Suggested Activities

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Suggested Activities

• Unit 2 Algebra Essentials

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Rate of Change

• An Introduction to Slope

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Schema Activator

• A rate of change is a ratio that shows a change
  in one quantity with respect to a change in
  another quantity.
• Examples
• hours worked vs. dollars earned
• miles ran vs. calories burned
• miles traveled vs. fuel in tank
• weight in pounds vs. price of bananas
• List 2 examples of your own.

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Rate of Change

• Independent variables are quantities that are
  manipulated or changed.
• hours worked
• miles ran
• miles traveled
• weight in pounds
• Dependent variables are quantities that are
  changed as a result of manipulating the
  independent variable.
• dollars earned
• calories burned
• fuel in tank
• price of bananas

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Rate of Change WRITE THIS DOWN!
Rate of Change Change in Dependent
Variable Change in
Independent Variable
RATIO!
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Rate of Change Example 1

• Independent variable? Dependent?
• The rate of change is constant in the table.
  Find the rate of change.What does this
  tell us?

Time (hours) Temperature(F)
1 -2
4 7
7 16
10 25
13 34
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Rate of Change Example 2

• Independent variable? Dependent?
• The rate of change is constant in the table.
  Find the rate of change.What does this
  tell us?

People Cost (dollars)
2 7.90
3 11.85
4 15.80
5 19.75
6 23.70
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Rate of Change You Try It!

• The rate of change is constant in each table.
  Find the rate of change.

Number of Days Rental Charge
1 60
2 75
3 90
4 105
5 120
Miles Ran Calories Burned
1 50
2 100
3 150
4 200
5 250
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Facebook Challenge The Solution
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Schema Activator

• The graph below represents the value of an iPad
  based on the number of years that have passed
  since it was originally purchased.
• Calculate the rate of changeas shown in the
  graph.
• What is the y-intercept?
• What does it mean in the contextof this problem?

11
Its Slinky Time!

• Materials your team needs
• A Slinky
• A foam cup
• Pennies
• Your task
• Attach the foam cup to one end of the Slinky.
• Hang the Slinky from a doorway, ceiling, corner
  of the room, etc.
• Measure the length of the Slinky from one end to
  the other (where the Slinky meets the cup).
• Add one penny to the cup.
• Measure the length of the Slinky again record!
• Repeat steps 4-5 to fill in the data table.
• Tonights homework
• Graph your data. Include labeled axes and a
  title!
• Remember ( of pennies is the independent
  variable, so it should be on the x-axis!)

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The Slinky Activity Follow-Up

• Return to your Slinky team. Compare each others
  graphs.
• Do they look the same? If not, what could be a
  cause for the variation between graphs?
• Do you see any pattern(s) when comparing the
  number of pennies to the length of the Slinky?
• Can you identify the independent/dependent
  variables?
• Select one graph to represent your teams
  findings.
• Be prepared to share.

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The Traffic Ticket Problem

• How much do you owe?

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You were caught speeding.

• Fill in your traffic ticket. In the SPEED
  LIMIT box list 65.
• Make up your own ALLEGED SPEED how fast were
  you actually driving?
• What type of car were you driving? Be creative!

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How much do you owe?

• The fine for speeding in your state is 85 plus
  5 for each mile above the speed limit you were
  driving.
• Calculate how much you need to pay.
• Lets compare our answers.

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Whats the equation?

• Can we write an equation that can be used to
  calculate any amount due based on the drivers
  speed?
• Whats the equation?
• Hint Notice that you must pay 85 regardless of
  your speed, in addition to 5 for every mile over
  the speed limit. Use a variable to represent the
  speed at which youre traveling.

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Heres the equation!

• Amount Owed 85 (Your Speed 65) 5
• Or, we can write it like this
• y 85 5(s 65)
• Now, lets graph that equation.
• Set your window to
• Xmin0
• Xmax120
• Xscl20
• Ymin0
• Ymax200
• Yscl20
• Xres1

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Make predictions.

• Using the Table feature on your calculator, about
  how much would somebody owe if they were driving
• 101 mph?
• 90 mph?
• 85 mph?
• Check your predictions by substituting for the
  variable s in our equation
• y 85 5(s 65)

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ExponentialGrowth Decay

• Real-World(practical) Applications!

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Schema Activator

• Do the following exponential functions represent
  growth or decay? (Think about the car and bank
  account examples weve worked on.)
• y (1.08)x
• y (½)x
• y (0.25)x
• y ½(8)x
• y (¼)x

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Team 1

• Population  The population of the popular town
  of Jersey City in 2008 was estimated to be
  250,000 people with an annual rate of increase
  (growth) of about 2.4. 
• Write an equation that models the population P
  based on the number of years x following 2008.
• How many people would you expect to be living in
  Jersey City in 2012?
• High-Five Challenge How long will it take for
  Jersey Citys population to double?

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Team 2

• Money  Jeiny invests 300 at a bank that offers
  5 interest compounded annually.
• Write an equation to model the growth of the
  investment.
• What would be the value of Angelis account after
  8 years?
• High-Five Challenge After how many years will
  Angelis account be worth four times her initial
  investment?

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Team 3

• Cars Matt bought a new car at a cost of
  25,000.  The car depreciates approximately 15
  of its value each year.
• Write an equation that models the decay of the
  cars value.
• What will be the value of the car in 4.5 years?
• How much money did Matt lose?
• High-Five Challenge When will the value of
  Matts car first fall below 3,500?

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Team 4

• More Money  Jordi invests 1,285 at a bank that
  offers 4.25 interest compounded annually.
• Write an equation to model the growth of the
  investment.
• What would be the value of Wills account after 2
  years?
• High-Five Challenge What is the minimum
  interest rate at which Will should invest 1,285
  to have at least 1,500 after 3 years?

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Exploring Quadratics

1. Today you will explore the graph of a quadratic
   function.
2. In groups of 6, you will complete the Kitchen
   Paraboloids handout and answer the questions that
   follow.
3. Group member roles
4. Water pourer
5. Measurement master
6. Data recorder
7. Results reporter