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.

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
	Numeral: 3 Word name: Three
	Numeral: Word name:
	Numeral: Word name:
	Numeral: Word name:
	Numeral: Word name:
	Numeral: Word name:
	Numeral: Word name:
	Numeral: Word name:
	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

Topic A 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. 
   2. 
   3. 
   4. 
2. Write the numerals from one to ten.

Answers to Topic A Self-Test

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

2. 1. 1

      2

      3

      4

      5

      6

      7

      8

      9

      10

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

The ones place tells how many ones there are.

• 3 means 3 ones.
• 0 means 0 ones
• 9 means 9 ones

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

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

Every ten is ten ones.

43 means 4 tens and 3 ones.

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

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

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

Reading and Writing Numerals

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

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

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

We use numerals to represent numbers.

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

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

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

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

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

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.

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”.

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.

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).

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.

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

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

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

 Topic B 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 B Self-Test

1. 1. tens
   2. tens
   3. hundreds
   4. ones
   5. ones
   6. hundreds
2. 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
3. 1. 547
   2. 380
   3. 275
   4. 416
   5. 923

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?

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

Example A: Compare 63 and 59

Look at the tens place.

• 63 has a 6 in the tens place
• 59 has a 5 in the tens place.
• 63 is larger than 59.

Example B: Compare 496 and 476

Look at the hundreds place.

• Both have 4’s.

Look at the tens place.

• 496 has a 9 in the tens place
• 476 has a 7 in the tens place.
• 496 is larger than 476.

Now use the same ideas to arrange more than two numerals in order. For example, to arrange 6, 616, 1, 66, 666, 61, and 16 in order from smallest to largest, use the following method.

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

• 6, 1
• 66, 61, 16, and
• 616, 666

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

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

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

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.

• 5 < 12 means 5 is less than 12
• 6 > 3 means 6 is greater than 3

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

Topic C 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 C Self Test

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

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:

• We may not know the exact number.
• The exact number may not be important for what we are doing.
• We may need a quick way to figure something out.

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

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

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

Topic D 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 D Self-Test

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

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

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.

The numbers above are called odd numbers.

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

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.

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.

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.

Topic E 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.
   2. How much money do you have?           dollars.
   3. How much money do you have?           cents.

Answers to Topic E Self-Test 

1. 1. 1, 3, 5, 7, 9, 11, 13, 15 17, 19
2. 1. 2, 4, 6, 8, 10, 12, 14, 16, 18, 20
3. 1. 75 cents
   2. 38 dollars
   3. 80 cents

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
   	Numeral: Word Name:
   	Numeral: Word Name:
   	Numeral: Word Name:
   	Numeral: Word Name:
   	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.
      
   4. 138 =            hundreds,           tens,           ones.
   5. 231 =            hundreds,           tens,           ones. Draw your picture below.
   6.            hundreds           tens           ones = 
      
      
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.          cents
    2.          dollars
    3.          cents
       
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. 1. 9, nine
   2. 7, seven
   3. 6, six
   4. 8, eight
   5. 5, five
2. 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
3. 1. hundreds
   2. tens
   3. ones
   4. hundreds
   5. tens
   6. ones
4. 1. 164
   2. 892
   3. 250
   4. 371
   5. 485
   6. 743
5. 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
6. 1. 47
   2. 19
   3. 65
   4. 38
   5. 24
   6. 535
   7. 360
   8. 204
7. 1. 23, 32, 258, 282, 345, 534
   2. 27, 155, 208, 335, 452, 635
8. 1. <
   2. >
   3. <
   4. =
9. 1. 40
   2. 340
   3. 70
   4. 30
10. 1. 70 cents
    2. 26 dollars
    3. 90 cents

11. 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

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

The plus sign + means to add.

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.

Adding Across

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

Example:

Another way to add numbers is across or horizontally.

4 + 5 = 9

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

Word Problems

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

Word such as:

• more than
• plus
• added to
• sum
• total
• have altogether
• in all

tell you to add the numbers together.

Look for these words when reading word problems and underline them before trying to solve a problem. Circle the information that is given.

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?

• You have circled 2 pages and 9 pages. This is the information you will use to find the answer.
• You have underlined “in all”. These words tell you to add.

Jane read 11 pages in all.

Topic A Self-Test

Mark       /22                 Aim       19/22

1. Find the sums. Be sure to check your answers. (12 marks)
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
   7. 
   8. 
   9. 
   10. 
   11. 
   12. 
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. 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

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:

1. Add the first two numbers together.
   
2. Add that sum to the next number.
   

The sum of:

Example B: 

1. Add the first two numbers together.
   
2. Add that sum to the third number.
   

The sum of:

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: Rectangle

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

• Perimeter = 3 + 2 + 3 + 2
• Perimeter = 10 meters

Topic B Self-Test

Mark      /18        Aim      15/18

1. Find the sums. Be sure to check your answers. (12 marks)
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
   7. 
   8. 
   9. 
   10. 
   11. 
   12. 
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.
      

Answers to Topic B Self-Test

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

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:

1. Add the ones to the ones. 3 ones + 6 ones = 9 ones. Write the answer in line with the ones in the equation.
   
2. Add the tens. 2 tens + 5 tens = 7 tens
   

The sum of 23 + 56 = 79

Example B:

1. Add the ones. 2 ones + 5 ones = 7 ones
   
2. Add the tens. 7 tens + 1 ten = 8 tens
   
3. Add the hundreds. 3 hundreds + 4 hundreds = 7 hundreds
   

The sum of 372 + 415 = 787

Topic C Self-Test

1. Find the sums. Be sure to check your answers. (12 marks)
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
   7. 
   8. 
   9. 
   10. 
   11. 
   12. 
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.
      

Answers to Topic C Self-Test

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

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

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

The minus sign − means to subtract.

says nine minus three equals six or nine take away three is six.

The difference between 9 and 3 is 6.

Subtraction is the opposite of addition.

Look at the examples:

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

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

Subtracting Across

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

Example:

Another way to subtract numbers is across or horizontally.

9 − 5 = 4

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

Word Problems

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

Words such as:

• less than
• minus
• subtracted from
• how many more
• how much more, and
• difference

tell you to subtract the numbers.

Look for these words when reading word problems and underline them before trying to solve a problem. Circle the information that is given.

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.

Topic A Self-Test

Mark    /21            Aim    18/27

1. Find the difference. Be sure to check your answers. (9 marks)
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
   7. 
   8. 
   9. 
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. 1. 8
   2. 9
   3. 6
   4. 7
   5. 6
   6. 8
   7. 4
   8. 2
   9. 9
2. 1. 1
   2. 8
   3. 7
   4. 6
   5. 7
   6. 0
3. 1. 9 fish
   2. $9
   3. 5 metres

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:

1. Subtract the ones from the ones. 7 ones − 6 ones = 1 one. Write the answer in line with the ones in the question.
   
2. Subtract the tens from the tens. 5 tens – 2 tens = 3 tens
   

The difference between 57 and 26 is 31.

Example B:

1.  Subtract the ones from the ones. 8 ones – 4 ones = 4 ones. Write the answer in line with the ones in the question.
   
2. Subtract the tens. 2 tens – 2 tens = 0 tens.
   
3. Subtract the hundreds. 6 hundreds – 5 hundreds = 1 hundred.
   

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

Topic B Self-Test

Mark       /27             Aim        23/27

1. Find the difference. Be sure to check your answers. (6 marks)
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
2. Find the difference. Be sure to check your answers. (6 marks)
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
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. 1. 8
   2. 9
   3. 6
   4. 7
   5. 6
   6. 8
2. 1. 474
   2. 257
   3. 231
   4. 234
   5. 211
   6. 412
3. 1. 22 degrees Celsius
   2. 56 kilometres
   3. 504 metres

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

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

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

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

• 60 minutes = 1 hour
• 60 seconds = 1 minute

Writing Time in Standard 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

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.

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.

Circle

The circle is a shape we all know.

These objects suggest the idea of a circle:

• rim of coffee cups and glasses
• top of lamp shades top of cans of food
• compact discs
• the ends of pipes and hoses (called the cross-section)
• the coloured part of your eye (the iris)

Add some examples of your own.

Triangle

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

Draw some different sized triangles here.

Rectangle

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

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

Square

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

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

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. 
   2. 
   3. 
   4. 
   5. 
   6. 
   7. 
   8. 
2. Estimate the following sums. Be sure to round to the nearest 10 before adding.
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
   7. 
   8. 
3. Estimate the following answers. Be sure to round to the nearest 10 before subtracting.
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
   7. 
   8. 
4. Estimate the following answers. Be sure to round to the nearest 10 before subtracting.
   1. 
   2. 
   3. 
   4. 
   5. 
   6. 
   7. 
   8. 
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 triangle
   2. A square
      
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. 1. 50
   2. 90
   3. 60
   4. 90
   5. 90
   6. 60
   7. 60
   8. 50
2. 1. 880
   2. 760
   3. 490
   4. 780
   5. 680
   6. 1090
   7. 950
   8. 570
3. 1. 10
   2. 30
   3. 20
   4. 60
   5. 40
   6. 30
   7. 40
   8. 60
4. 1. 220
   2. 500
   3. 850
   4. 620
   5. 420
   6. 200
   7. 270
   8. 740
5. 1. 10:20:12
   2. 8:45:06
   3. 5:32:45
   4. 1:07:28
   5. 12:55
   6. 6:05:39
6. 1. 6:45 p.m.
   2. 3:23 a.m.
   3. 2:35 p.m.
   4. 10:15 a.m.
7. 1. 1 hour
   2. 2 hours
8. 1. 
   2. 
9. 1. rectangle
   2. square
   3. circle
   4. triangle
10. 1. 550 metres
    2. 50 kilograms
    3. 150 kilograms
    4. 90 litres