Connecting Multiple Representations

1
Connecting Multiple Representations

• Christie McDougall

2
Getting Started

• Use the mind map to record connections between
  the terms.
• Talk about your connections with your table.
  Select two connections from the group and record
  on the master graphic organizer.
• How might you be able to use this type of graphic
  organizer with students?

3
Making Connections

• The concept of a variable can be developed by
  first looking at a variety of numerical
  replacements and discussing variables as
  representing a range of values.

4
Consider the following

• The Talks-A-Lot charges 20 for unlimited calling
  per month and 0.10 per text message. What
  would the bill for one month be if you sent 50
  text messages?
• What would the bill for one month be if you sent
  125 text messages?
• What changes and what stays the same?

5
How about this

• The Talks-A-Lot charges 20 for unlimited calling
  per month and 0.10 per text message. Write an
  equation to determine the cost of your monthly
  bill.
• Compare your equation to the verbal statement and
  test the equation with values.

6
Connecting Representations

• Provide experiences with data from a relationship
  that is expressed verbally, in a table, on a
  graph, and as a symbolic rule.

Language
Context
Table
Graph
Equation
7
Cell Phone Problem

• Which representations have we already created or
  used for the cell phone problem?
• What other representations might be useful to
  model this situation?

8
Think Dots

• Form a duo or triad for your work group.
• Roll the two number cubes.
• Use the number on the red cube to determine which
  of the problems you will explore.
• Use the number on the green cube to determine
  another representation to show the relationship.
• 1 Language
• 2 Context
• 3 Graph
• 4 Table
• 5 Equation
• 6 Group Choice
• Share your representation and process for
  translating from one representation to another
  with another group.

9
The Algebra Geometry Connection

• Explore the volume problem in groups of 4. There
  are materials on your table that may help you to
  visualize and explore the problem.
• Represent the relationship between the cut size
  and the volume of the box using multiple
  representations. Make a poster to demonstrate
  your process to other groups.
• Visit at least two other posters to see their
  approach to the problem. How did their process
  compare to your groups process?

10
Reflection

• What additional connections might you be able to
  add to the graphic organizer at this point?
• What are the implications of these ideas for
  classroom instruction in the middle grades?
• How might we improve this session? (evaluation
  form)