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LP8 QuadWords.notebook

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February 08, 2016

Warm Up: Factor completely and solve for x:a) 3x³ 12x² = 0 b) 2x² 10x = 12


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February 08, 2016

Quadratic Word Problems

1. In a dc circuit the power P dissipated in the circuit is given by the equaon P = RI² where R is the circuit resistance in ohms and I is the current in amperes. What current will produce 1440 was of power in a 10‐ohm resistor?

2. One side of a rectangular opening for a heating pipe is 3 in. longer than the other side. If the crosssectional area is 70 sq in., find the dimensions of the cross section.

3. Find the side length of a square whose area is 200 sq in.


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February 08, 2016

4. Find the diameter of a circular pipe whose crosssectional area is 3.00 sq in.

5. The SAE rating of a an engine is given by R = (D2N)/2.5, where D is the bore of the cylinder in inches, and N is the number of cylinders. What must the bore be for an eightcylinder engine to have an SAE rating of 33.8?

6. One side of a rectangular plate is 6 in. longer than the other. The total area is 216 sq in. How long is each side?


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February 08, 2016

Homework: p. 682683 C) 1, 8, 9, 151) The area of a square is 625 mm². Find its side length.

8) If P=RI² for a direct current circuit, find I (current in amperes) if:a) The power (P) is 405 watts and the resistance (R) is 5 ohms.b) The power is 800 watts and the resistance is 15 ohms.

9) Total piston displacement is given by the following formula:where P.D.=piston displacement in cubic inches

D=diameter of the bore cylinderL=length of stroke in inchesN=number of cylinders

Find the diameter if:a) P.D.=400 cu in. L = 4.5 in. N=8b) P.D.=392.7 cu in. L=4 in. N=6

15) The pressure loss F (in pounds per square inch of a hose is given bywhere Q is the flow rate (in hundreds of gallons per

minute) of water through the hose. If the pressure loss is 42.0 lb/sq in., what is the flow rate to the nearest gallon per minute?

Attachments

LP1 Signed Numbers Worksheet.doc

LP1 ZipZilchZero RecordSheet.pdf

LP2 exponents and PERMDAS.doc

LP3 PerfectSquares.pdf

LP3 Radicals.doc

Pretest6.pdf

review6.doc

TEST6.doc

test6.tst

xmas activity.doc

LP1 Ops w. Signed Numbers.doc

Name: _________________________________

Math In Trades

Period: _______________

OPERATIONS with SIGNED NUMBERS

MULTIPLICATION

DIVISION

X

_

+

_

+

_

_

+

+

ADDITION:

same = sum

different = difference

SAME SIGNS: add and keep the signDIFFERENT SIGNS: subtract and keep the

of both

sign of the bigger number

(+) + (+) = ____________

(big +) + (little -) = _____________

(-) + (-) = _____________

(little +) + (big -) = _____________

SUBTRACTION:

Subtracting when the second number is POSITIVE:

1) y – x ( y + (-x)

2) then follow the rules above (under addition)

Subtracting when the second number is NEGATIVE:

1) y – (-x) ( y + x

2) then follow the rules above (under addition)

SMART Notebook

© 2010 National Council of Teachers of Mathematics http://illuminations.nctm.org

Zip, Zilch, Zero Rules NAME _________________________

Setup: The game is for 3 or 4 players. Use a standard 52-card deck. Choose a dealer by drawing

for the high card. Shuffle the deck and deal 7 cards to each player. With the remaining cards,

form a draw pile in the middle of the table. Place the top card face up next to the draw pile to

start a discard pile.

Gameplay: Each turn, a player must follow this sequence.

1. Draw one card, either from the top of the draw pile or the top of the discard pile. A player

may choose to draw more than the top card from the discard pile but must take all the

cards on top of it and must play that bottom card in a zip during that turn.

2. Play any zips. (See “Zips” below.)

3. Discard one card, adding it (face up) to the top of the discard pile. The card should be

placed so that the cards below can still be seen. The previous discards are still available

for play.

If a player chooses to draw the top card on the discard pile in step 1, that card may not be

discarded during the same turn in step 3.

Zips: A zip consists of at least two cards from a player’s hand that sum to 0. Black cards count

as positive numbers and red cards count as negative numbers. Aces are worth one point, number

cards are worth face value, jacks are worth 11, queens are worth 12, and kings are worth 13.

Example 1: A red 6 and a black 6

Example 2: A black king, a red 2, a red 3, and a red 8

Going Out: A player goes out when the last card in his or her hand is played as a discard.

Scoring: When a player goes out, the hand is scored. Players subtract the absolute value of any

cards remaining in their hands from the absolute value of cards they played in zips.

SCORING EXAMPLES

ZIPPED CARDS REMAINING

CARDS

VALUE OF

ZIPPED CARDS

VALUE OF

REMAINING

CARDS

SCORE

Sample

Hand 1

red 6, black 6;

black king,

red 2, red 3,

red 8

black 7, red 3 38 10 28

Sample

Hand 2

red 7, black 2,

black 5; red 3,

black 2,

black ace

red king,

black queen 20 25 -5

Winning: The winner is the player with the most points after four hands are played.


Record

DATE OPPONENTS MY

SCORE

MY ORDER OF FINISH

(1ST

, 2ND

, 3RD

, 4TH

)

SMART Notebook

Topic: Exponents and Order of Operations

Standards:

Grade-Level:

Strand:

Performance Indicator:

Algebra

Number Sense and Operations- Students will understand meanings of operations and procedures, and how they relate to one another.

A.N.6- Evaluate expressions involving factorial(s), absolute value(s), and exponential expression(s)

Materials: warm-up overhead, wrap-up overhead, examples overhead

Procedures:

· Warm-Up Overhead ( The height of Mt. Whitney is +14,410 ft. The lowest point in Death Valley is –288 ft. What is the difference in altitude between these two points?

· Today: Exponents

· What are they?

· ab ( a = base, b = exponent, ab = power

· Example: 5³ = 5·5·5 = 125 and 7² = 7·7 = 49

· Show Ss how to do this in a calculator

· Example Overhead:

· 26

· 107

· (-3)4

· 5²

· –6³

· 45

· 12³

· 15

· 80

· (-2)²

· Let’s look at the powers with base 10… do 0 through 5

· How does the exponent relate to the number of zeros?

· So what is 1010?

· How does all this fit into PEMDAS?

· Example Overhead: Show all steps

· 12 + 54 / 3²

· 24·5³

· 6 + 3²

· (6 + 3)²

· (24 / 6)³

· 2² + 4² / 2³

· 4 + 3 · 24 / 6

· Wrap-Up Questions:

· What operation are exponents shorthand for? Give an example.

Homework:p. 353-354 A)35-39, C) 7

Slide 1

Slide 2

Slide 3

SMART Notebook

Resources for Teaching Math


In Search of Perfect Squares NAME _________________________ 1. Use your geoboard and rubber bands to model each square and complete the table below.

SIDE LENGTH AREA PERIMETER

5 units

8 units

49 units2

4 unit2

12 units

24 units

x units

y units2 2. A number is called a “perfect square” if it represents the area of a square whose side length is

a whole number. For example, 25 is a perfect square, because 25 square units represents the area of a square with a side length of 5 units. Which column above shows perfect squares?

3. Construct all the squares that are possible using your geoboard. Consider only squares with

horizontal and vertical sides. Record the side lengths and corresponding areas in the table below in order from least to greatest.

AREA

(UNITS2) SIDE LENGTH

(UNITS) SQUARE ROOT OF

THE AREA

Resources for Teaching Math


4. If you know the side length of a square, how can you find its area without a geoboard? 5. If you know the area of a square, how could you find the side length without a geoboard? 6. What is the relationship between the side length of a square and the square root of its area?

SMART Notebook

Topic: Radicals

Standards:

Grade-Level:

Strand:

Performance Indicator:

Algebra


A.N.2- Simplify radical terms (no variable in the radicand)

A.N.3- Perform the four arithmetic operations using like and unlike radical terms and express the result in simplest form

Algebra2/Trig


A2.N.2- Perform arithmetic operations (addition, subtraction, multiplication, division) with expressions containing irrational numbers in radical form

A2.N.4- Perform arithmetic operations on irrational expressions

Materials: warm-up overhead, examples overhead, geoboards, perfect squares activity

Procedures:

· Warm-Up Overhead ( 64 / 4² + 18

· Today: Radicals

· RADICALS ACTIVITY?

· What are perfect squares?

What are squares in a physical sense?

· Hand out perfect squares sheet and have Ss work on it for about 15 minutes

· Okay, so we’re actually going to work on square roots today though.

· What are square roots?

· Okay so square roots are only rational (no decimals) if we have a perfect square.

· Example: sqrt(16) = 4 and remember 4² = 16

· So they are inverses of each other, just like addition/subtraction and multiplication/division…now we have roots/exponents

· And how can we check to be sure our answer is correct?


· Sqrt(81)Sqrt(361)Sqrt(289)Sqrt(760)Sqrt(5.74)

· Okay now think of PEMDAS, ask why I write it differently?

· And so then where do square roots fit into this whole thing?

· So I like to call it PERMDAS, and rewrite with inverses on top of one another and explain why I do it that way

· Examples of why:

· (sqrt(225) – sqrt(81))/sqrt(36) * remember that numerators and denominators work like having a set of parenthesis

· sqrt((225-81)/36?

· Example Overhead: Calculate and show work

· 100 – sqrt(100)

(4² x sqrt(36))/3

· sqrt(9 + 16)

sqrt(9) + sqrt(16)

· 3sqrt49 + 2 + sqrt(64)

sqrt(169-144)

· sqt64 + sqrt121

6 + 4sqrt25

· 49 – 3²sqrt4

Homework:p. 353 B)1-12, 35

Slide 1

Slide 2

Slide 3

Slide 4

SMART Notebook

SMART Notebook

Name: _________________________________

Math in Trades

Unit 6: Pre-Algebra Review

Place each list of numbers in order from least to greatest. (Use of the number line is optional, but suggested.)

a) –8, 6, 0, 3, -4, 4, 7

b) -⅓, ⅔, ⅛, -⅜, -⅝, ⅞, -½

Simplify each of the following completely. (Remember to double-check your answer from your calculator based on the rules you know for operations with signed numbers.)

a) (-8) – (-8)

b) (-2.43671) x (-8.5) ( Round to two

significant digits

c) (4 x 3)² + 4 x 3²

d) 3⅝ - 8⅞

e)

( Round to the

f)

(Round to the

nearest thousand

nearest whole number

g)

( Round to three

h)

( Round to the nearest

decimal places

thousandth

i)

j)

( Round to two

decimal places

k) Find the side of a square whose area is 169 ft².

l) Joe’s Bagels was in the red $12,346 (negative) in the first half of the year and in the black $36,451 (positive) by the end of the year. What was the net gain over the year?

m) Use the formula ºF = 9/5(ºC) + 32 to convert –8 ºC to ºF. Round to the nearest degree.

n) Calculate the following and round to one significant digit. 20 – 19.5

0.6

SMART Notebook

Name: _________________________HINT: be sure to read all the directions! Math In Trades

Period: ______________ Unit 6: Pre-Algebra TEST TOTAL POINTS: 75

I. Multiple Choice. Each question is worth 3 points. If you get the wrong answer, but show all of the appropriate work, you may receive partial credit.

Total Value Section I: 30 pts

1. Written from smallest to largest, -13, 7, 4, -8, -2 would be written as:

(a) 7, 4, -2, -8, -13(b) –2, 4, 7, -8, -13(c) –13, -8, 7, 4, -2(d) –13, -8, -2, 4, 7

2. Simplified completely, -4 – (-4) is equal to:

(a) 0

(b) 8

(c) –8

(d) 16

3. Rounded to two significant digits, (2.4732) x (-6.4) is equal to:

(a) –15.82848

(b) 15.83

(c) –16

(d) 16

4. Simplified completely, (3 x 6)² + 3 x 6² is equivalent to:

(a) 432

(b) 3849444

(c) 11772

(d) 216

5. 2 ¼ - 4 ¾ equals:

(a) 7

(b) –2 ½

(c) 2 ½

(d) –7

6. Simplified, (-2.4) x (15) is equal to:

(a) 36

(b) –36

(c) –0.16

(d) –6.25

7. The Golden Gate Bridge is about 1 mile long. On a warm day is expands about 2 ft in length. If there were no expansion joints to compensate for the expansion, how high a bulge would this produce? Use the formula below for your calculation and round to the nearest foot.

(a) 89 feet

(b) 7922

(c) 2

(d) 1

8. Re-write

from least to greatest. (Hint: use their decimal equivalents to help you see the order)

(a)

(b)

(c)

(d)

9. The resistance, in ohms, in a certain silicon diode is found using the expression found below. Calculate the resistance to the nearest thousand ohms.

(a) 360000000

(b) 18973.666

(c) 18973

(d) 19000

10. Round

to two decimal places.

(a) 1.00

(b) 0.17

(c) 0.21

(d) 0.22

II. Calculations. Each question is worth 4 points. Partial credit will be allowed so SHOW ALL WORK in order to receive full credit.

Total Value Section II: 20 pts

11.

Round to two decimal places

12.


13. 14 – 46

(-4) · (-2)

14.


15.

III. Application. This section contains word problems. Each question is worth 5 points. REMEMBER, partial credit can be awarded so an attempt is much better than a blank.

Total Value Section III: 25 pts

16. Fire Protection. The flow rate (in gallons per minute) of water from 1 ½-in. hose at 65 psi is calculated from the expression

. Find the flow rate to the nearest gallon per minute.

17. Meteorology. Use the formula

to convert the following Fahrenheit temperatures to Celsius, rounded to the nearest degree.

a) –4ºF

b) 24ºF

18. Find the side of a square whose area is 225 sq ft. (Hint: what do you know about the sides of a square?)

19. Automotive Trades. An auto shop was $14,560 in the “red” (negative) at the beginning of the year and $47,220 in the “black” (positive) by the end of the year. How much profit did the shop make during the year?

20. Electronics. The following calculation is used to determine one of the voltages for a sweep generator: V = 10 – 9.5

0.03 Calculate the voltage and round to one significant digit.

SMART Notebook

SMART Notebook

Let it Snow ( Draw and label the x- and y-axes (including numbers) Graph each point and connect until STOP

(0, 21)

(3, 18)

(1, 16)

(1, 13)

(2, 12)

(0,10)

(1, 9)

(1, 6)

(3, 4)

(4, 5)

(4, 7)

(6, 7)

(8, 9)

(7, 10)

(6, 12)

(8, 15)

(11, 13)

(10, 10)

(12, 12)

(15, 9)

(13, 7)

(10, 7)

(9, 8)

(7, 6)

(7, 4)

(5, 4)

(5, 2)

(6, 1)

(8, 2)

(10, 1)

(12, 1)

(15, 4)

(17, 0)

(15, -4)

(12, -1)

(10, -1)

(8, -2)

(6, -1)

(5, -2)

(5, -4)

(7, -4)

(7, -6)

(9, -8)

(10, -7)

(13, -7)

(15, -9)

(12, -12)

(10, -10)

(11, -13)

(8, -15)

(6, -12)

(7, -10)

(8, -9)

(6, -7)

(4, -7)

(4, -5)

(3, -4)

(1, -6)

(1, -9)

(0, -10)

(2, -12)

(1, -13)

(1, -16)

(3, -18)

(0, -21)

(-3, -18)

(-1, -16)

(-1, -13)

(-2, -12)

(0, -10)

(-1, -9)

(-1, -6)

(-3, -4)

(-4, -5)

(-4, -7)

(-6, -7)

(-8, -9)

(-7, -10)

(-6, -12)

(-8, -15)

(-11, -13)

(-10, -10)

(-12, -12)

(-15, -9)

(-13, -7)

(-10, -7)

(-9, -8)

(-7, -6)

(-7, -4)

(-5, -4)

(-5, -2)

(-6, -1)

(-8, -2)

(-10, -1)

(-12, -1)

(-15, -4)

(-17, 0)

(-15, 4)

(-12, 1)

(-10, 1)

(-8, 2)

(-6, 1)

(-5, 2)

(-5, 4)

(-7, 4)

(-7, 6)

(-9, 8)

(-10, 7)

(-13, 7)

(-15, 9)

(-12, 12)

(- 10, 10)

(-11, 13)

(-8, 15)

(-6, 12)

(-7, 10)

(-8, 9)

(-6, 7)

(-4, 7)

(-4, 5)

(-3, 4)

(-1, 6)

(-1, 9)

(0, 10)

(-2, 12)

(-1, 13)

(-1, 16)

(-3, 18)

(0, 21)

( There are two sides to this paper

SMART Notebook

Topic: Operations with Signed Numbers

Materials: warm-up overhead, wrap-up overhead, examples overhead, signed numbers paper and overhead, HW passes, cards (playing)

Procedures:

· Warm-Up Overhead ( Simplify and show all steps. 6 + 8 x 2³ / 4

· Unit 4( Algbra

· Today: Operations with Signed Numbers

· What do I mean by this?

· Hand out worksheet and go over multiplication and division (without calculators)

· Examples:

· 5 · 6

· –5 · 6

· –5 · -6

· 5 · -6

· We know division works the same way, so I’m not going to bother with it

· Go over addition rules

· Examples:

· 5 + 6

· –5 + 6

· –5 + -6

· 5 + -6

· Go over subtraction rules

· Examples:

· 5 – 6

· –5 – 6

· –5 - -6

· 5 - -6

· Give calculators


· The temperatures in Killington, VT were recorded for one week including the wind-chill factor. They were 10º, –8º, 21º, 32º, 2º, -4º, and –6º. Find the average temperature for that week.

· ZIP ZILCH ZERO game

· Wrap-Up Questions:

· How is subtraction of signed numbers related to addition?

· How can absolute value be used to add and/or subtract signed numbers?

Homework:

pg. 334 #5; pg. 338 B)#2, 3; pg. 344 #4, 6

Slide 1

Slide 2

Slide 3

Slide 4

Slide 5

SMART Notebook

Page 1: Mar 7-5:12 AMPage 2: Mar 7-5:13 AMPage 3: Mar 7-5:14 AMPage 4: Jan 29-4:31 PMAttachments Page 1

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