Adult Literacy Fundamental Mathematics: Book 1 - 2nd Edition

Adult Literacy Fundamental Mathematics: Book 1 - 2nd Edition

Wendy Tagami and Liz Girard

Leslie Tenta; Marjorie E. Enns; Steve Ballantyne; Lynne Cannon; James Hooten; and Kate Nonesuch

BCcampus

Victoria, B.C.

Contents

1

Accessibility Statement

BCcampus Open Education believes that education must be available to everyone. This means supporting the creation of free, open, and accessible educational resources. We are actively committed to increasing the accessibility and usability of the textbooks we produce.

Accessibility of This Textbook

The web version of this resource has been designed to meet Web Content Accessibility Guidelines 2.0, level AA. In addition, it follows all guidelines in Appendix A: Checklist for Accessibility of the Accessibility Toolkit – 2nd Edition. It includes:

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This statement was last updated on September 22, 2021.

The Accessibility Checklist table was adapted from one originally created by the Rebus Community and shared under a CC BY 4.0 License.

2

For Students: How to Access and Use this Textbook

This textbook is available in the following formats:

For more information about the accessibility of this textbook, see the Accessibility Statement in the back matter.

You can access the online webbook and download any of the formats for free here: Adult Literacy Fundamental Mathematics: Book 1. To download the book in a different format, look for the “Download this book” drop-down menu and select the file type you want.

How can I use the different formats?
Format Internet required? Device Required apps Accessibility Features Screen reader compatible
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Tips for Using This Textbook

3

About BCcampus Open Education

Adult Literacy Fundamental Mathematics: Book 1 – 2nd Edition by Wendy Tagami and Liz Girard was funded by BCcampus Open Education.

BCcampus Open Education began in 2012 as the B.C. Open Textbook Project with the goal of making post-secondary education in British Columbia more accessible by reducing students’ costs through the use of open textbooks and other OER. BCcampus supports the post-secondary institutions of British Columbia as they adapt and evolve their teaching and learning practices to enable powerful learning opportunities for the students of B.C. BCcampus Open Education is funded by the British Columbia Ministry of Advanced Education and Skills Training and the Hewlett Foundation.

Open educational resources (OER) are teaching, learning, and research resources that, through permissions granted by the copyright holder, allow others to use, distribute, keep, or make changes to them. Our open textbooks are openly licensed using a Creative Commons licence and are offered in various eBook formats free of charge, or as printed books that are available at cost.

For more information about open education in British Columbia, please visit the BCcampus Open Education website. If you are an instructor who is using this book for a course, please fill out our Adoption of an Open Textbook form.

This book was produced using the following styles: ABE ALF Book 1 Style Sheet [Word file].

4

Acknowledgments

Curriculum Writers

Liz Girard, North Island College

Wendy Tagami, Selkirk College

Advisory Committee Members

Jill Auchinachie, Camosun College

Leanne Caillier-Smith, College of the Rockies

Mercedes de la Nuez, Northwest Community College

Barbara Stirsky, University of the Fraser Valley

Jan Weiten, Vancouver Community College

The Deans and Directors of Developmental Education

Stephanie Jewell, Vancouver Community College

Vivian Hermansen, North Island College

Lyle Olsen, Selkirk College

Allison Alder, Selkirk College

The Adult Literacy Fundamental Working Group

Cheryl Porter, North Island College

Stephen & Jennifer Marks, Layout Editors

5

To the Learner

Text that reads: To the learner, welcome to fundamental mathematics, book 1.

You have the skills you need to be a strong student in this class. Adult math learners have many skills. They have a lot of life experience. They also use math in their everyday lives. This means that adult math learners may already know some of what is being taught in this book. Use what you already know with confidence!

How to Use This Book

This textbook has:

  • A Table of Contents listing the units, the major topics and subtopics.
  • A Glossary giving definitions for mathematical vocabulary used in the course.
  • A Grades Record to keep track of your marks.

The textbook has many exercises; some are quite short, but others have a great number of questions. You do not have to do every single question!

  • Do as many questions as you feel are necessary for you to be confident in your skill. It is best to do all the word problems.
  • If you leave out some questions, try doing every second or every third question. Always do some questions from the end of each exercise because the questions usually get harder at the end. You might use the skipped questions for review before a test.
  • If you are working on a difficult skill or concept, do half the exercise one day and finish the exercise the next day. That is a much better way to learn.

Self-tests at the end of most topics have an Aim at the top. If you do not meet the aim, talk to your instructor, find what is causing the trouble, and do some more review before you go on.

A screenshot that shows that a mark for a self test is 18 and the aim is 15 out of 18.

A Review and Extra Practice section is at the end of each unit. If there is an area of the unit that you need extra practice in, you can use this. Or, if you want, you can use the section for more review.

A Practice Test is available for each unit. You may:

  • Write the practice test after you have studied the unit as a practice for the end-of-chapter test, OR
  • you might want to write it before you start the unit to find what you already know and which areas you need to work on.

Unit Tests are written after each unit. Again, you must reach the Aim before you begin the next unit. If you do not reach the aim, the instructor will assist you in finding and practising the difficult areas. When you are ready, you can write a B test to show that you have mastered the skills.

A Final Test is to be written when you have finished the book. This final test will assess your skills from the whole book. You have mastered the skills in each unit and then kept using many of them throughout the course. The test reviews all those skills.

Grades Record – Book 1

You have also been given a sheet to write down your grades. After each test, you can write in the mark. This way you can keep track of your grades as you go through the course. This is a good idea to use in all your courses.

Grade Record – Book 1
Unit Practice Test Date of Test A Test A Date of Test B Test B
Example A check mark. September 4, 2020 25/33 September 7, 2020 25/33
1
2
3
4
Final Test

I

Unit 1: Number Sense

1

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 learn math?
  • Are you breathing faster than normal?
  • Is your heart pounding?
  • Do you feel cold?

Add any other feelings.

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 breaking exercise.

Start by breathing 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:

“Breath in, two, three, four. Hold, two, three, four. Breath 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.

2

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:

0   1   2   3   4   5   6   7   8   9

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.

Two Ways to Write Numbers
Numeral Word Name
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.

Exercise 1

Count 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.

Picture Answer
Heart, heart, heart. Numeral: 3

Word name: Three

  1. Club, club
Numeral:

Word name:

  1. Heart, heart, heart, heart, heart, heart
Numeral:

Word name:

  1. Diamond, diamond, diamond, diamond, diamond, diamond, diamond, diamond.
Numeral:

Word name:

  1. Heart, heart, heart, heart, heart, heart, heart, heart, heart.
Numeral:

Word name:

  1. Diamond
Numeral:

Word name:

  1. Club, club, club, club, club.
Numeral:

Word name:

  1. Spade, spade, spade, spade, spade, spade, spade.
Numeral:

Word name:

  1. Heart, heart, heart, heart.
Numeral:

Word name:

Answers to Exercise 1

  1. 2, two
  2. 6, six
  3. 8, eight
  4. 9, nine
  5. 1, one
  6. 5, five
  7. 7, seven
  8. 4, four

Exercise 2

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

Answers to Exercise 2
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

Topic B Self-Test

Mark        /18        Aim      15/18

  1. Count the number of things in each picture, then write the numeral and the word name.
    1. There are no things in this picture.
    2. Dot, dot, dot, dot, dot, dot.
    3. Dot, dot, dot, dot, dot, dot, dot, dot.
    4. Dot, dot, dot, dot, dot, dot, dot, dot, dot.
  2. Write the numerals from one to ten.

Answers to Topic B Self-Test

    1. 0, zero
    2. 6, six
    3. 8, eight
    4. 9, nine
    1. 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.

3

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.

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 ten ones.

Ten ones equals ten.

43 means 4 tens and 3 ones.

Ten, ten, ten, ten, and one, one, one.

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

Ten and ten.

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

Ten, ten, ten, ten, ten, ten, ten, ten, ten and one, one, one, one, one, one, one, one, one.

Exercise 1

Fill 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    4    tens and    9    ones.

Ten, ten, ten, ten, and one, one, one, one, one, one, one, one, one.

  1. 37 means           tens and           ones.
  2. 65 means           tens and           ones.
  3. 56 means           tens and           ones.
  4. 87 means           tens and           ones
  5. 33 means           tens and           ones.
  6. 60 means           tens and           ones.

Answers to Exercise 1

  1. 3 tens, 7 ones
  2. 6 tens, 5 ones
  3. 5 tens, 6 ones
  4. 8 tens, 7 ones
  5. 3 tens, 3 ones
  6. 6 tens, 0 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 the same as ten tens, and every hundred is the same as one hundred ones.

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

100                                                        100                                                 100

425 means 4 hundreds, 2 tens, and 5 ones

354 means 3 hundreds, 5 tens, and 4 ones

Exercise 2

Fill in the blanks to make each sentence true. Draw a picture for questions b, c, d, and e, like the examples. Check your work using the answer key at the end of the exercise. Ask your instructor to check your sketches.

  1. 190 =     1     hundreds,     9     tens,    0     ones.
  2. 555 =           hundreds,           tens,           ones.
  3. 309 =           hundreds,           tens,           ones.
  4. 499 =           hundreds,           tens,           ones.
  5. 480 =           hundreds,           tens,           ones.

 

Answers to Exercise 2

  1. 5 hundreds, 5 tines, 5 ones
  2. 3 hundreds, 0 tens, 9 ones
  3. 4 hundreds, 9 tens, 9 ones
  4. 4 hundreds, 8 tens, 0 ones

Exercise 3

Count 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.

  1.      2     hundreds,      0     tens,      3     ones =     203

    hundred, hundred, and one, one, one
  2. hundreds, tens, ones =
    hundred, hundred, hundred, hundred. ten, ten, ten, one
  3. hundreds, tens, ones =
    hundred, and ten, ten, ten, ten, ten, ten, ten, ten.
  4. hundreds, tens, ones =
    hundred, hundred, and one, one, one

Answers to Exercise 3

  1. 4 hundreds, 3 tens, 1 ones
  2. 1 hundreds, 8 tens, 0 ones
  3. 2 hundreds, 0 tens, 3 ones

Need more practice?

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

four five-dollar bills are the same value as one twenty-dollar bill

Exercise 4

Write the place value name (ones, tens, hundreds) for each underlined digit. Check your work using the answer key at the end of the exercise.

  1. 622 hundreds
  2. 468 tens
  3. 920          
  4. 920          
  5. 648          
  6. 426          
  7. 534          
  8. 555          
  9. 451          
  10. 901          
  11. 226          
  12. 486          

Answers to Exercise 4

  1. ones
  2. hundreds
  3. tens
  4. ones
  5. hundreds
  6. tens
  7. tens
  8. ones
  9. hundreds
  10. ones

Exercise 5

Underline the digit for the place value named. Check your work using the answer key at the end of the exercise.

  1. hundreds, 416
  2. tens, 368
  3. tens, 364
  4. hundreds, 456
  5. ones, 206
  6. ones, 634

Answers to Exercise 5

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

Emotions Check

How are you feeling?

  1. Are your palms moist?
  2. 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.

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.

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.

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:

Numerals 1 to 12
Numeral Word Name
0 zero
1 one
2 two
3 three
4 four
5 five
6 six
7 seven
8 eight
9 nine
10 ten
11 eleven
12 twelve

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 1 ten.

Numerals 13 to 19
Numeral Word Name Meaning
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

Exercise 6

Write 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.

  1. 6
  2. 17
  3. 4
  4. 14
  5. 12
  6. 13

Answers to Exercise 6

  1. six
  2. seventeen
  3. four
  4. fourteen
  5. twelve
  6. thirteen

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”.

Numerals 20 to 90
Number Word Name Meaning
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.

Numerals Between Tens
Tens Ones 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).

Exercise 7

Write the word names for these numbers. Check your work using the answer key at the end of the exercise.

  1. 24 twenty-four
  2. 35 thirty-five
  3. 83          
  4. 46          
  5. 59          
  6. 20          
  7. 53          
  8. 25          
  9. 15          
  10. 38          

Answers to Exercise 7

  1. eighty-three
  2. forty-six
  3. fifty-nine
  4. twenty
  5. fifty-three
  6. twenty-five
  7. fifteen
  8. thirty-eight

Exercise 8

Write the numerals for these word names. Check your work using the answer key at the end of the exercise.

  1. ninety-nine  99   
  2. sixty-seven  67   
  3. eighty-one          
  4. eighteen          
  5. twenty-six          
  6. thirteen          
  7. thirty          
  8. forty-three          

Answers to Exercise 8

  1. 81
  2. 18
  3. 26
  4. 13
  5. 30
  6. 43

When we write hundreds in words, we need two words. The first word tells us how many hundreds. The second word tells us we are counting hundreds.

200      two hundred

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

Remember

  • hyphen (-) between the tens and units
  • no hyphen anywhere else
  • no “s” on the hundred
  • no “and” between the hundreds place and the tens place

\begin{array}{llll} \mathbf{367 } \text{ is made of:} & \mathbf{3} \text{ hundreds} & \mathbf{6} \text{ tens} & \mathbf{7} \text{ ones} \\ \text{Each is written:}& \text{three hundred} & \text{sixty} & \text{seven}\end{array} \\ \text{Put the parts together: } \textbf{three hundred sixty-seven}

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

\begin{array}{llll} \mathbf{504 } \text{ is made of:} & \mathbf{5} \text{ hundreds} & \mathbf{0} \text{ tens} & \mathbf{4} \text{ ones} \\ \text{Each is written:}& \text{fice hundred} & & \text{four}\end{array} \\ \text{Put the parts together: } \textbf{five hundred four}

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

\begin{array}{llll} \mathbf{890} \text{ is made of:} & \mathbf{8} \text{ hundreds} & \mathbf{9} \text{ tens} & \mathbf{0} \text{ ones} \\ \text{Each is written:}& \text{eight hundred} & \text{ninety} & \end{array} \\ \text{Put the parts together: } \textbf{eight hundred ninety}

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

\begin{array}{llll} \mathbf{100} \text{ is made of:} & \mathbf{1} \text{ hundreds} & \mathbf{0} \text{ tens} & \mathbf{0} \text{ ones} \\ \text{Each is written:}& \text{one hundred} & & \end{array} \\ \text{Put the parts together: } \textbf{one hundred}

Remember

Empty spaces are not written in words.

Exercise 9

Write the word names for these numerals. Check your work using the answer key at the end of the exercise.

  1. 623 is made of:         
    Each is written:         
    Put the parts together:         
  2. 364 is made of:         
    Each is written:         
    Put the parts together:         
  3. 213 is made of:         
    Each is written:         
    Put the parts together:         
  4. 405 is made of:         
    Each is written:         
    Put the parts together:         

Now, write the word name for each number. Check your work using the answer key at the end of the exercise.

  1. 704
  2. 470
  3. 993
  4. 100
  5. 972

Answers to Exercise 9

  1. 623 is made of: 6 hundreds, 2 tens, 3 ones
    Each is written: six hundred, twenty, three
    Put the parts together: six hundred twenty-three 
  2. 364 is made of:3 hundreds, 6 tens, 4 ones
    Each is written: three hundred, sixty, four
    Put the parts together: three hundred sixty-four
  3. 213 is made of: 2 hundreds. 1 ten, 3 ones
    Each is written: two hundred, thirteen
    Put the parts together: two hundred thirteen 
  4. 405 is made of:4 hundreds, 0 tens, 5 ones
    Each is written: four hundred, five
    Put the parts together: four hundred five 
  5. seven hundred four
  6. four hundred seventy
  7. nine hundred ninety-three
  8. one hundred
  9. nine hundred seventy-two

 Topic C Self-Test

Mark       /17                  Aim        14/17

  1. Write the place value for the underlined digit. (6 marks)
    1. 765
    2. 903
    3. 479
    4. 185
    5. 732
    6. 397
  2. Write the word names for these numerals. (6 marks)
    1. 79
    2. 492
    3. 378
    4. 820
    5. 405
    6. 583
  3. Write the numerals for these word names. (5 marks)
    1. five hundred forty-seven
    2. three hundred eighty
    3. two hundred seventy-five
    4. four hundred sixteen
    5. nine hundred twenty-three

Answers to Topic C Self-Test

    1. tens
    2. tens
    3. hundreds
    4. ones
    5. ones
    6. hundreds
    1. seventy-nine
    2. four hundred ninety-two
    3. three hundred seventy-eight
    4. eight hundred twenty
    5. four hundred five
    6. five hundred eighty-three
    1. 547
    2. 380
    3. 275
    4. 416
    5. 923

4

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 1

Draw a line under the larger numeral in each pair.

  1. 43, 48
  2. 27, 21
  3. 64, 63
  4. 24, 35
  5. 92, 89
  6. 72, 81

Answers to Exercise 1

  1. 27
  2. 64
  3. 35
  4. 92
  5. 81

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

Example A: Compare 63 and 59

Look at the tens place.

Example B: Compare 496 and 476

Look at the hundreds place.

Look at the tens place.

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

Exercise 2

Draw a line under the larger numeral in each pair. Check your work using the answer key at the end of the exercise.

  1. 36, 46
  2. 580, 59
  3. 87, 67
  4. 716, 116
  5. 429, 449
  6. 289, 283
  7. 471, 422
  8. 316, 322
  9. 876, 318

Answers to Exercise 2

  1. 580
  2. 87
  3. 716
  4. 449
  5. 289
  6. 471
  7. 322
  8. 876

Exercise 3

Draw a line under the larger numeral in each pair. Check your work using the answer key at the end of the exercise.

  1. 148, 151
  2. 129, 132
  3. 34, 37
  4. 325, 236
  5. 118, 13
  6. 489 423
  7. 471, 422
  8. 316, 322
  9. 876, 319

Answers to Exercise 3

  1. 132
  2. 37
  3. 325
  4. 118
  5. 489
  6. 471
  7. 322
  8. 876

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:

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.

Exercise 4

Arrange these numbers in order from smallest to largest. Check your work using the answer key at the end of the exercise.

  1. 323, 32, 332, 33, 3, 322, 2
  2. 44, 7, 474, 47, 744, 74, 77
  3. 123, 135, 152, 125
  4. 472, 427, 452, 475

Answers to Exercise 4

  1. 2, 3, 32, 33, 322, 323, 332
  2. 7, 44, 47, 74, 77, 474, 744
  3. 123, 125, 135, 152
  4. 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.

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

Remember

The hungry mouth goes to the biggest number.

seven is less than 8

Exercise 5

Write <, >, or = in each blank as needed. Check your work using the answer key at the end of the exercise.

  1. 3     <      5
  2.     >      7
  3. 12           9
  4. 28           28
  5. 48           84
  6. 376           376
  7. 520           530
  8. 582           521
  9. 674           296
  10. 214           251
  11. 879           900
  12. 784           784

Answers to Exercise 5

  1. >
  2. =
  3. <
  4. =
  5. <
  6. >
  7. >
  8. <
  9. <
  10. =

Topic D Self-Test

Mark     /12             Aim    10/12

  1. Box the larger number of each pair. (6 marks)
    1. 978, 789
    2. 566, 556
    3. 120, 142
    4. 701, 710
    5. 430, 403
    6. 879, 987
  2. Arrange these numerals in order from smallest to largest. (2 marks)
    1. 75, 754, 475, 47, 747, 574, 775
    2. 18, 237, 429, 824, 37, 994, 112
  3. Write >, <. or = in each blank to make a true statement. (4 marks)
    1. 678           768
    2. 102           100
    3. 463           846
    4. 101           101

Answers to Topic D Self Test

    1. 978
    2. 566
    3. 142
    4. 710
    5. 430
    6. 987
    1. 47, 75, 475, 574, 747, 754, 775
    2. 18, 37, 112, 237, 429, 824, 994
    1. <
    2. >
    3. <
    4. =

5

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 rounding numbers.

We round numbers for many reasons:

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 an important skill.

Rounding to the Nearest Ten

Here is a short method to round to the nearest ten. When rounding to the nearest ten, do this:

  1. Underline the tens digit. 83
  2. Look at the digit following in the ones place. 83
  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.
    • 42, rounds to 40 (42 is nearer to 40 than to 50)
    • 14, rounds to 10
    • 83, rounds to 80
  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.
    • 36, rounds to 40 (36 is nearer to 40 than to 30)
    • 25, rounds to 30
    • 98, rounds 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.

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

Exercise 1

Round each number to the nearest 10. Check your work using the answer key at the end of the exercise.

  1. 47 is between           tens and           tens.
    47 is closest to           tens.
    Rounded number is          .
  2. 81 is between           tens and           tens.
    81 is closest to           tens.
    Rounded number is          .
  3. 14 is between           tens and           tens.
    14 is closest to           tens.
    Rounded number is          .
  4. 26 is between           tens and           tens.
    26 is closest to           tens.
    Rounded number is          .
  5. 98 is between           tens and           tens.
    98 is closest to           tens.
    Rounded number is          .
  6. 57 is between           tens and           tens.
    57 is closest to           tens.
    Rounded number is          .
  7. 73 is between           tens and           tens.
    73 is closest to           tens.
    Rounded number is          .

Answers to Exercise 1

  1. 4 tens, 5 tens
    5 tens
    50
  2. 8 tens, 9 tens
    8 tens
    80
  3. 1 tens, 2 tens
    1 ten
    10
  4. 2 tens, 3 tens
    3 tens
    30
  5. 9 tens. 10 tens
    10 tens
    100
  6. 5 tens, 6 tens
    6 tens
    60
  7. 7 tens, 8 tens
    7 tens
    70

Exercise 2

Round each number to the nearest ten. Check your work using the answer key at the end of the exercise.

  1. 22 ≈    20   
  2. 86 ≈    90   
  3. 31 ≈          
  4. 96 ≈          
  5. 84 ≈          
  6. 55 ≈          
  7. 8 ≈          
  8. 2 ≈          
  9. 63 ≈          
  10. 49 ≈          
  11. 25 ≈          
  12. 71 ≈          
  13. 38 ≈          
  14. 51 ≈          
  15. 88 ≈          

Answers to Exercise 2

  1. 30
  2. 100
  3. 80
  4. 60
  5. 10
  6. 0
  7. 60
  8. 50
  9. 30
  10. 70
  11. 40
  12. 50
  13. 90

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

\large \begin{array}{rll} \downarrow &amp;&amp; \\ 2\underline{3}8 &amp; \approx &amp; 240 \end{array} \qquad \begin{array}{rll} \downarrow &amp;&amp; \\ 8\underline{8}3 &amp; \approx &amp; 880 \end{array}\qquad \begin{array}{rll} \downarrow &amp;&amp; \\ 2\underline{9}8 &amp; \approx &amp; 300 \end{array}

Exercise 3

Round each number to the nearest ten. Check your work using the answer key at the end of the exercise.

  1. 424 ≈          
  2. 867 ≈          
  3. 499 ≈          
  4. 132 ≈          
  5. 278 ≈          
  6. 617 ≈          
  7. 208 ≈          
  8. 851 ≈          
  9. 124 ≈          
  10. 576 ≈          
  11. 315 ≈          
  12. 742 ≈          
  13. 397 ≈          
  14. 952 ≈          
  15. 639 ≈          

Answers to Exercise 3

  1. 420
  2. 870
  3. 500
  4. 130
  5. 280
  6. 620
  7. 210
  8. 850
  9. 120
  10. 580
  11. 320
  12. 740
  13. 400
  14. 950
  15. 640

Exercise 4

For 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 Cost Rounded to nearest ten
Towels $14 $10
Dishes $32 $30
Saucepan $43 $40
Microwave $109 $110
Carving knife $18 $20
  1. Akkul walked 12 kilometres on Monday, 26 kilometres on Tuesday and 6 kilometres on Wednesday. Round each number to the nearest ten.
    Day Number Rounded Number
    Monday 12  
    Tuesday 26  
    Wednesday 6  
  2. 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 Rounded Number
    Monday 57  
    Tuesday 124  
    Wednesday 31  
    Thursday 75  
  3. Jamir drove 678 kilometres, 493 kilometres, 387 kilometres and 914 kilometres in one week. Round each mileage to the nearest ten.
    Day Kilometres Rounded Number
    #1 678  
    #2 493  
    #3 387  
    #4 914  

Answers to Exercise 4

  1. 10, 30, 10
  2. 60, 120, 30, 80
  3. 680, 490, 390, 910

Topic E Self-Test

Mark     /12          Aim      10/12

  1. Round your answer to the nearest ten. (8 marks)
    1. 47 ≈          
    2. 123 ≈          
    3. 4 ≈          
    4. 945 ≈          
    5. 329 ≈          
    6. 481 ≈          
    7. 865 ≈          
    8. 916 ≈          
  2. 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
    78  
    91  
    79  
    67  
    102  

Answers to Topic E Self-Test

    1. 50
    2. 120
    3. 0
    4. 950
    5. 330
    6. 480
    7. 870
    8. 920
    1. 80, 90, 80, 70, 100

6

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 twos 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 by 5s.

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 10s.

Exercise 1

Count how much money you have. Check your work using the answer key at the end of the exercise.

Example:

Three nickles.

How many nickels?      3     

How much money do you have?    15 cents    

  1. How many toonies do you have?
    How much money do you have?           dollars.Four toonies.
  2. How many dimes do you have?
    How much money do you have?           cents.Seven dimes.
  3. How many nickels do you have?
    How much money do you have?           cents.Nine nickles.
  4. How many dimes do you have?
    How much money do you have?           cents.Four dimes.
  5. How many nickels do you have?
    How much money do you have?           cents.Ten nickles.
  6. How many toonies do you have?
    How much money do you have?           dollars.Thirteen toonies.
  7. How many dimes do you have?
    How much money do you have?           cents.Nine dimes.

Answers to Exercise 1

  1. 4 toonies, 8 dollars
  2. 7 dimes, 70 cents
  3. 9 nickels, 45 cents
  4. 4 dimes, 40 cents
  5. 10 nickels, 50 cents
  6. 13 toonies, 26 dollars
  7. 9 dimes, 90 cents

Topic F Self-Test

Mark   /16             Aim    13/16

  1. Write the first 10 odd numbers starting with 1. (5 marks)
  2. Write the first 10 even numbers starting at 2. (5 marks)
  3. How much money do you have? (6 marks, 2 marks each)
    1. How much money do you have?           cents.Fifteen nickles.
    2. How much money do you have?           dollars.Nineteen toonies.
    3. How much money do you have?           cents.Eight dimes.

Answers to Topic F Self-Test 

    1. 1, 3, 5, 7, 9, 11, 13, 15 17, 19
    1. 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
    1. 75 cents
    2. 38 dollars
    3. 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.

7

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.

  1. Count the number of things in each picture. Write the number and word name.
    Picture Answer
    1. club. club, club, club, club, and club. club, club, club.
    Numeral:
    Word Name:
    1. diamond, diamond, diamond, diamond, and diamond, diamond, diamond
    Numeral:
    Word Name:
    1. heart, heart, heart, and heart, heart, heart
    Numeral:
    Word Name:
    1. dot, dot, dot, dot, dot, dot, and dot, dot.
    Numeral:
    Word Name:
    1. dot, dot, and dot, dot, dot
    Numeral:
    Word Name:
  2. Fill in the blanks to make each sentence true. Draw a picture for questions b and e.
    1. 46 means           tens and           ones.
    2. 25 means           tens and           ones. Draw your picture below.
    3.            means           tens and           ones.
      ten. ten. ten, ten, ten, ten and one, one, one
    4. 138 =            hundreds,           tens,           ones.
    5. 231 =            hundreds,           tens,           ones. Draw your picture below.
    6.            hundreds           tens           ones = 
      hundred, hundred, hundred, and ten, ten, and one, one, one, one, one
  3. Write the place value names (ones, tens, hundreds) for each individual digit.
    1. 821
    2. 294
    3. 638
    4. 417
    5. 346
    6. 573
  4. Underline the digit for the place value named.
    1. hundreds, 164
    2. tens, 892
    3. tens, 250
    4. hundreds, 371
    5. ones, 485
    6. ones, 743
  5. Write the word names for the numbers.
    1. 73
    2. 14
    3. 5
    4. 39
    5. 52
    6. 496
    7. 803
    8. 640
  6. Write the numerals for these word names.
    1. forty-seven
    2. nineteen
    3. sixty-five
    4. thirty-eight
    5. twenty-four
    6. five hundred thirty-five
    7. three hundred sixty
    8. two hundred four
  7. Arrange these numbers in order from smallest to largest.
    1. 258, 32, 23, 282, 345, 534
    2. 452, 208, 27, 335, 635, 155
  8. Write <, > or = in each blank as needed.
    1. 37            52
    2. 4            0
    3. 349            394
    4. 67            67
  9. Round each number to the nearest ten.
    1. 37 ≈          
    2. 344 ≈          
    3. 68 ≈          
    4. 25 ≈          
    5. 51 ≈          
    6. 876 ≈          
  10. How much money do you have?
    1.          centsnickel, nickel, nickel, nickel, nickel, and nickel, nickel, nickel, nickel, nickel, and nickel, nickel, nickel, nickel
    2.          dollarstoonie, toonie, toonie, toonie, and toonie, toonie, toonie, and toonie, toonie, toonie, toonie, and toonie, toonie
    3.          cents
      dime, dime, dime, dime, dime, and dime, dime, dime, dime,
  11. Word problems.
    1. 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
      Honeydews
      Cantaloupes
    2. 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

    1. 9, nine
    2. 7, seven
    3. 6, six
    4. 8, eight
    5. 5, five
    1. 4 tens, 6 ones
    2. 2 tens, 5 ones
    3. 63, 6 tens, 3 ones
    4. 1 hundred, 3 tens, 8 ones
    5. 2 hundreds, 3 tens, 1 one
    6. 325, 3 hundreds, 2 tens, 5 ones
    1. hundreds
    2. tens
    3. ones
    4. hundreds
    5. tens
    6. ones
    1. 164
    2. 892
    3. 250
    4. 371
    5. 485
    6. 743
    1. seventy-three
    2. fourteen
    3. five
    4. thirty-nine
    5. fifty-two
    6. four hundred ninety-six
    7. eight hundred three
    8. six hundred forty
    1. 47
    2. 19
    3. 65
    4. 38
    5. 24
    6. 535
    7. 360
    8. 204
    1. 23, 32, 258, 282, 345, 534
    2. 27, 155, 208, 335, 452, 635
    1. <
    2. >
    3. <
    4. =
    1. 40
    2. 340
    3. 70
    4. 30
    1. 70 cents
    2. 26 dollars
    3. 90 cents
    1. Melon Number Rounded Number
      Watermelons 114 110
      Honeydews 287 290
      Cantaloupes 345 350
    2. Kilometres Number Rounded Number
      Saturday 106 110
      Sunday 187 190
      Monday 285 290

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!

 

II

Unit 2: Addition

8

Topic A: Addition

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

The plus sign + means to add.

Three diamons plus two diamonds equals five diamons.

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 1

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.

  1. \begin{align} 2 \\+4 \\ \hline 6 \end{align}
  2. \begin{align} 3 \\ +1 \\ \hline 4 \end{align}
  3. \begin{align} 1 \\ +2 \\ \hline \\ \end{align}
  4. \begin{align}7 \\ +0 \\ \hline \\ \end{align}
  5. \begin{align}0 \\ +4 \\ \hline \\ \end{align}
  6. \begin{align} 1 \\ +4\\ \hline \\ \end{align}
  7. \begin{align} 5 \\ +2\\ \hline \\ \end{align}
  8. \begin{align} 3 \\ +3 \\ \hline \\ \end{align}
  9. \begin{align} 2 \\ +0\\ \hline \\ \end{align}
  10. \begin{align} 6 \\ +3 \\ \hline \\ \end{align}
  11. \begin{align} 4\\ +4\\ \hline \\ \end{align}
  12. \begin{align} 3 \\ +0\\ \hline \\ \end{align}
  13. \begin{align} 5 \\ +3\\ \hline \\ \end{align}
  14. \begin{align} 1 \\ +6\\ \hline \\ \end{align}
  15. \begin{align} 0 \\ +5\\ \hline \\ \end{align}
  16. \begin{align} 8 \\ +1\\ \hline \\ \end{align}

Answers to Exercise 1

  1. 6
  2. 4
  3. 3
  4. 7
  5. 4
  6. 5
  7. 7
  8. 6
  9. 2
  10. 9
  11. 8
  12. 3
  13. 8
  14. 7
  15. 5
  16. 9

Exercise 2

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.

  1. \begin{align} 4 \\ +5 \\ \hline 9\end{align}
  2. \begin{align} 1 \\ +8\\ \hline 9 \end{align}
  3. \begin{align} 8 \\ +0 \\ \hline \\ \end{align}
  4. \begin{align}3 \\ +3 \\ \hline \\ \end{align}
  5. \begin{align}0 \\ +0 \\ \hline \\ \end{align}
  6. \begin{align} 2 \\ +3\\ \hline \\ \end{align}
  7. \begin{align} 7 \\ +1\\ \hline \\ \end{align}
  8. \begin{align} 0 \\ +9 \\ \hline \\ \end{align}
  9. \begin{align} 4 \\ +2\\ \hline \\ \end{align}
  10. \begin{align} 0 \\ +2 \\ \hline \\ \end{align}
  11. \begin{align} 0\\ +7\\ \hline \\ \end{align}
  12. \begin{align} 1 \\ +1\\ \hline \\ \end{align}
  13. \begin{align} 2 \\ +7\\ \hline \\ \end{align}
  14. \begin{align} 0 \\ +1\\ \hline \\ \end{align}
  15. \begin{align} 6 \\ +2\\ \hline \\ \end{align}
  16. \begin{align} 0 \\ +6\\ \hline \\ \end{align}

Answers to Exercise 2

  1. 9
  2. 9
  3. 8
  4. 6
  5. 0
  6. 5
  7. 8
  8. 9
  9. 6
  10. 2
  11. 7
  12. 2
  13. 9
  14. 1
  15. 8
  16. 6

Exercise 3

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.

  1. \begin{align} 3 \\ +6\\ \hline 9\end{align}
  2. \begin{align} 4\\ +5\\ \hline 9 \end{align}
  3. \begin{align} 4\\ +1\\ \hline \\ \end{align}
  4. \begin{align} 9\\ +0\\ \hline \\ \end{align}
  5. \begin{align} 2\\ +2\\ \hline \\ \end{align}
  6. \begin{align} 3 \\ +4\\ \hline \\ \end{align}
  7. \begin{align} 0\\ +6\\ \hline \\ \end{align}
  8. \begin{align} 5\\ +2 \\ \hline \\ \end{align}
  9. \begin{align} 4\\ +0\\ \hline \\ \end{align}
  10. \begin{align} 1\\ +8\\ \hline \\ \end{align}
  11. \begin{align} 2\\ +3\\ \hline \\ \end{align}
  12. \begin{align} 0\\ +5\\ \hline \\ \end{align}

Answers to Exercise 3

  1. 9
  2. 9
  3. 5
  4. 9
  5. 4
  6. 7
  7. 6
  8. 7
  9. 4
  10. 9
  11. 5
  12. 5

Exercise 4

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.

  1. \begin{align} 6 \\ +5\\ \hline 11\end{align}
  2. \begin{align} 8\\ +2\\ \hline 10 \end{align}
  3. \begin{align} 5\\ +3\\ \hline \\ \end{align}
  4. \begin{align} 5\\ +7\\ \hline \\ \end{align}
  5. \begin{align} 3\\ +4\\ \hline \\ \end{align}
  6. \begin{align} 2 \\ +6\\ \hline \\ \end{align}
  7. \begin{align} 7\\ +3\\ \hline \\ \end{align}
  8. \begin{align} 3\\ +9\\ \hline \\ \end{align}
  9. \begin{align} 9\\ +3\\ \hline \\ \end{align}
  10. \begin{align} 8\\ +1\\ \hline \\ \end{align}
  11. \begin{align} 4\\ +5\\ \hline \\ \end{align}
  12. \begin{align} 1\\ +9\\ \hline \\ \end{align}
  13. \begin{align} 2\\ +7\\ \hline \\ \end{align}
  14. \begin{align} 3\\ +5\\ \hline \\ \end{align}
  15. \begin{align} 6\\ +6\\ \hline \\ \end{align}
  16. \begin{align} 5\\ +6\\ \hline \\ \end{align}

Answers to Exercise 4

  1. 11
  2. 10
  3. 8
  4. 12
  5. 7
  6. 8
  7. 10
  8. 12
  9. 12
  10. 9
  11. 9
  12. 10
  13. 9
  14. 8
  15. 12
  16. 11

Exercise 5

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.

  1. \begin{align} 9\\ +2\\ \hline \\ \end{align}
  2. \begin{align} 6\\ +4\\ \hline \\ \end{align}
  3. \begin{align} 4\\ +7\\ \hline \\ \end{align}
  4. \begin{align} 2\\ +5\\ \hline \\ \end{align}
  5. \begin{align} 8\\ +3\\ \hline \\ \end{align}
  6. \begin{align} 7\\ +4\\ \hline \\ \end{align}
  7. \begin{align} 6\\ +3\\ \hline \\ \end{align}
  8. \begin{align} 5\\ +5 \\ \hline \\ \end{align}
  9. \begin{align} 9\\ +1\\ \hline \\ \end{align}
  10. \begin{align} 7\\ +5\\ \hline \\ \end{align}
  11. \begin{align} 4\\ +8\\ \hline \\ \end{align}
  12. \begin{align} 6\\ +2\\ \hline \\ \end{align}
  13. \begin{align} 7\\ +2\\ \hline \\ \end{align}
  14. \begin{align} 1\\ +2\\ \hline \\ \end{align}
  15. \begin{align} 3\\ +6\\ \hline \\ \end{align}
  16. \begin{align} 5\\ +4\\ \hline \\ \end{align}

Answers to Exercise 5

  1. 11
  2. 10
  3. 11
  4. 7
  5. 11
  6. 11
  7. 9
  8. 10
  9. 10
  10. 12
  11. 12
  12. 8
  13. 9
  14. 3
  15. 9
  16. 9

Exercise 6

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.

  1. \begin{align} 3 \\ +9\\ \hline \\ \end{align}
  2. \begin{align} 5\\ +3\\ \hline \\ \end{align}
  3. \begin{align} 4\\ +6\\ \hline \\ \end{align}
  4. \begin{align} 4\\ +3\\ \hline \\ \end{align}
  5. \begin{align} 6\\ +5\\ \hline \\ \end{align}
  6. \begin{align} 2\\ +8\\ \hline \\ \end{align}
  7. \begin{align} 9\\ +1\\ \hline \\ \end{align}
  8. \begin{align} 7\\ +5\\ \hline \\ \end{align}
  9. \begin{align} 3\\ +8\\ \hline \\ \end{align}
  10. \begin{align} 5\\ +2\\ \hline \\ \end{align}
  11. \begin{align} 6\\ +6\\ \hline \\ \end{align}
  12. \begin{align} 2\\ +9\\ \hline \\ \end{align}

Answers to Exercise 6

  1. 12
  2. 8
  3. 10
  4. 7
  5. 11
  6. 10
  7. 10
  8. 12
  9. 11
  10. 7
  11. 12
  12. 11

Need more practice?

Practice your addition facts using a set of dice.

Roll the dice and add the amounts on the dice.

Exercise 7

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 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.

  1. \begin{align} 7\\ +6\\ \hline 13\end{align}
  2. \begin{align} 5\\ +9\\ \hline 14\end{align}
  3. \begin{align} 10\\ +3\\ \hline \\ \end{align}
  4. \begin{align} 5\\ +7\\ \hline \\ \end{align}
  5. \begin{align} 7\\ +9\\ \hline \\ \end{align}
  6. \begin{align} 10\\ +9\\ \hline \\ \end{align}
  7. \begin{align} 8\\ +7\\ \hline \\ \end{align}
  8. \begin{align} 6\\ +4 \\ \hline \\ \end{align}
  9. \begin{align} 5\\ +10\\ \hline \\ \end{align}
  10. \begin{align} 8\\ +9\\ \hline \\ \end{align}
  11. \begin{align} 8\\ +2\\ \hline \\ \end{align}
  12. \begin{align} 10\\ +6\\ \hline \\ \end{align}
  13. \begin{align} 7\\ +4\\ \hline \\ \end{align}
  14. \begin{align} 1\\ +7\\ \hline \\ \end{align}
  15. \begin{align} 3\\ +6\\ \hline \\ \end{align}
  16. \begin{align} 5\\ +4\\ \hline \\ \end{align}

Answers to Exercise 7

  1. 13
  2. 14
  3. 13
  4. 12
  5. 16
  6. 19
  7. 15
  8. 10
  9. 15
  10. 17
  11. 10
  12. 16
  13. 11
  14. 8
  15. 9
  16. 9

Exercise 8

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 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.

  1. \begin{align} 10\\ +1\\ \hline \\ \end{align}
  2. \begin{align} 7\\ +7\\ \hline \\ \end{align}
  3. \begin{align} 10\\ +8\\ \hline \\ \end{align}
  4. \begin{align} 7\\ +8\\ \hline \\ \end{align}
  5. \begin{align} 4\\ +6\\ \hline \\ \end{align}
  6. \begin{align} 1 \\ +10\\ \hline \\ \end{align}
  7. \begin{align} 4\\ +7\\ \hline \\ \end{align}
  8. \begin{align} 3\\ +10\\ \hline \\ \end{align}
  9. \begin{align} 0\\ +7\\ \hline \\ \end{align}
  10. \begin{align} 3\\ +9\\ \hline \\ \end{align}
  11. \begin{align} 10\\ +7\\ \hline \\ \end{align}
  12. \begin{align} 6\\ +4\\ \hline \\ \end{align}

Answers to Exercise 8

  1. 11
  2. 14
  3. 18
  4. 15
  5. 10
  6. 11
  7. 11
  8. 13
  9. 7
  10. 12
  11. 17
  12. 10

Exercise 9

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 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.

  1. \begin{align} 4 \\ +9\\ \hline \\ \end{align}
  2. \begin{align} 7\\ +2\\ \hline \\ \end{align}
  3. \begin{align} 5\\ +5\\ \hline \\ \end{align}
  4. \begin{align} 3\\ +6\\ \hline \\ \end{align}
  5. \begin{align} 6\\ +10\\ \hline \\ \end{align}
  6. \begin{align} 8\\ +5\\ \hline \\ \end{align}
  7. \begin{align} 6\\ +9\\ \hline \\ \end{align}
  8. \begin{align} 6\\ +6\\ \hline \\ \end{align}
  9. \begin{align} 3\\ +7\\ \hline \\ \end{align}
  10. \begin{align} 9\\ +3\\ \hline \\ \end{align}
  11. \begin{align} 2\\ +8\\ \hline \\ \end{align}
  12. \begin{align} 5\\ +10\\ \hline \\ \end{align}
  13. \begin{align} 5\\ +5\\ \hline \\ \end{align}
  14. \begin{align} 10\\ +3\\ \hline \\ \end{align}
  15. \begin{align} 8\\ +8\\ \hline \\ \end{align}
  16. \begin{align} 2\\ +10\\ \hline \\ \end{align}

Answers to Exercise 9

  1. 13
  2. 9
  3. 10
  4. 9
  5. 16
  6. 13
  7. 15
  8. 12
  9. 10
  10. 12
  11. 10
  12. 15
  13. 10
  14. 13
  15. 16
  16. 12

Exercise 10

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 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.

  1. \begin{align} 7\\ +10\\ \hline \\ \end{align}
  2. \begin{align} 10\\ +4\\ \hline \\ \end{align}
  3. \begin{align} 8\\ +8\\ \hline \\ \end{align}
  4. \begin{align} 2\\ +9\\ \hline \\ \end{align}
  5. \begin{align} 4\\ +6\\ \hline \\ \end{align}
  6. \begin{align} 3 \\ +10\\ \hline \\ \end{align}
  7. \begin{align} 7\\ +4\\ \hline \\ \end{align}
  8. \begin{align} 3\\ +8\\ \hline \\ \end{align}
  9. \begin{align} 8\\ +3\\ \hline \\ \end{align}
  10. \begin{align} 7\\ +8\\ \hline \\ \end{align}
  11. \begin{align} 5\\ +9\\ \hline \\ \end{align}
  12. \begin{align} 9\\ +5\\ \hline \\ \end{align}

Answers to Exercise 10

  1. 17
  2. 14
  3. 16
  4. 11
  5. 10
  6. 13
  7. 11
  8. 11
  9. 11
  10. 15
  11. 14
  12. 14

Exercise 11

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 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.

  1. \begin{align} 7 \\ +2\\ \hline \\ \end{align}
  2. \begin{align} 4\\ +4\\ \hline \\ \end{align}
  3. \begin{align} 3\\ +5\\ \hline \\ \end{align}
  4. \begin{align} 4\\ +6\\ \hline \\ \end{align}
  5. \begin{align} 8\\ +1\\ \hline \\ \end{align}
  6. \begin{align} 9\\ +6\\ \hline \\ \end{align}
  7. \begin{align} 1\\ +3\\ \hline \\ \end{align}
  8. \begin{align} 0\\ +2 \\ \hline \\ \end{align}
  9. \begin{align} 4\\ +9\\ \hline \\ \end{align}
  10. \begin{align} 9\\ +2\\ \hline \\ \end{align}
  11. \begin{align} 4\\ +1\\ \hline \\ \end{align}
  12. \begin{align} 8\\ +8\\ \hline \\ \end{align}

Answers to Exercise 11

  1. 9
  2. 8
  3. 8
  4. 10
  5. 9
  6. 15
  7. 4
  8. 2
  9. 13
  10. 11
  11. 5
  12. 16

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.

Exercise 12

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

  1. \begin{align} 6\\ +7\\ \hline 13 \end{align}
  2. \begin{align} 8\\ +3\\ \hline 11 \end{align}
  3. \begin{align} 4\\ +2\\ \hline \\ \end{align}
  4. \begin{align} 8\\ +7\\ \hline \\ \end{align}
  5. \begin{align} 1\\ +2\\ \hline \\ \end{align}
  6. \begin{align} 6\\ +4\\ \hline \\ \end{align}
  7. \begin{align} 5\\ +8\\ \hline \\ \end{align}
  8. \begin{align} 2\\ +5\\ \hline \\ \end{align}
  9. \begin{align} 7\\ +6\\ \hline \\ \end{align}
  10. \begin{align} 0\\ +3\\ \hline \\ \end{align}
  11. \begin{align} 9\\ +7\\ \hline \\ \end{align}
  12. \begin{align} 7\\ +2\\ \hline \\ \end{align}
  13. \begin{align} 4\\ +4\\ \hline \\ \end{align}
  14. \begin{align} 3\\ +5\\ \hline \\ \end{align}
  15. \begin{align} 4\\ +6\\ \hline \\ \end{align}
  16. \begin{align} 8\\ +1\\ \hline \\ \end{align}

Answers to Exercise 12

  1. 13
  2. 11
  3. 6
  4. 15
  5. 3
  6. 10
  7. 13
  8. 7
  9. 13
  10. 3
  11. 16
  12. 9
  13. 8
  14. 8
  15. 10
  16. 9

Adding Across

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

Example:

\begin{align} 4 \\ +5 \\ \hline 9 \end{align}

Another way to add numbers is across or horizontally.

4 + 5 = 9

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

Exercise 13

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.

  1. 10 + 0 =
  2. 2 + 2 =
  3. 5 + 3 =
  4. 1 + 1 =
  5. 8 + 4 =
  6. 7 + 1 =
  7. 0 + 4 =
  8. 6 + 3 =
  9. 3 + 2 =
  10. 1 + 10 =
  11. 9 + 3 =
  12. 4 + 9 =
  13. 3 + 7 =
  14. 4 + 8 =

Answers to Exercise 13

  1. 10
  2. 4
  3. 8
  4. 2
  5. 12
  6. 8
  7. 4
  8. 9
  9. 5
  10. 11
  11. 12
  12. 13
  13. 10
  14. 12

Exercise 14

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.

  1. 9 + 6 =
  2. 8 + 9 =
  3. 9 + 9 =
  4. 2 + 3 =
  5. 7 + 3 =
  6. 10 + 8 =
  7. 9 + 7 =
  8. 8 + 8 =
  9. 8 + 10 =
  10. 3 + 9 =
  11. 9 + 2 =
  12. 4 + 4 =

Answers to Exercise 14

  1. 15
  2. 17
  3. 18
  4. 5
  5. 10
  6. 18
  7. 16
  8. 16
  9. 18
  10. 12
  11. 11
  12. 8

Word Problems

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

Word such as:

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.

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 2 pages. After lunch she read 9 pages. How many pages did she read in all?

\begin{align} 2\text{ pages}\\+9\text{ pages}\\ \hline 11\text{ pages} \end{align}

Jane read 11 pages in all.

Exercise 15

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.

  1. 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?
  2. 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?
  3. 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?
  4. 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?
  5. 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 15

  1. 16 cans
  2. 12 shots
  3. 10 people
  4. 17 runs
  5. 14 apples

Topic A Self-Test

Mark       /22                 Aim       19/22

  1. Find the sums. Be sure to check your answers. (12 marks)
    1. \begin{align}9\\+6\\ \hline\\ \end{align}
    2. \begin{align}5\\+8\\ \hline\\ \end{align}
    3. \begin{align}4\\+2\\ \hline\\ \end{align}
    4. \begin{align}7\\+6\\ \hline\\ \end{align}
    5. \begin{align}3\\+5\\ \hline\\ \end{align}
    6. \begin{align}1\\+9\\ \hline\\ \end{align}
    7. \begin{align}2\\+3\\ \hline\\ \end{align}
    8. \begin{align}6\\+4\\ \hline\\ \end{align}
    9. \begin{align}8\\+1\\ \hline\\ \end{align}
    10. \begin{align}9\\+8\\ \hline\\ \end{align}
    11. \begin{align}7\\+4\\ \hline\\ \end{align}
    12. \begin{align}5\\+6\\ \hline\\ \end{align}
  2. Find the sums. Be sure to check your answers. (4 marks)
    1. 6 + 7 =
    2. 3 + 8 =
    3. 4 + 6 =
    4. 8 + 5 =
  3. Solve each of the following word problems. Be sure to include the unit of measure in your answer. Be sure to circle the information and underline what’s being asked.(6 marks, 2 marks each)
    1. Paco worked 5 hours on Monday and 9 hours on Tuesday. How many hours did Paco work in total?
    2. 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?
    3. Omari bought 3 bananas on Monday. He bought 5 bananas on Tuesday. How many bananas did he buy altogether?

Answers to Topic A Self Test

    1. 15
    2. 13
    3. 6
    4. 13
    5. 8
    6. 10
    7. 5
    8. 10
    9. 9
    10. 17
    11. 11
    12. 11
    1. 13
    2. 11
    3. 10
    4. 13
    1. 14 hours
    2. 14 robins
    3. 8 bananas

9

Topic B: Addition of Three or More Numbers

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

  1. Add the first two numbers together.
  2. Add that sum to the next number.
  3. Add that sum to the next number (if needed).

Example A:

\begin{align} 6\\ 1\\ +3\\ \hline \\ \end{align}

  1. Add the first two numbers together.
    \begin{align} 6 \\ +1\\ \hline 7 \end{align}
  2. Add that sum to the next number.
    \begin{align} 7\\ +3 \\ \hline 10 \end{align}

The sum of:

\begin{align} 6 \\ 1\\ +3\\ \hline 10 \end{align}

Example B: 

\begin{align} 4\\ 5\\ +7\\ \hline \\ \end{align}

  1. Add the first two numbers together.
    \begin{align} 4\\ +5\\ \hline 9 \end{align}
  2. Add that sum to the third number.
    \begin{align} 9\\ +7\\ \hline 16 \end{align}

The sum of:

\begin{align} 4\\ 5\\ +7\\ \hline 16 \end{align}

Exercise 1

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

  1. \begin{align} 1\\ 2\\ +5\\ \hline \\ \end{align}
  2. \begin{align} 6\\ 3\\ +2\\ \hline \\ \end{align}
  3. \begin{align} 7\\ 1\\ +6\\ \hline \\ \end{align}
  4. \begin{align} 3\\ 6\\ +5\\ \hline \\ \end{align}
  5. \begin{align} 8\\ 1\\ +4\\ \hline \\ \end{align}
  6. \begin{align} 5\\ 4\\ +8\\ \hline \\ \end{align}
  7. \begin{align} 1\\ 5\\ +7\\ \hline \\ \end{align}
  8. \begin{align} 7\\ 2\\ +5\\ \hline \\ \end{align}
  9. \begin{align} 1\\ 8\\ +3\\ \hline \\ \end{align}
  10. \begin{align} 4\\ 5\\ +9\\ \hline \\ \end{align}
  11. \begin{align} 2\\ 2\\ +8\\ \hline \\ \end{align}
  12. \begin{align} 6\\ 3\\ +5\\ \hline \\ \end{align}
  13. \begin{align} 7\\ 2\\ +5\\ \hline \\ \end{align}
  14. \begin{align} 3\\ 2\\ +5\\ \hline \\ \end{align}
  15. \begin{align} 6\\ 2\\ +5\\ \hline \\ \end{align}
  16. \begin{align} 4\\ 4\\ +5\\ \hline \\ \end{align}

Answers to Exercise 1

  1. 8
  2. 11
  3. 14
  4. 14
  5. 13
  6. 17
  7. 13
  8. 14
  9. 12
  10. 18
  11. 12
  12. 14
  13. 14
  14. 10
  15. 13
  16. 13

Exercise 2

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

  1. \begin{align} 3\\ 5\\ +7\\ \hline \\ \end{align}
  2. \begin{align} 2\\ 6\\ +8\\ \hline \\ \end{align}
  3. \begin{align} 4\\ 1\\ +9\\ \hline \\ \end{align}
  4. \begin{align} 5\\ 4\\ +2\\ \hline \\ \end{align}
  5. \begin{align} 3\\ 6\\ +4\\ \hline \\ \end{align}
  6. \begin{align} 2\\ 5\\ +4\\ \hline \\ \end{align}
  7. \begin{align} 6\\ 3\\ +2\\ \hline \\ \end{align}
  8. \begin{align} 3\\ 5\\ +3\\ \hline \\ \end{align}
  9. \begin{align} 3\\ 4\\ +7\\ \hline \\ \end{align}
  10. \begin{align} 4\\ 5\\ +9\\ \hline \\ \end{align}
  11. \begin{align} 6\\ 3\\ +2\\ \hline \\ \end{align}
  12. \begin{align} 5\\ 2\\ +9\\ \hline \\ \end{align}

Answers to Exercise 2

  1. 15
  2. 16
  3. 14
  4. 11
  5. 13
  6. 11
  7. 11
  8. 11
  9. 14
  10. 18
  11. 11
  12. 16

Exercise 3

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

  1. \begin{align} 3\\ 2\\ +8\\ \hline \\ \end{align}
  2. \begin{align} 2\\ 1\\ +4\\ \hline \\ \end{align}
  3. \begin{align} 4\\ 3\\ +1\\ \hline \\ \end{align}
  4. \begin{align} 1\\ 2\\ +8\\ \hline \\ \end{align}
  5. \begin{align} 3\\ 2\\ +2\\ \hline \\ \end{align}
  6. \begin{align} 5\\ 1\\ +2\\ \hline \\ \end{align}
  7. \begin{align} 7\\ 2\\ +8\\ \hline \\ \end{align}
  8. \begin{align} 4\\ 2\\ +6\\ \hline \\ \end{align}
  9. \begin{align} 7\\ 2\\ +7\\ \hline \\ \end{align}
  10. \begin{align} 6\\ 1\\ +1\\ \hline \\ \end{align}
  11. \begin{align} 2\\ 7\\ +6\\ \hline \\ \end{align}
  12. \begin{align} 3\\ 4\\ +2\\ \hline \\ \end{align}
  13. \begin{align} 3\\ 4\\ +1\\ \hline \\ \end{align}
  14. \begin{align} 7\\ 1\\ +9\\ \hline \\ \end{align}
  15. \begin{align} 2\\ 6\\ +4\\ \hline \\ \end{align}
  16. \begin{align} 3\\ 1\\ +2\\ \hline \\ \end{align}

Answers to Exercise 3

  1. 13
  2. 7
  3. 8
  4. 11
  5. 7
  6. 8
  7. 17
  8. 12
  9. 16
  10. 8
  11. 15
  12. 9
  13. 8
  14. 17
  15. 12
  16. 6

Exercise 4

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

  1. \begin{align} 1\\ 3\\ 4\\ +5\\ \hline \\ \end{align}
  2. \begin{align} 2\\ 3\\ 4\\ +6\\ \hline \\ \end{align}
  3. \begin{align} 4\\ 3\\ 2\\ +8\\ \hline \\ \end{align}
  4. \begin{align} 3\\ 1\\ 5\\ +6\\ \hline \\ \end{align}
  5. \begin{align} 2\\ 2\\ 3\\ +2\\ \hline \\ \end{align}
  6. \begin{align} 3\\ 3\\ 1\\ +2\\ \hline \\ \end{align}
  7. \begin{align} 2\\ 1\\ 2\\ +4\\ \hline \\ \end{align}
  8. \begin{align} 1\\ 2\\ 4\\ +6\\ \hline \\ \end{align}
  9. \begin{align} 2\\ 4\\ 1\\ +6\\ \hline \\ \end{align}
  10. \begin{align} 3\\ 2\\ 3\\ +3\\ \hline \\ \end{align}
  11. \begin{align} 2\\ 1\\ 4\\ +0\\ \hline \\ \end{align}
  12. \begin{align} 3\\ 1\\ 4\\ +1\\ \hline \\ \end{align}

Answers to Exercise 4

  1. 13
  2. 15
  3. 17
  4. 15
  5. 9
  6. 9
  7. 9
  8. 13
  9. 13
  10. 11
  11. 7
  12. 9

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: RectangleA rectangle. The length of the sides are 3 metres, 2 metres, 3 metres and two metres.

To find the perimeter, add the lengths of the sides of the rectangle.

Exercise 5

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.

  1. Find the perimeter of the swimming pool.
    a rectangular-shape swimming pool whose sides are 3 metres, four metres, three metres and four metres.
  2. Find the perimeter of the garden.
    a triangle shape garden whose sides are 3 metres, 4 metres and 6 metres
  3. Find the perimeter of the greenhouse.
    a square-shape greenhouse whose sides are 3 metres long
  4. Find the perimeter of the sign.
    a rectangular shape sign whose sides are 2 metres, 3 metres, 2 metres, and 3 metres

Answers to Exercise 5

  1. 14 metres
  2. 13 metres
  3. 12 metres
  4. 10 metres

Topic B Self-Test

Mark      /18        Aim      15/18

  1. Find the sums. Be sure to check your answers. (12 marks)
    1. \begin{align} 4\\ 6\\ +2\\ \hline \end{align}
    2. \begin{align} 3\\ 6\\ +9\\ \hline \end{align}
    3. \begin{align} 7\\ 2\\ +8\\ \hline \end{align}
    4. \begin{align} 2\\ 1\\ +4\\ \hline \end{align}
    5. \begin{align} 3\\ 5\\ +8\\ \hline \end{align}
    6. \begin{align} 4\\ 6\\ +7\\ \hline \end{align}
    7. \begin{align} 3\\ 1\\ 5\\ +2\\ \hline \end{align}
    8. \begin{align} 4\\ 2\\ 3\\ +7\\ \hline \end{align}
    9. \begin{align} 5\\ 3\\ 1\\ +8\\ \hline \end{align}
    10. \begin{align} 3\\ 5\\ 1\\ +3\\ \hline \end{align}
    11. \begin{align} 1\\ 5\\ 4\\ +6\\ \hline \end{align}
    12. \begin{align} 2\\ 1\\ 6\\ +5\\ \hline \end{align}
  2. Solve each of the following word problems. Be sure to include the unit of measure in your answer. Be sure to circle the information and underline what’s being asked.(6 marks, 2 marks each)
    1. 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?
    2. 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?
    3. Find the perimeter of the garden.
      a rectangular shape garden whose sides are 4 metres, 2 metres, 4 metres and 2 metres

Answers to Topic B Self-Test

    1. 12
    2. 18
    3. 17
    4. 7
    5. 16
    6. 17
    7. 11
    8. 16
    9. 17
    10. 12
    11. 16
    12. 14
    1. 16 hours
    2. 9 metres
    3. 12 metres

10

Topic C: Addition of Larger Numbers

Use these steps to complete each addition question.

  1. Add the ones to the ones.
  2. Add the tens to the tens.
  3. Add the hundreds to the hundreds.

Example A:

\begin{align} 23\\ +56\\ \hline \\ \end{align}

  1. Add the ones to the ones. 3 ones + 6 ones = 9 ones. Write the answer in line with the ones in the equation.
    \begin{align} 23\\ +56\\ \hline 9 \end{align}
  2. Add the tens. 2 tens + 5 tens = 7 tens
    \begin{align} 23\\ +56\\ \hline 79\end{align}

The sum of 23 + 56 = 79

Example B:

\begin{align} 372\\ +415\\ \hline \\ \end{align}

  1. Add the ones. 2 ones + 5 ones = 7 ones
    \begin{align} 372\\ +415\\ \hline 7\end{align}
  2. Add the tens. 7 tens + 1 ten = 8 tens
    \begin{align} 372\\ +415\\ \hline 87\end{align}
  3. Add the hundreds. 3 hundreds + 4 hundreds = 7 hundreds
    \begin{align} 372\\ +415\\ \hline 787\end{align}

The sum of 372 + 415 = 789

Exercise 1

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

  1. \begin{align} 23\\ +56\\ \hline \\ \end{align}
  2. \begin{align} 20\\ +69\\ \hline \\ \end{align}
  3. \begin{align} 58\\ +21\\ \hline \\ \end{align}
  4. \begin{align} 62\\ +13\\ \hline \\ \end{align}
  5. \begin{align} 73\\ +14\\ \hline \\ \end{align}
  6. \begin{align} 44\\ +54\\ \hline \\ \end{align}
  7. \begin{align} 10\\ +75\\ \hline \\ \end{align}
  8. \begin{align} 36\\ +22\\ \hline \\ \end{align}
  9. \begin{align} 10\\ +36\\ \hline \\ \end{align}
  10. \begin{align} 16\\ +23\\ \hline \\ \end{align}
  11. \begin{align} 40\\ +50\\ \hline \\ \end{align}
  12. \begin{align} 37\\ +32\\ \hline \\ \end{align}
  13. \begin{align} 14\\ +50\\ \hline \\ \end{align}
  14. \begin{align} 23\\ +16\\ \hline \\ \end{align}
  15. \begin{align} 41\\ +38\\ \hline \\ \end{align}
  16. \begin{align} 40\\ +11\\ \hline \\ \end{align}

Answers to Exercise 1

  1. 79
  2. 89
  3. 79
  4. 75
  5. 87
  6. 98
  7. 85
  8. 58
  9. 46
  10. 39
  11. 90
  12. 69
  13. 64
  14. 39
  15. 79
  16. 51

Exercise 2

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

  1. \begin{align} 47\\ +51\\ \hline \\ \end{align}
  2. \begin{align} 65\\ +24\\ \hline \\ \end{align}
  3. \begin{align} 78\\ +21\\ \hline \\ \end{align}
  4. \begin{align} 84\\ +12\\ \hline \\ \end{align}
  5. \begin{align} 73\\ +22\\ \hline \\ \end{align}
  6. \begin{align} 64\\ +13\\ \hline \\ \end{align}
  7. \begin{align} 25\\ +64\\ \hline \\ \end{align}
  8. \begin{align} 51\\ +38\\ \hline \\ \end{align}
  9. \begin{align} 26\\ +43\\ \hline \\ \end{align}
  10. \begin{align} 40\\ +57\\ \hline \\ \end{align}
  11. \begin{align} 76\\ +23\\ \hline \\ \end{align}
  12. \begin{align} 86\\ +13\\ \hline \\ \end{align}

Answers to Exercise 2

  1. 98
  2. 89
  3. 99
  4. 96
  5. 95
  6. 77
  7. 89
  8. 89
  9. 69
  10. 97
  11. 99
  12. 99

Exercise 3

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

  1. \begin{align} 32\\ +64\\ \hline \\ \end{align}
  2. \begin{align} 23\\ +54\\ \hline \\ \end{align}
  3. \begin{align} 62\\ +22\\ \hline \\ \end{align}
  4. \begin{align} 83\\ +11\\ \hline \\ \end{align}
  5. \begin{align} 32\\ +45\\ \hline \\ \end{align}
  6. \begin{align} 63\\ +33\\ \hline \\ \end{align}
  7. \begin{align} 75\\ +24\\ \hline \\ \end{align}
  8. \begin{align} 46\\ +12\\ \hline \\ \end{align}
  9. \begin{align} 44\\ +35\\ \hline \\ \end{align}
  10. \begin{align} 25\\ +42\\ \hline \\ \end{align}
  11. \begin{align} 41\\ +38\\ \hline \\ \end{align}
  12. \begin{align} 54\\ +45\\ \hline \\ \end{align}
  13. \begin{align} 25\\ +32\\ \hline \\ \end{align}
  14. \begin{align} 35\\ +42\\ \hline \\ \end{align}
  15. \begin{align} 32\\ +44\\ \hline \\ \end{align}
  16. \begin{align} 22\\ +14\\ \hline \\ \end{align}

Answers to Exercise 3

  1. 96
  2. 77
  3. 84
  4. 94
  5. 77
  6. 96
  7. 99
  8. 58
  9. 79
  10. 67
  11. 79
  12. 99
  13. 57
  14. 77
  15. 76
  16. 36

Exercise 4

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

  1. \begin{align} 286\\ +513\\ \hline \\ \end{align}
  2. \begin{align} 649\\ +250\\ \hline \\ \end{align}
  3. \begin{align} 156\\ +542\\ \hline \\ \end{align}
  4. \begin{align} 503\\ +361\\ \hline \\ \end{align}
  5. \begin{align} 273\\ +620\\ \hline \\ \end{align}
  6. \begin{align} 27\\ +961\\ \hline \\ \end{align}
  7. \begin{align} 852\\ +36\\ \hline \\ \end{align}
  8. \begin{align} 300\\ +50\\ \hline \\ \end{align}
  9. \begin{align} 364\\ +523\\ \hline \\ \end{align}

Answers to Exercise 4

  1. 799
  2. 899
  3. 698
  4. 864
  5. 893
  6. 988
  7. 888
  8. 350
  9. 887

Exercise 5

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

  1. \begin{align} 171\\ +401\\ \hline \\ \end{align}
  2. \begin{align} 314\\ +553\\ \hline \\ \end{align}
  3. \begin{align} 431\\ +317\\ \hline \\ \end{align}
  4. \begin{align} 213\\ +384\\ \hline \\ \end{align}
  5. \begin{align} 163\\ +224\\ \hline \\ \end{align}
  6. \begin{align} 412\\ +513\\ \hline \\ \end{align}
  7. \begin{align} 731\\ +142\\ \hline \\ \end{align}
  8. \begin{align} 314\\ +524\\ \hline \\ \end{align}
  9. \begin{align} 253\\ +401\\ \hline \\ \end{align}

Answers to Exercise 5

  1. 572
  2. 867
  3. 748
  4. 597
  5. 387
  6. 925
  7. 873
  8. 838
  9. 654

Topic C Self-Test

  1. Find the sums. Be sure to check your answers. (12 marks)
    1. \begin{align} 46\\ +23\\ \hline \\ \end{align}
    2. \begin{align} 32\\ +13\\ \hline \\ \end{align}
    3. \begin{align} 72\\ +25\\ \hline \\ \end{align}
    4. \begin{align} 56\\ +12\\ \hline \\ \end{align}
    5. \begin{align} 65\\ +34\\ \hline \\ \end{align}
    6. \begin{align} 25\\ +51\\ \hline \\ \end{align}
    7. \begin{align} 324\\ +263\\ \hline \\ \end{align}
    8. \begin{align} 183\\ +514\\ \hline \\ \end{align}
    9. \begin{align} 753\\ +145\\ \hline \\ \end{align}
    10. \begin{align} 618\\ +120\\ \hline \\ \end{align}
    11. \begin{align} 224\\ +465\\ \hline \\ \end{align}
    12. \begin{align} 563\\ +216\\ \hline \\ \end{align}
  2. Solve each of the following word problems. Be sure to include the unit of measure in your answer. Be sure to circle the information and underline what’s being asked.(6 marks, 2 marks each)
    1. Mahala’s dad worked 45 hours one week and 52 hours the next week. How many hours did he work during those two weeks?
    2. A trucker drove 526 kilometers on the first trip and 341 kilometers on the next. How many kilometers did the trucker drive altogether?
    3. Find the perimeter of the garden.
      a rectangular shape garden whose sides are 11 metres, 12 metres, 11 metres and 12 metres

Answers to Topic C Self-Test

    1. 69
    2. 45
    3. 97
    4. 68
    5. 99
    6. 76
    7. 587
    8. 697
    9. 898
    10. 738
    11. 689
    12. 779
    1. 97 hours
    2. 867 kilometres
    3. 46 metres

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.

11

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.

  1. Check out your addition facts.
    1. \begin{align} 5\\ +6\\ \hline \\ \end{align}
    2. \begin{align} 8\\ +2\\ \hline \\ \end{align}
    3. \begin{align} 3\\ +4\\ \hline \\ \end{align}
    4. \begin{align} 9\\ +7\\ \hline \\ \end{align}
    5. \begin{align} 7\\ +10\\ \hline \\ \end{align}
    6. \begin{align} 6\\ +8\\ \hline \\ \end{align}
    7. \begin{align} 9\\ +4\\ \hline \\ \end{align}
    8. \begin{align} 2\\ +3\\ \hline \\ \end{align}
    9. \begin{align} 8\\ +4\\ \hline \\ \end{align}
    10. \begin{align} 3\\ +3\\ \hline \\ \end{align}
    11. \begin{align} 9\\ +9\\ \hline \\ \end{align}
    12. \begin{align} 5\\ +4\\ \hline \\ \end{align}
    13. \begin{align} 1\\ +2\\ \hline \\ \end{align}
    14. \begin{align} 3\\ +1\\ \hline \\ \end{align}
    15. \begin{align} 6\\ +9\\ \hline \\ \end{align}
    16. \begin{align} 5\\ +3\\ \hline \\ \end{align}
  2. Add across or horizontally.
    1. 8 + 7 =
    2. 0 + 3 =
    3. 8 + 10 =
    4. 5 + 2 =
    5. 2 + 2 =
    6. 7 + 5 =
    7. 9 + 8 =
    8. 3 + 6 =
    9. 9 + 5 =
    10. 1 + 5 =
  3. Find the sums.
    1. \begin{align} 6\\ 2\\ +4\\ \hline \\ \end{align}
    2. \begin{align} 5\\ 2\\ +1\\ \hline \\ \end{align}
    3. \begin{align} 4\\ 4\\ +8\\ \hline \\ \end{align}
    4. \begin{align} 3\\ 4\\ +5\\ \hline \\ \end{align}
    5. \begin{align} 2\\ 3\\ +4\\ \hline \\ \end{align}
    6. \begin{align} 6\\ 4\\ +7\\ \hline \\ \end{align}
    7. \begin{align} 3\\ 4\\ +6\\ \hline \\ \end{align}
    8. \begin{align} 7\\ 2\\ +4\\ \hline \\ \end{align}
    9. \begin{align} 3\\ 6\\ +8\\ \hline \\ \end{align}
  4. Find the sums.
    1. \begin{align} 26\\ +30\\ \hline \\ \end{align}
    2. \begin{align} 42\\ +57\\ \hline \\ \end{align}
    3. \begin{align} 44\\ +32\\ \hline \\ \end{align}
    4. \begin{align}32\\ +81\\ \hline \\ \end{align}
    5. \begin{align} 83\\ +13\\ \hline \\ \end{align}
    6. \begin{align} 76\\ +12\\ \hline \\ \end{align}
    7. \begin{align} 34\\ +51\\ \hline \\ \end{align}
    8. \begin{align} 54\\ +22\\ \hline \\ \end{align}
    9. \begin{align} 52\\ +43\\ \hline \\ \end{align}
    10. \begin{align} 25\\ +42\\ \hline \\ \end{align}
    11. \begin{align} 72\\ +35\\ \hline \\ \end{align}
    12. \begin{align} 66\\ +12\\ \hline \\ \end{align}
  5. Find the sums.
    1. \begin{align} 342\\ +523\\ \hline \\ \end{align}
    2. \begin{align} 725\\ +142\\ \hline \\ \end{align}
    3. \begin{align}362\\ +417\\ \hline \\ \end{align}
    4. \begin{align} 425\\ +172\\ \hline \\ \end{align}
    5. \begin{align} 284\\ +314\\ \hline \\ \end{align}
    6. \begin{align} 315\\ +132\\ \hline \\ \end{align}
    7. \begin{align} 363\\ +415\\ \hline \\ \end{align}
    8. \begin{align} 741\\ +225\\ \hline \\ \end{align}
    9. \begin{align} 404\\ +445\\ \hline \\ \end{align}
    10. \begin{align} 654\\ +215\\ \hline \\ \end{align}
    11. \begin{align} 234\\ +352\\ \hline \\ \end{align}
    12. \begin{align} 525\\ +431\\ \hline \\ \end{align}
  6. 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.
    1. a rectangle. the length of the sides are 3 metres, 1 metre, 3 metres, and 1 metre
    2. a square whose sides are 5 metres long
    3. 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?
    4. Seung weighs 36 kilograms. His father weighs 62 kilograms. How much do they weigh altogether?

Answers to Unit 2 Review

    1. 11
    2. 10
    3. 7
    4. 16
    5. 17
    6. 14
    7. 13
    8. 5
    9. 12
    10. 6
    11. 18
    12. 9
    13. 3
    14. 4
    15. 15
    16. 8
    1. 15
    2. 3
    3. 18
    4. 7
    5. 4
    6. 12
    7. 17
    8. 9
    9. 14
    10. 6
    1. 12
    2. 8
    3. 16
    4. 12
    5. 9
    6. 17
    7. 13
    8. 13
    9. 17
    1. 56
    2. 99
    3. 76
    4. 113
    5. 96
    6. 88
    7. 85
    8. 76
    9. 95
    10. 67
    11. 107
    12. 78
    1. 865
    2. 867
    3. 779
    4. 597
    5. 598
    6. 447
    7. 778
    8. 966
    9. 849
    10. 869
    11. 586
    12. 956
    1. 8 metres, rectangle
    2. 20 metres, square
    3. 676 metres
    4. 98 kilograms

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!

III

Unit 3: Subtraction

12

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.

nine minus three is six

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:

\large \begin{array}{cc}5+4=9 &amp; 9-4=5 \\ 4+5=9 &amp; 9-5=4\end{array}

\large \begin{array}{cc}\begin{array}{r}8\\+3\\ \hline 11\end{array} &amp; \begin{array}{r}11\\-3\\ \hline 8 \end{array} \\ \begin{array}{r}3\\+8\\ \hline 11 \end{array} &amp; \begin{array}{r}11\\-8\\ \hline 3\end{array}\end{array}

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

Exercise 1

Check out your subtraction facts by doing the following exercises 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 exercises. Then, make a list of any subtraction facts you do not know or which are slow for you and practice them.

  1. \begin{align}5\\-4\\ \hline\\ \end{align}
  2. \begin{align}3\\-2\\ \hline\\ \end{align}
  3. \begin{align}7\\-7\\ \hline\\ \end{align}
  4. \begin{align}1\\-0\\ \hline\\ \end{align}
  5. \begin{align}8\\-2\\ \hline\\ \end{align}
  6. \begin{align}9\\-7\\ \hline\\ \end{align}
  7. \begin{align}4\\-3\\ \hline\\ \end{align}
  8. \begin{align}6\\-1\\ \hline\\ \end{align}
  9. \begin{align}7\\-2\\ \hline\\ \end{align}
  10. \begin{align}2\\-2\\ \hline\\ \end{align}
  11. \begin{align}7\\-6\\ \hline\\ \end{align}
  12. \begin{align}8\\-7\\ \hline\\ \end{align}

Answers to Exercise 1

  1. 1
  2. 1
  3. 0
  4. 1
  5. 6
  6. 2
  7. 1
  8. 5
  9. 5
  10. 0
  11. 1
  12. 1

Exercise 2

  1. \begin{align}8\\-4\\ \hline\\ \end{align}
  2. \begin{align}9\\-1\\ \hline\\ \end{align}
  3. \begin{align}7\\-5\\ \hline\\ \end{align}
  4. \begin{align}6\\-4\\ \hline\\ \end{align}
  5. \begin{align}9\\-4\\ \hline\\ \end{align}
  6. \begin{align}5\\-2\\ \hline\\ \end{align}
  7. \begin{align}2\\-0\\ \hline\\ \end{align}
  8. \begin{align}6\\-3\\ \hline\\ \end{align}
  9. \begin{align}8\\-3\\ \hline\\ \end{align}
  10. \begin{align}6\\-5\\ \hline\\ \end{align}
  11. \begin{align}4\\-4\\ \hline\\ \end{align}
  12. \begin{align}9\\-0\\ \hline\\ \end{align}

Answers to Exercise 2

  1. 4
  2. 8
  3. 2
  4. 2
  5. 5
  6. 3
  7. 2
  8. 3
  9. 5
  10. 1
  11. 0
  12. 9

Exercise 3

  1. \begin{align}8\\-4\\ \hline\\ \end{align}
  2. \begin{align}5\\-5\\ \hline\\ \end{align}
  3. \begin{align}2\\-1\\ \hline\\ \end{align}
  4. \begin{align}4\\-3\\ \hline\\ \end{align}
  5. \begin{align}3\\-3\\ \hline\\ \end{align}
  6. \begin{align}6\\-3\\ \hline\\ \end{align}
  7. \begin{align}7\\-6\\ \hline\\ \end{align}
  8. \begin{align}9\\-2\\ \hline\\ \end{align}
  9. \begin{align}9\\-0\\ \hline\\ \end{align}
  10. \begin{align}5\\-4\\ \hline\\ \end{align}
  11. \begin{align}8\\-8\\ \hline\\ \end{align}
  12. \begin{align}4\\-2\\ \hline\\ \end{align}
  13. \begin{align}7\\-7\\ \hline\\ \end{align}
  14. \begin{align}2\\-0\\ \hline\\ \end{align}
  15. \begin{align}6\\-1\\ \hline\\ \end{align}
  16. \begin{align}9\\-8\\ \hline\\ \end{align}

Answers to Exercise 3

  1. 4
  2. 0
  3. 1
  4. 1
  5. 0
  6. 3
  7. 1
  8. 7
  9. 9
  10. 1
  11. 0
  12. 2
  13. 0
  14. 2
  15. 5
  16. 1

Exercise 4

  1. \begin{align}11\\-7\\ \hline\\ \end{align}
  2. \begin{align}10\\-4\\ \hline\\ \end{align}
  3. \begin{align}12\\-7\\ \hline\\ \end{align}
  4. \begin{align}8\\-6\\ \hline\\ \end{align}
  5. \begin{align}10\\-8\\ \hline\\ \end{align}
  6. \begin{align}7\\-4\\ \hline\\ \end{align}
  7. \begin{align}9\\-3\\ \hline\\ \end{align}
  8. \begin{align}9\\-5\\ \hline\\ \end{align}

Answers to Exercise 4

  1. 4
  2. 6
  3. 5
  4. 2
  5. 2
  6. 3
  7. 6
  8. 4

Exercise 5

  1. \begin{align}12\\-3\\ \hline\\ \end{align}
  2. \begin{align}9\\-6\\ \hline\\ \end{align}
  3. \begin{align}11\\-9\\ \hline\\ \end{align}
  4. \begin{align}10\\-5\\ \hline\\ \end{align}
  5. \begin{align}8\\-8\\ \hline\\ \end{align}
  6. \begin{align}10\\-4\\ \hline\\ \end{align}
  7. \begin{align}12\\-4\\ \hline\\ \end{align}
  8. \begin{align}7\\-6\\ \hline\\ \end{align}

Answers to Exercise 5

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

Exercise 6

  1. \begin{align}11\\-7\\ \hline\\ \end{align}
  2. \begin{align}12\\-6\\ \hline\\ \end{align}
  3. \begin{align}10\\-9\\ \hline\\ \end{align}
  4. \begin{align}8\\-3\\ \hline\\ \end{align}
  5. \begin{align}12\\-5\\ \hline\\ \end{align}
  6. \begin{align}10\\-4\\ \hline\\ \end{align}
  7. \begin{align}9\\-7\\ \hline\\ \end{align}
  8. \begin{align}7\\-3\\ \hline\\ \end{align}
  9. \begin{align}8\\-4\\ \hline\\ \end{align}
  10. \begin{align}11\\-9\\ \hline\\ \end{align}
  11. \begin{align}9\\-5\\ \hline\\ \end{align}
  12. \begin{align}7\\-2\\ \hline\\ \end{align}

Answers to Exercise 6

  1. 4
  2. 6
  3. 1
  4. 5
  5. 7
  6. 6
  7. 2
  8. 4
  9. 4
  10. 2
  11. 1
  12. 5

Exercise 6

  1. \begin{align}11\\-7\\ \hline\\ \end{align}
  2. \begin{align}12\\-6\\ \hline\\ \end{align}
  3. \begin{align}10\\-9\\ \hline\\ \end{align}
  4. \begin{align}8\\-3\\ \hline\\ \end{align}
  5. \begin{align}12\\-5\\ \hline\\ \end{align}
  6. \begin{align}10\\-4\\ \hline\\ \end{align}
  7. \begin{align}9\\-7\\ \hline\\ \end{align}
  8. \begin{align}7\\-3\\ \hline\\ \end{align}
  9. \begin{align}8\\-4\\ \hline\\ \end{align}
  10. \begin{align}11\\-9\\ \hline\\ \end{align}
  11. \begin{align}6\\-5\\ \hline\\ \end{align}
  12. \begin{align}7\\-2\\ \hline\\ \end{align}

Answers to Exercise 6

  1. 4
  2. 6
  3. 1
  4. 5
  5. 7
  6. 6
  7. 2
  8. 4
  9. 4
  10. 2
  11. 4
  12. 5

Exercise 7

  1. \begin{align}13\\-5\\ \hline\\ \end{align}
  2. \begin{align}10\\-1\\ \hline\\ \end{align}
  3. \begin{align}9\\-4\\ \hline\\ \end{align}
  4. \begin{align}5\\-4\\ \hline\\ \end{align}
  5. \begin{align}9\\-9\\ \hline\\ \end{align}
  6. \begin{align}16\\-8\\ \hline\\ \end{align}
  7. \begin{align}11\\-7\\ \hline\\ \end{align}
  8. \begin{align}6\\-3\\ \hline\\ \end{align}
  9. \begin{align}18\\-9\\ \hline\\ \end{align}
  10. \begin{align}7\\-2\\ \hline\\ \end{align}
  11. \begin{align}13\\-7\\ \hline\\ \end{align}
  12. \begin{align}8\\-6\\ \hline\\ \end{align}

Answers to Exercise 7

  1. 8
  2. 9
  3. 5
  4. 1
  5. 0
  6. 8
  7. 4
  8. 3
  9. 9
  10. 5
  11. 6
  12. 2

Practice your subtraction facts using dominoes. Place all the dominoes face down.

Exercise 8

  1. \begin{align}12\\-3\\ \hline\\ \end{align}
  2. \begin{align}6\\-2\\ \hline\\ \end{align}
  3. \begin{align}10\\-4\\ \hline\\ \end{align}
  4. \begin{align}11\\-9\\ \hline\\ \end{align}
  5. \begin{align}1\\-0\\ \hline\\ \end{align}
  6. \begin{align}8\\-1\\ \hline\\ \end{align}
  7. \begin{align}12\\-5\\ \hline\\ \end{align}
  8. \begin{align}11\\-2\\ \hline\\ \end{align}
  9. \begin{align}3\\-2\\ \hline\\ \end{align}
  10. \begin{align}11\\-8\\ \hline\\ \end{align}
  11. \begin{align}14\\-7\\ \hline\\ \end{align}
  12. \begin{align}8\\-3\\ \hline\\ \end{align}
  13. \begin{align}15\\-9\\ \hline\\ \end{align}
  14. \begin{align}9\\-7\\ \hline\\ \end{align}
  15. \begin{align}7\\-1\\ \hline\\ \end{align}
  16. \begin{align}11\\-5\\ \hline\\ \end{align}

Answers to Exercise 8

  1. 9
  2. 4
  3. 6
  4. 2
  5. 1
  6. 7
  7. 7
  8. 9
  9. 1
  10. 3
  11. 7
  12. 5
  13. 6
  14. 2
  15. 6
  16. 6

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 get 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.

Subtracting Across

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

Example:

\begin{align}9\\-5\\ \hline 4 \end{align}

Another way to subtract numbers is across or horizontally.

9 − 5 = 4

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

Exercise 9

Practice subtracting across or horizontally. Check your work using the answer key at the end of the exercise.

  1. 6 − 3 =
  2. 12 − 8 =
  3. 4 − 1 =
  4. 8 − 6 =
  5. 18 − 9 =
  6. 11 − 4 =
  7. 7 − 2 =
  8. 16 − 7 =
  9. 10 − 5 =
  10. 2 − 0 =
  11. 9 − 5 =
  12. 17 − 8 =

Answers to Exercise 9

  1. 3
  2. 4
  3. 3
  4. 2
  5. 9
  6. 7
  7. 5
  8. 9
  9. 5
  10. 2
  11. 4
  12. 9

Exercise 10

Practice subtracting across or horizontally. Check your work using the answer key at the end of the exercise.

  1. 9 − 6 =
  2. 14 − 5 =
  3. 8 − 4 =
  4. 7 − 1 =
  5. 11 − 7 =
  6. 5 − 0 =
  7. 4 − 3 =
  8. 15 − 8 =
  9. 11 − 9 =
  10. 10 − 2 =
  11. 9 − 2 =
  12. 8 − 3 =

Answers to Exercise 10

  1. 3
  2. 9
  3. 4
  4. 6
  5. 4
  6. 5
  7. 1
  8. 7
  9. 2
  10. 8
  11. 7
  12. 5

Exercise 11

Practice subtracting across or horizontally. Check your work using the answer key at the end of the exercise.

  1. 3 − 2 =
  2. 17 − 9 =
  3. 14 − 7 =
  4. 9 − 3 =
  5. 12 − 5 =
  6. 8 − 8 =
  7. 6 − 1 =
  8. 13 − 4 =
  9. 11 − 6 =
  10. 4 − 0 =
  11. 8 − 1 =
  12. 16 − 9 =
  13. 7 − 0 =
  14. 13 − 8 =
  15. 12 − 3 =
  16. 9 − 4 =
  17. 15 − 7 =
  18. 10 − 6 =
  19. 11 − 5 =
  20. 5 − 2 =

Answers to Exercise 11

  1. 1
  2. 8
  3. 7
  4. 6
  5. 7
  6. 0
  7. 5
  8. 9
  9. 5
  10. 4
  11. 7
  12. 7
  13. 7
  14. 5
  15. 9
  16. 5
  17. 8
  18. 4
  19. 6
  20. 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:

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.

Example: 

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

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

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.

\begin{align} 14 \text{ nails} \\ -7 \text{ nails} \\ \hline 7 \text{ nails} \end{align}

Exercise 12

  1. Wolfgang walked 11 blocks. Ingrid walked 6 blocks. Wolfgang walked how much farther than Ingrid?
  2. Mika and her father went fishing. Mika caught 18 fish and her father caught 9 fish. How many more fish did Mika catch?
  3. 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?
  4. Malik counted 12 cars in the parking lot where he worked. One hour later, he counted only 4 cars. How many cars left?

Answers to Exercise 12

  1. 5 blocks
  2. 9 fish
  3. 8 moon cakes
  4. 8 cars

Topic A Self-Test

Mark    /21            Aim    18/27

  1. Find the difference. Be sure to check your answers. (9 marks)
    1. \begin{align}16\\-8\\ \hline\\ \end{align}
    2. \begin{align}18\\-9\\ \hline\\ \end{align}
    3. \begin{align}14\\-8\\ \hline\\ \end{align}
    4. \begin{align}11\\-4\\ \hline\\ \end{align}
    5. \begin{align}9\\-3\\ \hline\\ \end{align}
    6. \begin{align}17\\-9\\ \hline\\ \end{align}
    7. \begin{align}10\\-6\\ \hline\\ \end{align}
    8. \begin{align}7\\-5\\ \hline\\ \end{align}
    9. \begin{align}15\\-6\\ \hline\\ \end{align}
  2. Find the difference. Be sure to check your answers. (6 marks)
    1. 3 − 2 =
    2. 17 − 9 =
    3. 14 − 7 =
    4. 9 − 3 =
    5. 12 − 5 =
    6. 8 − 8 =
  3. Solve each of the following word problems. Be sure to include the unit of measure in your answer. Be sure to circle the information and underline what’s being asked.(6 marks, 2 marks each)
    1. Shada caught 17 fish. She gave 8 fish to her grandmother. How many fish did she have left?
    2. Yuan went to the store with $15 to buy some rice. The rice cost $6. How much did he have left?
    3. 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-Test

    1. 8
    2. 9
    3. 6
    4. 7
    5. 6
    6. 8
    7. 4
    8. 2
    9. 9
    1. 1
    2. 8
    3. 7
    4. 6
    5. 7
    6. 0
    1. 9 fish
    2. $9
    3. 5 metres

13

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 minus sign.

Use these steps to complete each subtraction question.

  1. Subtract the ones from the ones.
  2. Subtract the tens from the tens.
  3. Subtract the hundreds from the hundreds.

Example A:

\begin{align}57\\-26\\ \hline \\ \end{align}

  1. Subtract the ones from the ones. 7 ones − 6 ones = 1 one. Write the answer in line with the ones in the question.
    \begin{align}57\\-26\\ \hline 1 \end{align}
  2. Subtract the tens from the tens. 5 tens – 2 tens = 3 tens
    \begin{align}57\\-26\\ \hline 31 \end{align}

The difference between 57 and 26 is 31.

Example B:

\begin{align}628\\-524\\ \hline \\ \end{align}

  1.  Subtract the ones from the ones. 8 ones – 4 ones = 4 ones. Write the answer in line with the ones in the question.
    \begin{align}628\\-524\\ \hline 4 \end{align}
  2. Subtract the tens. 2 tens – 2 tens = 0 tens.
    \begin{align}628\\-524\\ \hline 04 \end{align}
  3. Subtract the hundreds. 6 hundreds – 5 hundreds = 1 hundred.
    \begin{align}628\\-524\\ \hline 104 \end{align}

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

Exercise 1

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

  1. \begin{align}87\\-36\\ \hline\\ \end{align}
  2. \begin{align}29\\-21\\ \hline\\ \end{align}
  3. \begin{align}48\\-40\\ \hline\\ \end{align}
  4. \begin{align}99\\-63\\ \hline\\ \end{align}
  5. \begin{align}75\\-45\\ \hline\\ \end{align}
  6. \begin{align}73\\-20\\ \hline\\ \end{align}
  7. \begin{align}92\\-21\\ \hline\\ \end{align}
  8. \begin{align}58\\-27\\ \hline\\ \end{align}
  9. \begin{align}84\\-23\\ \hline\\ \end{align}
  10. \begin{align}69\\-38\\ \hline\\ \end{align}
  11. \begin{align}45\\-23\\ \hline\\ \end{align}
  12. \begin{align}49\\-19\\ \hline\\ \end{align}
  13. \begin{align}59\\-14\\ \hline\\ \end{align}
  14. \begin{align}87\\-63\\ \hline\\ \end{align}
  15. \begin{align}88\\-15\\ \hline\\ \end{align}
  16. \begin{align}56\\-44\\ \hline\\ \end{align}

Answers to Exercise 1

  1. 51
  2. 8
  3. 8
  4. 36
  5. 30
  6. 53
  7. 71
  8. 31
  9. 61
  10. 31
  11. 22
  12. 30
  13. 45
  14. 24
  15. 73
  16. 12

Exercise 2

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

  1. \begin{align}46\\-23\\ \hline\\ \end{align}
  2. \begin{align}65\\-42\\ \hline\\ \end{align}
  3. \begin{align}45\\-13\\ \hline\\ \end{align}
  4. \begin{align}53\\-20\\ \hline\\ \end{align}
  5. \begin{align}34\\-21\\ \hline\\ \end{align}
  6. \begin{align}48\\-32\\ \hline\\ \end{align}
  7. \begin{align}56\\-13\\ \hline\\ \end{align}
  8. \begin{align}26\\-15\\ \hline\\ \end{align}
  9. \begin{align}49\\-22\\ \hline\\ \end{align}
  10. \begin{align}58\\-27\\ \hline\\ \end{align}
  11. \begin{align}95\\-71\\ \hline\\ \end{align}
  12. \begin{align}89\\-14\\ \hline\\ \end{align}
  13. \begin{align}69\\-19\\ \hline\\ \end{align}
  14. \begin{align}86\\-71\\ \hline\\ \end{align}
  15. \begin{align}99\\-50\\ \hline\\ \end{align}
  16. \begin{align}89\\-55\\ \hline\\ \end{align}

Answers to Exercise 2

  1. 23
  2. 23
  3. 32
  4. 33
  5. 13
  6. 16
  7. 43
  8. 11
  9. 27
  10. 31
  11. 24
  12. 75
  13. 50
  14. 15
  15. 49
  16. 34

Exercise 3

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

  1. \begin{align}23\\-11\\ \hline\\ \end{align}
  2. \begin{align}53\\-21\\ \hline\\ \end{align}
  3. \begin{align}32\\-20\\ \hline\\ \end{align}
  4. \begin{align}77\\-32\\ \hline\\ \end{align}
  5. \begin{align}32\\-21\\ \hline\\ \end{align}
  6. \begin{align}38\\-15\\ \hline\\ \end{align}
  7. \begin{align}33\\-13\\ \hline\\ \end{align}
  8. \begin{align}92\\-30\\ \hline\\ \end{align}
  9. \begin{align}94\\-23\\ \hline\\ \end{align}
  10. \begin{align}54\\-42\\ \hline\\ \end{align}
  11. \begin{align}74\\-33\\ \hline\\ \end{align}
  12. \begin{align}88\\-72\\ \hline\\ \end{align}
  13. \begin{align}46\\-36\\ \hline\\ \end{align}
  14. \begin{align}75\\-41\\ \hline\\ \end{align}
  15. \begin{align}85\\-12\\ \hline\\ \end{align}
  16. \begin{align}56\\-45\\ \hline\\ \end{align}

Answers to Exercise 3

  1. 12
  2. 32
  3. 12
  4. 45
  5. 11
  6. 23
  7. 20
  8. 62
  9. 71
  10. 12
  11. 41
  12. 16
  13. 10
  14. 34
  15. 73
  16. 11

Exercise 4

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

  1. \begin{align}476\\-413\\ \hline\\ \end{align}
  2. \begin{align}873\\-560\\ \hline\\ \end{align}
  3. \begin{align}589\\-384\\ \hline\\ \end{align}
  4. \begin{align}793\\-170\\ \hline\\ \end{align}
  5. \begin{align}228\\-123\\ \hline\\ \end{align}
  6. \begin{align}995\\-452\\ \hline\\ \end{align}
  7. \begin{align}869\\-423\\ \hline\\ \end{align}
  8. \begin{align}769\\-405\\ \hline\\ \end{align}
  9. \begin{align}788\\-435\\ \hline\\ \end{align}
  10. \begin{align}579\\-234\\ \hline\\ \end{align}
  11. \begin{align}958\\-403\\ \hline\\ \end{align}
  12. \begin{align}696\\-251\\ \hline\\ \end{align}
  13. \begin{align}657\\-435\\ \hline\\ \end{align}
  14. \begin{align}745\\-412\\ \hline\\ \end{align}
  15. \begin{align}967\\-143\\ \hline\\ \end{align}

Answers to Exercise 4

  1. 63
  2. 313
  3. 205
  4. 623
  5. 105
  6. 543
  7. 446
  8. 364
  9. 353
  10. 345
  11. 555
  12. 445
  13. 222
  14. 333
  15. 824

Topic B Self-Test

Mark       /27             Aim        23/27

  1. Find the difference. Be sure to check your answers. (6 marks)
    1. \begin{align}16\\-8\\ \hline\\ \end{align}
    2. \begin{align}18\\-9\\ \hline\\ \end{align}
    3. \begin{align}14\\-8\\ \hline\\ \end{align}
    4. \begin{align}11\\-4\\ \hline\\ \end{align}
    5. \begin{align}9\\-3\\ \hline\\ \end{align}
    6. \begin{align}17\\-9\\ \hline\\ \end{align}
  2. Find the difference. Be sure to check your answers. (6 marks)
    1. \begin{align}896\\-422\\ \hline\\ \end{align}
    2. \begin{align}788\\-531\\ \hline\\ \end{align}
    3. \begin{align}549\\-318\\ \hline\\ \end{align}
    4. \begin{align}936\\-702\\ \hline\\ \end{align}
    5. \begin{align}936\\-725\\ \hline\\ \end{align}
    6. \begin{align}654\\-242\\ \hline\\ \end{align}
  3. Solve each of the following word problems. Be sure to include the unit of measure in your answer. Be sure to circle the information and underline what’s being asked.(6 marks, 2 marks each)
    1. 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?
    2. Misha’s family is on a 179 kilometer trip. They have already gone 123 kilometers. How much farther to they have to go?
    3. 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 Test

    1. 8
    2. 9
    3. 6
    4. 7
    5. 6
    6. 8
    1. 474
    2. 257
    3. 231
    4. 234
    5. 211
    6. 412
    1. 22 degrees Celsius
    2. 56 kilometres
    3. 504 metres

14

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.

  1. Check out your subtraction facts.
    1. \begin{align}5\\-2\\ \hline\\ \end{align}
    2. \begin{align}8\\-7\\ \hline\\ \end{align}
    3. \begin{align}3\\-1\\ \hline\\ \end{align}
    4. \begin{align}9\\-5\\ \hline\\ \end{align}
    5. \begin{align}18\\-9\\ \hline\\ \end{align}
    6. \begin{align}11\\-4\\ \hline\\ \end{align}
    7. \begin{align}13\\-5\\ \hline\\ \end{align}
    8. \begin{align}10\\-5\\ \hline\\ \end{align}
    9. \begin{align}6\\-6\\ \hline\\ \end{align}
    10. \begin{align}14\\-8\\ \hline\\ \end{align}
    11. \begin{align}16\\-7\\ \hline\\ \end{align}
    12. \begin{align}12\\-9\\ \hline\\ \end{align}
    13. \begin{align}17\\-9\\ \hline\\ \end{align}
    14. \begin{align}9\\-3\\ \hline\\ \end{align}
    15. \begin{align}13\\-6\\ \hline\\ \end{align}
    16. \begin{align}15\\-8\\ \hline\\ \end{align}
  2. Subtract across or horizontally.
    1. 8 − 6 =
    2. 12 − 5 =
    3. 10 − 10 =
    4. 9 − 8 =
    5. 11 − 6 =
    6. 8 − 4 =
    7. 7 − 3 =
    8. 14 − 9 =
  3. Find the differences.
    1. \begin{align}45\\-23\\ \hline\\ \end{align}
    2. \begin{align}78\\-15\\ \hline\\ \end{align}
    3. \begin{align}84\\-52\\ \hline\\ \end{align}
    4. \begin{align}57\\-10\\ \hline\\ \end{align}
    5. \begin{align}78\\-21\\ \hline\\ \end{align}
    6. \begin{align}69\\-43\\ \hline\\ \end{align}
    7. \begin{align}96\\-45\\ \hline\\ \end{align}
    8. \begin{align}88\\-35\\ \hline\\ \end{align}
    9. \begin{align}95\\-33\\ \hline\\ \end{align}
  4. Find the differences.
    1. \begin{align}583\\-163\\ \hline\\ \end{align}
    2. \begin{align}799\\-265\\ \hline\\ \end{align}
    3. \begin{align}629\\-305\\ \hline\\ \end{align}
    4. \begin{align}847\\-406\\ \hline\\ \end{align}
    5. \begin{align}978\\-252\\ \hline\\ \end{align}
    6. \begin{align}797\\-652\\ \hline\\ \end{align}
    7. \begin{align}765\\-243\\ \hline\\ \end{align}
    8. \begin{align}854\\-344\\ \hline\\ \end{align}
    9. \begin{align}536\\-314\\ \hline\\ \end{align}
    10. \begin{align}897\\-246\\ \hline\\ \end{align}
    11. \begin{align}669\\-238\\ \hline\\ \end{align}
    12. \begin{align}769\\-564\\ \hline\\ \end{align}
  5. Word problems.
    1. 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?
    2. 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 Review

    1. 3
    2. 1
    3. 2
    4. 4
    5. 9
    6. 7
    7. 8
    8. 5
    9. 0
    10. 6
    11. 9
    12. 3
    13. 8
    14. 6
    15. 7
    16. 7
    1. 2
    2. 7
    3. 0
    4. 1
    5. 5
    6. 4
    7. 4
    8. 5
    1. 22
    2. 63
    3. 32
    4. 47
    5. 57
    6. 26
    7. 51
    8. 53
    9. 62
    1. 420
    2. 534
    3. 324
    4. 441
    5. 726
    6. 145
    7. 522
    8. 510
    9. 222
    10. 651
    11. 431
    12. 205
    1. 117 light bulbs
    2. 235 kilometres

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!

IV

Unit 4: Estimating, Time, and Shapes

15

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 Estimate
\begin{align}23\\+45\\ \hline \\ \end{align} \begin{align}20\\+50\\ \hline 70\end{align}
\begin{align}67\\-31\\ \hline \\ \end{align} \begin{align}70\\-30\\ \hline 40\end{align}
\begin{align}372\\+416\\ \hline\\ \end{align} \begin{align}370\\+420\\ \hline 790\end{align}
\begin{align}564\\-243\\ \hline \\ \end{align} \begin{align}560\\-240\\ \hline 320\end{align}

Exercise 1

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.

  1. \begin{align}27\\+31\\ \hline \\ \end{align}
  2. \begin{align}42\\+51\\ \hline \\ \end{align}
  3. \begin{align}26\\+32\\ \hline \\ \end{align}
  4. \begin{align}14\\+52\\ \hline \\ \end{align}
  5. \begin{align}44\\+24\\ \hline \\ \end{align}
  6. \begin{align}31\\+27\\ \hline \\ \end{align}
  7. \begin{align}65\\+22\\ \hline \\ \end{align}
  8. \begin{align}46\\+23\\ \hline \\ \end{align}
  9. \begin{align}23\\+72\\ \hline \\ \end{align}
  10. \begin{align}42\\+36\\ \hline \\ \end{align}
  11. \begin{align}64\\+14\\ \hline \\ \end{align}
  12. \begin{align}32\\+20\\ \hline \\ \end{align}
  13. \begin{align}423\\+324\\ \hline \\ \end{align}
  14. \begin{align}526\\+345\\ \hline \\ \end{align}
  15. \begin{align}123\\+541\\ \hline \\ \end{align}
  16. \begin{align}752\\+243\\ \hline \\ \end{align}

Answers to Exercise 1

  1. 60
  2. 90
  3. 60
  4. 60
  5. 60
  6. 60
  7. 90
  8. 70
  9. 90
  10. 80
  11. 70
  12. 50
  13. 740
  14. 880
  15. 660
  16. 990

Exercise 2

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.

  1. \begin{align}35\\-16\\ \hline \\ \end{align}
  2. \begin{align}52\\-14\\ \hline \\ \end{align}
  3. \begin{align}67\\-19\\ \hline \\ \end{align}
  4. \begin{align}51\\-23\\ \hline \\ \end{align}
  5. \begin{align}36\\-17\\ \hline \\ \end{align}
  6. \begin{align}72\\-44\\ \hline \\ \end{align}
  7. \begin{align}38\\-19\\ \hline \\ \end{align}
  8. \begin{align}74\\-26\\ \hline \\ \end{align}
  9. \begin{align}93\\-89\\ \hline \\ \end{align}
  10. \begin{align}82\\-57\\ \hline \\ \end{align}
  11. \begin{align}56\\-27\\ \hline \\ \end{align}
  12. \begin{align}93\\-48\\ \hline \\ \end{align}
  13. \begin{align}752\\-342\\ \hline \\ \end{align}
  14. \begin{align}765\\-439\\ \hline \\ \end{align}
  15. \begin{align}673\\-424\\ \hline \\ \end{align}
  16. \begin{align}645\\-309\\ \hline \\ \end{align}

Answers to Exercise 2

  1. 20
  2. 40
  3. 50
  4. 30
  5. 20
  6. 30
  7. 20
  8. 40
  9. 0
  10. 20
  11. 30
  12. 40
  13. 410
  14. 330
  15. 250
  16. 340

Exercise 3

Estimate the following answers. Be sure to round to the nearest ten before adding or subtracting.

Be sure to circle the information and underline what’s 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?

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

\begin{align}186\\-103\\ \hline \\ \end{align}

Estimate:

\begin{align}190\\100\\ \hline 90 \end{align}

About 90 people are adults.

  1. The bus has 84 passenger seats. All the seats are filled and 39 passengers are standing. How many passengers are on the bus?
  2. Trisha counted 67 boxes on one shelf. She counted 78 boxes on the next shelf. How many boxes were there altogether?
  3. The library loaned out 157 books on Monday. It loaned out 118 books on Tuesday. How many books did it loan on both days?
  4. 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?
  5. 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?
  6. Mr. Martinez needs 257 metres of fencing. He has 125 metres. How much more fencing does he need to buy?

Answers to Exercise 3

  1. 120 passengers
  2. 150 boxes
  3. 280 books
  4. 30 minutes
  5. 20 people
  6. 130 metres

16

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.

Writing Time in Standard Format

Time is written in a standard format.

Hours: Minutes: Seconds

Example:

12 noon

would be written as 12:00:00

or 12:00 (without the seconds)

Example:

4 o’clock

would be written as 4:00:00

or 4:00 (without the seconds)

Example:

8 hours, 47 minutes, 3 seconds

would be written as 8:47:03

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

Example:

3 hours, 9 minutes, 3 seconds

would be written as 3:09:03

Exercise 1

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

  1. 3 hours, 56 minutes, 42 seconds
  2. 12 hours, 2 minutes, 29 seconds
  3. 1 hour, 23 minutes, 54 seconds
  4. 6 hours, 7 minutes, 39 seconds
  5. 11 hours, 41 minutes
  6. 7 hours, 14 minutes, 59 seconds
  7. 21 hours, 36 minutes
  8. 1 hour, 51 minutes, 41 seconds
  9. 5 hours, 18 minutes, 10 seconds

Answers to Exercise 1

  1. 3:56:42
  2. 12:02:29
  3. 1:23:54
  4. 6:07:39
  5. 11:41
  6. 7:14:59
  7. 21:36
  8. 1:51:41
  9. 5:18:10

A.M. 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.

Exercise 2

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.

  1. Your shift at work starts at 8:30 in the morning.
  2. Your class starts at 1:00 in the afternoon.
  3. Your son has soccer practice at 4:00 in the afternoon.
  4. You catch your bus at 6:15 in the morning.
  5. You need to go to the doctor at 3:20 in the afternoon.

Answers to Exercise 2

  1. 8:30 a.m.
  2. 1:00 p.m.
  3. 4:00 p.m.
  4. 6:15 a.m.
  5. 3:20 p.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.

Exercise 3

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.

  1. You needed 2 hours and 15 minutes for grocery shopping.
  2. It took 1 hour and 50 minutes to cook dinner.
  3. You drove for 9 hours and 23 minutes.
  4. Your baby slept for 1 hour and 47 minutes.
  5. You visited with friends for 3 hours and 11 minutes.
  6. It took 2 hours and 35 minutes to play the hockey game.
  7. You rode on the bus for 1 hour and 28 minutes.
  8. You walked to work in 38 minutes.
  9. How long does it take you to get to school?

Answers to Exercise 3

  1. 2 hours
  2. 2 hours
  3. 9 hours
  4. 2 hours
  5. 3 hours
  6. 3 hours
  7. 1 hour
  8. 1 hour
  9. Check with your instructor.

17

Topic C: Shapes

Circle

The circle is a shape we all know.

a medium size red circle, a small yellow circle, a big blue circle

These objects suggest the idea of a circle:

Add some examples of your own.

Triangle

A triangle is a three-sided shape. Triangles have three sides and three angles.three different sized triangles in different colours

Draw some different sized triangles here.

Rectangle

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

three different sized rectangles in different colours

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

Square

A square is a special kind of rectangle. Squares have square corners and all four sides are the same length.three different sized circles in different colours

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

Exercise 1

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

Example: 

A cookie is a circle.a circle

  1. A door is a          .
  2. This page is a          .
  3. A yield sign is a          .
  4. A room is usually a          .
  5. A coin is a          .
  6. A ten dollar bill is a          .
  7. The rim of a jar is a          .
  8. This warning sign is a          .a warning sign with three sides and three angles
  9. A pizza is a          .

Answers to Exercise 1

  1. rectangle
  2. rectangle
  3. triangle
  4. rectangle
  5. circle
  6. rectangle
  7. circle
  8. triangle
  9. circle

Exercise 2

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.

  1. A circle          .
  2. A rectangle          .
  3. A square          .
  4. A triangle          .

Exercise 3

Circle the correct shape in each line. Have your instructor check your answers.

  1. A rectangle
    a circle, a rectangle, a square, a triangle
  2. A circlea square, a triangle, a rectangle, a circle
  3. A squarea rectangle, a circle, a square, a triangle
  4. A trianglea triangle, a square, a circle, a rectangle

Exercise 4

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

  1. a round clock
  2. a pine tree
  3. a cell phone
  4. a chess board
  5. a photograph of a house
  6. a bowl
  7. a frying pan with 4 corners and 4 equal sides
  8. the Canadian flag

Answers to Exercise 4

  1. circle
  2. triangle
  3. rectangle
  4. square
  5. rectangle or triangle
  6. circle
  7. square
  8. rectangle

18

Unit 4 Review: Estimating, Time, and 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.

  1. Estimate the following answers. Be sure to round to the nearest 10 before adding.
    1. \begin{align}23\\+32\\ \hline \\ \end{align}
    2. \begin{align}68\\+17\\ \hline \\ \end{align}
    3. \begin{align}34\\+28\\ \hline \\ \end{align}
    4. \begin{align}42\\+53\\ \hline \\ \end{align}
    5. \begin{align}74\\+24\\ \hline \\ \end{align}
    6. \begin{align}33\\+28\\ \hline \\ \end{align}
    7. \begin{align}17\\+42\\ \hline \\ \end{align}
    8. \begin{align}27\\+18\\ \hline \\ \end{align}
  2. Estimate the following sums. Be sure to round to the nearest 10 before adding.
    1. \begin{align}625\\+254\\ \hline \\ \end{align}
    2. \begin{align}432\\+325\\ \hline \\ \end{align}
    3. \begin{align}328\\+163\\ \hline \\ \end{align}
    4. \begin{align}529\\+248\\ \hline \\ \end{align}
    5. \begin{align}536\\+137\\ \hline \\ \end{align}
    6. \begin{align}867\\+215\\ \hline \\ \end{align}
    7. \begin{align}843\\+107\\ \hline \\ \end{align}
    8. \begin{align}435\\+127\\ \hline \\ \end{align}
  3. Estimate the following answers. Be sure to round to the nearest 10 before subtracting.
    1. \begin{align}43\\-28\\ \hline \\ \end{align}
    2. \begin{align}64\\-25\\ \hline \\ \end{align}
    3. \begin{align}73\\-47\\ \hline \\ \end{align}
    4. \begin{align}83\\-24\\ \hline \\ \end{align}
    5. \begin{align}68\\-28\\ \hline \\ \end{align}
    6. \begin{align}54\\-22\\ \hline \\ \end{align}
    7. \begin{align}67\\-29\\ \hline \\ \end{align}
    8. \begin{align}85\\-29\\ \hline \\ \end{align}
  4. Estimate the following answers. Be sure to round to the nearest 10 before subtracting.
    1. \begin{align}625\\-407\\ \hline \\ \end{align}
    2. \begin{align}908\\-413\\ \hline \\ \end{align}
    3. \begin{align}976\\-134\\ \hline \\ \end{align}
    4. \begin{align}882\\-257\\ \hline \\ \end{align}
    5. \begin{align}572\\-154\\ \hline \\ \end{align}
    6. \begin{align}908\\-713\\ \hline \\ \end{align}
    7. \begin{align}965\\-702\\ \hline \\ \end{align}
    8. \begin{align}988\\-254\\ \hline \\ \end{align}
  5. Write the following times in standard format.
    1. 10 hours, 20 minutes, 12 seconds
    2. 8 hours,45 minutes, 6 seconds
    3. 5 hours, 32 minutes, 45 seconds
    4. 1 hour, 7 minutes, 28 seconds
    5. 12 hours, 55 minutes
    6. 6 hours, 5 minutes, 39 seconds
  6. Write the following times using a.m. or p.m.
    1. The movie starts at 6:45 in the evening.
    2. Your friend calls and wakes you up at 3:23 in the morning.
    3. Your dog barks at the mailman at 2:35 in the afternoon.
    4. Your morning break is at 10:15.
  7. Round the following times to the nearest hour.
    1. You took a walk for 47 minutes.
    2. Your round trip (there and back) to the mall took 2 hours and 12 minutes.
  8. Circle the correct shape in each line.
    1. A trianglea triangle, a square, a circle, a rectangle
    2. A square
      a rectangle, a circle, a square, a triangle
  9. The following things give the idea of a shape. Write the name of the shape in each blank.
    1. A window is a          .
    2. A checkerboard is a          .
    3. A watch is a          .
    4. A yield sign is a          .
  10. Word Problems. Estimate the following answers. Be sure to round to the nearest 10 before adding or subtracting. Be sure to circle the information and underline what’s being asked.
    1. 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.
    2. A restaurant used 76 kilograms of potatoes and 68 kilograms of meat. Estimate how many kilograms of potatoes and meat the restaurant used altogether.
    3. Paolo’s father weighs 78 kilograms. Paolo weighs 29 kilograms. Estimate how much more Paolo’s father weighs.
    4. Chi bought 54 litres of gasoline on Tuesday. He ought 38 litres of gasoline on Friday. Estimate how many litres of gas he bought altogether.

Answers to Unit 4 Review

    1. 50
    2. 90
    3. 60
    4. 90
    5. 90
    6. 60
    7. 60
    8. 50
    1. 880
    2. 760
    3. 490
    4. 780
    5. 680
    6. 1090
    7. 950
    8. 570
    1. 10
    2. 30
    3. 20
    4. 60
    5. 40
    6. 30
    7. 40
    8. 60
    1. 220
    2. 500
    3. 850
    4. 620
    5. 420
    6. 200
    7. 270
    8. 740
    1. 10:20:12
    2. 8:45:06
    3. 5:32:45
    4. 1:07:28
    5. 12:55
    6. 6:05:39
    1. 6:45 p.m.
    2. 3:23 a.m.
    3. 2:35 p.m.
    4. 10:15 a.m.
    1. 1 hour
    2. 2 hours
    1. a triangle
    2. a square
    1. rectangle
    2. square
    3. circle
    4. triangle
    1. 550 metres
    2. 50 kilograms
    3. 150 kilograms
    4. 90 litres

1

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.

If you can’t remember how to do a question, 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

  1. Count the number of things in each picture. Write the number and word name.
    Picture Answer
    1. diamond, diamond, diamond, diamond
    Numeral:

    Word Name:

    1. heart, heart, heart
    Numeral:

    Word Name:

    1. dot, dot, and dot, dot, dot, dot, dot, dot
    Numeral:

    Word Name:

    1. dot, and dot, dot, dot, dot, dot
    Numeral:

    Word Name:

1-C

  1. Fill in the blanks to make each sentence true. Draw a picture for B and D.
    1. 58 means           tens and           ones.
    2. 18 means           tens and           ones.
    3. 471 means           hundreds,           tens and           ones.
    4. 127 means           hundreds,           tens and           ones.
  2. Write the place value names (ones, tens, hundreds) for each underlined digit.
    1. 56         
    2. 239          
    3. 98         
    4. 534          
  3. Name the digit for the place value named from the number 5782.
    1. Ten          
    2. Hundreds          
  4. Write the word names for the numbers.
    1. 17
    2. 342
    3. 625
  5. Write numerals for these word names.
    1. seventy-five
    2. nineteen
    3. seven hundred fifty
    4. nine hundred five
    5. eight hundred seventy-three

1-D

  1. Place a box around the larger number.
    1. 452, 245
    2. 678, 687
  2. H. Arrange these numbers in order from smallest to largest.
    1. 86, 668, 886, 686, 868, 66, 866
    2. 23, 323, 223, 33, 332, 322, 232
  3. Write <, > or = in each blank as needed.
    1. 23           34
    2. 118           118
    3. 667           576
    4. 405           450

1-E

  1. Round each number to the nearest ten.
    1. 52
    2. 123
    3. 178
    4. 89
  2. Word problems. For each problem, round the numbers to the nearest 10.
    1. 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 Rounded Number
      Polar Bear
      Koala Bear
      Panda Bear
      Kodiak Bear
      Black Bear
  3. How much money do you have?
    1.           cents
      dime, dime, dime, dime
    2.           dollars
      toonie, toonie, toonie, toonie, and toonie, toonie

2-A

  1. Check out your addition facts.
    1. \begin{align}0\\+8\\ \hline \\ \end{align}
    2. \begin{align}2\\+3\\ \hline \\ \end{align}
    3. \begin{align}8\\+2\\ \hline \\ \end{align}
    4. \begin{align}1\\+4\\ \hline \\ \end{align}
    5. \begin{align}5\\+0\\ \hline \\ \end{align}
    6. \begin{align}9\\+5\\ \hline \\ \end{align}
    7. \begin{align}6\\+7\\ \hline \\ \end{align}
    8. \begin{align}3\\+6\\ \hline \\ \end{align}
  2. Add across or horizontally.
    1. 7 + 4 =
    2. 3 + 0 =
    3. 2 + 9 =
    4. 9 + 8 =
    5. 6 + 2 =
    6. 5 + 6 =
    7. 8 + 9 =
    8. 4 + 2 =
  3. Find the sums.
    1. \begin{align}4\\5\\+3\\ \hline \\ \end{align}
    2. \begin{align}2\\7\\+8\\ \hline \\ \end{align}
    3. \begin{align}4\\2\\+8\\ \hline \\ \end{align}
    4. \begin{align}4\\6\\+7\\ \hline \\ \end{align}
    5. \begin{align}3\\2\\+3\\ \hline \\ \end{align}
    6. \begin{align}6\\1\\+5\\ \hline \\ \end{align}
  4. Find the sums.
    1. \begin{align}5\\2\\3\\+4\\ \hline \\ \end{align}
    2. \begin{align}2\\3\\4\\+7\\ \hline \\ \end{align}
    3. \begin{align}3\\0\\1\\+2\\ \hline \\ \end{align}
    4. \begin{align}2\\3\\1\\+2\\ \hline \\ \end{align}
    5. \begin{align}5\\1\\3\\+2\\ \hline \\ \end{align}
    6. \begin{align}4\\3\\2\\+6\\ \hline \\ \end{align}
  5. 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.
    1. a rectangle whose length is 3 metres, and width is 2 metres
    2. a triangle whose adjacent is 4 metres, opposite is 3 metres, and hypothesis is 5 metres
    3. a square whose side is 2 metres
  6. Find the sums.
    1. \begin{align}46\\+33\\ \hline \\ \end{align}
    2. \begin{align}35\\+93\\ \hline \\ \end{align}
    3. \begin{align}82\\+56\\ \hline \\ \end{align}
    4. \begin{align}91\\+17\\ \hline \\ \end{align}
    5. \begin{align}740\\+859\\ \hline \\ \end{align}
    6. \begin{align}638\\+610\\ \hline \\ \end{align}
  7. Word problems.
    1. Seven cars were in the first row. Four cars were in the second row. How many cars are there in the first two rows?
    2. One bicycle stored ordered 56 bikes. Another store ordered 72 bikes. How many bikes did both stores order?
    3. 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

  1. Check out your subtraction facts.
    1. \begin{align}9\\-5\\ \hline \\ \end{align}
    2. \begin{align}6\\-3\\ \hline \\ \end{align}
    3. \begin{align}17\\-8\\ \hline \\ \end{align}
    4. \begin{align}14\\-7\\ \hline \\ \end{align}
    5. \begin{align}14\\-9\\ \hline \\ \end{align}
    6. \begin{align}11\\-2\\ \hline \\ \end{align}
    7. \begin{align}12\\-5\\ \hline \\ \end{align}
    8. \begin{align}9\\-3\\ \hline \\ \end{align}
  2. Subtract across or horizontally
    1. 4 − 1 =
    2. 8 − 2 =
    3. 17 − 8 =
    4. 11 − 6 =
    5. 6 − 4 =
    6. 11 − 3 =

3-B

  1. Find the differences.
    1. \begin{align}76\\-25\\ \hline \\ \end{align}
    2. \begin{align}84\\-43\\ \hline \\ \end{align}
    3. \begin{align}95\\-74\\ \hline \\ \end{align}
    4. \begin{align}69\\-16\\ \hline \\ \end{align}
    5. \begin{align}852\\-321\\ \hline \\ \end{align}
    6. \begin{align}789\\-650\\ \hline \\ \end{align}
  2. Word problems. Solve each work problem.
    1. There were 18 roses in a bouquet. Milton gave 9 roses away. How many roses were left?
    2. A city has 89 mail carriers. One day only 54 were at work. How many were not at work?
    3. Mariko and Stefan went 5-pin bowling. Mariko scored 274 points while Stefan scored 152. How many more points did Mariko score?

4-A

  1. Estimate the following answers. Be sure to round to the nearest 10 before adding.
    1. \begin{align}81\\+74\\ \hline \\ \end{align}
    2. \begin{align}53\\+39\\ \hline \\ \end{align}
    3. \begin{align}43\\+68\\ \hline \\ \end{align}
    4. \begin{align}733\\+719\\ \hline \\ \end{align}
    5. \begin{align}907\\+448\\ \hline \\ \end{align}
    6. \begin{align}623\\+914\\ \hline \\ \end{align}
  2. Estimate the following answers. Be sure to round to the nearest 10 before subtracting.
    1. \begin{align}82\\-59\\ \hline \\ \end{align}
    2. \begin{align}67\\-38\\ \hline \\ \end{align}
    3. \begin{align}61\\-17\\ \hline \\ \end{align}
    4. \begin{align}968\\-426\\ \hline \\ \end{align}
    5. \begin{align}577\\-171\\ \hline \\ \end{align}
    6. \begin{align}742\\-533\\ \hline \\ \end{align}
  3. Word problems. Estimate the following answers. Be sure to round to the nearest 10 before adding or subtracting.
    1. 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?
    2. 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

  1. Write the following times in standard format.
    1. 3 h, 22 min, 51 s
    2. 8 h, 38 min, 9 s
    3. 10 h, 18 min, 23 s
    4. 7 h, 43 min, 34 s
  2. Write the following times using a.m. or p.m.
    1. The movie begins at 8:30 in the evening.
    2. The coffee shop opens at 5:15 in the morning.
    3. The shopping mall closes at 10:00 at night.
  3. Round the following times to the nearest hour.
    1. The running time for the movie was 2 hours and 25 minutes.
    2. It took 5 hours and 53 minutes to go the hockey and return home after the game.
  4. The following things give the idea of a shape. Write the name of the shape in each blank.
    1. A tree is a          .
    2. A swimming pool is a          .
    3. A quarter is a          .
  5. What shape are the following things? Write triangle, square, rectangle or circle.
    1. a blackboard
    2. a sudoku board

Answers to Book 1 Review

    1. 4, four
    2. 3, three
    3. 8, eight
    4. 6, six
    1. 5 tens, 8 ones
    2. 1 ten, 8 ones
    3. 4 hundreds, 7 tens, 1 one
    4. 1 hundred, 2 tens, 7 ones
    1. tens
    2. ones
    3. tens
    4. hundreds
    1. 8
    2. 7
    1. seventeen
    2. three hundred forty-two
    3. six hundred twenty-five
    1. 75
    2. 19
    3. 750
    4. 905
    5. 873
    1. 452
    2. 687
    1. 66, 86, 668, 686, 866, 868, 886
    2. 23, 33, 223, 232, 322, 323, 332
    1. <
    2. =
    3. >
    4. <
    1. 50
    2. 120
    3. 180
    4. 90
    1. Bear Number Rounded Number
      Polar Bear 1002 1000
      Koala Bear 14 10
      Panda Bear 113 110
      Kodiak Bear 679 680
      Black Bear 272 270
    1. 40 cents
    2. 12 dollars
    1. 8
    2. 5
    3. 10
    4. 5
    5. 5
    6. 14
    7. 13
    8. 9
    1. 11
    2. 3
    3. 11
    4. 17
    5. 8
    6. 11
    7. 17
    8. 6
    1. 12
    2. 17
    3. 14
    4. 17
    5. 8
    6. 12
    1. 14
    2. 16
    3. 6
    4. 8
    5. 11
    6. 15
    1. 10 metres, rectangle
    2. 12 metres, triangle
    3. 8 metres, square
    1. 79
    2. 128
    3. 138
    4. 108
    5. 1599
    6. 1248
    1. 11 cars
    2. 128 bikes
    3. 99 kilometres
    1. 4
    2. 3
    3. 9
    4. 7
    5. 5
    6. 9
    7. 7
    8. 6
    1. 3
    2. 6
    3. 9
    4. 5
    5. 2
    6. 8
    1. 51
    2. 41
    3. 21
    4. 53
    5. 531
    6. 139
    1. 9 roses
    2. 35 mail carriers
    3. 122 points
    1. 80 + 70 = 150
    2. 50 + 40 = 90
    3. 40 + 70 = 110
    4. 730 + 720 = 1450
    5. 910 + 450 = 1360
    6. 620 + 910 = 1530
    1. 80 − 60 = 20
    2. 70 − 40 = 30
    3. 60 − 20 = 40
    4. 970 − 430 = 540
    5. 580 − 170 = 410
    6. 740 − 530 = 210
    1. 50 years
    2. 220 metres
    1. 3:22:51
    2. 8:38:09
    3. 10:18:23
    4. 7:43:34
    1. 8:30 p.m.
    2. 5:15 a.m.
    3. 10:00 p.m.
    1. 2 hours
    2. 6 hours
    1. triangle
    2. rectangle
    3. circle
    1. rectangle
    2. square

2

Versioning History

This page provides a record of edits and changes made to this book since its initial publication. Whenever edits or updates are made in the text, we provide a record and description of those changes here. If the change is minor, the version number increases by 0.01. If the edits involve substantial updates, the version number increases to the next full number.

The files posted by this book always reflect the most recent version. If you find an error in this book, please fill out the Report an Error form.

Version Date Change Details
1.00 October 3, 2014 Book initially published in the BC Open Textbook Collection.
2.00 September 22, 2021 Book updated and republished in Pressbooks as the second edition.