The Role of Mathematical Tools

1
The Role of Mathematical Tools

• By Sandra
• Kari
• Nancy
• Jamie

2
Manipulative Tools

• Concrete see-hear-do activities
• Aid student thinking (Communication)
• Are visual (picture) representation of concepts
• Allow students to focus on strategies for problem
  solving rather than mechanical calculations

3
Manipulative Tools Cont.

• Increases exploration to develop concepts
• Serve as a method to test hypothesis
• Bring senses into learning
• Are varied presentations for different learning
  styles
• Represents numbers and the operation on those
  numbers

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Manipulative Tools In Lesson Sequences

• Overhead
• Transparencies
• Charts
• Oral Presentations
• Pictures

• Diagrams
• Tables
• Dry Erase Boards
• Fingers
• Chips

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Partitioning (Monkeys in a Tree)

• Overhead (diagrams, table, numbers, and trees) as
  visual imagery to aid in problem solving.
• Various ways to partition (encourage thinking
  communication), How did you figure that out.
• Table (way to test hypothesis if all
  possibilities are correct).

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Double Decker Bus

• Table serves as simulated double-decker bus
  (visual image)
• Promotes student thinking when combined with
  questioning and discussion (communication)
• Introduces the concept of addition (rational
  counting)

7
Dot Patterns

• Spatial patterns used for numbers less than six
  (visual recognition)
• Encourage grouping rather than counting (number
  sense)
• Promote conceptual subitizing (Number sense)

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Single Ten Frame 12

• Single ten frame transparencies and chips serve
  as a spatial representation of object
  organization.
• Promotes mental imaging, and rational counting.
• Aids in the understanding of partitioned items up
  to ten.

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Double Ten Frame

• Double ten frame transparencies serve as a
  concrete representation of numbers.
• Aids in partitioning concepts of items 1 and up.
• Encourages students to group items rather than
  match counting.
• Promotes rational counting.

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Tiles and Their Uses
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Sensai Says

• Using Yourself As A Manipulative

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Conclusion!!!

• Manipulative tools are concrete material that
  enable the teacher and the students to have
  grounded conversations
• Concrete material furnish something on which the
  students can act, which should be consistent with
  our goals as successful teachers