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Unit 1 – Multiple Representations 1
Name: ____________________ Teacher: _____________ Per: ___
Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8
Unit 9
Unit 10
– Unit 1 – [Multiple Representations]
Unit 1 – Multiple Representations 2
To be a Successful Algebra class,
TIGERs will show…
#TENACITY during our practice, have…
I attempt all practice I attempt all homework I never give up when I don’t understand
#INTEGRITY as we help others with their work, maintain a…
I always check my answers I correct my work, I never just copy answers I explain answers, I never just give them
#GO-FOR-IT attitude, continually…
I write down all notes, even if I’m confused I remain positive about my goals I treat each day as a chance to reset
#ENCOURAGE each other to succeed as a team, and always…
I offer help when I understand the material I push my teammates to reach their goals I never let my teammates give up
#REACH-OUT and ask for help when we need it!
I ask my questions during homework check I ask my teammates for help during practice I attend enrichment/tutorials when I need to
Unit 1 – Multiple Representations 3
Unit Calendar
MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY
August 25 26 27 28 29 1st day
Introduction to Multiple
Representations
Multiple Representations /
Vocabulary
Definition of a Function
Discrete & Continuous Relations / Functions
QUIZ
Sept 1 2 3 4 5
NO SCHOOL
Multiple Representations/
Vocabulary
Domain & Range
Multiple Representations/
Vocabulary
Independent & Dependent
Function notation QUIZ
8 9 10 11 12
Pattern Poster
Sequences Sequences Review TEST
Essential Questions
In what ways can I represent numerical relationships?
Why would one representation be more useful than another?
How are the different representations the same and how are they different?
Unit 1 – Multiple Representations 4
Critical Vocabulary
Function
Function notation
Continuous
Discrete
Dependent variable
Independent variable
Domain of a function
Range of a function
Unit 1 – Multiple Representations 5
Multiple Representations
Picture / Story
1 2
3
Table
Picture
#
Lines
Ordered Pairs Graph
Pattern:
Picture / Story
1 2
3
Table
Picture
#
Blocks
Ordered Pairs Graph
Pattern:
Unit 1 – Multiple Representations 6
Unit 1 – Multiple Representations 7
y = 10x + 40
You are studying for a test. For
every ______ hour(s) you study,
your grade increases by _______
points.
Unit 1 – Multiple Representations 8
Picture / Story
1 2
3
Table
Picture
#
Stars
Ordered Pairs Graph
Pattern:
Picture / Story In a savings account, Martin has $5. He plans to save $2 each week from is allowance.
Table
Week Money
Ordered Pairs Graph
Pattern:
Unit 1 – Multiple Representations 9
Unit 1 – Multiple Representations 10
You have $100 for lunch money.
For every ______ weeks(s) that
you buy lunch, you spend _______
dollars.
Write the first 3 ordered pairs for
this situation.
How much money do you have
after 3 weeks?
How many weeks until you run out
of money?
Unit 1 – Multiple Representations 11
Unit 1 – Multiple Representations 12
Unit 1 – Multiple Representations 13
Definition of a Function
Foldable Goes Here
Unit 1 – Multiple Representations 14
Ordered Pairs
{(−1, 6), (1, 3), (2, 5), (1, 7)} ____
{(−1, 2), (0, 5), (5, 0), (2, −1)} ____
{(4, 7), (2, 1), (3, 6), (3, 4)} ____
{(1, 5), (2, 6), (3, 6), (4, 7)} ____
Table
___ ___
Mapping
__
__
__ __
Graph
___ ___
___ ___
Determine if each
representation is
A function or (√)
Not a function (X)
Unit 1 – Multiple Representations 15
Discrete and Continuous
Discrete
A relation/function/situation that is represented by _____________.
Continuous A relation/function/situation that is represented by a _____________.
Would the following situations be represented by a Discrete or Continuous Graph? ____ The number of students in a classroom throughout the day. ____ The temperature as it changes throughout the day. ____ The height of an ice sculpture as it melts. ____ The amount of money in your savings account. ____ The number of math problems on your homework each night.
Unit 1 – Multiple Representations 16
x y 0 0
1 15
You are mowing yards for extra
money. For every _______ yards(s)
you mow, you earn _______ dollars.
Equation:
Is this Discrete or Continuous?
Unit 1 – Multiple Representations 17
x y
5
4
3
2
1
1 2 3 4 5
How many hours will it take to
travel 6 miles?
How many miles will you travel in
8 hours?
You are pulling a heavy cart down a
road. For every _________ hours,
you travel _______miles.
Unit 1 – Multiple Representations 18
x y
Billy collects stamps and can afford
to buy 8 new stamps each week.
His dad gave him 20 stamps to start
with before he began buying his
own.
Equation:
Is this Discrete or Continuous?
Unit 1 – Multiple Representations 19
Unit 1 – Multiple Representations 20
Unit 1 – Multiple Representations 21
Domain and Range
Domain
For a discrete relationship, it is a list of the ____ _________.
Range For a discrete relationship, it is a list of the ____ _________.
Unit 1 – Multiple Representations 22
Unit 1 – Multiple Representations 23
Unit 1 – Multiple Representations 24
Ashley is able to read ______ book(s)
for every ______ week(s).
x y
1 3
2 5
3 7
4 9
5 11
6 13
7 15
Equation:
Discrete or Continuous?
Function or Not a Function?
For the Domain values {1, 3, 7},
List the cooresponding Range:
Unit 1 – Multiple Representations 25
How much would it cost for 6 glasses?
Unit 1 – Multiple Representations 26
Unit 1 – Multiple Representations 27
Independent and Dependent Variables
Foldable Goes Here
Unit 1 – Multiple Representations 28
Examples of Dependent Relationships
Circle the Independent Variable and Double Underline the Dependent Variable.
1. How fast I wake up in the morning depends on how much sleep I get.
2. Our height is a function of our age.
3. The amount of the change in my pocket depends on the type of coins found there.
4. The amount of studying determines the grade we make.
5. As my car gets older, it is worth less money.
6. The grass gets greener as I put more fertilizer on it.
7. The amount of money I make at my job depends on the number of hours I work.
8. The number of cavities in your teeth depends on the number of times you floss your teeth.
9. The amount of homework I have will effect how many hours I can play games.
10. My battery life goes down as I use my phone.
11. The weather outside will influence the number of icecream cones sold.
Examples of Dependent Relationships in Equations/Formulas
12. y = -2x + 4 What you plug in: ________
Your result or answer: ________
13. Cost = $3(Pizzas) + 2 Input: ________
Output: ________
14. C = 2πr Independent Variable: ________
(Circumference) Dependent Variable: ________
Unit 1 – Multiple Representations 29
Unit 1 – Multiple Representations 30
Function Notation
Mathemticians devloped function notation for two main reasons:
You can name different functions with different letters to keep track of them.
They could shorten questions like “What is the value of y if x is 3?” into only 2 symbols.
Let’s take a look:
1. What major difffernece do you see between “y=” notation and function notation?
2. Why do you think they chose b(x) and p(x)?
The symbol b(x) in this problem means “the cost of x bottles bought at Barking Lot Grooming”
b(4) in this problem means “the cost of 4 bottles bought at Barking Lot Grooming”
b(x) = 38 in this problem means “for some number x, the cost at Barking Lot Grooming is $38”
3. How would I represent finding the cost of 8 bottles bought at Tidy Paws using function notation?
Interpret the following written in function notation: p(10) = 51
4. What does the 10 represent? 5. What does the 51 represent?
Unit 1 – Multiple Representations 31
Here’s funtion notation in action:
Plugging into an equation/function:
Given f(x) = 2x – 3 find…
f(2) f(-3) f(7) f(3) + f(0)
Reading points on a graph:
Find f(0) Find f(2)= Find x, if f(x)=4
Application Problem:
Swine flu is attacking Porkopolis. The function below determines how many people have swine flu where t = time in days and S = the number of people in thousands.
a. Find S(4).
b. What does S(4) mean?
c. Fill in the whole table.
d. Graph the function.
e. Find t when S(t) = 23.
f. What does S(t) = 23 mean?
t S(t)
1
2
3
4
5
6
7
49)( ttS
Unit 1 – Multiple Representations 32
Unit 1 – Multiple Representations 33
Sequences
2, 4, 6, 8, 10, ____, ____ 8, 11, 14, 17, 20, ____, ____ 12, 8, 4, 0, -4, ____, ____ -14, -12, -10, -8, -6, ____, ____
Rules: 2n 3n + 5 -4n + 16 2n – 16
1. Verify that the Rule matches each sequence above.
2. What does the “n” represent in the rules above?
3. Where is the number in front of “n” coming from in the rules above?
4. How do I know if the number in front of “n” is negative or positive?
5. What about the number after “n.” where does that come from?
Examples:
7, 9, 11, 13, 15, 17, ____, ____. Rule: ____________ Find the 50th term: ________
25, 21, 17, 13, 9, 5, ____, ____. Rule: ____________ Find the 20th term: ________
-100, -90, -80, -70, -60, ____, ____. Rule: ____________ Find the 25th term: ________
-30, -36, -42, -48, -54, ____, ____. Rule: ____________ Find the 100th term: ________
Unit 1 – Multiple Representations 34