Lesson 1: Exploring Large Numbers
1. Write each number in standard form.
a) 2 million 186 thousand 23
b) 4 000 000 000 + 6 000 000 + 900 000 + 60 000 + 5000 + 400 + 80 + 4
c) 50 000 000 + 5 000 000 + 70 000 + 2000 + 9
d) six billion two hundred seventeen million three thousand eleven
2. Write each number in expanded form.
a) 184 267 317 b) 4 300 627 803
c) 17 652 425 d) 85 697 304 281
3. Write each number in words.
a) 1 856 374 021 356
b) 85 609 327 004
c) 2 000 351 246
4. Write the value of each underlined digit.
a) 184 267 317
b) 4 300 627 803
c) 17 662 425
d) 55 247 361 401
5. Use the digits from 1 to 8. Use each digit only once.
Make an 8-digit number as close to 17 000 000 as possible.
6. Explain the difference between the two 4s in the number 546 347 658 123.
7. Write the number that is:
a) 10 000 less than 987 624 325
b) 100 000 more than 2 325 678 141
Lesson 2: Numbers All Around Us Use a calculator when you need to.
1. Use the data in the table.
a) Find the total population of the 3 territories in 2006.
b) How much greater is the population of British Columbia than the population of Alberta?
c) What is the combined population of Manitoba and Saskatchewan?
d) Find the total population of all the provinces and territories in the table.
2. Nadia’s property is 937 m long and 641 m wide. What is the perimeter of Nadia’s property?
3. Cecil planted 744 maple trees in 24 equal rows. How many trees were planted in each row?
4. Twenty-seven nuts and bolts are needed to assemble a picnic table. How many nuts and bolts are needed for 256 picnic tables?
5. One package of sugar-free gum has 14 pieces. How many packages can be made with 3680 pieces?
6. The population of Nunavut was 26 745 in 2001 and 29 474 in 2006. By how much did the population increase from 2001 to 2006?
2006 Population Counts Province or
Territory Population
Manitoba 1 148 401 Saskatchewan 968 157 Alberta 3 290 350 British Columbia 4 113 487 Yukon Territory 30 372 Northwest
Lesson 3: Exploring Multiples
1. List the first 10 multiples of each number.
a) 4 b) 9 c) 6 d) 25 e) 12
2. Find the first 3 common multiples of each pair of numbers.
a) 6 and 8 b) 3 and 7 c) 9 and 10
d) 4 and 7 e) 2 and 9 f) 5 and 8
3. Find the first 2 common multiples of each set of numbers.
a) 3, 4, and 6 b) 2, 4, and 5
c) 4, 6, and 8 d) 2, 3, and 4
4. Draw a large Venn diagram with 2 overlapping loops. Label the loops Multiples of 3 and Multiples of 4. Sort these numbers in the Venn diagram:
48, 15, 24, 33, 60, 73, 56, 40, 42, 21, 16, 28
5. Draw a large Venn diagram with 3 overlapping loops.
Label the loops Multiples of 2, Multiples of 3, and Multiples of 5. Sort these numbers in the Venn diagram:
20, 12, 21, 8, 9, 15, 29, 25, 30, 36
6. Kimi saw 13 animals in the barnyard.
Some were chickens and some were sheep. Altogether there were 36 legs.
Lesson 4: Prime and Composite Numbers
1. Tell if each number is prime or composite.
a) 73 b) 48 c) 23 d) 59 e) 39
2. Copy the table.
Sort the numbers from 20 to 40 in the table.
3. Write 3 numbers less than 50 that have exactly 4 factors each.
4. Write 3 numbers less than 50 that have exactly 2 factors each.
5. Which numbers below are factors of 35? How do you know?
2, 3, 4, 5, 6, 7, 8, 9, 10
6. Lemons are packaged in bags of 6.
Which of these numbers of lemons can be packaged in full bags? How do you know?
96, 46, 42, 60, 63, 72, 85
7. Chioke goes to the gym every 4th day. He works at the soup kitchen every 3rd day.
Chioke went to the gym and worked at the soup kitchen today. When will he next do both on the same day?
Even Odd Prime
Lesson 5: Investigating Factors
1. List all the factors of each number.
a) 24 b) 36 c) 50 d) 19
e) 84 f) 48 g) 51 h) 16
2. Draw a factor tree to find the factors of each number that are prime.
a) 32 b) 60 c) 42
3. Use division to find the factors of each number that are prime.
a) 80 b) 32 c) 48
4. Find the common factors of each pair of numbers.
a) 12, 18 b) 16, 32 c) 21, 35 d) 45, 60
5. Draw 2 different factor trees for each number.
a) 66 b) 90 c) 48 d) 24
6. List 3 different numbers that have exactly 2 factors. What are these numbers called?
7. Draw a Venn diagram to show the factors of 12 and 30.
Where did you place the common factors of 12 and 30 in the diagram?
8. List the factors of each number that are prime.
a) 38 b) 40 c) 85
9. a) Is 42 a perfect number? Explain how you know.
Lesson 7: Order of Operations
1. Evaluate each expression. Use the order of operations.
a) 24 6 7 b) 38 – 16 4 c) 55 + 15 3
d) 7 (4 + 8) e) 28 (16 – 9) f) 50 – 16 + 4
2. Use a calculator to evaluate.
a) 1256 – 57 8 b) 684 23 4
c) 96 342 – (573 29) d) 4094 89 + 318
3. Use brackets to make each number sentence true.
a) 15 – 6 3 + 7 = 20 b) 50 – 6 6 = 14
c) 60 + 14 2 = 67 d) 100 + 44 12 = 12
4. Use mental math to evaluate.
a) (70 2) 7 b) 10 000 – 3000 3
c) 500 + 250 2 d) 2500 (50 2)
e) (3000 + 2000) 50 f) 180 (2 9)
5. How many different answers can you get by inserting one pair of brackets in this expression?
15 + 9 3 + 6
Write each expression, then evaluate it.
6. Danny bought 6 shirts for $26 each and 2 pairs of pants for $55 a pair. Which expression shows how much Danny spent, in dollars?
a) 6 26 × 2 55
b) 6 26 + 2 55
c) (6 + 2) (26 + 55)
7. Callie bought 3 packages of drinking boxes. Each package has 6 drinking boxes.
Callie shared the drinking boxes equally among 9 children. How many drinking boxes did each child get?
Lesson 8: What Is an Integer?
1. Write an integer to represent each situation.
a) The temperature is 8° below 0°C.
b) The valley was 700 m below sea level.
c) Victor spent $89 of his savings.
d) The plane flew at an altitude of 20 000 m.
e) Chuck’s golf score was 5 under par.
2. Write the opposite of each integer.
a) +7 b) –4 c) +8 d) –17 e) +32
3. Describe a situation that could be represented by each integer.
a) 73 b) –14 c) –450 d) +845 e) –2
4. A photo of a close finish of a race showed: • Jan 3 m before the finish line
• Simon 1 m before the finish line • Bryn 2 m after the finish line • Nikki 4 m after the finish line. Suppose 0 represents the finish line.
Use first initials to show the position of each racer on the number line.
5. Draw red or yellow tiles to model each integer.
Lesson 9: Comparing and Ordering Integers
1. Order the integers in each set from least to greatest.
a) 0, +6, –6, –10, +9 b) +25, +17, –23, –8, +12
c) +4, –9, +16, –25, +1 d) –52, +45, +76, –30, –121
2. Order these elevations from highest to lowest.
Caspian Sea Shore: 28 m below sea level Elbrus, Russia: 5642 m above sea level Lake Assal, Djibouti: 156 m below sea level Eurasia Basin, Arctic Ocean: 5450 m below sea level McKinley, Alaska: 6194 m above sea level
3. Copy and complete by placing < or > in each box.
a) –8 –7 b) +9 +20 c) –12 + 4
d) 0 –11 e) –23 –32 f) +15 –3
4. The data show the temperatures in different cities on one day in March. Use these temperatures to answer the questions below.
Victoria: +10°C Calgary: –6°C Regina: +5°C Winnipeg: –3°C Toronto: +7°C Quebec: –8°C Moncton: +2°C Halifax: –2°C St. John’s: –7°C
Charlottetown: 0°C Iqaluit: –35°C Whitehorse: –12°C Yellowknife: –31°C
a) Which city has the highest temperature?
b) Which city has the lowest temperature?
c) Which cities have temperatures greater than –1°C?
d) Which cities have temperatures between –6°C and +6°C?
e) Which cities have temperatures that are opposite integers?
Extra Practice 1 – Master 2.25
Lesson 1
1. a) 2 186 023 b) 4 006 965 484 c) 55 072 009 d) 6 217 003 011
2. a) 100 000 000 + 80 000 000 + 4 000 000 + 200 000 + 60 000 + 7000 + 300 + 10 + 7 b) 4 000 000 000 + 300 000 000 + 600 000
+ 20 000 + 7000 + 800 + 3
c) 10 000 000 + 7 000 000 + 600 000 + 50 000 + 2000 + 400 + 20 + 5 d) 80 000 000 000 + 5 000 000 000
+ 600 000 000 + 90 000 000 + 7 000 000 + 300 000 + 4000 + 200 + 80 + 1
3. a) one trillion eight hundred fifty-six billion three hundred seventy-four million twenty-one thousand three hundred fifty-six b) eighty-five billion six hundred nine million
three hundred twenty-seven thousand four c) two billion three hundred fifty-one thousand
two hundred forty-six
4. a) 80 000 000 b) 600 000 c) 7 000 000 d) 5 000 000 000
5. 16 875 432
6. The first 4 is in the ten billions place. It has a value of 40 billion.
The second 4 is in the ten millions place. It has a value of 40 million.
7. a) 987 614 325 b) 2 325 778 141 c) 865 273 424 850
Extra Practice 2 – Master 2.26
6. 2729
Extra Practice 3 – Master 2.27
Lesson 3
1. a) 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 b) 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 c) 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 d) 25, 50, 75, 100, 125, 150, 175, 200,
225, 250
e) 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
2. a) 24, 48, 72 b) 21, 42, 63 c) 90, 180, 270 d) 28, 56, 84 e) 18, 36, 54 f) 40, 80, 120
3. a) 12 and 24 b) 20 and 40 c) 24 and 48 d) 12 and 24
4.
3. 10, 21, 35
4. 17, 23, 47
5. 5, 7
6. 96, 42, 60, 72
7. In 12 days
Extra Practice 5 – Master 2.29
Lesson 5
1. a) 1, 2, 3, 4, 6, 8, 12, 24 b) 1, 2, 3, 4, 6, 9, 12, 18, 36 c) 1, 2, 5, 10, 25, 50 d) 1, 19
e) 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84 f) 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 g) 1, 3, 17, 51
h) 1, 2, 4, 8, 16
2. a) 2
b) 2, 3, 5
c) 2, 3, 7
5. a)
b)
c)
d)
6. 23, 37, and 73 are prime numbers.
So, 42 is not a perfect number.
b) The factors of 32 are: 1, 2, 4, 8, 16, and 32. If I add all the factors except 32, I get 31. So, 32 is an almost-perfect number.
Extra Practice 7 – Master 2.30
Lesson 7
1. a) 28 b) 34 c) 60 d) 84 e) 4 f) 38
2. a) 800 b) 3933 c) 79 725 d) 364
3. a) 15 – (6 3) + 7 = 20 b) 50 – (6 6) = 14 c) 60 + (14 2) = 67 d) (100 + 44) 12 = 12
4. a) 20 b) 1000 c) 1000 d) 25 e) 100 f) 10
5. (15 + 9) 3 + 6 = 14 (15 + 9 3) + 6 = 24 15 + (9 3) + 6 = 24 15 + (9 3 + 6) = 24 15 + 9 (3 + 6) = 16
6. 6 26 + 2 55
7. (3 6) 9 = 2
Extra Practice 8 – Master 2.31
Lesson 8
1. a) –8 b) –700 c) –89 d) +20 000 e) –5
2. a) –7 b) +4 c) –8
c) d)
e)
Extra Practice 9 – Master 2.32
Lesson 9
1. a) –10, –6, 0, +6, +9 b) –23, –8, +12, +17, +25 c) –25, –9, +1, +4, +16 d) –121, –52, –30, +45, +76
2. 6194 m, 5642 m, –28 m, –156 m, –5450 m
3. a) < b) < c) < d) > e) > f) >
4. a) Victoria b) Iqaluit
c) Victoria, Moncton, Toronto, Regina, Charlottetown
d) Winnipeg, Moncton, Halifax, Regina, Charlottetown
e) Moncton and Halifax, Toronto and St. John’s
f) Winnipeg, Calgary, Halifax, Quebec, St. John’s, Yellowknife, Iqaluit, Whitehorse g) Calgary, Quebec, St. John’s, Yellowknife,
