Grade Eight Classroom Strategies Blackline...

Classroom Strategies Blackline Master Page 69

Grade Eight

Classroom

Strategies

Blackline Masters

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

Classroom Strategies Blackline Master I - 2

Real Number Race


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


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


Ratio

nal

Betw

een 1

0 and

15

4

Integer


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


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


10.33

33


- 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 5 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


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.


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


-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


- 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


-

-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)


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)


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


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


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


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


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


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


STOP STOP STOP

STOP STOP STOP

CHASE CHASE CHASE

CHASE STOP STOP


GO GO GO

GO GO GO

GO GO GO

CHASE STOP GO


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


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


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


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.


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


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

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


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

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


0

98

7

6

5 1

23

4

EXPONENT EXPERTS


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

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