Name: ______Date: ______
Extra Practice BLM 8.1
8.1 Investigate and Describe Patterns
Copyright Ó 2007 McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies.
This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.
Name: ______Date: ______
1. a) Describe the pattern of the letters D, H, L, P, ... How would you identify the next letter?
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b) Determine the next two letters.
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2. a) A circular pool has a circumference of 18.3 m. Estimate the diameter of the pool to the nearest metre. Explain your reasoning.
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b) Another pool has a diameter of 18.3m. Estimate the circumference.
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3. Describe how you can find the value of the next term in each pattern. Then find the values of the next two terms.
a) 9, 18, 27, 36, ...
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b)
Term Number / 1 / 2 / 3 / 4Value of term / 12 / 9 / 6 / 3
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c)
Term Number / 1 / 2 / 3 / 4Value of term / 7 / 14 / 28 / 56
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4. Refer to question 3, part a).
a) Write an algebraic expression for the value of a term. Use n for the term number.
______
b) Suppose the numbers in the sequence represent the cost of 1, 2, 3, 4, … movie tickets. Find the cost of the tickets when n = 3.5, 6.5, –4, and 12. Which numbers make sense and why?
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5. a) Determine the number of shelves and posts in each diagram of the following pattern. Complete the table.
Number of Posts / 2 / 3 / 4Number of Shelves / 4
b) Determine the number of shelves when there are • 5 posts • 6 posts
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c) Write an algebraic expression to model the pattern, using the variable s to represent the number of shelves and the variable p to represent the number of posts.
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d) Determine the number of shelves when there are 20 posts.
Extra Practice BLM 8.2
Chapter 8.2 Describe Relationships with Algebraic Equations
Copyright Ó 2007 McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies.
This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.
Name: ______Date: ______
1. For each statement, indicate whether it can be represented by an algebraic expression or equation. Explain your choice. Then, write an algebraic expression or equation for each statement. Choose your own variables and indicate what they represent.
a) one-third of Dexter’s earnings
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b) the area of a rectangle is length times width
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c) five more years than Miriam’s age
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2. Louis is nine years older than Erika.
a) Write an equation that relates Louis’ age to Erika’s age.
______
b) Find Louis’ age when Erika is 3.
______
c) How old is Erika when Louis is 26?
______
3. A taxi charges $6 plus $2.75 for every kilometre driven.
a) Create a table of values for the cost of trips of between 1 km and 5 km.
b) Graph the relationship.
c) Use the graph to find the cost of a 10-km trip.
______
d) Write an equation that relates cost and trip distance.
______
e) Use the equation to find the cost of a 10-km trip. Do your answers to parts c) and e) agree? Explain.
______
4. Kim is making a tile
border along a wall.
She always starts with
a corner pattern and
makes the rest of the
border with the trim pattern.
a) Create a table of values to shows the number of grey tiles are required for:
• 1 pattern piece (1 corner)?
• 2 pattern pieces (1 corner, 1 trim)?
• 3 pattern pieces (1 corner, 2 trim)?
b) Extend the pattern to find the number of grey tiles required for 4 and 5 pattern pieces.
______
c) Describe how you can find the number of grey tiles required if you know the number of pattern pieces.
______
d) Write an equation to relate the number of grey tiles, t, and the number of pattern pieces, p.
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e) Use the equation to find the number of grey tiles in a boarder of 25 pattern pieces.
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f) A border requires 55 grey tiles. How many pattern pieces are there?
______
Extra Practice BLM 8.3
Chapter 8.3 Collect Like Terms
Copyright Ó 2007 McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies.
This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.
Name: ______Date: ______
1. Classify each pair of terms as like or unlike. Explain your choice.
a) 2x and 2y ______
b) 4x and 3 ______
c) –3 and 6 ______
d) 2n and –6n ______
2. Simplify each expression, if possible. If it is not possible, explain why.
a) 3x + 4x ______
b) 2x + 5y ______
c) 4x + 1 ______
d) 7 + 3 ______
3. Model each expression using algebra tiles. Draw the models.
a) 5x + 3x b) 4y + y
c) 6p + 2p d) 5m + 2m + 4m
4. Write three different expressions that can be simplified to 6y – 2.
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5. Simplify each expression. Give a realistic situation that each expression could represent.
a) 7y – 2y
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b) 5x + (–x)
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c) 5t – 4t
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6. Simplify by collecting like terms.
a) 8x + 4x + 6y – 2y _______
b) 3x – 5x + 4 – 13 ______
c) 5y + 2 – 7y + 8 ______
d) 5x + 6y – 1 + x + (–9y) + 2
______
7. Liam and Tilda both tutor Grade 8 students in mathematics. Liam charges $8.00 per house visit plus an hourly rate of $10.00. Tilda charges $12 per house visit plus an hourly rate of $7.00.
a) Use algebra tiles to model the total cost of a tutoring session with each person.
b) Write expressions to model the cost of a tutoring session by each person.
______
c) Write a simplified expression that describes the total for both tutoring sessions.
______
d) Find the combined total earnings for both tutors for 1 h and for 3 h.
______
Chapter 8 Extra Practice Answer Key
Get Ready
1. a) –8 b) –2 c) –8 d) 7 e) 1 f) 4 g)–15 h)–4 i) –5 j) –6
2. a) –6 b) 15 c) 1 d) 21
3. perimeter: 26 m; area: 32 m2
4. Natalie has $30 in her savings account and she adds $5 at the end of each week.
a) For table, w is week and s is savings in dollars.
w / 1 / 2 / 3 / 4 / 5s / 35 / 40 / 45 / 50 / 55
b) Graph should show the points (1, 35), (2, 40), (3, 45), (4, 50), (5, 55). c) $70 d) 12 weeks
5. a) = b) ≠ c) ≠ d) =
6. Answers for e) to h) may vary. a) 2 b) 8 c) 6 d) 5 e) 4, 3 f) 24, 5 g) 3, 5 h) –18, 3
8.1 Investigate and Describe Patterns
1. a) Write every 4th consecutive letter in the alphabet. Find the 4th letter after P. b) T, X
2. a) 6 m. Explanations may vary. b) 54.9 m
3. Descriptions may vary. a) Start with 9 and then add 9 to each term following. 45, 54.
b) Start with 12 and then subtract 3 from each term following. 0, –3. c) Start with 7 and then multiply each term following by 2. 112, 224.
4. a) 9n b) $31.50, $58.50, $–36.00, $108.00. Only 12 tickets makes sense because you cannot buy negative or fractional parts of a ticket.
5. a)
Number of Posts / 2 / 3 / 4Number of Shelves / 4 / 8 / 12
b) 16 shelves, 20 shelves c) s = 4p – 4 or s = 4(p – 1) d) 80 shelves
8.2 Describe Relationships With Algebraic Equations
1. a) expression; e ¸ 3, where e represents Dexter’s earnings.
b) equation; A = l ´ w, where A represents area, l represents length, and w represents width.
c) expression; m + 5, where m represents Miriam’s age.
2. a) L = E + 9, where L represents Louis’ age, and E represents Erika’s age.
b) 12 years old c) 17 years old
3. a) For table, d is distance in kilometres and c is cost in dollars.
d / 1 / 2 / 3 / 4 / 5c / 8.75 / 11.50 / 14.25 / 17.00 / 19.75
b) Graph should show the points (1, 8.75), (2, 11.5), (3, 14.25), (4, 17), (5, 19.75). c) $33.50
d) c = 2.75d + 6 e) $33.50, yes
4. a)
Number of Pattern Pieces / 1 / 2 / 3Number of Grey Tiles / 7 / 11 / 15
b) 19 grey tiles; 23 grey tiles c) The number of grey tiles is 7 for the first pattern piece (the corner) plus 4 for every additional pattern piece (trim). d) t = 7 + 4(p – 1) or t = 4p + 3
e) 103 grey tiles f) 13 pattern pieces
8.3 Collect Like Terms
1. Explanations may vary. a), b) unlike terms c), d) like terms.
2. a) 7x b) unlike terms c) unlike terms. d) 10
3. a) 5 x-tiles and 3 x-tiles b) 4 y-tiles and 2 y-tiles c) Use x-tiles to represent p. 6 x-tiles and 1 x-tile d) Use y-tiles to represent m. 5 y-tiles, 2 y-tiles and 4 y-tiles.
4. Answers may vary.
5. Situations may vary. a) 5y b) 4x c) t
6. a) 12x + 4y b) –2y + 10 c) x – 5y d) 6x – 3y + 1
7. a) Use an x-tile to represent the number of hours worked by each tutor. Liam: 10 x-tiles and 8 unit tiles. Tilda: 7 x-tiles and 12 unit tiles.
b) Liam: 10h + 8. Tilda: 7h + 12 c) 17h + 20 d) $37; $71
Review
1. a)
b) For table, s is the stage number and n is the number of white triangle in each stage.
s / 1 / 2 / 3 / 4 / 5n / 1 / 3 / 5 / 7 / 9
c) Graph should show the points (1, 1), (2, 3), (3, 5), (4, 7), (5, 9). Scatterplot. The stage number and triangles are whole numbers. d) 13
f) First stage has a triangle made of 3 white triangles surrounding 1 black triangle. For each new stage, 1 black and 2 white triangles are added to the right side of the shape.
g) n = 2s + 1 h) 15 white triangles; yes
2. a) 23.6 mm b) 30.8 cm
3. a) 7 x-tiles and 3 unit tiles b) 2 y-tiles and 1 x-tile c) 5 y-tiles, 3 x-tiles, and 4 unit tiles
d) 4 x-tiles, 1 y-tile, and 2 unit tiles
4. a) Start with 3, and then add 4 to each term following. 19, 23, 27. b) Start with 9 and then add 10 to each term following. 49, 59, 69. c) Start with 20 and then subtract 8 from each term following. –12, –20, –28.
5. a) 11x b) 6y c) 5x + 2y d) 5p e) –2x f) 7a – 5b
6. a) 22 b) –6 c) 8 d) 5 e) –4 f) –36
Practice Test
1. C 2. A 3. B 4. B
5. a) 51.5 cm b) 17.0 mm
6. a) i) 12x; 72 b) –2m; 8 c) 10y + 2; 2 d) 2k; 0
7. Explanations may vary. 5 m
8. a) White squares: start with 4 and multiply the number by 4 each day. Grey squares: use consecutive square numbers starting with 1. b) Day 4: a square of 16 grey squares with a row of 4 white squares on each side. Day 5: a square of 25 grey squares with a row of 5 white squares on each side. c) For table, d is day and b is the number of blocks after each day.
d / 1 / 2 / 3 / 4 / 5b / 5 / 12 / 21 / 32 / 45
d) d2 + 4d e) 252 blocks f) 18 days
Extra Practice BLM 9.1
9.1 Solve Equations
Copyright Ó 2007 McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies.
This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher.
Name: ______Date: ______
1. a) What equation is modelled?
______
b) What do you need to add to or subtract from both sides of the balance to solve the equation?
______
c) Find the solution.
______
2. How many cubes must go into each box in order to make the following scales balance?
a)
_____
b) Each box must contain the same number of cubes.
_____
3. Solve. You can model, use systematic trials, or the cover-up method.
a) 4z = 16 z = _____
b) 3q = 18 q = _____
c) 8 + x = 12 x = _____
d) 6 – y = 30 y = _____
e) 5n = 35 n = _____
f) 29 – m = 3 m = _____
g) 3a + 7 = –2 a = _____
h) 4b + 17 = 41 b = _____
4. Pick any equation from question 3. Draw a diagram to illustrate each solution.