Honors Math 3 Ms. J. Blackwell, nbct ... · Domain & Range – Video Clip Notes: State the domain, the range, tell if the graph is a function (write yes or no), and state whether

Honors Math 3 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 1

Honors Math 3

Ms. J. Blackwell, nbct

https://sites.google.com/site/blackwellsbutterflyworld/home

Unit 1 – Functions & Inverses

(August is National Catfish, Back to School, Goat Cheese,

Peach, & Sandwich Month) Day Date Topic Homework

1

8/27

Mon

(Due Dates

are on the

Website.)

4.1 – 4.2 Absolute Value, Domain & Range, and

Step Functions

4.1 RS # 3, 4, 6 & 4.2 RS # 1- 15 odd

2 8/28

Tues

4.1 – 4.3 Point – Slope Form & Absolute Value

Functions

(August 28th

– National Bow Tie & Cherry

Turnover Day)

4.1 Set # 7, 4.2 # 1 – 6,

4.2 Go # 19, 4.3 # 11 – 14

3 8/29

Wed

4.2 – 4.3 Absolute Value Equations & Graphs

(August 29

th – National Chop Suey Day)

4.2 # 13 – 19 and

4.3 RS # 2 – 10b Even

4 8/30

Thurs

4.3 – 4.4 Quadratics & Absolute Value

(August 30th

– National Toasted Marshmellow Day)

Study,

4.4 RS due Tues,

& Project

5 8/31

Fri

Quiz

(August 31st – National Trail Mix Day)

Thurs’ HW & Give 3 People a

Compliment! (Graded HW due Sept 5th)

Assignments are due the day before or the morning of a pre-planned Absence / Field Trip. Anyone

checking into school after math class will need to turn in assignments by the end of the school day.

Thank You!



(September is National Whole Grain, Classical Music, & Chicken Month)

6 9/3

Mon

Holiday

7

9/4

Tues

4.1 – 4.2 Desmos Lab & Project Plan Time

(September 4

th – National Wildlife Day)

Graded HW # 1 =

Google Classroom by

9pm = 1 – page Word

Doc using Desmos for

graphs on page 1 &

page 3 & Project

8

9/5

Wed

4.5 – 4.6 Direct & Inverse Variation & Intro to Inverse

Functions

(September 5th

– National Cheese Pizza Day)

4.5 SG, 4.6 # 5 – 11,

& Give Your Parents a

Compliment!

9 9/6

Thurs

4.6 – 4.7 Graph Characteristics

(September 6th

– National Coffee Ice Cream Day)

4.7 # 4, 8, 12 and

4.7 RSG # 2, 6, 10, 14,

18, 2, 6

10

9/7

Fri

Quiz

(September 7th

– National Acorn Squash & Salami

Day) (September 8th

– National Ampersand Day ) (September 9

th – National Teddy Bear Day)

4.7, 4.7 RSG Odd, &

Baggie of Healthy

Snacks

11

9/10

Mon

Review & Problem Set – Delta Math (September 10

h – National TV Dinner Day )

Study, PS # 1 due Th, &

Penny/Quarter Tread =

Graded HW # 2 due Fri

12 9/11

Tues

Unit Test 1

(September 11h – National Remembrance Day)

Say Something nice to 3

People

& PS # 1


Honors Math 3

Ms. J. Blackwell, nbct


Unit 2 – Inverse Applications

(September is also National Mushroom, Potato, Honey,

& Self Improvement Month) Day Date Topic Homework

1

9/12

Wed

(Due Dates

are on the

Website.)

1.3 Aesop’s Fables

(September 12

th – National Encouragement

& Chocolate Milkshake Day)

1.3 RSG Odd & Prj

2 9/13

Thurs

1.1 Absolute Value & Inverse Word Problems

(September 13h – National Peanut Day)

1.1 RSG Odd, Tire

Tread GH # 2, Baggie

of Cheesy Snack, &

Napkin

3 9/14

Fri

1.2 & 1.5 Skid Marks & Inverse Relation Activity

(September 14h – National Cream Filled Donut Day)

(September 15h – National Cheese Toast Day)

(September 16th

– National Cinnamon Raisin Bread Day)

1.2 All, 1.5 RSG Even, &

Prj

Assignments are due the day before or the morning of a pre-planned Absence / Field Trip. Anyone

checking into school after math class will need to turn in assignments by the end of the school day.

Thank You!



4

9/17

Mon

1.4 Inverse Number Theory

(September 17th

– National Apple Dumpling Day)

1.4 # 1 – 6,

Set # 15, &

Go # 27 - 30

5 9/18

Tues

Quiz

(September 18th

– National Cheeseburger Day)

PS # 2 due Fri 6 am

& Give Yourself a $1

6

9/19

Wed

Vacation Day

(September 19

th – National Butterscotch Pudding Day)

7 9/20

Thurs

Review

(September 20th

– National String Cheese &

Punch Day)

Study, PS # 2, &

Project

8 9/21

Fri

Unit Test 2

(September 21stth

– National Pecan Cookie Day)

Project, On – line

Ted Talk Link, 2.2

RSG Even, & Power

Rule Song


“It’s All About The Brain” – Graphic Organizer

Tell what each part means from the video clip.

PC _______________________________________________________________

MC _______________________________________________________________

BA _______________________________________________________________

AC _______________________________________________________________

VC _______________________________________________________________

WA _______________________________________________________________

LS _______________________________________________________________


Class Activity – Names _____________________________________

SLOPE INTERCEPT FORM OF A LINE:_________________

What is the equation of the line in the graph displayed below:

Let’s graph the equation 1

23

y x

Slope:______ Y-Intercept:_______

Domain:_________________ Range:__________________

Given f(x) = 4x + 8, find each:

f(2)

f(-3) f(x)= -10 f(4a)

Slope:_____ Y-Intercept:____

Equation:___________________

Write the slope as a fraction & y-intercept as a

point!


Class work

Absolute Value Video Notes

1.

2. 3.

4.

5. Additional Notes:

“Less Thand” “Great –

or”

Absolute Value Equations & Inequalities

6 Groups – Solve each Graph each Good Luck!

1. 9x

2. 14642 s

3. 24 n

4. 472 w

5. 246 p

6. 862 x

7. 26 x

8. 30543 m

9. 453 y

10. 1334 p

11. 1152 s

12. 123 y


( 2) ______

(5) ______

f

f

Domain & Range – Video Clip Notes:

State the domain, the range, tell if the graph is a function (write yes or no), and state whether the graph is

discrete, continuous or neither.

1) List the Points for # 1

Inequality Notation: Inequality Notation:

Domain 2) Domain 3) Domain

Range Range Range

Function? Function? Function?

____________________ _____________________ _____________________

Interval Notation

2) Domain 3) Domain

2) Range 3) Range

5.

2

2, 5

( ) 2 , 2 3

2 , 2

x

f x x x

x x

_____________

_____________

f

f

D

R

evaluate:


3. For the following function g, decide if each of the statements is correct. If it is incorrect,

fix the equation or restriction to make it true.

Check one: Statement Correction to the

Statement (if false) True False

From A to B, the restriction is 4 > x > -2.

From B to C, the equation is g(x) = 2x + 0.5.

3

From C to D, the equation is g(x) = 7.

To the right of E, the equation is g(x) = -3x + 3.

4

To the right of E, the restriction is x < 8.

4. Application: There are 25 bikes and trikes at the park. The bikes and trikes have

60 wheels in all. How many bikes and trikes are in the park?

4 Evaluate each of

the following for

function g.

a. g(3) _______

b. g(-1) _______

c. g(-3) _______

d. g(8) _______

e. g(40) _______


STUDENT ACTIVITY SHEET

Fire Hose Friction Loss – The Varying Variables for the One That Got Away – Part 1

The questions:

How does Friction Loss change with the quality of the fire hose?

How does Friction Loss change with the length of the fire hose?

How does Friction Loss change with the velocity of the water in the fire

hose?

How does Friction Loss change with various diameters of the fire hose?

You will need:

Activity sheet

Access to the internet to view website and YouTube video information

Assignment:

Investigation # 1 – Direct & Inverse Variation Formulas

In the fire service, Friction Loss is defined

as the loss of energy in pressure whenever

water runs through hoses, fittings, and

appliances. As water runs through the

hose, it rubs against the lining of the hose,

the couplings, and even itself. Each time

this happens, friction causes the water to

slow down.

View the following video “Firefighter Gets Owned by the Hose - Rookie Mistake”:

https://www.youtube.com/watch?v=Ci_sfp1rGjE . Investigate the four rules of Friction Loss below and

determine the rookie’s mistakes.

https://www.youtube.com/watch?v=Ci_sfp1rGjE


Friction Loss in a fire hose is governed by several rules:

Rule 1 – Friction loss varies with the quality of the hose.

a. What do you think this means? Explain this statement using at least 2 sentences.

b. How does Rule 1 affect the “rookie’s” mistake?

Rule 2 – Friction loss varies directly with the length of the hose.

c. Write the variation formula for the 2nd

Friction Rule.

d. Given the following example, Identify the values for the formula in part a.

Friction loss is calculated in 100-foot lengths; the total friction loss is figured when all lengths are added

together. For example, if the friction loss in one length of 1¾-inch hose is 15 psi, then if four 100-foot

lengths are added together, the total friction loss would be 60 psi.


Using the formula from part a, fill in the numerical values below:

e. What are the factors that would cause the “K” value to change?

f. How does Rule 2 affect the “rookie’s” mistake?

Rule 3 – Friction Loss varies with the square of the velocity.

a. Write the variation formula for the 3rd

Friction Rule and identify the variables.

b. What if the velocity is doubled? What will happen to the Friction Loss?


c. What if the velocity is quadrupled? Will the Fl double from the previous answer?

d. How does Rule 3 affect the “rookie’s” mistake?

Rule 4 – For a given flow, the Friction Loss varies inversely as the fifth power of the

diameter of the hose.

e. Write the variation formula for the 4thd

Friction Rule and identify the variables.

f. What if the hose size is doubled, but the flow rate is kept the same, what happens to the

friction loss?

g. How does Rule 4 affect the “rookie’s” mistake?

(Fire Hose Friction Activity written by J. Blackwell, nbct in connection w/ Wake Tech Community College)


Four Worksheet Create the following “Number” by only using 4 – fours! Good Luck!

1

11

2

12

3

13

4

14

5

15

6

16

7

17

8

18

9

19

10

20


STUDENT ACTIVITY SHEET

Predicting Car Speeds from Skid Marks Analysis

The question:

Given a skid mark length and a road surface type and condition, predict the car’s speed entering the skid?

Such information could be used in court to prove certain aspects of a crime.

You will need:

Excel or a calculator with regression capabilities

Assignment:

First, you will determine the coefficient of friction for two

surface types. To do this, a weighted tire drag sled is used

with an instrument to measure the force being applied. From

Newton’s second law, it can be determined that the friction

f = F/W, where F is the force applied to pull the drag sled and

W is the weight of the drag sled. Below you will find 10 samples

of forces required to move a 38 pound drag sled on a certain new

asphalt road. Determine the coefficient of friction of each force

and then find the average f for this particular asphalt. Below you will also find 10 samples of forces

required to move a 52 pound drag sled on a certain heavy traveled concrete road. Determine the

coefficient of friction of each force and then find the average f for this particular concrete road.

New Asphalt (38 pound sled):

Force 32 34 35 33 35 34 33 32 33 36

Friction

Now, find the friction average to be used for this certain road type later in this activity.

F = ________________

Heavy Traveled Concrete (52 pound sled):

Force 28 27 29 30 26 27 30 25 29 28

Friction

Now, find the friction average to be used for this certain road type later in this activity.

F = ________________


Second and after knowing the road’s coefficient of friction,

you can now use test skids to determine the relationship

between the vehicle speed entering the skid and the skid

mark length. To determine this relationship, one could create

test skids recording the speed entering the skid and then

measuring the skid length. Below you will find 8 samples

of mph recorded and the corresponding skid length. The

first set of data is for the New Asphalt and the second set

of data is for the Heavy Traveled Concrete.

New Asphalt:

Speed at

breaking(mph) 30 35 40 45 50 55 60 65

Skid Length

(ft)

34 46 60 76 94 114 135 159

Using regression, find the best model for this relationship: ______________________________________

Heavy Traveled Concrete:

Speed at

breaking(mph) 30 35 40 45 50 55 60 65

Skid Length

(ft)

56 76 99 126 155 188 224 262

Using regression, find the best model for this relationship: _____________________________________

Third, now compare your models with the accepted standard used in the criminal field. In the field, the

skid mark is measured and then the speed is determined or predicted, so what should be the independent

variable and what should be the dependent variable? ________________________________

Now, rearrange both equations above so that the input variable is the skid length and the output variable is

the predicted speed.

New Asphalt Equation for Speed: _________________________________________

Heavy Traveled Concrete Equation for Speed: __________________________________________


The accepted standard model used in the field is , where D is the skid length in feet and f is

the road surface coefficient of friction. Is this formula consistent with your two formulas? If not, then

what is different?

Fourth, predict the vehicle’s speed entering the skid for each situation below.

Situation 1: A car closely strikes a child getting off a school bus in a 45 mph speed limit zone. The skid

mark is measured to be 134 feet long and the asphalt coefficient of friction is estimated to be 0.8. Is the

driver guilty of any crime? What crimes?

Situation 2: A car strikes another car entering the intersection in a 45 mph speed limit zone. The skid

mark is measured to be 154 feet long and the older used asphalt coefficient of friction is estimated to be

0.63. Is the driver guilty of any crime? What crimes?

134 feet

f = 0.8

154 feet

f = 0.63


Situation 3: A car strikes another car entering the highway in a 55 mph speed limit zone. The skid mark

is measured to be 112 feet long and the concrete coefficient of friction is estimated to be 0.72. At the point

of impact between the two cars, it is also estimated by analyzing the impact damage that the car traveling

down the highway was still moving at 35 mph at the point of impact with the second car. The standard

formula used when combining two speeds ( like one from a skid mark into another speed at an impact) is

given to be , where and are the two speeds to be combined. Is the

driver guilty of any crime?

Situation 4: A car travels off road to avoid an accident and creates a skid mark across two different types

of surfaces. The first surface is concrete and the second surface is a grass area. If the skid mark on the

concrete is 38 feet and the skid mark on the grass area is 80

feet, was the drive speeding if the area is in a 35 mph speed

zone? Assume the concrete f = .75 and the grass area f = .47 .

(Skid Mark Activity written by J. Martin – Wake Tech Community College)

f = 0.72

112 feet

Documents

Honors Math 3 Ms. J. Blackwell, nbct ... · Domain & Range – Video Clip Notes: State the domain, the range, tell if the graph is a function (write yes or no), and state whether