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Classroom Strategies Blackline MasterPage 220

Luis is a master craftsman who can make incredible snowboards.To open a shop he needs a license to operate a business ($50)and a sign for his shop ($400).For each snowboard he makes, he spends $35 in materials and he pays $6 for labor.

This formula gives him the cost, C, for making n snowboards. C = 450 + 41n

1. Explain why the formula works.

2. If Luis can find a sign maker to make the sign for $250, what will the formulalook like?

3. Using the original formula above, if Luis makes 20 snowboards, how much willit cost him?

4. How much does it cost to make 100 snowboards?

5. At the end of one week, Luis had spent $860 in production costs. How manysnowboards did he make that week?

6. Luis sells each snowboard for $125. If he sells 100 snowboards, how muchmoney does he bring in from the sales?

7. What will his profit be if he sells 100 snowboards?

8. Write a profit formula for Luis that shows his profit if he sells n snowboards.

9. Luis decides he needs to use more outside labor. He will now pay $15 in laborfor each snowboard made. What will his cost formula look like now?

10. How much will it now cost to make 100 snowboards.

11. After increasing the amount he pays for labor, what will his profit formula looklike?

12. Using the new profit formula, determine his profit is he sells 100 snowboards?

III - 1

Name____________________________________________Date________

Classroom Strategies Blackline Master Page 221

Music Lover’s Special

At the Music Barn, all CDs are $12.50. All cassette tapes are $7.25, and thereare some old record albums that cost $25.00 each. Stevie loves music and he’sgoing shopping. He has $200 that he can spend. The prices listed include tax.

A formula for the total amount spent on music isP = 12.50C + 7.25T + 25A

where P is the total price of all the music purchased,C is the number of CDs purchased,T is the number of tapes purchased, andA is the number of albums purchased.

1. If Stevie buys 5 CDs, 3 tapes and 1 album, how much does he spend?

2. What is the maximum number of CDs he can buy?

3. What is the maximum number of tapes he can buy?

4. The shop owner has a special deal. For every purchase of a CD or tape, theshopper can buy one album at half price. With this deal, what is the maximumnumber of albums Stevie can buy?

5. Stevie really wants one album badly. If he buys that, what is the maximumnumber of tapes he can buy? (Remember the special offer described in problemfour.)

6. Stevie has a CD player in his home and a cassette player in his car. He hasdecided to buy a tape every time he buys a CD so he can enjoy the music inboth places. If he forgets the album, what is the maximum number of CDs hecan buy?

7. Can you make up a problem using this formula? Make a difficult one thatmight stump others in the class.

III - 2

Name____________________________________________Date________


Perimeter and Area Patterns

A

B

C

D

III - 3

1 2 3 4

Classroom Strategies Blackline Master Page 223III - 4

Perimeter and Area Patterns Recording Page

Complete the charts below for the four geometric patterns on the previous page.

Can you predict the areas and perimeters for the figures not shown? Can you find a

formula for the nth figure in the pattern? That is, can you find a formula with n as a

variable that will help you calculate the area or perimeter when you plug in a num-

ber for n, the figure number in the pattern?

Name____________________________________________Date________

Pattern Number Perimeter Area

A 1 _____ _____

A 2 _____ _____

A 3 _____ _____

A 4 _____ _____

A 5 _____ _____

A 10 _____ _____

A 100 _____ _____

A 1000 _____ _____

A n _____ _____


B 1 _____ _____

B 2 _____ _____

B 3 _____ _____

B 4 _____ _____

B 5 _____ _____

B 10 _____ _____

B 100 _____ _____

B 1000 _____ _____

B n _____ _____


C 1 _____ _____

C 2 _____ _____

C 3 _____ _____

C 4 _____ _____

C 5 _____ _____

C 10 _____ _____

C 100 _____ _____

C 1000 _____ _____

C n _____ _____


D 1 _____ _____

D 2 _____ _____

D 3 _____ _____

D 4 _____ _____

D 5 _____ _____

D 10 _____ _____

D 100 _____ _____

D 1000 _____ _____

D n _____ _____


1. Mark an X on the slide at the point where he was 1 second

after he started sliding.

2. Mark a P on the slide at the point where he will

be after 2 seconds.

3. How many feet did he drop between the

first and second seconds?

4. How many feet did he drop

between the

second and third seconds?

5. About how long did it take him to reach a height of 30 feet above the ground?

6. About how long will it take him to travel half way down the slide?

7. About how long will it take him to reach the bottom?

8. How many feet did he drop between the fourth and fifth seconds?

Jeff is on a giant water slide 50 feet tall. His science teacher gave him a formula that

he can use to determine how high he is above the ground after sliding for a given

amount of time. H represents his height above the ground; the variable t represents

how many seconds he has been sliding.

H = 50 – 2t2

Fast Formula

50 feet

40 feet

30 feet

20 feet

10 feet

0 feet

III - 5

Name____________________________________________Date________


Prickly Gift

On the planet Vulcan, there is an especially long-lived species of cactus. When eachcactus is one year old, it produces exactly two offshoots (baby cacti) and then neverreproduces again. Mr. Spock gives Captain Kirk a newly sprouted cactus plant whichhe gives to his nephew in Iowa. Complete the chart to find out how many cacti therewill be in the following years.

Name____________________________________________Date________

YEAR NEW CACTI TOTAL CACTI

0

1

2

3

4

5

6

7

N

1

2 3

1

Classroom Strategies Blackline MasterPage 226 III - 7

Cube Exploration

A cube is painted and then cut up into smaller congruent cubes. Complete the chart todetermine how many cubes fall into the categories.

Number ofsmaller cubesper edge

Total number ofsmaller cubes

Number of cubes with paint on ___ side(s).

20 1 3

4

3

2

6

5

1

n

Name____________________________________________Date________


Solving Equations Square Puzzle

Cut out the squares above. Fit the squares together so that touching edges match an equation toits solution.

10

3x + 4 = 13

+ 4x

= 3

1

-3

7

4x – 1 = 1

-10

4.5

4 – 3x = 34 7 –

2x =

15

-20

-4

5 – 12x = 2

-15

-1

-8

4

0.5

5 – 8x = 11

12x +6 = -10

1 – 9x = 4

5x – 3 = 2

3 +

30x

= 0

_

-0.1

8

2

2x-7 = 12 – 6x = 5

-5

7x + 2 = 3

4-x = 9

15

20x

+ 3

= 5

1

0.1

4x + 1 = 40

3x + 1 = 25

3x – 6 = -6

-7-0.5

5 –

3x =

11

-2

12 –x = -3

0.5x

+ 1

= 1

120

5

3

6-6

5 – 2x = 19

10 – 2x = 4

14

43

17

43

52

17

3 4 1 3

14

1 3

34

25

III - 8


Solving Inequalities Square Puzzle

Cut out the squares above. Fit the squares together so that touching edges match an equation to

its solution.

y > 7

y <

4/3

3y – 4 < 11

-2y

< 2

y > -4

y >

-1

-16y > 8

y >

-1 /

2

y < 1/2

3 –

4y

< 6 y

+ 3

< 5

y > -4/3

y <

21 – 8y > -5

y >

-5

y < 5

y <

- 1/3

y > -1/2

y <

-3

y <-1/2

-2y

+ 5

> 1

1

y <

-7

6y + 1 < 3

-4y

– 1

> 2

7y – 6 > -3

3y

< 3

y < 3/4

y <

1

y > 4

y >

-3

-6y < 3

y <

-2

2 – 6y > 10

Y <

-1

1 – 5y > 21

y –

4 <

-5

2 –

9y

< 5

y > 3

y >

-1/3

14y > 7

y >

5

5 – 2y < -3

-2y

+ 4

< -1

4

y > -7

y < -4/3

y <

- 3/4

-2y

< -

4 y >

2

12 –3y < 8

10

+ 3

y <

22

y > 1/2

y<

4

y < -5

y <

3

y > 1/3

Y >

1

3y – 1 > -7

4y

– 1

< 1

1

y >

3 /4

y < 1/3

y < -4

y > -2

y > 0

y > 4/3


Cut the triangles apart. Reassemble the puzzle

so that touching edges match an equation with its solution.The result should be the shape shown in miniature below.

4

x - 15 = -18

522x =

44

-3

3

x =

2-2

-4

7x = 28

-5

x + 17 = 20

1

- 1/2

x +

3 =

2

x - 4 = 4

5 - x = 0 -2

x = -

2-1

2

x =

- 1

4

2

8x +

3/2 =

2-2

24x = -12

One-Step Equations Triangle Puzzle

15 - x = 20

1/2


Border Patrol

Y =

Name____________________________________________Date________


Border Patrol

y =

2

35

6

-1

-2

-3

-5

1

4

-40

y

2

35

6

0

-2

-3

-5

1

4

-4-6

x


.Target Game

.. ... . . ... .. .. .. . ..

Name____________________________________________Date________


Target Game

2

35

6

-1

-2

-3-5

1

4

-40

Y-intercept

2

3

1/3 4

3/2

4/3

Pick any

empty spot

Remove

one of your

spots

Lose

turn

Pick any

empty spot

2/3

1

0

3/4 +

-

+

+

+

++

+

+

+

++

+

-

-

-

--

-

-

-

-

- -

Slope

1/2

1/4


The Troll Kings

Two Troll Kings, Able and Ben, plan to dig for treasure in the mountain below their castle. They will take the

elevator down to a given floor and then start to dig along a given path (straight line) until they reach one of the

treasures. The treasures are indicated by circular regions with a number giving the value of the treasure. Able

and Ben each dig five tunnels. You are to determine who finds the most treasure.

Roll a die to determine which floor to start on (this will correspond to the y-intercept).

Use a domino (with no zero) to determine the slope of the line (path) that each king will dig. The domino with 2

and 3 could represent a slope of 2/3, -2/3,

3/2, or -3/2. The choice is yours.

Able Ben

1) floor ______ path _______ treasure _______ 1) floor ______ path _______ treasure _______




5) floor path treasure 5) floor path treasure

1

1 2

1

5

6

3

6

6

2

6

4

1

4

4 4

1

4

12 12

1

4

4

1

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

-8

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

8

9

1

1

1

2

2

2

2

2

2

4

4

4

4

4

4

elevator

Nam

e___

____

____

____

____

____

____

____

____

____

____

_Dat

e___

____

_


1. Consider the geometric “stair step” pattern below. What is the area of the 15th figure in this

pattern?

What is the total of all blocks used in 15 figures of this pattern?

2. An ice cream shop claims to have 31 different flavors. How many different triple-scoop

cones can be made? Note: chocolate, chocolate, then vanilla is the same as chocolate,

vanilla, then chocolate. Hint: Start with a simpler problem. What if there were fewer flavors

to consider?

Number of flavors Number of Triple Scoop Possibilities

1 1

2 4 (CCC, VVV, CCV, CVV)

3 ______

4 ______

5 ______

31 ______

3. How many paths are there from A to B in this diagram, if you may only travel up and to the

right?

Problem Solving with Pascal

1 2 3 4 5 . . .

A

B

...

Name___________________Date_______


4. How many different ways are there to trace the letters in the given order in the word

“Mathematics” in the figure below?

M

M A

M A T

M A T H

M A T H E

M A T H E M

M A T H E M A

M A T H E M A T

M A T H E M A T I

M A T H E M A T I C

M A T H E M A T I C S

Hint: Start with a simpler problem.

How many ways to trace M in this figure? M 1

How many ways to trace MA in this figure? M

M A 2

How many ways to trace MAT in this figure?

M

M A

M A T

Can you find a pattern?

5. “On the first day of Christmas my True Love gave to me a partridge in a pear tree.

On the second day of Christmas my True Love gave to me, two turtle doves AND a partridge

in a pear tree.” Wow, that’s one gift on the first day, and 3 more gifts on the second day!

How many gifts will this lover get in all the twelve days of Christmas?

6. Coin Connection – When you toss a given number of coins, how many ways are there to get

a fixed number of heads? Complete this chart and find a connection to Pascal’s Triangle.

Number of Coins Ways to Get This Number of Heads

0 1 2 3 4 5 6

2

3

4

5

6

III - 17


Patterns in Pascal’s Triangle Name____________Date____

1. What patterns do you see in Pascal’s triangle? How would you generate the next row?

2. What pattern do you see from adding the numbers in each row?

3. What pattern do you see when you add up the diagonals as shown?

4. Choose any number in the triangle. Shade the six numbers surrounding the number

you chose, so that the petals alternate between two colors. Multiply the three numbers

of matching color. What do you find about these two products? Can you explain why

this happens?

5. Color in all the multiples of 2. What pattern do you see? Color in all the multiples of

3 or 4 or five. What patterns do you see?

6. Pick five colors and assign each one to a number 0,1,2,3, or 4. Divide the numbers in

Pascal’s triangle by 5. Note whether the remainder of each number is 0,1,2,3, or 4.

Color code the cells in the triangle by matching the color to the remainder number.

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1


1 1

1 2 1

1 3 3 1

1

5 5 110 10

1 19 936 3684 84126 126

PASCAL'S TRIANGLE

10

1 1

45 45120 120210 210252

1

1

1

1 16 615 1520

1

17 721 2135 35

188 28 2856 5670

1

1

1

1

1

1

1

1

1

1

1

10

1

1

1

1

1

1

11 55 165 330 462462 330 165 55 11

1266220495792924792495220 66 12

13 78 286 715 1287 1716 17161287 715 286 78 13

14 913641001200230033432300320021001364 91 14

15 105 10545513653003500564356435500530031365455 15

16 120 560182043688008114401287011440800843681820560 120 16

816

17 136 2380618812376194482431024310194481237661882380680 680 136 17

18 153 85681856431824437584862043758318241856485683060816 3060 153 18

4 6 4


Equations and Inequalities - 8th Grade Name Date

Solve each of the following. Show your work.

1. x + 7 = 24 __________ 2. x + 130 = 100 ________

3. x - 70 = 42 __________ 4. x - 24 = -30 _________

5. 7x = 105 __________ 6. 5x = 2 _________

7. x = 15 __________ 8. x = -5 _________

6 12

9. 3x - 5 = 35 ___________ 10. 7x + 16 = 9 _________

11. -5x + 6 = 16 ___________ 12. -3x - 4 = 47 _________

Graph the solution for each of the following.

13. 3x < 12

14. -7x < 14

15. 2x - 1 > 15

16. 6 - 5x > 21


17. y = 2x - 8 ( , )( , )( , )( , )

18. y = 4 - .5x ( , )( , )( , )( , )


Find 4 ordered pairs to fit the equations shown. Draw the graphs of the lines.

Y

X

Find four ordered pairs that satisfy the equations shown. Draw the graphs of the lines.


Y

X


19. Which of the points shown belong to the graph of y < x + 5? Circle the ones that belong to the graph. Mark an X on the points which do not belong.


21. Draw a line that passes through the point (-5,-8) and has a slope of 1.

22. Draw a line that passes through the point (5,0) and has a slope of - 1/2.

Y

X


20. Find the slope of the line shown.

Equations and Inequalities - 8th Grade Name Date________


’s NumbersStart:A = B = sum difference product quotient

III - 24

Documents

Name Date - SharpSchoolp1cdn4static.sharpschool.com/UserFiles/Servers... · Classroom Strategies Blackline Master Page 223III - 4 Perimeter and Area Patterns Recording Page Complete