Unit 1 – Multiple Representations 1

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– 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?

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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:

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y = 10x + 40

You are studying for a test. For

every ______ hour(s) you study,

your grade increases by _______

points.

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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:

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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?

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Definition of a Function

Foldable Goes Here

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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.

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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.

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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?

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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 ____ _________.

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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:

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How much would it cost for 6 glasses?

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Independent and Dependent Variables

Foldable Goes Here

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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: ________

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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

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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: ________

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