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.