Classroom Strategies Blackline Master Page 69
Grade Eight
Classroom
Strategies
Blackline Masters
Page 70 Classroom Strategies Blackline Master s
Classroom Strategies Blackline Master Page 71 I - 1
Real numbers
Irrationals
Rationals
NaturalIntegers
-3
3
3
Real numbers: the set of rational and irrational numbers
Natural numbers: the counting numbers: {1,2,3 …}
Whole numbers: the set of counting numbers plus zero:
{0,1,2,3, …}
Integers: the set of counting numbers and their opposites plus
zero {… -3,-2,-1, 0, 1, 2, 3 …}
Rational numbers: numbers that can be expressed as the ratio of
two integers
Decimal representations of rational numbers either
terminate or repeat. Ex. 2.375 , 4, -.25, -.14
Irrational numbers: numbers that cannot be expressed as a ratio
of two integers Their decimal representations neither
terminate nor repeat.
Ex. 3 , π , 0.14114111411114 …
IntegersWholes
Naturals
Page 72 Classroom Strategies Blackline Master I - 2
Real Number Race
Classroom Strategies Blackline Master Page 73 I - 3
Spinner for Real Number Race
Integer
Natural
Real
Rational Irrational
Lose a Turn
Number Real Rational Irrational Integer Natural
4 x x x xx x x x
-3 x x x
0.333 x x 0.25 x x 0.171771777... x x
π x x
x x
x x
x x
12
A fair number cube labeled 1 to 6 can also be used in place of the spinner above.1 = Rational; 2 = Real; 3 = Irrational; 4 = Natural; 5 = Integer; 6 = Lose a turn
REAL NUMBER RACE
4
19
7
Page 74 Classroom Strategies Blackline Master I - 4
ππππ
Irrational
Between –10 and -15
Integ
erBe
twee
n –20
and -
25
- 14
40
2ππππ
Irrati
onal
Betw
een –
20 an
d -25
NaturalBetween 0 and 5
ππππ+8
NaturalBetween 15 and 20
- 4 ππππ
Rational
Between –5 and -10
Ratio
nal
Betw
een 1
0 and
15
4
Integer
Between –10 and -15
4 36
16.1010010001…
Irrational
Between 0 and -5
Integ
er
Betw
een 0
.1 an
d –0.5
- 12
4
-21.21121112…
64
Irrati
onal
Betw
een –
15 an
d -20
IntegerBetween 5 and 10
-22
Irrational
Between –5 and -10
Irrati
onal
Betw
een 1
0 and
15- 4 24
500
Integer
Between 0 and -5
Ratio
nal
Betw
een –
15 an
d -20
IrrationalBetween 0 and 5
- 2
-15.75
32 2
Natural
Between 20 and 25IrrationalBetween 15 and 20
- 80
IrrationalBetween 20 and 25
10.33
33
IrrationalBetween 5 and 10
- 15
2
Subsets of Real NumbersArrange the pieces so that touching edges are a number and a description of that number.
Classroom Strategies Blackline Master Page 75 I - 5
1 9
24( 1/3 + 1/4 )
1 1 / 4
15
100%
of 1
60 divided by 0.6
56
1 of 5255 60 x 0.6
6
10% of 640
13.5
1 of 48
2
21
1 of 1
005
1 • 1 • 49 • 243 7
3200 divided by 200
24
16
105 2
3 of 3
6
4
1 of 2008
36
10
1 of 3603
35
1 of 1
44
2
45
10 decreased by 40%
25%
of 8
7 + 38 8
1 of 633
10 15
30
25% of 60
12
1 of
210
7
23
120
1 of 808
25
18
60(1/3 + 1/4)
0.9 • 9
100
14
724 of 605
20
2 • 4 20 d
ecre
ased
by 1
0%
10 decreased by 10%
8
49
50 decreased by 2%
40
1 of 160
4
5 2/3 + 6 1/3
64
48 50 d
ecre
ased
by 1
0%
1.3 + 9.5 + 2.7
8.1
27
Rational Review Triangle Puzzle
Page 76 Classroom Strategies Blackline Master I - 6
Building Rectangles from Cubes
.
Materials needed: Enough colored cubes or color tiles for each group to have 6 red, 5 blue, 5 yellow, 5 green. Graph paper and colored pencils for recording solutions.
Tasks
1. Build a rectangle that is half blue and half green. Can you do this in more than one way?Can you think of various ways to write the name of the rectangle you made? Draw a pictureof each method and label it with the various forms of the fraction name.
2. Build a rectangle that is 1/2 blue, 1/4 green and the rest red. How many cubes did you use?Can you solve this problem another way? Draw a picture of the solutions you found.What fraction of the rectangle is red? Write a number sentence that shows how thedifferent colors represent fractions that add up to one.
3. Build a rectangle that is 1/3 blue, 1/6 green and the rest red. How many cubes did you use?Can you solve this problem another way? Draw a picture of the solutions you found.What fraction of the rectangle is red? Write a number sentence that shows how thedifferent colors represent fractions that add up to one.
4. Build a rectangle that is 1/4 blue, 1/8 green and the rest red. How many cubes did you use?Could you solve this problem another way if you had more cubes? Draw a picture of thesolutions you found. What fraction of the rectangle is red? Write a number sentencethat shows how the different colors represent fractions that add up to one.
5. Build a rectangle that is 1/4 blue, 1/2 red, 1/3 green and the rest yellow. How many cubes didyou use? Could you solve this problem another way if you had more cubes? Draw apicture of the solutions you found. What fraction of the rectangle is red?Write a number sentence that shows how the different colors represent fractions thatadd up to one.
6. Build a rectangle that is 3/5 red, 1/2 blue and the rest green. How many cubes did you use?Could you solve this problem another way if you had more cubes? Draw a picture of thesolutions you found. What fraction of the rectangle is red? Write a number sentencethat shows how the different colors represent fractions that add up to one.
7. Suppose you were to build a rectangle that is 3/8 blue, 1/4 green, 1/3 red and the restyellow. How many cubes would you need? Draw a picture of this rectangle andwrite the number sentence that shows how it is constructed.
Classroom Strategies Blackline Master Page 77 I - 7
Fill in the card above with integers of your choice from –30 to 29. Choose numbers
for each column as indicated on the card. For example, under B, choose numbers
from –30 to –19. The numbers in each column may be in any order as long as they are
from the indicated number range and not repeated.
Rational Math Bingo
B-30 to -19
I-18 to -7
N-6 to 5
G6 to 17
018 to 29
Free
Page 78 Classroom Strategies Blackline Master I - 8
-42 + 12
9.00 x -3.0 2600 ÷ (-100) -1 x (-5)2
6 ( -10 + 6) -4 x 5 - 3 -2 - 4 x 5
3 x (-7) 2 x 105 -104
-14 -
-0.017 x 1000 -(2)4
-49 + 20
- x 27
15 3
2 3
-21 4 3
x
Classroom Strategies Blackline Master Page 79 I - 9
- 1 x 60 4
-6 ÷ 0.5 1 + 3(-4) -(4)2 + 6
-1(4-7)2 (-1 -3) ÷ 1 2 3 - 2 x 5
-18 + 12 5 x 103
-103 - (22 x 12)
-248 ÷124 - (3/4 + 1/4)
-8 -6
- 1 x 32
3
-23 -5
Page 80 Classroom Strategies Blackline Master I - 10
-
-1 ÷ - -8 + (-2)(-6) 1.25 ÷ .25
x 1 + 22 + 2 23
105
104 99 ÷ 9
39 ÷ 3 7 + 6 Inches inone foot
7 14
1 2 +
1 2
13 26
1 3
14 5
15 7
20 + 7 3
3 4
1 4
16 - 2(7)
Classroom Strategies Blackline Master Page 81 I - 11
27.17-12.17
-6 ÷ - -1 + (-5)(-4) 5 ÷ .25
x 7 + 5(3) -2 + 52
55
53 (1+1)(6+7)
-7 x (-4) 23 + 5
24
1 3
14 5
15 2
3 8
5 8
24 + 23
34
3
-34 ÷ (-2)
Page 82 Classroom Strategies Blackline Master I - 12
Four in a Row
Algebraic Expression
Suggested expressions: x + y x - y -x + 2y x - y -(x + y) 2x - 3y y +
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
-7
-4
-6
6
7
-5
-3
3
4
2
1
-2
-1
5
1x
Classroom Strategies Blackline Master Page 83 I - 13
I. Use your calculator to change each fraction below to a decimal form.
1. 1 _________________ 2. 2 _________________
9 9
3. 4 _________________ 4. 17 _________________
9 99
5. 25 _________________ 6. 32 _________________
99 99
7. 422 _________________ 8. 535 _________________
999 999
9. 683 _________________
999
Use the pattern you see to determine which fraction is equivalent to the decimals below.
Check your answer with the calculator.
10. .555 ________ 11. .77 ________
12. .8383 ________ 13. .2626 ________
14. .137 ________ 15. .184 ________
16. How would you explain this pattern to someone else?
II. Examine the equivalent fractions and decimals below. Look for a pattern.
0.233 = 0.411 = 0.5777 =
0.84444 = 0.41212 = 0.73535 =
0.39191 = 0.56262 =
17. Use the pattern to determine the ratio equivalent to:
0.622222 = _______ 0.3717171… = _______
18. Can you determine a ratio equivalent to 0.4315315 ? ______________
Patterns for Repeating Decimals
2190
3790
5290
7690
408990
388990
728990
557990
Page 84 Classroom Strategies Blackline Master I - 14
Thousand Mile Race
Cards in Play
Score
Hazards or Stockpiled Cards
Team 1 Team 2 Team 3
Classroom Strategies Blackline Master Page 85 I -15
50 50 50
50 50 50
50 50 50
50 50 50
10% of 120 50% of 200 25% of 8
20% of 100 10% of 1300 50% of 650
25% of 160 20% of 600 10% of 450
110% of 100 75% of 120 120% of 35
Page 86 Classroom Strategies Blackline Master I - 16
100 100 100
100 100 100
100 100 100
100 100 100
50% of 810 10% of 37 20% of 455
25% of 8004 150% of 20 90% of $4.50
33 1/3% of 120 75% of 60 80% of 250
200% of 18 150% of 6 125% of 20
Classroom Strategies Blackline Master Page 87 I - 17
150 150 150
150 150 150
150 150 150
150 150 150
10% of 75 20% of 800 50% of 6.008
25% of 32 110% of 80 80% of 350
150% of 62 cents 75% of 840 110% of $1.20
80% of $3.00 150% of $5.00 90% of $3.40
Page 88 Classroom Strategies Blackline Master I - 18
200 200 200
200 200 200
200 200 200
200 200 200
20% of 15 37
25% of $1.08 50% of 2 3
10% of $9.60 66 2/3% of 330 75% of 820
80% of 300 75% of 480 150% of $2.40
110% of 90 80% of 525 125% of 600
Classroom Strategies Blackline Master Page 89 I - 19
STOP STOP STOP
STOP STOP STOP
CHASE CHASE CHASE
CHASE STOP STOP
Page 90 Classroom Strategies Blackline Master I - 20
GO GO GO
GO GO GO
GO GO GO
CHASE STOP GO
Classroom Strategies Blackline Master Page 91 I - 21
Four’s A Winner!
320 400 10 250 50 225
90 20 270 100 150 15
150 120 80 30 240 75
180 60 25 200 5 125
40 100 50 135 90 45
75 10 360 20 60 300
25% of 25% increase 25% decrease50% of 50% increase 100% increase
20 40 60 80 100 120 160 180 200
Page 92 Classroom Strategies Blackline Master I - 22
Scientific Notation Square Puzzle
7,800
6.1 x 103
4.5 x 101
1.7
x 10
2
61,000
170
1 x 10-1
350
4.5
3.5 x 102
4.2
7.8
x 10
2
6.1
780
0.0023
0.42
450.023
0.078
3500
0.1
3.5 x 103
0.45
1700
4.2 x 100
1.7 x 103
23,000
7.8
x 10
-1
2.3 x 10-3
0.78
610
1.7
x 10
-3
7.8 x 10-2
0.0045
1 x 10-4
2300
4.5 x 10-12.3 x 10
3
7.8
3.5
x 10
-1
2.3 x 104
0.35
1 x 10-2
0.04
5
3500
00
6.1 x 102
4.5 x 10-2
420.0001
2.3 x 10-1
0.00017
3.5
x 10
5
0.001
350,000
7.8 x 100
2.3
x 10
-4
0.010.00023
7.8 x 101
0.17
450
6.1
x 10
1
4.2 x 101
1.7 x 10-1
Cut out the squares above. Fit the squares together so that touching edges are equivalent.
Scientific Notation Square Puzzle
Classroom Strategies Blackline Master Page 93 I - 23
Scientific Notation Team Game
Number in Play
Team Answer
The leader begins the game by writing a number in scientificnotation in one of the rectangles at the top of the board. On a team’sturn, they change the number according to the directions on thespinner. If they are correct, they move ahead one space; and thenumber in play is changed to the number the team just constructed. Ifincorrect, they move back one space, and the number in play remainsthe same. The winner is the first team to reach the finish. Suggestion:Play this on a laminated board or on transparency with dry erasemarker.
*Between decimal and scientificnotation.
Divideby 100
Change Form*
Go Back 2
Divide by 10
Lose a Turn
Multiply.by
100
Multiply by 1000 Multiply
By 10
Divide by 2
Mult.by 2
Start Finish
MULTIPLY BY 100
MULTIPLY BY 10
MULTIPLY BY 1000
DIVIDE BY 10
DIVIDE BY 2
MULTIPLY BY 2
GO BACK 2
LOSE A TURN
CHANGE FORM *
DIVIDE BY 100
* Between decimal and scientific notation
SCIENTIFIC NOTATION TEAM GAME
Page 94 Classroom Strategies Blackline Master I - 24
Rules of Exponents Triangle Puzzle
Cut the triangles apart. Reassemble the puzzle so that touching edges have equivalentexpressions. The result should be the shape shown in miniature below.
Classroom Strategies Blackline Master Page 95 I - 25
POWER BINGOPOWER BINGO
PP OO WW EE RR
2
2
2
2
2
3
3
3
3
3
4
4
4
4
4
5
5
5
5
5
10
10
10
10
10
Page 96 Classroom Strategies Blackline Master I - 26
26•2-11 2-6•22 23
26
223
25
26 26•2-6
25
2426•2-4 2•22
2-6•210 2•(22)2 3•3-6
Classroom Strategies Blackline Master Page 97
3-1•3-3 3-6•33 33
35
34
3535
35 32•3-1
35
3337•3-4 (22)2
3•34 4-11•(42)3 42•4-6
I - 27
Page 98 Classroom Strategies Blackline Master
40•4-3 4-3•4 43
44
44
4445
44 41•4
45•42
444•43
5-1•5-4 5-7•(5-1)-3 54•5-7
(42)4
43
I - 28
Classroom Strategies Blackline Master Page 99 I - 29
5•5-3 5-3•52 52
52
57
5655
53 51•52
54•52
525•54
10-11•109 10-10•(102)3 104•10-7
(102)4
10-13
Page 100 Classroom Strategies Blackline Master
10-11•1011 105
106 104•10-3
10-10•(103)4 (102)4
105106•10 103
106
10
I - 30
Classroom Strategies Blackline Master Page 101 I - 31
0
98
7
6
5 1
23
4
EXPONENT EXPERTS
Page 102 Classroom Strategies Blackline Master I - 32
3x2 n3 – n2 n2
n4
5a2 - a 2x2 + 1
x2 + x x2 + 4
x3 + x2
4
w3 + 8 x4
5x3 2x2 + 10 x3
-2x2
x2 + 5
2