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Agenda:IntroductionQuick activity Discussion on ManipulativesCRA…Concrete Representational, AbstractSome common, but powerful manilulatives
Geoboard, base-10 blocks, Algebra tiles
Algebra TilesA couple of activities
Visualizing mathematics …Three Act Math.
A small task (3 minutes)1. Each of you has a tangram in your group. 2. Your job is to figure out what fraction the
smallest triangle represents of the complete tangram.
Answer………
What concepts could be introduced using Tangrams?
Role Of The Teacher “The mere use of manipulatives does not
guarantee that students understand concepts and procedures and be able to connect these concepts to abstract symbols without teachers making these connections explicit.”
(Reimer & Moyer 2005)
A Question
Could we become master teachers by just watching a master teacher?
What Are Manipulatives?
•Physical objects used to visualizeabstract concepts and promote learning
•Concrete materials that can beused when exploring math ideas, performing math tasks or solving math problems
What the Research Says….
Let’s face the objections…Why should I use manipulatives…?
“They can’t use them on the test” “My students don’t behave when they have
toys in front of them.”
Why I should Use ManipulativesMotivate students
Feel like they are playingMake math learning real and concretePrompt discussions about math ideasAllow teachers to see students at work doing mathematics Increase engagementAccommodate various learning styles
Visual learnersAuditory learnersLogical/MathematicalMusical/RhythmicBodily/Tactile/Kinesthetic learners
Learn through moving, touching, and doing
C-R-ACONCRETE: The “doing” stage. Uses hands-on
physical (concrete) models or manipulatives to represent numbers and unknowns.
REPRESENTATIONAL : The “seeing” stage. Draws or uses pictorial representations of the models
ABSTRACT: The “symbolic” stage. Involves numbers as abstract symbols of pictorial displays
What grade should we start introducing manipulatives?
Role Of The TeacherPLANNING IS KEY!!!!Choose manipulatives to support the lesson’s
objectives!!
Provide opportunity to become acquainted with manipulatives before they are used in the lesson
Encourage the students to talk and write about what they have learned.
Help the students to move from concrete to paper-and-pencil abstraction.
GeoboardsAid in the teaching of basic geometric
concepts and in developing conceptual understanding of area and perimeter
Excellent Investigation for MYP Criteria B.
Pick’s Theorem
Base 10 Blocks
Aid to teach Base 10 place value
Basic arithmetic operations
Build an understanding of number sense
… other bases?
Algebra Tiles
Algebra tiles enable students to access algebraic concepts through geometric understanding.
They are the real representations of a abstraction
Arithmetic operations are facilitated easily with tiles representing both numbers and variables.
What are the most difficult idea in mathematics?
Can algebra tiles help?
Virtual ManipulativesNational Library of Manipulative
Gizmos
Math Playground
… there are millions of apps available for free. Okay, maybe not millions, but certainly enough
to get the job done.
Three Act Math…. Dan MeyersProblem Solving with a twist
Accessible at all age groups
Natural “story arc” that takes us from the concrete to the abstract.
Students will participate as the resolution of the story demands it.