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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!
Honors Math 3 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 2
(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 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 3
Honors Math 3
Ms. J. Blackwell, nbct
https://sites.google.com/site/blackwellsbutterflyworld/home
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!
Honors Math 3 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 4
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
Honors Math 3 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 5
“It’s All About The Brain” – Graphic Organizer
Tell what each part means from the video clip.
PC _______________________________________________________________
MC _______________________________________________________________
BA _______________________________________________________________
AC _______________________________________________________________
VC _______________________________________________________________
WA _______________________________________________________________
LS _______________________________________________________________
Honors Math 3 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 6
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!
Honors Math 3 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 7
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
Honors Math 3 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 8
( 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:
Honors Math 3 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 9
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) _______
Honors Math 3 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 10
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.
Honors Math 3 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 11
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.
Honors Math 3 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 12
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?
Honors Math 3 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 13
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)
Honors Math 3 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 14
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
Honors Math 3 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 15
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 = ________________
Honors Math 3 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 16
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: __________________________________________
Honors Math 3 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 17
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
Honors Math 3 Fall 2018 Have a Good Day! Ms. J. Blackwell, nbct 18
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
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