unit 1: number sense name: quiz (lessons 1 to 3) date:

Unit 1: Number Sense Name: ________________________

Quiz (Lessons 1 to 3) Date: ________________

Sample Unit Quizzes and Tests for Workbook 7.1 K-1

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1. Write the number with the correct spacing, then write the place value of the bold digit. a) 12098532 = ___________________________________ place value: ________________ b) 36982 = _______________________________________ place value: ________________ 2. Circle the larger number in each pair. a) 3 001 and 30 001 b) 5 679 142 and 5 789 142 3. Evaluate each expression. Use the correct order of operations. a) (2 + 5) × 3 ÷ 7 b) 25 ÷ 5 × 3 + 2 4. Verify that each equation is true. a) 18 – 4 – 7 = 1 + 2 + 4 b) 20 × 2 ÷ 4 – 5 = 6 ÷ 2 + 2 BONUS: Add brackets where necessary to make the following equations true. a) 6 + 2 × 10 – 4 = 18 b) 24 ÷ 6 – 2 + 3 = 9

Unit 1: Number Sense Answer Key

Quiz (Lessons 1 to 3)

K-2 Sample Unit Quizzes and Tests for Workbook 7.1

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1. a)

12 098 532, hundred thousands

b) 36 982, tens

2. a) 30 001, more digits

b) 5 789 142, same number of digits, so look at the left most place - they are different

3. a) 3

b) 17

4. a) 18 – 4 – 7 = 14 – 7 = 7

1 + 2 + 4 = 3 + 4 = 7

b) 20 × 2 ÷ 4 – 5 = 40 ÷ 4 – 5 = 10 – 5 = 5

6 ÷ 2 + 2 = 3 + 2 = 5

BONUS

a) 6 + 2 × (10 – 4) = 18

b) 24 ÷ (6 – 2) + 3 = 9


Test (Lessons 1 to 8) Date: ________________


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1. Write the number with the correct spacing, then write the place value of the bold digit.

95135498467 = ______________________________ place value: __________________

2. Rewrite each number in expanded form.

a) 378 403

b) 16 021

3. Evaluate each expression. Use the correct order of operations.

a) 3 – 1 × 4 ÷ 2 b) 2 + 3 × (8 ÷ 4)

4. Rewrite the expressions below without brackets by changing only the operation symbols. Keep the answers the same.

a) 24 ÷ (4 × 3) b) 5 × 12 ÷ (4 ÷ 2)

_______________________ ________________________

5. Verify that each equation is true.

a) 14 + 3 – 2 = 22 – 8 + 1 b) (19 + 5) ÷ 6 + 2 = 14 ÷ (9 – 2) × 3

6. Each rectangle in a) and b) is cut in half and rearranged. Label the lengths of the resulting sides, then write an area expression for the new rectangle and find the area.

a)

6 × 10 = _____ × _____ = ______

b)

2 × 4 = _____ × _____ = _______

10

6

4

2

Unit 1: Number Sense continued

Test (Lessons 1 to 8)


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7. Circle the larger number in each pair.

a) 5 367 098 and 536 798 b) 498 753 and 498 743

8. From the given product make two more products with the same answer. Do not use the same numbers.

a) 12 × 15 = ____ × ____ b) 24 × 27 = _____ × _____

= ____ × ____ = _____ × _____

9. Draw rectangles to show why:

a) 10 × 2 = 5 × 4 b) 3 × 6 = 9 × 2

10. Fill in the blanks with the correct operation and number.

a) 6 × 9 = 54 so 6 × 18 = 54 _____ b) 24 ÷ 8 = 3 so 96 ÷ (8 _____) = 3 c) 7 – 3 = (7 + 2) – (3 _____) d) 18 × 5 = (18 ÷ 3) × (5 _____)

11. Either write the unique answer or explain why you cannot (too many answers or no answer).

a) 0 × 7 = ___________ b) 0 × ___________ = 0 c) 3 ÷ 0 = ___________ BONUS: 5 ÷ _________ = No answer

12. Finish writing the equations to show how to find the area of the shaded region in two ways.

Area = 4 × ( _____ – _____ )

Area = 4 × _____ – 4 × _____

9

4

3




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13. Use multiples of 10 or 100 to break each problem into simpler problems.

a) 5 × 34 = 5 ______ + 5 × ______ b) 3 × 332 = 3 × _____ + 3 × ____ + 3 ×___

= _____ + _____ = _____ + _____ + _____

= _____ = _____

14. Use long multiplication to find each product.

a) b) c) d)

BONUS: Add brackets in different ways to get as many different answers as you can. Rewrite the statement each time and show the answers.

a) 8 – 3 – 2 – 1 b) 8 ÷ 2 × 2 × 2

BONUS: Find the product 6 × 41 632.

2 7

3

×

2 4

5

×

4 5 6× 7

5 2×

3 9

+




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1. 95 135 498 467, billions

2. a) 300 000 + 70 000 + 8 000 + 400 + 3

b) 10 000 + 6 000 + 20 + 1

3. a) 1

b) 8

4. a) 24 ÷ 4 ÷ 3

b) 5 × 12 ÷ 4 × 2

5. a) 14 + 3 – 2 = 15 22 – 8 + 1 = 15

b) (19 + 5) ÷ 6 + 2 = 6 14 ÷ (9 – 2) × 3 = 6

6. a) 12 × 5 = 60

b) 1 × 8 = 8

7. a) 5 367 098, more digits

b) 498 753 8. a) Answers may vary.

Samples:

3 × 60 4 × 45 2 × 90 6 × 30

b) 12 × 54 6 × 108 3 × 216 8 × 81

9. a) Draw a 10 × 2 rectangle and move the bottom half to beside the top half:

b) Draw a 3 × 6 rectangle, and divide it into 3 equal vertical sections (three 3 × 2 rectangles) and move the middle section underneath the left most section and the right section underneath again:

10. a) × 2

b) × 4

c) + 2

d) × 3

11. a) 0

b) Too many answers

c) No answer

BONUS 0

12. 4 × (9 – 3) = 4 × 9 – 4 × 3

13. a) 5 × 30 + 5 × 4 = 150 + 20 = 170

b) 3 × 300 + 3 × 30 + 3 × 2 = 900 + 90 + 6 = 996

14. a) 81

b) 120

c) 3 192

d) 2 028

BONUS

a) 8 – 3 – 2 – 1 = 2 8 – (3 – 2 – 1) = 8 8 – 3 – (2 – 1) = 4 8 – (3 – 2) – 1 = 6

b) 8 ÷ 2 × 2 × 2 = 16 8 ÷ (2 × 2 × 2) = 1 8 ÷ (2 × 2) × 2 = 4

BONUS 249 792

Unit 2: Patterns and Algebra Name: ________________________



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1. Continue the sequence, and then find the rule.

a) 41, 38, 35, _____, _____, _____ The rule is: _____________________________

b) 1, 4, 16, _____, _____ The rule is: _____________________________

c) 10, 15, 20, 10, 15, 20, _____, _____ The rule is: _____________________________

2. A company charges a flat fee of $6 plus $4 per hour to rent a bicycle.

a) Write an expression representing the cost to rent a bicycle for h hours.

b) How much would it cost to rent a bike for 3 hours?

3. There are 14 apples in total. Write an equation and solve it to find the number of apples in each bag.

4. Circle all the expressions that mean the same thing as 5m + 3. 3m + 5 5r + 3 3 + 5s m × 5 + 3 3 + 5t 5 + 3m BONUS: Circle the equation that doesn’t have the same answer as the other three. 4x + 5 = 21 21 = 5 + 4x 4x + 21 = 5 21 – 4x = 5

Unit 2: Patterns and Algebra Answer Key



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1. a) 32, 29, 26 Rule: Start at 41 and subtract 3.

b) 64, 256 Rule: Start at 1 and multiply by 4.

c) 10, 15 Rule: 10, 15, 20, then repeat.

2. a) 4h + 6 or 6 + 4h

b) $18

3. 3x + 2 = 14 x = 4

4. 5r + 3 3 + 5s m × 5 + 3 3 + 5t

BONUS 4x + 21 = 5

Unit 2: Patterns and Algebra Name: ________________________



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Section A

1. Find how each sequence was made. Then extend each pattern.

a) 24 , 21 , 18 , ____ , ____ , ____ b) 2 , 6 , 10 , ____ , ____ , ____

c) 1 , 3 , 9 , ____ , ____ d) 64 , 32 , 16 , ____ , ____ , ____

2. Match each sequence to the description.

A. Decreases by the same amount ____ 13 , 20 , 27 , 34 , 41

B. Increases by different amounts ____ 9 , 6 , 9 , 12 , 9

C. Increases by 7 each time ____ 8 , 12 , 15 , 19 , 25

D. Increases and decreases by 3 ____ 45 , 43 , 41 , 39 , 37

3. Andrea planted an apple tree when she was four years old and recorded its height every year since. Some of her data got lost.

a) How much does the tree grow each year? ___________

b) Complete the table.

BONUS When the apple tree is 240 cm high, it will start to grow fruit. How old will Andrea be when the tree produces apples? ______

4. Underline the variable. Then write an expression for each cost. Use n for the variable.

Cost ($)

DVDs are on sale for $5 each

A grocery store charges $0.39 for each lemon.

A car rental company charges a $50 flat fee plus $20 per day

BONUS: Chocolate bars are on sale for 99¢ each.

Andrea’s age

Height of tree (cm)

4 100

5

6 140

7 160

8

Unit 2: Patterns and Algebra continued



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Section B

5. Circle the expressions that get you back to m.

5m ÷ 5 5 + m – 5 3m – 3 4 – m + 4

6. Solve for the variable by undoing each operation in the equation.

a) 3x + 6 = 18 b) 5y – 10 = 35 c) 6z + 3 = 9

7. Each weighs x kg and each weighs 1 kg. Scale A is balanced perfectly.

Draw scale B so that there are only triangles on the first side.

Draw scale C to show what balances one triangle.

Under each scale write an algebraic equation.

a)

b)

8. Solve the following equations.

a) x + x + x + x = 20 b) 6x + 2 = 8

BONUS: x3 = 5 BONUS: 3x + 4 = 5x

9. Write an algebraic expression for each description.

a) 5 times a number _______________________

b) A number decreased by 15 _______________________

BONUS: 3 more than half of a number _______________________

10. The sum of three consecutive numbers is 21. What are the three numbers?

11. The perimeter of this triangle is 18. Find the missing side lengths.

B C A

B C A

8

x x

Unit 2: Patterns and Algebra Answer Key



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Section A

1. a) – 3

15, 12, 9

b) + 4

14, 18, 22

c) × 3

27, 81

d) ÷ 2

8, 4, 2

2. C, D, B, A

3. a) 20 cm

b) 120 cm, 180 cm

BONUS 11

4. a) DVDs, 5n

b) Lemon, 0.39n

c) Day, 50 + 20n

BONUS Chocolate bars, 0.99n

Section B 5. 5m ÷ 5, 5 + m – 5

6. a) x = 4

b) y = 9 c) z = 1

7. a)

3x = 9

x = 3

b)

4x = 8

x = 2

8. a) x = 5

b) x = 1

BONUS x = 15

BONUS x = 2

9. a) 5n

b) n – 15

BONUS n2 + 3 or 3 + n2

10. 6, 7, 8

11. x = 5

B

C

B

C


Quiz (Lessons 9 to 13) – Ontario Date: ________________


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1. a) List the next few multiples of these numbers.

10: 0, ____, ____, ____, ____, ____, ____, ____, ____

12: 0, ____, ____, ____, ____, ____, ____, ____, ____

b) What is the LCM of 10 and 12? ______

2. a) Find the factors of these numbers.

24: __________________________

42: __________________________ b) What is the GCF of 24 and 42? ______

3. In the list below, circle each perfect square. 2 4 6 9 10 11 15 18 23 28 33 36 44

4. Between each pair of numbers, use the symbol < or > to indicate which number is greater.

a) 42 ___ 15 b) 7 ___ 64 c) 27 ___ 52 d) 32 ___ 100

5. Evaluate each expression.

a) 25 + 9 b) 62 ÷ 32 BONUS: Evaluate 22 × 25 ÷ 10.


Quiz (Lessons 9 to 13) – Ontario


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1. a) 10: 0, 10, 20, 30, 40, 50, 60, 70, 80

12: 0, 12, 24, 36, 48, 60, 72, 84, 96

b) LCM (10,12) = 60

2. a) 24: 1, 2, 3, 4, 6, 8, 12, 24

42: 1, 2, 3, 6, 7, 14, 21, 42

b) GCF (24,42) = 6

3. Circle: 4, 9, 36

4. a) 42 > 15

b) 7 < 64

c) 27 > 52

d) 32 < 100

5 a) 5 + 3 = 8

b) 36 ÷ 9 = 4

BONUS 4 × 5 ÷ 10 = 20 ÷ 10 = 2


Quiz (Lessons 18 to 22) – Review Date: ________________


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1. Write these numbers as mixed fractions and as improper fractions.

a) b)

2. Write the mixed numbers as improper fractions.

a) 2 45 b) 3

14

3. Write the improper fractions as mixed numbers.

a) 116 b) 7

3

4. a) How many months are there in 14 of a year?

b) How many months are there in 34 of a year?

c) How many months are in 2 23 of a year?

d) How many months are in 1 16 of a year?


Quiz (Lessons 18 to 22) – Review


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1. a) 4 35 , 23

5

b) 2 14 , 94

2. a) 145

b) 134

3. a) 1 56

b) 2 13

4. a) 3 months

b) 9 months

c) 32 months

d) 14 months


Test (Lessons 18 to 31) – Ontario Date: ________________


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1. Find the factors of 18 and 30, then write their greatest common factor (GCF).

18: ____________________________ 30: ____________________________

GCF = _____

2. Between each pair of numbers, write < (less than) or > (greater than).

a) 52 ___ 24 b) 8 ___ 81

3. a) Express the mixed number

146

as an improper fraction.

b) Express the improper fraction 238

as a mixed number.

4. Consider the fractions 14 ,

25 and

310 .

a) Write equivalent fractions with denominator 20.

14 =

20

25 =

20

310 =

20

b) Write the fractions you found in a) in order from smallest to largest.

20 20 20

c) Write equivalent fractions with numerator 6.

14 =

6

25 =

6

310 =

6

d) Write the fractions you found in c) in order from smallest to largest.

6 6 6

e) Do your answers to parts b) and d) agree? Explain.

5. Calculate.

a) 37 +

27 –

17 = b)

1213 –

713 +

313 =


Test (Lessons 18 to 31) – Ontario


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6. The lowest common multiple of the denominators of a pair of fractions is called the:

L___________________ C_________________ D________________________ of the fractions.

7. a) Find the LCD of each pair of fractions.

i) 38 and

14 ii)

34 and

13 iii)

58 and

310

LCD = ______ LCD = ______ LCD = _______

b) Use the LCD you found in a) to add each pair of fractions.

i) 38 +

14 ii)

34 +

13 iii)

58 +

310

c) Which pair of fractions from part b) adds to more than 1? How can you tell from your answers?

8. Reduce the fractions below by dividing the numerator and the denominator by their GCF.

a)

812

= b)

2025

= c)

39

=

9. Add or subtract. Write your answer in lowest terms.

a) 1 36 10

b) 3 1

3 24 6

c) 5 1

2 18 2

d) 4 2

2 19 3

10. Melissa plans to bike for 1

212 kilometres today.

If she has already biked 137 kilometres, how much farther must she go?

BONUS: Which fraction is larger, 301900

or 20016000

? Explain your choice.


Test (Lessons 18 to 31) – Ontario


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1. 18: 1, 2, 3, 6, 9, 18 30: 1, 2, 3, 5, 6, 10, 15, 30 GCF = 6

2. a) 52 > 24

b) 8 < 81

3. a) 256

b) 2 78

4. a) 520 ,

820 ,

620

b) 520 ,

620 ,

820

c) 624 ,

615 ,

620

d) 624 ,

620 ,

615

e) Yes, the same numbers are put in the same order. 14 is smallest in

both cases, and 25 is largest.

5. a) 47

b) 813

6. Lowest Common Denominator

7. a) i) 8

ii) 12

iii) 40

b) i) 58

ii) 1312

iii) 3740

c) 1312

because 13 > 12

8. a) 23 (÷ 4)

b) 45 (÷ 5)

c) 13 (÷ 3)

9. a) 715

b) 1 7

12

c) 4 18

d) 79

10. 5 16 km farther

BONUS 301900 is 1

900 more than 13 and

20016000 is 1

6000 more than 13 .

Since 1900 > 1

6000 , we know

that 301900 > 2001

6000 .

Unit 4: Geometry Name: ________________________



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1. Draw and label diagrams for the following situations. Use a protractor and a ruler.

a) A line segment and its perpendicular bisector b) Two lines that intersect at 30o

2. Draw a line parallel to AB. Draw a line perpendicular to AB. Label the parallel and the

perpendicular lines on your diagram.

3. Use arrow symbols to mark the sides of these shapes that look like they are parallel.

a) b)

c) BONUS

A

B

Unit 4: Geometry Answer Key



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A

30o

1. Teacher to check. Sample solutions:

a)

b)

2. Teacher to check. Sample solution:

3. a)

b)

c)

BONUS

Unit 4: Geometry Name: ________________________ Test (Lessons 4 to 12) Date: ________________


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1. Use a protractor. Draw a line segment perpendicular to AB that passes through P.

a) b)

c) Are either of the lines you drew perpendicular bisectors of AB? How can you tell?

2. Sketch a rectangle. Clearly label any parallel or perpendicular line segments in your sketch.

3. The angles ∠a and ∠b are a linear pair. Identify the three other linear pairs in the diagram. ∠ ______ and ∠ ______

∠ ______ and ∠ ______

∠ ______ and ∠ ______ BONUS: If ∠a = 110°, what are the values of the other angles? 4. Draw ∆ABC, an equilateral triangle with AC = 5 cm. Use a ruler and a protractor. Label all sides and all angles.

a d

c b

A

B

P

A

B

P

Unit 4: Geometry continued



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5. Lines of symmetry in polygons are either angle bisectors, perpendicular bisectors of sides or both. Sketch three polygons to show each of these three situations:

angle bisector perpendicular bisector of side both BONUS: In a regular hexagon there are two types of lines of symmetry. Which ones? Use a sketch to show your answer. 6. The foot of a ladder makes a 60o angle with the ground. The top of the ladder rests on a wall

perpendicular to the ground. a) Make a sketch to show this situation. b) What angle does the ladder form with the wall? ___________

How do you know?

c) How can you tell that the distance from the top of the ladder to the ground is longer than the

distance from the base of the ladder to the wall? BONUS:

The ladder is moved so that the angle formed by the foot of the ladder and the ground is 45°. How does the distance from the top of the ladder to the ground compare to the distance from the

foot of the ladder to the wall? Explain.

Unit 4: Geometry Answer Key



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1. a)

b)

c) Yes, the line in a) is a perpendicular bisector since P = 90° and AP = BP.

IMPORTANT: Students must use a ruler to find that AP = BP – they can’t just assume so by looking).

2. Teacher to check.

Sample answer:

3. a and d

c and d

b and c

BONUS c = 110°

d = 70°

b = 70°


Note that all sides should be marked as 5 cm and all angles should be marked as 60°.


Sample answers:

Angle bisector

Perpendicular bisector of side

Both

BONUS

Two types: the opposite side bisectors and the diagonal angle bisectors

6. a) Teacher to check.

Sample sketch:

b) 30°

The angles in the triangle must add up to 180° and, in addition to the 60° angle given, we know that a wall is 90° to the ground.

c) The distance from the top of the ladder to the ground is longer. (The longer side is opposite the larger angle and, since 60° > 30°, the vertical side is longer.)

BONUS

They are equal because both opposite angles are now 45°.

B

A

P

B

P

A

30°

60°




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1. Write the decimal as a fraction or a mixed number.

a) 0.4 = b) 2.53 = c) 0.017 = 2. Write a decimal for the fraction or the mixed number.

a) 20431000

= b) 79100

= c) 1000

=23

3. Arrange the numbers in increasing order: 2.534, 2.354, 2.43, 2.345 4. Add the decimals, then round your answer to the nearest tenth.

a) 0.183 + 0.314 b) 2.23 + 4.68 5. Subtract the decimals, then round your answer to the nearest tenth.

a) 0.74 – 0.47 b) 5.65 – 0.51




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1. a) 410

b) 2 53

100

c) 171000

2. a) 3.204

b) 0.79

c) 0.023

3. From smallest to largest: 2.345, 2.354, 2.43, 2.534

4. a) 0.497 ≈ 0.5

b) 6.91 ≈ 6.9

5. a) 0.27 ≈ 0.3

b) 5.14 ≈ 5.1




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1. Put a decimal in each number so that the digit 4 has the value of 410 .

a) 4 3 2 b) 3 4 2 c) 3 2 4 d) 4

2. Round to the digit indicated.

a) 173.64 (tens) _____________________________ b) 21.4377 (hundredths) _____________________________ c) 88.092 (tenths) _____________________________ d) 47.71 (ones) _____________________________ e) 39.0832 (thousandths) _____________________________

3. Add or subtract the decimals by lining up the decimal points. a) 3.84 + 6.3 b) 3.07 – 1.54 c) 12.9 + 4.56 4. Multiply or divide.

a) 10 × 2.43 = _____________________________ b) 1000 × 7.18 = _____________________________ c) 100 × 4.39 = _____________________________ d) 1.09 ÷ 1000 = _____________________________ e) 6.58 ÷ 10 = _____________________________ f) 5.36 ÷ 100 = _____________________________




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5. Divide.

a) 82.5 ÷ 5 b) 7.56 ÷ 6 c) 87.6 ÷ 3 d) 43.12 ÷ 8

6. Janelle plans to buy a skirt that costs $15.85 and two tops that cost $11.35 each. How much will she be spending in total? 7. Which is a better deal, 6 pencils for $5.34 or 7 pencils for $6.09? 8. The average daily rainfall for the month of December in Vancouver is 5.2 mm. How much rain (on average) does Vancouver receive each December? BONUS : A box of paper contains 10 reams of paper (1 ream = 500 sheets) and costs $65.50. What is the cost of each sheet of paper to the nearest tenth of a cent?

) –

–

–

) –

–

–

)–

–

–

–

–

–

)




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1. a) 0.432

b) 3.42

c) 32.4

d) 0.4

2. a) 170

b) 21.44

c) 88.1

d) 48

e) 39.083

3. a) 10.14

b) 1.53

c) 17.46

4. a) 24.3

b) 7 180

c) 439

d) 0.001 09

e) 0.658

f) 0.053 6

5. a)

b)

c)

d)

6. Janelle will be spending $38.55 in total.

7. 7 pencils for $6.09 is a better deal ($0.87 per pencil).

8. 161.2 mm of rain

BONUS 1.3¢

) –

–

–

1 6 5

5 8 2 5

5

3 2

3 0

2 5

2 5

0

) –

–

–

1 2 6

6 7 5 6

6

1 5

1 2

3 6

3 6

0

) –

–

–

2 9 2

3 8 7 6

6

2 7

2 7

0 6

0 6

0

–

–

–

) 5 3 9

8 4 3 1 2

4 0

3 1

2 4

7 2

7 2

0

Unit 6: Measurement Name: ________________________

Quiz (Lessons 11 to 17) – Ontario Date: ________________


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1. Write each ratio in lowest terms.

a) 14 : 35 = b) 48 : 28 = 2. Solve the proportions.

a) 6 : 20 = 24 : b) : 18 = 55 : 30 3. Your car’s fuel efficiency is 11.2 km/L.

How far can you travel on 45 L of gas? Show your work. 4. Chaundra runs 2 km in 1

5 of an hour.

How far can she run in 2 hours? Show your work.

Unit 6: Measurement Answer Key

Quiz (Lessons 11 to 17) – Ontario


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1. a) 2 : 5

b) 12 : 7

2. a) 80

b) 33

3. 504 km

4. 20 km

Unit 6: Measurement Name: ________________________

Test (Lessons 1 to 3 & 7 to 17) – Ontario Date: ________________


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1. Change the units.

a) 18.67 g = __________ kg b) 1.89 m = __________ km c) 2.74 L = __________ mL

d) 4 174 mL = __________ L e) 0.072 g = __________ mg f) 73.3 mm = __________ m

2. Change the units of area.

a) 813.1 cm2 = __________ m2 b) 0.086 m2 = __________ cm2

3. Find the area of the trapezoid. 4. Find the area of the shaded part of the diagram below.

5. A triangle has a height of 3.2 cm and an area of 19.2 cm2. What is the length of its base? Do not use a calculator. 6. A trapezoid of area 35 cm2 has bases of length 7 cm and 13 cm. What is the height of the trapezoid? Show your work.

18 cm

5.2 cm

3.8 cm

Unit 6: Measurement continued

Test (Lessons 1 to 3 & 7 to 17) – Ontario


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7. Write each ratio in lowest terms.

a) 30 : 18 = b) 32 : 40 = 8. Solve the proportions.

a) 9 : 24 = : 32 b) 16 : = 56 : 35

9. An individual paper clip has a mass of 1 g. How many paper clips can be made from a 10 kg piece of metal? Show your work. 10. A 2-cup measuring cup holds 500 mL of liquid. How many measuring cups of water would it take to fill an Olympic sized swimming pool with a volume of 2 500 000 L? Show your work. 11. It takes Sharon 350 strides to run around a 400 m track. How long, in whole cm, is each of her strides? Do not use a calculator. 12. A 4 L bag of milk that costs $5.49. A 2 L carton of milk that costs $3.49.

a) What is the price per litre for each? Do not use a calculator.

b) Which is the better buy? Explain. 13. Some of the world’s fastest runners can sprint 100 m in 10 seconds. At this rate, how far (in km) would they run in an hour? BONUS 14. Of all the countries on Earth, Bangladesh has one of the highest population densities in the world,

at about 1130 people per km2. Canada has a population of approximately 34 000 000 people, spread over an area of about 10 000 000 km2.

a) What is Canada’s population density, in people per km2?

b) How many times greater is the population density of Bangladesh compared to that of Canada?

Unit 6: Measurement Answer Key

Test (Lessons 1 to 3 & 7 to 17) – Ontario


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1. a) 0.018 67 kg

b) 0.001 89 km

c) 2 740 mL

d) 4.174 L

e) 72 mg

f) 0.073 3 m

2. a) 0.081 31 m2

b) 860 cm2

3. 22 units2

4. 115.2 cm2

5. 12 cm

6. 3.5 cm

7. a) 5 : 3

b) 4 : 5

8. a) 12

b) 10

9. 10 000

10. 5 000 000

11. 114 cm

12. a) $1.37/L, $1.75/L

b) The 4 L bag is the better buy.

13. 36 km

BONUS

14. a) 3.4 people/km2

b) 332 times greater

Unit 7: Probability and Data Management Name: ______________________

Test (Lessons 1 to 5) Date: ______________


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Section A

1. For the data set 37, 21, 30, 17, 22, 13, 45, 24:

a) Build a stem and leaf plot.

b) Which number has a stem of 4? _____

c) Which two numbers have the same leaf? __________ 2. Using the stem and leaf plot shown, find the range, the median

and the mode.

Range: ______

Median: ______

Mode: ______

3. Ten people work in a sales office. They get paid different salaries per year, depending on their job.

Manager: $95 000 Associate: $48 000 Administrator: $35 000 There are 2 managers, 5 associates and 3 administrators.

a) Calculate the mean salary in the office.

b) What is the mode of the salaries? ______________

c) Will the mean salary increase or decrease if a new associate is hired? ___________________

d) Will the mean salary increase or decrease if an administrator retires? ___________________

e) Which better reflects the salaries in the company, the mean or the mode? Explain. 4. The mean of a set of data is 12. The data values are 7, 3, 14, 11, 19, and x. What is the value of x? 5. A set of 5 data values has modes of 13 and 4. If the mean of this data set is 9, what are the data

values in this set?

Stem Leaf

Stem Leaf 3 4 6 4 0 3 3 35 2 7 6 3 8 8 7 0 1

Unit 7: Probability and Data Management continued



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Section B

6. Irene’s math test scores (out of 30) are 25, 28, 26, 25, 8, 29, 28, 24, 23.

a) What is the outlier in this set? _____

b) Why might Irene’s teacher decide to remove this outlier when calculating the average for her report card?

c) Which average is affected more by the removal of the outlier, the mean or the median?

Justify your answer. 7. Write true or false beside each statement. Then explain why the statement is true, or give an

example to show that it is false.

a) Two numbers with the same leaf always have the same number of digits. _______ b) Two numbers with the same stem always have the same number of digits. _______ c) The greater number always has the greater leaf. _______ BONUS 8. Create a set of 6 data values with mode 8, median 7 and mean 11.

Unit 7: Probability and Data Management Answer Key



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Section A 1. a)

b) 45

c) 37, 17

2. Range = 71 – 34 = 37 Median = 52 Mode = 43

3. a) [(2 × 95 000) + (5 × 48 000) + (3 × 35 000)] ÷ 10 = $53 500

b) $48 000

c) Decrease

d) Increase

e) The mode is better reflection since 8 of 10 employees are below mean, which is raised because of outliers (managers).

4. Sum of all is 6 × 12 = 72, so: 7 + 3 + 14 + 11 + 19 + x = 72 ∴ x = 18

5. (4 + 4 + y + 13 + 13) ÷ 5 = 9, which means y = 11 ∴the data values are: 4, 4, 11, 13, 13

Section B

6. a) 8

b) The outlier does not reflect the quality of her work over the year; Irene may have been sick or had a bad day on the day of the test.

c) With outlier: Mean = 24 Median = 25 Removing outlier: Mean = 26 Median = 25.5 The mean is affected more than the median (it increased by 2 points vs 0.5).

7. a) False

Sample counter-example:The numbers 34 and 174 have the same leaf but have a different number of digits (because their stems have a different number of digits).

b) True

Sample explanation: Since the leaf is always one digit long, two numbers with the same stem will always have the same number of digits (the number in their stem plus one).

c) False

Sample counter-example:The number 73 is greater than the number 29, even though the leaf of 29 is greater (what determines the greater number is usually the stem).

BONUS


Sample answer: 4, 5, 6, 8, 8, 35 Note that answers will vary, but should have two values of 8, one value greater than 8, one value of 6 (to give median of 7) and two unique values less than 6 (to keep mode of 8). The sum of all six values must be 66 (to give mean of 11).

Stem Leaf 1 3 7 2 1 2 4 3 0 7 4 5

unit 1: number sense name: quiz (lessons 1 to 3) date:

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