)

573

b)

867

c)

748

d)

597

e)

387

f)

943

g)

873

h)

838

i)

654

j)

668

k)

1087

l)

879

m)

942

n)

985

o)

748

p)

938

q)

379

r)

996

s)

985

t)

568

u)

698

v)

869

w)

738

x)

795

ExerciseSix

Find the sums. Check your work using the answer key at the

end of the exercise.

a)
754

b)
410

c)
653

+ 231

+ 257

+ 142

d)
815

e)
243

f)
615

+ 170

+ 146

+ 303

g)
124

h)
451

i)
705

+ 762

+ 206

+ 261

j)
627

k)
357

l)
725

+ 512

+ 130

+ 273

m)
753

n)
425

o)
652

+ 902

+ 203

+ 137

p)
357

q)
675

r)
802

+ 132

+ 214

+ 254

s)
524

t)
723

u)
243

+ 321

+ 306

+152

v)
145

w)
262

x)
545

+ 213

+ 321

+ 131

Answers to ExerciseSix

a)

985

b)

667

c)

795

d)

985

e)

389

f)

918

g)

886

h)

657

i)

966

j)

1 139

k)

487

l)

998

m)

1 655

n)

628

o)

789

p)

489

q)

889

r)

1 056

s)

845

t)

1 029

u)

395

v)

358

w)

583

x)

676

Topic C: Self-Test

Mark

/22
Aim

19/22

Find the sums. Be sure to check your answers.
12 marks

a)
46

b)
32

c)
72

+ 23

+ 13

+ 25

d)
56

e)
65

f)
25

+ 21

+ 34

+ 51

g)
324

h)
183

i)
753

+ 263

+ 514

+ 145

j)
618

k)
224

l)
563

+ 120

+ 465

+ 216

Solve each of the following word problems.

6 marks Be sure to include the unit of measure in your answer.
(2 marks each) Be sure to circle information and underline what is being asked.

- Mahala’s dad worked 45 hours one week and 52 hours the next week. How many hours did he work during those two weeks?

- A trucker drove 526 kilometers on the first trip and 341 kilometers on the next. How many kilometers did the trucker drive altogether?

- Find the perimeter of the garden.

12 metres

Garden
11 metres
11 metres

12 metres

a)

69

b)

45

c)
97

d)

77

e)
99

f)

76

g)

587

h)

697

i)
898

j)

738

k) 689

l)

779

B.

a)

97 hours

b)
867

kilometres

c)

46 metres

Answers to Topic C Self-Test A.
EmotionsCheck

How are you feeling? Are your palms moist? How is your breathing? Take control. Be the boss. If you are feeling anxious, practice your breathing exercise.

Remember: breathe in slowly to the count of four, hold it for the count of four, and breathe out slowly to the count of four.

Unit 2 Review – Addition

You will now practice all the skills you learned in Unit 2. Check your work using the answer key at the end of the review.

Check out your addition facts.

a)
5

b)
8

c)
3

d)
9

+ 6

+ 2

+ 4

+ 7

e)
7

f)
6

g)
9

h)
2

+ 10

+ 8

+ 4

+ 3

i)
8

j)
3

k)
9

l)
5

+ 4

+ 3

+ 9

+ 4

m)
1

n)
3

o)
6

p)
5

+ 2

+ 1

+ 9

+ 3

Add across or horizontally.

a)

8

+

7 =

b)

0

+

3

=

c)

8

+

10 =

d)

5

+

2

=

e)

2

+

2

=

f)

7

+

5

=

g)

9

+

8

=

h)

3

+

6

=

i)

9

+

5

=

j)

1

+

5

=

k)
6 + 10 =
l)
4 + 1 =

m)
7 + 3 =
n)
5 + 8 =

o)
2 + 6 =
p)
8 + 3 =

Find the sums.

a)
6

b)
5

c)
4

2

2

4

+ 4

+ 1

+ 8

d)
3

e)
2

f)
6

4

3

4

+ 5

+ 4

+ 7

g)
3

h)
7

i)
3

4

2

6

+ 6

+ 4

+ 8

Find the sums.

a)
26

b)
42

c)
44

+ 30

+ 57

+ 32

d)
32

e)
83

f)
76

+ 81

+ 13

+ 12

g)
34

h)
54

i)
52

+ 51

+ 22

+ 43

j)
25

k)
72

l)
66

+ 42

+ 35

+ 12

Find the sums.

a)
342

b)
725

c)
362

+ 523

+ 142

+ 417

d)
425

e)
284

f)
315

+ 172

+ 314

+ 132

g)
363

h)
741

i)
403

+ 415

+ 225

+ 445

j)
654

k)
234

l)
525

+ 215

+ 352

+ 431

Word Problems.

- Find the perimeter of the shape. Be sure to put the unit of measure in your answer. Write the name of the shape below the picture.

3 metres

1 metre
1 metre

3 metres

- 5 metres

5 metres
5 metres

5 metres

- The CN Tower in Toronto is 554 metres high. On top of the tower is a TV mast that is 122 metres high. What is the total height of the tower and TV mast?

- Answers to Unit 2 ReviewA.a)8 metres, rectangleb)20 metres, squarec)676 metresd)98 kilograms
Seung weighs 36 kilograms. His father weighs 62 kilograms. How much do they weigh altogether?

a)

11

b)

10

c)

7

d)

16

e)

17

f)

14

g)

13

h)

5

i)

12

j)

6

k)

18

l)

9

m)

3

n)

4

o)

15

p)

8

B.

a)

15

b)

3

c)

18

d)

7

e)

4

f)

12

g)

17

h)

9

i)

14

j)

6

k)

16

l)

5

m)

10

n)

13

o)

8

p)

11

C.

a)

12

b)

8

c)

16

d)

12

e)

9

f)

17

g)

13

h)

13

i)

17

D.

a)

56

b)

99

c)

76

d)

113

e)

96

f)

88

g)

85

h)

76

i)

95

j)

67

k)

107

l)

78

E.

a)

865

b)

867

c)

779

d)

597

e)

598

f)

447

g)

778

h)

966

i)

848

j)

869

k)

586

l)

956

F.

CONGRATULATIONS!!Now you have finished Unit 2.TEST TIME!Ask your instructor for the Practice Test for this unit.Once you’ve done the practice test, you need to do the unit 2 test.Again, ask your instructor for this.Good luck!

148
Book 1

3

Unit 3

Subtraction

Topic A: Subtraction

Subtraction takes an amount away from another amount. The result of subtraction is called the difference.

The minus sign ─ means to subtract.

says nine minus three equals six or nine take away three is six The difference between 9 and 3 is 6.

Subtraction is the opposite of addition. Look at the examples:

5 + 4 = 9

4 + 5 = 9

9 – 4 = 5

9 – 5 = 4

8

+ 3

11

11

─ 3

8

3

11

+ 8

11

─ 8

3

Subtraction facts are a tool that you will use to do subtraction questions.

Exercise One

Check out your subtraction facts by doing this exercise as

quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them.

a)
5

b)
3

c)
7

d)
1

─ 4

─ 2

─ 7

─ 0

e)
8

f)
9

g)
4

h)
6

─ 2

─ 7

─ 3

─ 1

i)
7

j)
2

k)
7

l)
8

─ 2

─ 2

─ 6

─ 7

m)
0

n)
7

o)
3

p)
6

─ 0

─ 1

─ 0

─ 6

q)
4

r)
6

s)
9

t)
8

─ 2

─ 2

─ 5

─ 6

u)
5

v)
8

w)
1

x)
7

─ 3

─ 1

─ 1

─ 0

y)
9

z)
3

aa)

2

bb)

7

─ 9

─ 1

─ 1

─ 4

Answers to ExerciseOne

a)

1

b)

1

c)

0

d)

1

e)

6

f)

2

g)

1

h)

5

i)

5

j)

0

k)

1

l)

1

m)

0

n)

6

o)

3

p)

0

q)

2

r)

4

s)

4

t)

2

u)

2

v)

7

w)

0

x)

7

y)

0

z)

2

aa)

1

bb)

3

ExerciseTwo

Check out your subtraction facts by doing this exercise as

quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them.

a)
8

b)
9

c)
7

d)
6

─ 4

─ 1

─ 5

─ 4

e)
9

f)
5

g)
2

h)
6

─ 4

─ 2

─ 0

─ 3

i)
8

j)
6

k)
4

l)
9

─ 3

─ 5

─ 4

─ 0

m)
7

n)
5

o)
9

p)
3

─ 3

─ 5

─ 8

─ 3

q)
5

r)
9

s)
4

t)
8

─ 0

─ 2

─ 1

─ 5

u)
5

v)
9

w)
6

x)
8

─ 1

─ 3

─ 0

─ 8

y)
9

z)
4

aa)

8

bb)

7

─ 6

─ 0

─ 0

─ 4

a)

4

b)

8

c)

2
d) 2
e) 5
f) 3
g) 2

h)

3

i)

5

j)

1
k) 0
l) 9
m) 4
n) 0

o)

1

p)

0

q)

5

r)

7

s)

3

t)
3

u) 4

v)

6

w)

6

x)

0

y)

3

z)

4

aa) 8

bb) 3

Answers to Exercise Two
ExerciseThree

Check out your subtraction facts by doing this exercise as

quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you – practice the.

a)
8

b)
5

c)
2

d)
4

─ 4

─ 5

─ 1

─ 3

e)
3

f)
6

g)
7

h)
9

─ 3

─ 3

─ 6

─ 2

i)
9

j)
5

k)
8

l)
4

─ 0

─ 4

─ 8

─ 2

m)
7

n)
2

o)
6

p)
9

─ 7

─ 0

─ 1

─ 8

q)
6

r)
3

s)
9

t)
8

─ 4

─ 1

─ 9

─ 7

u)
3

v)
7

w)
8

x)
9

─ 2

─ 5

─ 3

─ 5

y)
8

z)
5

aa)

7

bb)

6

─ 6

─ 3

─ 1

─ 5

cc)

4

dd)

1

ee)

0

ff)

8

─ 1

─ 1

─ 0

─ 0

gg)

9

hh)

6

ii)
9

jj)

7

─ 7

─ 6

─ 6

─ 4

kk)

9

ll)

8

mm)

7

nn)

5

─ 3

─ 5

─ 2

─ 1

Answers to ExerciseThree

a)

4

b)

0

c)

1

d)

1

e)

0

f)

3

g)

1

h)

7

i)

9

j)

1

k)

0

l)

2

m)

0

n)

2

o)

5

p)

1

q)

2

r)

2

s)

0

t)

1

u)

1

v)

2

w)

5

x)

4

y)

2

z)

2

aa)

6

bb)

1

cc)

3

dd)

0

ee)

0

ff)

8

gg)

2

hh)

0

ii)

3

jj) 3
kk) 6
ll) 3
mm) 5
nn) 4

ExerciseFour

Check out your subtraction facts by doing this exercise as

quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them.

a)
11

b)
10

c)
12

d)
8

─ 7

─ 4

─ 7

─ 6

e)
10

f)
7

g)
9

h)
9

─ 8

─ 4

─ 3

─ 5

i)
7

j)
10

k)
12

l)
10

─ 3

─ 9

─ 8

─ 7

m)
8

n)
11

o)
10

p)
12

─ 3

─ 4

─ 6

─ 5

q)
10

r)
12

s)
8

t)
11

─ 4

─ 9

─ 5

─ 2

u)
11

v)
12

w)
10

x)
11

─ 8

─ 6

─ 2

─ 6

Answers to ExerciseFour

a)

4

b)

6

c)

5

d)

2

e)

2

f)

3

g)

6

h)

4

i)

4

j)

1

k)

4

l)

3

m)

5

n)

7

o)

4

p)

7

q)

6

r)

3

s)

3

t)

9

u)

3

v)

6

w)

8

x)

5

ExerciseFive

Check out your subtraction facts by doing this exercise as

quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them.

a)
12

b)
9

c)
11

d)
10

─ 3

─ 6

─ 9

─ 5

e)
8

f)
10

g)
12

h)
7

─ 8

─ 3

─ 4

─ 6

i)
9

j)
11

k)
9

l)
11

─ 8

─ 5

─ 7

─ 3

m)
10

n)
9

o)
12

p)
11

─ 2

─ 9

─ 6

─ 2

q)
12

r)
11

s)
10

t)
8

─ 9

─ 6

─ 4

─ 4

u)
9

v)
11

w)
12

x)
8

─ 4

─ 8

─ 2

─ 5

Answers to ExerciseFive

a)

9

b)

3

c)

2

d)

5

e)

0

f)

7

g)

8

h)

1

i)

1

j)

6

k)

2

l)

8

m)

8

n)

0

o)

6

p)

9

q)

3

r)

5

s)

6

t)

4

u)

5

v)

3

w)

10

x)

3

ExerciseSix

Check out your subtraction facts by doing this exercise as

quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them.

a)
11

b)
12

c)
10

d)
8

─ 7

─ 6

─ 9

─ 3

e)
12

f)
10

g)
9

h)
7

─ 5

─ 4

─ 7

─ 3

i)
8

j)
11

k)
6

l)
7

─ 4

─ 9

─ 5

─ 2

m)
10

n)
9

o)
12

p)
9

─ 7

─ 6

─ 8

─ 2

q)
11

r)
10

s)
12

t)
7

─ 4

─ 2

─ 7

─ 5

u)
11

v)
12

w)
10

x)
7

─ 6

─ 9

─ 3

─ 6

y)
10

z)
8

aa)

11

bb)

9

─ 6

─ 2

─ 5

─ 1

cc)

10

dd) 12

ee)

9

ff)

11

─ 5

─ 3

─ 4

─ 3

Answers to ExerciseSix

a)

4

b)

6

c)

1

d)

5

e)

7

f)

6

g)

2

h)

4

i)

4

j)

2

k)

1

l)

5

m)

3

n)

3

o)

4

p)

7

q)

7

r)

8

s)

5

t)

2

u)

5

v)

3

w)

7

x)

1

y)

4

z)

6

aa)

6

bb)

8

cc)

5

dd)

9

ee)

5

ff)

8

Need more practice?

Practice your subtraction facts using dominoes. Place all the dominoes face down. Flip over two dominoes and subtract.

ExerciseSeven

Check out your subtraction facts by doing this exercise as

quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them.

a)
13

b)
10

c)
9

d)
5

─ 5

─ 1

─ 4

─ 4

e)
9

f)
16

g)
11

h)
6

─ 9

─ 8

─ 7

─ 3

i)
18

j)
7

k)
13

l)
8

─ 9

─ 2

─ 7

─ 6

m)
4

n)
14

o)
2

p)
17

─ 3

─ 5

─ 0

─ 8

q)
14

r)
16

s)
12

t)
3

─ 6

─ 7

─ 4

─ 0

u)
5

v)
13

w)
10

x)
8

─ 2

─ 6

─ 7

─ 8

y)
13

z)
7

aa)

15

bb)

12

─ 9

─ 5

─ 7

─ 9

Answers to ExerciseSeven

a)

8

b)

9

c)

5

d)

1

e)

0

f)

8

g)

4

h)

3

i)

9

j)

5

k)

6

l)

2

m)

1

n)

9

o)

2

p)

9

q)

8

r)

9

s)

8

t)

3

u)

3

v)

7

w)

3

x)

0

y)

4

z)

2

aa)

8

bb)

3

ExerciseEight

Check out your subtraction facts by doing this exercise as

quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them.

a)
12

b)
6

c)
10

d)
11

─ 3

─ 2

─ 4

─ 9

e)
1

f)
8

g)
12

h)
11

─ 0

─ 1

─ 5

─ 2

i)
3

j)
11

k)
14

l)
8

─ 2

─ 8

─ 7

─ 3

m)
15

n)
9

o)
7

p)
11

─ 9

─ 7

─ 1

─ 5

q)
12

r)
10

s)
8

t)
6

─ 7

─ 8

─ 7

─ 5

u)
9

v)
7

w)
10

x)
9

─ 6

─ 3

─ 0

─ 1

y)
16

z)
9

aa)

9

bb)

8

─ 7

─ 2

─ 0

─ 4

Answers to ExerciseEight

a)

9

b)

4

c)

6

d)

2

e)

1

f)

7

g)

7

h)

9

i)

1

j)

3

k)

7

l)

5

m)

6

n)

2

o)

6

p)

6

q)

5

r)

2

s)

1

t)

1

u)

3

v)

4

w)

10

x)

8

y)

9

z)

7

aa)

9

bb)

4

ExerciseNine

Check out your subtraction facts by doing this exercise as

quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them.

a)
1

b)
7

c)
12

d)
5

─ 1

─ 6

─ 3

─ 0

e)
11

f)
4

g)
8

h)
14

─ 3

─ 1

─ 0

─ 9

i)
6

j)
12

k)
9

l)
2

─ 6

─ 8

─ 3

─ 1

m)
17

n)
6

o)
13

p)
4

─ 9

─ 0

─ 4

─ 2

q)
2

r)
10

s)
7

t)
5

─ 2

─ 3

─ 7

─ 1

u)
15

v)
3

w)
16

x)
9

─ 8

─ 1

─ 9

─ 5

y)
13

z)
7

aa)

12

bb)

4

─ 8

─ 4

─ 6

─ 0

Answers to ExerciseNine

a)

0

b)

1

c)

9

d)

5

e)

8

f)

3

g)

8

h)

5

i)

0

j)

4

k)

6

l)

1

m)

8

n)

6

o)

9

p)

2

q)

0

r)

7

s)

0

t)

4

u)

7

v)

2

w)

7

x)

4

y)

5

z)

3

aa)

6

bb)

4

ExerciseTen

Check out your subtraction facts by doing this exercise as

quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them.

a)
15

b)
3

c)
6

d)
11

─ 6

─ 3

─ 4

─ 4

e)
5

f)
10

g)
6

h)
14

─ 5

─ 2

─ 1

─ 8

i)
12

j)
8

k)
4

l)
7

─ 3

─ 2

─ 4

─ 0

m)
11

n)
5

o)
8

p)
10

─ 6

─ 3

─ 5

─ 9

q)
16

r)
9

s)
7

t)
4

─ 7

─ 8

─ 2

─ 3

u)
13

v)
2

w)
9

x)
17

─ 6

─ 2

─ 2

─ 8

y)
14

z)
1

aa)

12

bb)

3

─ 5

─ 0

─ 8

─ 1

cc)

8

dd) 10

ee)

13

ff)

7

─ 6

─ 6

─ 4

─ 4

Answers to ExerciseTen

a)

9

b)

0

c)

2

d)

7

e)

0

f)

8

g)

5

h)

6

i)

9

j)

6

k)

0

l)

7

m)

5

n)

2

o)

3

p)

1

q)

9

r)

1

s)

5

t)

1

u)

7

v)

0

w)

7

x)

9

y)

9

z)

1

aa)

4

bb)

2

cc)

2

dd)

4

ee)

9

ff)

3

ExerciseEleven

Check out your subtraction facts by doing this exercise

as quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them.

a)
18

b)
1

c)
3

d)
14

─ 9

─ 1

─ 0

─ 7

e)
8

f)
12

g)
6

h)
15

─ 3

─ 5

─ 4

─ 7

i)
11

j)
5

k)
6

l)
10

─ 3

─ 1

─ 0

─ 9

m)
5

n)
11

o)
4

p)
15

─ 3

─ 7

─ 0

─ 9

q)
16

r)
7

s)
10

t)
6

─ 8

─ 5

─ 2

─ 3

u)
13

v)
9

w)
2

x)
8

─ 8

─ 4

─ 0

─ 5

y)
10

z)
5

aa)

11

bb)

12

─ 1

─ 5

─ 5

─ 6

cc)

8

dd)

7

ee)

11

ff)

9

─ 2

─ 1

─ 2

─ 6

gg)

12

hh)

8

ii)
10

jj)

6

─ 3

─ 0

─ 7

─ 6

kk)

14

ll)
10

mm)

8

nn)

7

─ 9

─ 3

─ 7

─ 0

Answers to ExerciseEleven

a) 9

b)

0

c)

3

d)

7

e)

5

f)

7

g)

2

h) 8

i)

8

j)

4

k)

6

l)

1

m)

2

n)

4

o) 4

p)

6

q)

8

r)

2

s)

8

t)

3

u)

5

v) 5

w)

2

x)

3

y)

9

z)

0

aa)

6

bb)

6

cc) 6

dd)

6

ee)

9

ff)

3

gg)

9

hh)

8

ii) 3

jj) 0
kk) 5
ll) 7
mm) 1
nn) 7

Need some extra practice? Find a partner and play this card game. Using a regular deck of cards, a jack will be eleven, a queen will be twelve and a king will be thirteen. Shuffle the cards and deal them out. Keep your cards in a pile in front of you. Each player flips over a card. Take turns subtracting the numbers on the cards. If the person gets the right answer that person gets to keep the cards. If the person gets the wrong answer the other player gets the cards. The person who collects all the cards is the winner. You could also set a time limit and the person with the most cards when time is up is the winner.

ExerciseTwelve

Check out your subtraction facts by doing this exercise as

quickly as you can. Use your addition facts to help find the subtraction facts. Check your work using the answer key at the end of the exercise. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them.

a)
5

b)
9

c)
12

d)
4

─ 2

─ 1

─ 4

─ 2

e)
17

f)
2

g)
11

h)
7

─ 9

─ 1

─ 9

─ 7

i)
14

j)
16

k)
9

l)
8

─ 6

─ 9

─ 3

─ 1

m)
9

n)
14

o)
10

p)
15

─ 0

─ 8

─ 5

─ 8

q)
12

r)
13

s)
6

t)
5

─ 9

─ 5

─ 5

─ 0

u)
13

v)
8

w)
10

x)
7

─ 9

─ 4

─ 0

─ 3

y)
11

z)
9

aa)

6

bb)

4

─ 8

─ 9

─ 1

─ 4

cc)

13

dd)

3

ee)

11

ff)

5

─ 7

─ 2

─ 4

─ 4

gg)

11

hh)

9

ii)
6

jj)

3

─ 6

─ 5

─ 2

─ 3

kk)

4

ll)
7

mm)

10

nn)

12

─ 1

─ 6

─ 4

─ 7

oo)

15

pp) 10

qq)

9

rr)

8

─ 6

─ 8

─ 7

─ 8

a)

3

b)

8

c)

8

d)

2

e)

6

f)

1

g)

2

h)

0

i)

8

j)

7

k)

6

l)

7

m)

9

n)

6

o)

5

p)

7

q)

3

r)

8

s)

1

t)

5

u)

4

v)

4

w)

10

x)

4

y)

3

z)

0

aa)

5

bb)

0

cc)

6

dd)

1

ee)

7

ff)

1

gg)

5

hh)

4

ii)

4

jj)

0

kk)

3

ll)

1

mm) 6

nn)

5

oo)

9

pp)

2

qq)

2

rr)

0

Answers to Exercise Twelve
Emotions Check

How are you feeling? Are your palms moist? How is your breathing? Take control. Be the boss. If you are feeling anxious, practice your breathing exercise.

Remember: breathe in slowly to the count of four, hold it for the count of four and breathe out slowly to the count of four.

Subtracting Across

So far you have only been subtracting numbers when they are up and down or vertical.

Example:
9

─ 5

4

Another way to subtract numbers is across or horizontally.

Example:

9 ─ 5 = 4

When you subtract numbers across, you work from left to right.

Exercise One

Practice subtracting across or horizontally. Check your work

using the answer key at the end of the exercise.

a)
6 ─ 3 =
b)
12 ─ 8 =

c)
4 ─ 1 =
d)
8 ─ 6 =

e)
18 ─ 9 =
f)
11 ─ 4 =

g)
7 ─ 2 =
h)
16 ─ 7 =

i)
10 ─ 5 =
j)
2 ─ 0 =

k)
9 ─ 5 =
l)
17 ─ 8 =

m)
5 ─ 3 =
n)
14 ─ 9 =

o)

15

─

6

=

p)

3

─

1

=

q)

13

─

7

=

r)

1

─

0

=

s)

10

─

4

=

t)

6

─

2

=

174

Book 1

Answers to ExerciseOne

a)

3

b)

4

c)

3

d)

2

e)

9

f)

7

g)
5

h)

9

i)

5

j)

2

k)

4

l)

9

m)

2

n)
5

o)

9

p)

2

q)

6

r)

1

s)

6

t)

4

ExerciseTwo

Practice subtracting across or horizontally. Check your work

using the answer key at the end of the exercise

a)
9 ─ 6 =
b)
14 ─ 5 =

c)
8 ─ 4 =
d)
7 ─ 1 =

e)
11 ─ 7 =
f)
5 ─ 0 =

g)
4 ─ 3 =
h)
15 ─ 8 =

i)
11 ─ 9 =
j)
10 ─ 2 =

k)
9 ─ 2 =
l)
8 ─ 3 =

m)
13 ─ 5 =
n)
12 ─ 6 =

o)
10 ─ 7 =
p)
7 ─ 4 =

q)
5 ─ 1 =
r)
16 ─ 8 =

s)
10 ─ 9 =
t)
6 ─ 0 =

Answers to ExerciseTwo

a)

3

b)

9

c)

4

d)

6

e)

4

f)

5

g)
1

h)

7

i)

2

j)

8

k)

7

l)

5

m)

8

n)
6

o)

3

p)

3

q)

4

r)

8

s)

1

t)

6

ExerciseThree

Practice subtracting across or horizontally. Check your work

using the answer key at the end of the exercise

a)

3 ─ 2 =

b)

17 ─ 9 =

c)

14 ─ 7 =

d)

9 ─ 3 =

e)

12 ─ 5 =

f)

8 ─ 8 =

g)

6 ─ 1 =

h)

13 ─ 4 =

i)

11 ─ 6 =

j)

4 ─ 0 =

k)

8 ─ 1 =

l)

16 ─ 9 =

m)

7 ─ 0 =

n)

13 ─ 8 =

o)

12 ─ 3 =

p)

9 ─ 4 =

q)

15 ─ 7 =

r)

10 ─ 6 =

s)

11 ─ 5 =

t)

5 ─ 2 =

Answers to ExerciseThree

a)

1

b)

8

c)

7

d)

6

e)

7

f)

0

g)
5

h)

9

i)

5

j)

4

k)

7

l)

7

m)

7

n)
5

o)

9

p)

5

q)

8

r)

4

s)

6

t)

3

Word Problems

Learning subtraction facts is very important because once you know them all they become a tool to use when solving problems.

Words such as less than, minus, subtracted from, how many more, how much more, and difference tell you to subtract the numbers. Look for these words when reading word problems and underline them before trying to solve a problem.
Circle
the information that is given.

used 7
Example:There were 14 nails in a box. Lu used 7 of them. How many nails were still in the box?

14 nails
There were box?

in a box. Lu

of them. How many nails were still in the

You have circled 14 nails and 7. This is the information you will use to find the answer.

You have underlined “How many”. These words tell you to subtract.

14 nails

— 7 nails

7 nails

Exercise One

Solve each of the following word problems. Be sure to

underline the words that tell you to subtract. Circle

the information that is given. Check your work usingthe answer key at the end of the exercise. Have your instructor check your underlining and circling.

- Wolfgang walked 11 blocks. Ingrid walked 6 blocks. Wolfgang walked how much farther than Ingrid?

- Mika and her father went fishing. Mika caught 18 fish and her father caught 9 fish. How many more fish did Mika catch?

- Kuan-Lin was making moon cakes for the class party. She needed 15 cakes for the party.

On Monday she had made 7 moon cakes. How many moon cakes did she still need to make?

- Malik counted 12 cars in the parking lot where he worked. One hour later, he counted only 4 cars. How many cars left?

- There were 17 chairs in a room. Eight of them were being used. How many chairs were not being used?

- Answers to Exercise One
Amelie had $12 in her wallet. She bought a latté for $4. Find the difference.

a)
5 blocks

b)

9 fish

c)

8 moon cakes

d)
8 cars

e)

9 chairs

f)

$8

Topic A: Self-Test

Mark

/21
Aim
18/27

Find the differences. Be sure to check your answers.
9 marks

a)
16

b)
18

c)
14

─ 8

─ 9

─ 8

d)
11

e)
9

f)
17

─ 4

─ 3

─ 9

g)
10

h)
7

i)
15

─ 6

─ 5

─ 6

- Find the differences. Be sure to check your answers.
6
marks

a)

10 ─ 6 =

b)

7 ─ 5 =

c)

15 ─ 9 =

d)

9 ─ 4 =

e)

11 ─ 3 =

f)

10 ─ 7 =

Solve each of the following word problems.

6 marks Be sure to include the unit of measure in your answer.
(2 marks each) Be sure to circle information and underline what is being asked.

- Shada caught 17 fish. She gave 8 fish to her grandmother. How many fish did she have left?

- Yuan went to the store with $15 to buy some rice. The rice cost $6. How much did he have left?

- Carlo had 13 metres of fencing. He used 8 metres around his flower garden. How many metres did he have left?

Answers to Topic A Self-TestA.

a)

8

b)

9

c)

6

d) 7

e)
6

f)

8

g)

4

h)

2

i)

9

B.

a)

4

b)

2

c)

6

d) 5

e)
8

f)

3

C.

a)

9 fish

b)
$9

c)
5 metres

Topic B: Subtraction of Larger Numbers

You can find the difference between two large numbers using the basic subtraction facts you have been practicing. Always take away or subtract the number after the minussign.

Use these steps to complete each subtraction question.

Step 1: Subtract the ones from the ones.

Step 2: Subtract the tens from the tens.

Step 3: Subtract the hundreds from the hundreds.

Example A:
57

– 26

Step 1: Subtract the ones from the ones. 7 ones – 6 ones = 1 one

57

– 26

1

Write the answer in line with the ones in the question.

Step2:
Subtract the tens from the tens. 5 tens – 2 tens = 3 tens

57

– 26

31

The difference between 57 and 26 is 31.

Example B:

628

─ 524

Step1:

Subtract the ones from the ones. 8 ones – 4 ones = 4 ones

628

─ 524

4

Write the answer in line with the ones in the question.

Step2:
Subtract the tens. 2 tens – 2 tens = 0 tens

628

─ 524

04

Write the answer in line with the tens in the question. The 0 must be placed in the answer to hold the tens place.

Step3:
Subtract the hundreds. 6 hundreds – 5 hundreds = 1 hundred

628

─ 524

104

Write the answer in line with the hundreds in the question. The difference between 628 and 524 is 104.

Exercise One

Find the differences. Check your work using the answer key at

the end of the exercise.

a)
87

b)
29

c)
48

d)
99

─ 36

─ 21

─ 40

─ 63

e)
75

f)
73

g)
92

h)
58

─ 45

─ 20

─ 21

─ 27

i)
84

j)
69

k)
45

l)
49

─ 23

─ 38

─ 23

─ 19

m)
59

n)
87

o)
88

p)
56

─ 14

─ 63

─ 15

─ 44

q)
96

r)
37

s)
70

t)
38

─ 75

─ 17

─ 50

─ 24

u)
31

v)
27

w)
74

x)
45

─ 10

─ 12

─ 53

─ 20

Answers to ExerciseOne

a)

51

b)

8

c)

8

d)

36

e)

30

f)

53

g)

71

h)

31

i)

61

j)

31

k)

22

l)

30

m)

45

n)

24

o)

73

p)

12

q)

21

r)

20

s)

20

t)

14

u)

21

v)

15

w)

21

x)

25

ExerciseTwo

Find the differences. Check your work using the answer key at

the end of the exercise.

a)
46

b)
65

c)
45

d)
53

─ 23

─ 42

─ 13

─ 20

e)
34

f)
48

g)
56

h)
26

─ 21

─ 32

─ 13

─ 15

i)
49

j)
58

k)
95

l)
37

─ 22

─ 27

─ 71

─ 14

m)
69

n)
86

o)
99

p)
89

─ 19

─ 71

─ 50

─ 55

q)
97

r)
87

s)
48

t)
36

─ 13

─ 25

─ 26

─ 11

u)
46

v)
86

w)
59

x)
84

─ 12

─ 43

─ 32

─ 14

Answers to ExerciseTwo

a)

23

b)

23

c)

32

d)

33

e)

13

f)

16

g)

43

h)

11

i)

27

j)

31

k)

24

l)

23

m)

50

n)

15

o)

49

p)

34

q)

84

r)

62

s)

22

t)

25

u)

34

v)

43

w)

27

x)

70

ExerciseThree

Find the differences. Check your work using the answer key at

the end of the exercise.

a)
23

b)
53

c)
32

d)
77

─ 11

─ 21

─ 20

─ 32

e)
31

f)
38

g)
33

h)
92

─ 21

─ 15

─ 13

─ 30

i)
94

j)
54

k)
74

l)
88

─ 23

─ 42

─ 33

─ 72

m)
46

n)
75

o)
85

p)
56

─ 36

─ 41

─ 12

─ 45

q)
64

r)
27

s)
76

t)
63

─ 22

─ 15

─ 53

─ 41

u)
52

v)
57

w)
69

x)
77

─ 41

─ 44

─ 46

─ 42

Answers to ExerciseThree

a)

12

b)

32

c)

12

d)

45

e)

10

f)

23

g)

20

h)

62

i)

71

j)

12

k)

41

l)

16

m)

10

n)

34

o)

73

p)

11

q)

42

r)

12

s)

23

t)

22

u)

11

v)

13

w)

23

x)

35

ExerciseFour

Find the differences. Check your work using the answer key at

the end of the exercise.

a)
476

b)
873

c)
589

─ 413

─ 560

─ 384

d)
793

e)
228

f)
995

─ 170

─ 123

─ 452

g)
896

h)
769

i)
788

─ 450

─ 405

─ 435

j)
579

k)
958

l)
696

─ 234

─ 403

─ 251

m)
657

n)
745

o)
967

─ 234

─ 412

─ 143

p)
456

q)
627

r)
878

─ 214

─ 512

─ 425

s)
357

t)
725

u)
678

─ 130

─ 214

─ 623

v)
526

w)
724

x)
429

─ 116

─ 221

─ 316

Answers to ExerciseFour

a)

63

b)

313

c)

205

d)

623

e)

105

f)

543

g)

446

h)

364

i)

353

j)

345

k)

555

l)

445

m)

423

n)

333

o)

824

p)

242

q)

115

r)

453

s)

227

t)

511

u)

55

v)

410

w)

503

x)

113

ExerciseFive

Find the differences. Check your work using the answer key at

the end of the exercise.

a)
543

b)
752

c)
328

─ 132

─ 150

─ 115

d)
758

e)
587

f)
857

─ 341

─ 425

─ 143

g)
545

h)
466

i)
964

─ 302

─ 115

─ 231

j)
679

k)
757

l)
467

─ 424

─ 136

─ 132

m)
536

n)
897

o)
979

─ 325

─ 287

─ 465

p)
907

q)
496

r)
778

─ 605

─ 144

─ 635

s)
573

t)
859

u)
735

─ 232

─ 734

─ 420

v)
912

w)
966

x)
578

─ 811

─ 732

─ 343

Answers to ExerciseFive

a)

411

b)

602

c)

213

d)

417

e)

162

f)

714

g)

243

h)

351

i)

733

j)

255

k)

621

l)

335

m)

211

n)

610

o)

514

p)

302

q)

352

r)

143

s)

341

t)

125

u)

315

v)

101

w)

234

x)

235

ExerciseSix

Find the differences. Check your work using the answer key

at the end of the exercise.

a)
353

b)
896

c)
786

─142

─ 675

─ 325

d)
743

e)
548

f)
685

─ 623

─ 336

─ 143

g)
393

h)
965

i)
478

─ 241

─ 130

─ 352

j)
968

k)
435

l)
694

─ 605

─ 234

─ 523

m)
576

n)
946

o)
664

─ 314

─ 615

─ 532

p)
824

q)
768

r)
497

─ 513

─ 633

─ 335

s)
985

t)
679

u)
598

─ 843

─ 436

─ 365

v)
984

w)
569

x)
747

─ 672

─ 238

─ 636

Answers to ExerciseSix

a)

211

b)

221

c)

461

d)

120

e)

212

f)

542

g)

152

h)

835

i)

126

j)

363

k)

201

l)

171

m)

262

n)

331

o)

132

p)

311

q)

135

r)

162

s)

142

t)

243

u)

233

v)

312

w)

331

x)

111

Topic B: Self-Test

Mark

/27
Aim

23/27

A.
Find the differences. Be sure to check your answers.
6 marks

a)
59

b)
27

c)
78

─ 33

─ 14

─ 23

d)
93

e)
67

f)
86

─ 81

─ 45

─ 56

- Find the differences. Be sure to check your answers.
6
marks

a)
896

b)
788

c)
467

─ 422

─ 531

─ 126

d)
549

e)
936

f)
654

─ 318

─ 725

─ 242

Solve each of the following word problems.

6 marks Be sure to include the unit of measure in your answer.
(2 marks each) Be sure to circle information and underline what is being asked.

- At noon the temperature was 34 degrees Celsius. At nine o’clock in the evening, it was 12 degrees Celsius. How many degrees did the temperature drop?

- Misha’s family is on a 179 kilometer trip. They have already gone 123 kilometers. How much farther to they have to go?

- The Burj Khalifa in Dubai is one of the tallest buildings in the world at 828 metres. The Eiffel Tower in Paris is 324 metres tall. How much taller is the Burj Khalifa than the Eiffel Tower?

Answers to Topic B Self-TestA.a)22 degrees Celsiusb) 56 kilometresc) 504 metres

a)

B.

26

b)
13

c)

55

d) 12

e)
22

f)

30

a)

474

b)
257

c)

341

d) 231

e)
211

f)

412

C.

Unit 3 Review – Subtraction

You will now practice all the skills you learned in Unit 3. Check your work using the answer key at the end of the review.

Check out your subtraction facts.

a)
5

b)
8

c)
3

d)
9

─ 2

─ 7

─ 1

─ 5

e)
18

f)
11

g)
13

h)
10

─ 9

─ 4

─ 5

─ 5

i)
6

j)
14

k)
16

l)
12

─ 6

─ 8

─7

─ 9

m)
17

n)
9

o)
13

p)
15

─ 9

─ 3

─ 6

─ 8

Subtract across or horizontally.

a)
8 ─ 6 =
b)
12 ─ 5 =

c)
10 ─ 10 =
d)
9 ─ 8 =

e)
11 ─ 6 =
f)
8 ─ 4 =

g)
7 ─ 3 =
h)
14 ─ 9 =

i)
10 ─ 8 =
j)
8 ─ 5 =

k)
13 ─ 4 =
l)
15 ─ 7 =

m)
14 ─ 7 =
n)
7 ─ 1 =

o)
17 ─ 8 =
p)
13 ─ 7 =

Find the differences.

a)
45

b)
78

c)
84

─ 23

─ 15

─ 52

d)
57

e)
78

f)
69

─ 10

─ 21

─ 43

g)
96

h)
88

i)
95

─ 45

─ 35

─ 33

j)
45

k)
85

l)
87

─ 15

─ 31

─ 45

Find the differences

a)
583

b)
799

c)
629

─ 163

─ 265

─ 305

d)
847

e)
978

f)
797

─ 406

─ 252

─ 652

g)
765

h)
854

i)
536

─ 243

─ 344

─ 314

j)
897

k)
669

l)
769

─ 246

─ 238

─ 564

Word Problems

- One week, Tiago changed 258 light bulbs in the building. The next week, Tiago changed 141 light bulbs. How many more bulbs did Tiago change the first week?

- Anoki drove 769 kilometres while his friend Dasan drove 534 kilometres on their trip. How many more kilometres did Anoki drive?

Answers to Unit 3 ReviewA.E.a) 117 light bulbsb) 235 kilometres

a)

3

b)

1

c)

2

d)

4

e)

9

f)

7

g)

8

h)

5

i)

0

j)

6

k)

9

l)

3

m)

8

n)

6

o)

7

p)

7

B.

a)

2

b)

7

c)

0

d)

1

e)

5

f)

4

g)

4

h)

5

i)

2

j)

3

k)

9

l)

8

m)

7

n)

6

o)

9

p)

6

C.

a)

22

b)

63

c)

32

d)

47

e)

57

f)

26

g)

51

h)

53

i)

62

j)

30

k)

54

l)

42

D.

a)

420

b)

534

c)

324

d)

441

e)

726

f)

145

g)

522

h)

510

i)

222

j)

651

k)

431

l)

205

CONGRATULATIONS!!Now you have finished Unit 3.TEST TIME!Ask your instructor for the Practice Test for this unit.Once you’ve done the practice test, you need to do the unit 3 test.Again, ask your instructor for this.Good luck!

4

Unit 4

Estimating, Time and Shapes

Topic A: Estimating

You use numbers in your everyday life. You often use estimating in your everyday life.

You go shopping and you only have twenty dollars, you may need to estimate how much your groceries are going to cost before you go to pay for them.

You commute by bus each day to work and it takes thirty-three minutes going to work and thirty-three minutes coming home at the end of the day. You would say that it takes you about one hour on the bus.

These are examples of estimating.

You have already learned about rounding numbers. You need to be able to round numbers in order to be able to estimate.

When you solve math problems, it is a good idea to estimate what the answer may be. Estimating the answer means finding an answer that is close to the real answer. Estimating helps you to see if the real answer is sensible. To estimate an answer, you need to round the numbers then add or subtract the rounded numbers. Remember to round to the nearest ten.

Example:

23

+ 45

Estimate:

20

+ 50

70

Example:

67

Estimate:

70

─ 31

─ 30

40

Example:

372

Estimate:

370

+ 416

+ 420

790

Example:

564

Estimate:

560

─ 243

─ 240

320

Exercise One

Estimate the following answers. Be sure to round to the

nearest 10 before adding. Check your work using the answer key at the end of the exercise.

a)
27

Estimate:

b)
42

Estimate:

+ 31

+ 51

c)
26

Estimate:

d)
14

Estimate:

+ 32

+ 52

e)
44

Estimate:

f)
31

Estimate:

+ 24

+ 27

g)
65

Estimate:

h)
46

Estimate:

+ 22

+ 23

i)
23

Estimate:

j)
42

Estimate:

+ 72

+ 36

k)
64

Estimate:

l)
32

Estimate:

+ 14

+ 20

m) 423

Estimate:

n) 526

Estimate:

+ 324

+ 345

o) 123

Estimate:

p) 752

Estimate:

+ 541

+ 243

q) 429

Estimate:

r) 324

Estimate:

+ 316

+ 115

s) 162

Estimate:

t)
156

Estimate:

+ 531

+ 322

u) 302

Estimate:

v) 326

Estimate:

+ 473

+ 607

w) 312

Estimate:

x) 341

Estimate:

+ 148

+ 248

Answers to ExerciseOne

a)

60

b)

90

c)

60

d)

60

e)

60

f)

60

g)

90

h)

70

i)

90

j)

80

k)

70

l)

50

m)

740

n)

880

o)

660

p)

990

q)

750

r)

440

s)

690

t)

480

u)

770

v)

940

w)

460

x)

590

ExerciseTwo

Estimate the following answers. Be sure to round to the

nearest 10 before subtracting. Check your work using the answer key at the end of the exercise.

a)
35

Estimate:

b)
52

Estimate:

─ 16

─ 14

c)
67

Estimate:

d)
51

Estimate:

─ 19

─ 23

e)
36

Estimate:

f)
72

Estimate:

─ 17

─ 44

g)
38

Estimate:

h)
74

Estimate:

─ 19

─ 26

i)
93

Estimate:

j)
82

Estimate:

─ 89

─ 57

k)
56

Estimate:

l)
94

Estimate:

─ 27

─ 48

m) 752

Estimate:

n) 765

Estimate:

─ 342

─ 439

o) 673

Estimate:

p) 645

Estimate:

─ 424

─ 309

q) 811

Estimate:

r) 591

Estimate:

─ 502

─ 57

s) 972

Estimate:

t)
178

Estimate:

─ 447

─ 152

u) 471

Estimate:

v) 316

Estimate:

─ 146

─ 222

w) 678

Estimate:

x) 486

Estimate:

─ 425

─ 211

Answers to ExerciseTwo

a)

20

b)

40

c)

50

d)

30

e)

20

f)

30

g)

20

h)

40

i)

0

j)

20

k)

30

l)

40

m)

410

n)

330

o)

250

p)

340

q)

310

r)

540

s)

520

t)

30

u)

320

v)

100

w)

250

x)

280

ExerciseThree

Estimate the following answers. Be sure to

round to the nearest ten before adding or subtracting. Remember to circle the information and underline what is being asked. Check your work using the answer key at the end of the exercise.

Example:

There are 186 people living in my apartment building. If 103 are children, how many are adults?

103

There are
186
people living in my apartment building. If how many are adults?

are children,

186
Estimate:

190

─ 103
─ 100

90

About 90 people are adults.

- The bus has 84 passenger seats. All the seats are filled and 39 passengers are standing. How many passengers are on the bus?

- Trisha counted 67 boxes on one shelf. She counted 78 boxes on the next shelf. How many boxes were there altogether?

- The library loaned out 157 books on Monday. It loaned out 118 books on Tuesday. How many book did it loan on both days?

- Ryan worked on the computer for 78 minutes. Helen worked on the computer for 54 minutes. How much longer did Ryan work on the computer?

- The Ludlow factory has 73 people working in the factory. The Watson factory has 48 people working in their factory. How many more people work in the Ludlow factory?

- Mr. Martinez needs 257 metres of fencing. He has 125 metres. How much more fencing does he need to buy?

Answers to Exercise Threea)120 passengersd)30 minutesb) 150 boxese)20 peoplec)280 booksf)130 meters

Topic B: Time

The ancient Babylonians used a number system based on 60. We still use their number system when we talk about time.

There are 60 minutes in an hour, and there are 60 seconds in a minute.

60 minutes = 1 hour

60 seconds = 1 minute

Writing Time in Standard FormatTime is written in a standard format. Hours: Minutes: SecondsExample:12 noonwould be written as 12:00:00 or 12:00 (without the seconds)Example:4 o’clockwould be written as 4:00:00 or 4:00 (without the seconds)Example:8 hours, 47 minutes, 3 secondswould be written as 8:47:03Note:When there is only one number, put in a zero to hold the tens place.Example:3 hours, 9 minutes, 3 secondswould be written as 3:09:03

Exercise One

Write the following times in standard format. Check your

work using the answer key at the end of the exercise.

Example:

2 hours, 7 minutes, 31 seconds

2:07:31

Note: If there is only one number, remember to put in a zero to hold the tens place.

- 3 hours, 56 minutes, 42 seconds

- 12 hours, 2 minutes, 29 seconds

- 1 hour, 23 minutes, 54 seconds

- 6 hours, 7 minutes, 39 seconds

- 11 hours, 41 minutes

- 7 hours, 14 minutes, 59 seconds

- 21 hours, 36 minutes

- 1 hour, 51 minutes, 41 seconds

- Answers to Exercise One
5 hours, 18 minutes, 10 seconds.

a)

3:56:42

b)

12:02:29

c)

1:23:54

d)

6:07:39

e)

11:41

f)

7:14:59

g)

21:36

h)

1:51:41

i)

5:18:10

and P.M.

You need to go to the dentist at 9:00 a.m. This is in the morning because of the a.m. The abbreviation a.m. means ante meridiem or before noon. We use a.m. for any times between 12 midnight and 12 noon.

You are meeting friends for dinner at 6:00 p.m. This is at night because of the p.m. The abbreviation p.m. means post meridiem or after noon. We use p.m. for any times between 12 noon and 12 midnight.

Example:

You catch the bus at 7 o’clock in the morning.

The time would be written as 7:00 a.m.

Example:

You are meeting friends to go fishing at 6:30 at night.

The time would be written as 6:30 p.m.

ExerciseTwo

Write the following times using a.m. or p.m. Check your

work using the answer key at the end of the exercise.

Example:

The sun rises at 7:07 in the morning.

7:07 a.m.

- Your shift at work starts at 8:30 in the morning.

- Your class starts at 1:00 in the afternoon.

- Your son has soccer practice at 4:00 in the afternoon.

- Answers to Exercise Two
You catch your bus at 6:15 in the morning.

- You need to go to the doctor at 3:20 in the afternoon.

- You eat dinner at 6:30 in the evening.

- Your children go to bed at 8:45 in the evening.

- Your alarm goes off at 5:50 in the morning.

- Your friend called at 11:25 in the morning.

a)

8:30 a.m.

b)

1:00 p.m.

c)

4:00 p.m.

d)

6:15 a.m.

e)

3:20 p.m.

f)

6:30 p.m.

g)

8:45 p.m.

h)

5:50 a.m.

i)

11:25 a.m.

Rounding Time

When you round time, if the minutes are more than thirty, you round up to the next number of hours. If the minutes are less than thirty, you remain at the same number of hours.

Example:

If it took 45 minutes to drive to school, you would round that to one hour because 45 minutes is greater than 30 minutes.

Example:

If it took one hour and 15 minutes to get to school by bus, you would round that to one hour because 15 minutes is less than 30 minutes.

Example:

If it took 8 hours and 37 minutes to complete the painting job, you would round that to 9 hours because 37 minutes is greater than 30 minutes.

ExerciseThree

Round the following times to the nearest hour. Check

your work using the answer key at the end of the exercise.

Example:

The movie lasted 3 hours and 13 minutes.

3 hours

- You needed 2 hours and 15 minutes for grocery shopping.

- It took 1 hour and 50 minutes to cook dinner.

- You drove for 9 hours and 23 minutes.

- Your baby slept for 1 hour and 47 minutes.

- Answers to Exercise Three
You visited with friends for 3 hours and 11 minutes.

- It took 2 hours and 35 minutes to play the hockey game.

- You rode on the bus for 1 hour and 28 minutes.

- You walked to work in 38 minutes.

- How long does it take you to get to school?

a)

2 hours

b)

2 hours

c)

9 hours

d)

2 hours

e)

3 hours

f)

3 hours

g)

1 hour

h)

1 hour

i)

check with your instructor

Topic C: Shapes

Circle

The circle is a shape we all know.

These objects suggest the idea of a circle.

rim of coffee cups and glasses
top of lamp shades top of cans of food
compact discs

the ends of pipes and hoses (called the cross-section) the coloured part of your eye (the iris)

Add some examples of your own.

Triangle

A triangle is a three-sided shape. Triangles have three sides and threeangles.

Draw some different sized triangles here.

Rectangle

A rectangle is a four-sided shape. Rectangles have four sides and four right angles (square corners).

Can you think of anything that has a rectangle shape? Write it here.

Squares

A square is a special kind of rectangle. Squares have square corners and four sides are the same length

Can you think of anything that has a square shape? Write it here.

Exercise One

The following things give the idea of a shape. Write

the nameof the shape in each blank. Then draw the shape.

Example:

A cookie is a
circle
.

- A door is a

.

- This page is a
.

- A yield sign is a
.

- A room is usually a
.

- A coin is a
.

- A ten dollar bill is a
.

- The rim of a jar is a
.

- This warning sign

is a
.

- Answers to Exercise One
A pizza is a
.

a)

rectangle

b)

rectangle

c)

triangle

d)

rectangle

e)

circle

f)

rectangle

g)

circle

h)

triangle

i)

circle

ExerciseTwo

Look around the room and find each of the following shapes.

Write the name on the line. Have your instructor check your answers.

Example:

A rectangle
door

- A circle

- A rectangle

- A square

- A triangle

ExerciseThree

Circle the correct shape in each line. Have your

instructor check your answers.

- A rectangle.

- A circle

- A square

- A triangle

ExerciseFour

What shape are the following things? Write triangle,square, rectangle or circle on the line.

a)
b)

Answers to Exercise Four
c)
d)

e)
f)

g)
h)

a) circle

b)
triangle

c)
rectangle

d) square

e)
rectangle or triangle

f) circle

g) square

h) rectangle

Unit 4 Review – Estimating, Time, Shapes

You will now practice all the skills you learned in Unit 4. Check your work using the answer key at the end of the review.

Estimate the following sums. Be sure to round to the nearest 10 before adding.

a)
23

Estimate:

b)
68

Estimate:

+ 32

+ 17

c)
34

Estimate:

d)
42

Estimate:

+ 28

+ 53

e)
74

Estimate:

f)
33

Estimate:

+ 24

+ 28

g)
17

Estimate:

h)
27

Estimate:

+ 42

+ 18

- Estimate the following sums. Be sure to round to the nearest 10 before adding.

a) 625

Estimate:

b) 432

Estimate:

+ 254

+ 325

c) 328

Estimate:

d) 529

Estimate:

+ 163

+ 248

e) 536

Estimate:

f)
867

Estimate:

+ 137

+ 215

g) 843

Estimate:

h) 435

Estimate:

+ 107

+ 127

Estimate the following answers. Be sure to round to the nearest 10 before subtracting.

a)
43

Estimate:

b)
64

Estimate:

─ 28

─ 25

c)
73

Estimate:

d)
83

Estimate:

─ 47

─ 24

e)
68

Estimate:

f)
54

Estimate:

─ 28

─ 22

g)
67

Estimate:

h)
85

Estimate:

─ 29

─ 29

Estimate the following answers. Be sure to round to the nearest 10 before subtracting.

a) 625

Estimate:

b) 908

Estimate:

─ 407

─ 413

c) 976

Estimate:

d) 882

Estimate:

─ 134

─ 257

e) 572

Estimate:

f)
908

Estimate:

─ 154

─ 713

g) 965

Estimate:

h) 988

Estimate:

─ 702

─ 254

- Write the following times in standard format.

- 10 hours, 20 minutes, 12 seconds

- 8 hours,45 minutes, 6 seconds

- 5 hour, 32 minutes, 45 seconds

- 1 hour, 7 minutes, 28 seconds

- 12 hours, 55 minutes

- 6 hours, 5 minutes, 39 seconds

Write the following times using a.m. or p.m.

- The movie starts at 6:45 in the evening.

- Your friend calls and wakes you up at 3:23 in the morning.

- Your dog barks at the mailman at 2:35 in the afternoon.

- Your morning break is at 10:15.

Round the following times to the nearest hour.

- You took a walk for 47 minutes.

- Your round trip (there and back) to the mall took 2 hours and 12 minutes.

Circle the correct shape in each line.

- A triangle

- A square

The following things give the idea of a shape. Write the name of the shape in each blank.

- A window is a
.

- A checkerboard is a
.

- A watch is a
.

- A yield sign is a
.

J.
Word Problems.
Estimate the following answers. Be sure to round to the nearest 10 before adding or subtracting. Remember to circle
the information and underline what is being asked.

- The Sears Tower is 443 metres tall. It has a 105 metre TV antenna on top.

Estimate the height of the building and the antenna.

- A restaurant used 76 kilograms of potatoes and 68 kilograms of meat.

Estimate how many kilograms of potatoes and meat the restaurant used altogether.

- Paolo’s father weighs 78 kilograms. Paolo weighs 29 kilograms. Estimate how much more Paolo’s father weighs.

- Chi bought 54 litres of gasoline on Tuesday. He bought 38 litres of gasoline on Friday. Estimate how many litres of gas he bought altogether.

a)50b)90c)60d)90e)90f)60g)60h)50B.a)880b)760c)490d)780e)680f)1 090g)950h)570C.a)10b)30c)20d)60e)40f)30g)40h)60D.a)220b)500c)850d)620e)420f)200g)270h)740E.a)10:20:12b)8:45:06c)5:32:45d)1:07:28e)12:55f)6:05:39F.a)6:45 p.m.b)3:23 a.m.c)2:35 p.m.d)10:15 a.m.G.a)1 hourb)2 hours
Answers to Unit 4 Review A.

H.

Have your instructor check these.

I.

a)

rectangle

b) square

c)

circle

d)

triangle

J.

a)

550 metres

b) 150 kilograms

c)

50 kilograms

d)

90 litres

CONGRATULATIONS!!Now you have finished Unit 4.TEST TIME!Ask your instructor for the Practice Test for this unit.Once you’ve done the practice test, you need to do the unit 4 test.Again, ask your instructor for this.Good luck!

Book 1 Review

You will now practice all the skills you learned in Book 1. Check your work using the answer key at the end of the review.

Ifyoucan‟trememberhowtodoaquestion, go back to the lesson on this topic to refresh your memory. The unit and topic for where each question came from is listed next to the question.

Example: 1-B means Unit 1, Topic B

1-B

- Count the number of things in each picture. Write the number and word name.

Numeral: Word Name
Numeral: Word Name
a)
b)

●●● ● ●● ● ●
●●●●●●
c)
d)

Numeral:
Numeral:

Word Name:
Word
Name:

1-C

- Fill the blanks to make each sentence true. Draw a picture for b and d.

- 58 means
tens and
ones.

- 18 means
tens and
ones. Draw your picture below.

- 471 means
hundreds,
tens,
ones.

- 127 means
hundreds,
tens,
ones. Draw your picture below.

Write the place value name (ones, tens, hundreds) for each underlined digit.

a)
564

b)
239

c)
986

d)
534

Name the digit for the place value named from the number below.

5 782

- tens

b)
hundreds

Write the word names for the numbers.

a)
17

b)
342

c)
625

Write numerals for these word names.

- seventy-five

b) nineteen

c) seven hundred fifty

d) nine hundred five

e) eight hundred seventy-three

1-D

- Place a box around the larger number.

a) 452
245
b) 678
687

Arrange these numbers in order from smallest to largest.

a) 86
668
886
686
868
66
866

b) 23
323
223
33
332
322
232

Write <, > or = in each blank as needed.

a) 23
34

b)

118
118

c) 667
576

d)

405
450

1-E

- Round each number to the nearest 10.

a)
52

b) 123

c)
178

d) 89

Word Problems. For each problem, round the numbers to the nearest 10.

- The polar bear can weigh 1 002 kilograms, a koala bear can weigh 14 kilograms, a panda bear can weigh 113 kilograms, a kodiak bear can weigh 679 kilograms and a black bear can weigh 272 kilograms. Round each number to the nearest 10.

Bear

Number

RoundedNumber

Polar bear

Koala bear

Panda bear

Kodiak bear

Black bear

How much money do you have?

a)

How much money to you have?
cents

b)

How much money do you have?
dollars

2-A

- Check out your addition facts.

a)
0

b)
2

c)
8

d)
1

+ 8

+ 3

+ 2

+ 4

e)
5

f)
9

g)
6

h)
3

+ 0

+ 5

+ 7

+ 6

Add across or horizontally.

a)

7

+

4

=

b)

3

+

0

=

c)

2

+

9

=

d)

9

+

8

=

e)

6

+

2

=

f)

5

+

6

=

g)

8

+

9

=

h)

4

+

2

=

- Find the sums.

a)
4

b)
2

c)
4

5

7

2

+ 3

+ 8

+ 8

d)
4

e)
3

f)
6

6

2

1

+ 7

+ 3

+ 5

- Find the sums.

a)
5

b)
2

c)
3

2

3

0

3

4

1

+ 4

+ 7

+ 2

d)
2

e)
5

f)
4

3

1

3

1

3

2

+ 2

+ 2

+ 6

Find the perimeter of the shape. Be sure to put the unit of measure in your answer. Write the name of the shape below the picture.

- 3 metres

2 metres

b)

5 metres
3 metres

4 metres

c)

2 metres

Find the sums.

a)
46

b)
35

c)
82

+ 33

+ 93

+ 56

d)
91

e)
740

f)
638

+ 17

+ 859

+ 610

g)
521
h)
970

+ 848
+ 625

Word Problems.

- Seven cars were in the first row. Four cars were in the second row. How many cars are there in the first two rows?

- One bicycle stored ordered 56 bikes. Another store ordered 72 bikes. How many bikes did both stores order?

- A mail carrier walked 51 kilometres in a week. The next week she walked 48 kilometres the next week. How far did she walk in two weeks?

3-A

- Check out your subtraction facts.

a)
9

b)
6

c)
17

d)
14

− 5

− 3

− 8

− 7

e)
14
g)
11
g)
12
h)
9

U.
Subtract
acrossorhorizontally.

a)
4 − 1 =

b)

8 − 2 =

c)
17 − 8 =

d)

11 − 6 =

e)
6 − 4 =

f)

11 − 3 =

g)
10 − 1 =

h)

13 − 8 =

3-B

- Find the differences.

a)
76
b)
84
c)
95

d)
69
e)
852
f)
789

g)
938
h)
959

Word Problems. Solve each work problem.

- There were 18 roses in a bouquet. Milton gave 9 roses away. How many roses were left?

- A city has 89 mail carriers. One day only 54 were at work. How many were not at work?

- Mariko and Stefan went 5-pin bowling. Mariko scored 274 points while Stefan scored 152. How many more points did Mariko score?

4-A

- Estimate the following answers. Be sure to round to the nearest 10 before adding.

a)
81

Estimate:

b)
53

Estimate:

+ 74

+ 39

c)
43

Estimate:

d) 733

Estimate:

+ 68

+ 719

e) 907

Estimate

f)
623

Estimate:

+ 448

+ 914

- Estimate the following answers. Be sure to round to the nearest 10 before subtracting.

- 82
Estimate:

b)
67
Estimate:

c)
61
Estimate:

d) 968
Estimate:

e) 577
Estimate

f)
742
Estimate:

Word Problems. Estimate the following answers. Be sure to round to the nearest 10 before adding or subtracting.

- Mr. Han worked in his store for 33 years. Before owning a store, he had worked in a bank for 24 years. How many years has Mr. Han worked?

- The longest span of the Lions Gate Bridge in Vancouver is 473 metres. The longest span of the Confederation Bridge in Prince Edward Island is 247 metres. What is the difference?

4-B

AA.
Write
the following times in standard format.

- 3 h, 22 min, 51 s

- 8 h, 38 min, 9 s

c) 10 h, 18 min, 23 s

d) 7 h, 43 min, 34 s

BB.
Write the following times using a.m. or p.m.

- The movie begins at 8:30 in the evening.

- The coffee shop opens at 5:15 in the morning.

- The shopping mall closes at 10:00 at night.

CC.
Round the following times to the nearest hour.

- The running time for the movie was 2 hours and 25 minutes.

- It took 5 hours and 53 minutes to go the hockey and return home after the game.

DD.
The following things give the idea of a shape. Write the name of the shape in each blank.

- A Christmas tree is a
.

- A swimming pool is a
.

- A quarter is a
.

EE.
What shape are the following things. Write triangle, square, rectangle or circle on the line.

- b)

Answers to Book 1 Review A.

- 4, four
b) 3, three
c)
8, eight
d) 6, six

B.

a) 5 tens, 8 ones
b) 1 ten, 8 ones
c)
4 hundreds, 7 tens, 1 one

d) 1 hundred, 2 tens, 7 ones

C.

a)
tens
b)
ones
c)
tens
d) hundreds

D.

a)
8
b)
7

E.

a)
seventeen
b)
three hundred forty-two
c)
six hundred twenty-five

F.

a)
75
b)
19
c)
750
d) 905
e) 873

452
687
G.

a)
b)

H.

a)
66 86 668 686 866 868 886
b) 23 33 223 232 322 323 332

I.

a)
<
b)
=
c)
>
d) <

J.

a)
50
b)
120
c)
180
d) 90

K.

a)

Bear

Number

RoundedNumber

Polar bear

1 002

1 000

Koala bear

14

10

Panda bear

113

110

Kodiak bear

679

680

Black bear

272

270

L.

a)

40 cents

b)

12 dollars

M.

a)

8

b)

5

c)

10

d)

5

e)

5

f)

14

g)

13

h)

9

N.

a)

11

b)

3

c)

11

d)

17

e)

8

f)

11

g)

17

h)

6

O.

a) 12

b) 17

c)
14

d) 17

e)
8

f)
12

P.

a) 13
b) 16
c)
6
d) 8
e)
11
f)
15

Q.

- 10 metres, rectangle
b) 12 metres, triangle
c)
8 metres, square

R.

a)

79

b)

128

c)

138

d)

108

e)

1 799

f)

1 248

g)

1 369

h)

1 595

S.

a)

11 cars

b)

128 bikes

c)

99 kilometres

T.

a)

4

b)

3

c)

9

d)

7

e)

5

f)

9

g)

7

h)

6

U.

a)

3

b)

6

c)

9

d)

5

e)

2

f)

8

g)

9

h)

5

V.

a)

51

b)

41

c)

21

d)

53

e)

531

f)

139

g)

137

h)

427

W.a)9 rosesb)35 mail carriersc)122 pointsX.a)80 + 70 = 150d)730 + 720 = 1 450b) 50 + 40 = 90e)910 + 450 = 1 360c)40 + 70 = 110f)620 + 910 = 1 530Y.a)d)b)e)c)f)Z.a)50 yearsb) 220 metresAA.a)3:22:51b)8:38:09c)10:18:23d) 7:43:34BB.a)8:30 p.m.b)5:15 a.m.c)10:00 p.m.CC.a)2 hoursb)6 hoursDD.a)triangleb)rectanglec)circleEE.a)rectangleb)square

Glossary

addends The numbers to be added together in an addition question. In 3 + 5 = 8, the addends are 3 and 5.

axis Any straight line used for measuring or as a reference.

balance Balance has many meanings. In money matters, the balance is the amount left. It might be the amount left in a bank account (bank balance) or it might be the amount you still must pay on a bill (balance owing).

cancelled cheque A cheque that has been cashed. The cheque is stamped, or cancelled, so it is no longer negotiable.

circumference The distance around a circle; the perimeter of a circle.

commission Salespeople may be paid a percentage of the money made in sales. The commission is part or all their earnings.

common fractions eg, , ,

cross multiply In a proportion, multiply the numerator of the first fraction times the denominator of the second fraction. Then multiply the denominator of the first fraction times the numerator of the second fraction. In a true proportion, the products of the cross multiplication are equal.

denominator The bottom number in a common fraction; tells into how many equal parts the whole thing has been divided.

diameter The distance across a circle through its centre.

difference The result of a subtraction question, the answer. Subtraction gives the difference between two numbers.

digitAny of the ten numerals (0 to 9) are digits. This term comes from our ten fingers which are called digits. The numerals came to be called “digits” from the practice of counting on the fingers!

discount An amount taken off the regular cost. If something is bought “at a discount” it is bought at less than the regular price.

divide To separate into equal parts.

dividend The number or quantity to be divided; what you start with before you divide.

divisor The number of groups or the quantity into which a number (the dividend) is to be separated.

equal = The same as

equation A mathematical statement that two quantities are equal. An equation may use numerals with a letter to stand for an unknown quantity. 6 + Y = 9

equivalent Equal in value; equivalent numbers (whole or fractions) can be used interchangeably; that is, they can be used instead of each other.

estimate Make an approximate answer. Use the sign
to mean approximately equal.

factors The numbers or quantities that are multiplied together to form a given product.

5
2 = 10, so 5 and 2 are factors of 10.

fraction Part of the whole; a quantity less than one unit.

horizontal in a flat position; we are horizontal when we lie in a bed. A horizontal line goes across the page.

improper fractionA common fraction with a value equal to or more than one.

infinite Without end, without limit.

invert To turn upside down.

like fractions With the same denominators.

lowest termsWhen the terms of a common fraction or ratio do not have a common factor (except 1), the fraction or ratio are in lowest terms (also called simplest form).

minuend The first number in a subtraction question.

mixed number A whole number and a common fraction. 1

mixed decimal A whole number and a decimal fraction. 1.75

multiple If a certain number is multiplied by another number, the product is a multiple of the numbers. Think of the multiplication tables. For example, 2, 4, 6, 8, 10, 12, 14. . . are multiples

of 2.

multiplicand The number to be multiplied.

multiplier The number you multiply by.

negotiable Something which can be cashed, that is, exchanged or traded as money.

numbers Numbers represent the amount, the place in a sequence; number is the idea of quantity or order.

numerals The digits 1,2,3,4,5,6,7,8,9,0 are also called numerals. These ten digits are combined to make infinite numerals. Digits are like the letters, numerals are like the words and numbers are the meaning.

numerator The top number in a common fraction; the numerator tells how many parts of the whole thing are being considered.

overdrawn If the value of the cheques or money taken from a bank account is higher than the amount of money in the account, then the account is overdrawn. The account is “in the hole” or “in the red” are expressions sometimes used.

parallel Two objects or lines side by side, never crossing and always the same distance from each other. Railway tracks are parallel, the lines on writing paper are parallel.

percent % For every one hundred.

perimeter The distance around the outside of a shape.

place value We understand numbers by the way the digits (numerals) are arranged in relationship to each other and to the decimal point. Each position has a certain value. Our number system is a decimal system. The place value is based on ten.

prime number A number that can only be divided evenly by itself and 1.

product The result of a multiplying question, the answer.

proper fractionA common fraction with a value less than one.

proportion Generally, proportion is a way of comparing a part of something to the whole thing. Eg. his feet are small in proportion to his height. In mathematics, proportion is used to describe two or more ratios that are equivalent to each other.

quotient The result of a division question; the quotient tells how many times one number is contained in the other.

radius The distance from the centre of a circle to the outside of the circle.

ratio The relationship between two or more quantities. Eg. the ratio of men to women in the armed forces is 10 to 3 (10:3)

reciprocal A number, when multiplied by its reciprocal, equals 1. To find the reciprocal of a common fraction, invert it.
= 1

reduce Write a common fraction in lowest terms. Divide both terms by same factor.

remainder The amount left when a divisor does not divide evenly into the dividend. The remainder must be less than the divisor.

sign In mathematics, a symbol that tells what operation is to be performed or what the relationship is between the numbers.

+

plus, means to add

–

minus, means to subtract multiplied by, “times” divided by, division

=

equal, the same quantity as

not equal approximately equal

<

less than

>

greater than

less than or equal to greater than or equal to

simplify See reduce.

subtrahend The amount that is taken away in a subtraction question.

sum The result of an addition question, the answer to an addition question.

symbol A written or printed mark, letter, abbreviation etc. that stands for something else.

terma) A definite period of time, such as a school term or the term of a loan.

- Conditions of a contract; the terms of the agreement. c) In mathematics, the quantities in a fraction and in a ratio are called the termsof the fraction or the termsof the ratio. In an algebra equation, the quantities connected by a + or – sign are also called terms.

total The amount altogether.

transaction One piece of business. A transaction often involves money. When you pay a bill, take money from the bank or write a cheque, you have made a transaction.

unit Any fixed quantity, amount, distance or measure that is used as a standard. In mathematics, always identify the unit with which you are working. Eg. 3 km, 4 cups, 12 people,

$76, 70 books, 545 g.

unit price The price for a set amount. Eg. price per litre, price per gram.

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unlike fractions Fractions which have different denominators.

verticalin an up and down position; we are vertical when we are standing up. On a page, a vertical line is shown from the top to the bottom of the page.

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This is where you can add appendices or other back matter.