Variables and Patterns

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Variables and Patterns

• Introducing Algebra

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Investigation 1

• Variables, Tables, and Coordinate Graphs

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1.1 Preparing for a Bike Tour

• What do you know about bicycle tours?

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1.1 Preparing for a Bike Tour

• 1. How far do you think you could ride in a day?
• How do you think the speed of your ride would
  change during the course of the day?
• What conditions would affect the speed and
  distance you could ride?

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1.1 Preparing for a Bike Tour
Jumping Jack Experiment
Test your endurance!
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Ticket-out-the-door
Think about the process of creating a table to
record data. In our experiment, we used
10-second intervals. Could you have chosen
different time intervals for recording data in
your table?
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Variables and Patterns

• 1.2 Making Graphs

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Math Dictionary

• Variable a quantity that changes
• EXAMPLE Time and the number of jumping jacks
  were the variables in our experiment

X
y
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Math Dictionary

• Coordinate graph displays data shows the
  relationship between two variables
• A coordinate graph relates
• the dependent variable
• (y-axis) and the independent
• variable (x-axis)

EXAMPLE
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Coordinate Graph
y-axis
Finger Model
x-axis
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Math Dictionary

• Dependent variable one of the two variables in
  a relationship its value depends on the other
  variable
• Independent variable one of the two variables
  in a relationship its value determines the value
  of the other variable

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Example

• The cost of a long-distance phone call (dependent
  variable) DEPENDS on how long you talk
  (independent variable).

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Math Dictionary

• Y-axis the number line that is vertical on a
  coordinate grid (dependent variable)

y
It's Dependent!
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Math Dictionary

• X-axis the number line that is horizontal on a
  coordinate grid (independent variable)

Miss Independent!
x-axis
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Math Dictionary

• Scale A labeling plan used on each of the axes
  on the coordinate grid (decide on the least and
  greatest values and how to space the scale marks)
• Coordinate pair an ordered pair of numbers used
  to locate a point on a coordinate grid (x,y)

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KWL Chart

• What do you already KNOW about the coordinate
  graph?
• What do you WANT to know about the coordinate
  graph?
• What did you LEARN about the coordinate graph?

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Notes Making Graphs
Create a Graphic Organizer
FLOW CHART
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Problem 1.2

• Complete A-C on page 9

Make a Graph!
Classwork/Homework CORE 1-3 Connections 18-20
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Day 1 Atlantic City to Lewes
Bike Tour 2008
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Google Maps
Cape May, NJ
Atlantic City, NJ
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Problem 1.3 Interpreting Graphs

• Learning Partners Complete A and B
• Summary What are some possible reasons for the
  changes in the riders speed and distance
  traveled?

Classwork/Homework Page 17-18 4-5 Page 26 26
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Day 2 Lewes to Chincoteague Island
Bike Tour 2008
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Map of Lewes to Chincoteague Island - Google Maps
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Pony Swim
YouTube - Chincoteague Pony Swim
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1.4 Reading Data from Graphs

• Complete Problem 1.4 A-F with your Learning
  Partner (page 13)

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Venn Diagram
Summary
Tables
Graphs
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Day 3 Chincoteague Island to Norfolk
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Google Maps
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1.5 Finding Average Speed
Learning Partner Activity

• Make a graph of the distance traveled on day 3.
  Answer questions A-E.

Classwork/Homework Page 21 10 Page 22 12
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Summary for Investigation 1

• The problems in this investigation asked you to
  think about variables and the patterns relating
  the values of variables. You made tables and
  graphs to show how different variables are
  related. The following questions will help you
  summarize what you have learned.

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Question 1

• Describe the steps you would take in making a
  graph to show the relationship between two
  related variables.

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Question 2

• How do you decide which variable should be on the
  x-axis and which should be on the y-axis?

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Question 3

• What are the advantages and disadvantages of
  representing a relationship between variables in
  a table?

Time (sec) 10 20 30 40
Number of JJ 12 21 31 40
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Question 4

• What are the advantages and disadvantages of
  representing a relationship between variables in
  a graph?

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Question 5

• What are the advantages and disadvantages of
  describing a relationship between variables in a
  written report?

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Congratulations!

• You have completed investigation one!