Julian DavenportEducation Transformation Office

Cisely ScottJesse J. McCrary

DATE: June 21, 2011

BENCHMARK: Manipulatives

MT 2.0.2011

OBJECTIVE:

Participants will explain the purpose of using math manipulatives and identify ways of enhancing math instruction through the use of manipulatives.

ESSENTIAL QUESTION:

How can we use concrete resources to move students to the understanding of representational and abstract math concepts.

VOCABULARY: manipulatives, tangram, learning styles, concrete, representational, abstract (CRA), base 10 blocks, geoboards, pattern blocks, virtual manipulatives

AGENDA: IcebreakerWhat Are Manipulatives? What the Research Shows Reaching Various Types of

LearnersHands-On Activities RotationsDemonstrations for Upcoming

Benchmarks Challenges with prizes

Virtual ManipulativesTake Aways:

Things learned during this session

Tangram Handout

EXIT SLIP: IN YOUR JOURNALConnect: How can we use concrete resources to move students to the understanding of representational and abstract math concepts.

Connect: 1 question you still have about the using manipulatives.

HOME LEARNING:

Review today’s lesson and develop your next steps to share this information with teachers at your school.

Common Board Configuration (CBC)

Ice Breaker (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 else could we use tangrams to teach?

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)

Random Thoughts…..How many of you feel you could become master

teachers by just watching a master teacher?

How many of you could build a computer after sitting in a computer programming class and listening to your professor tell you how to build a computer?

How many of you could fly a plane without ever touching the controls prior to your first flight?

Why is this important to the classroom?

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….

Some things you might encounter…..Why use manipulatives? They can’t use them

on the test? Concrete/Kinestethic Conceptual/Visual Understanding

Ability to Understand the Abstract

My students can’t behave when they have toys in front of them.

Allow students 1-2 minutes to play with the manipulatives before utilizing them.

Set specific rules i.e. if they hit the floor, you lose yours!

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

Conceptual understanding in math will usually follow this order. Therefore it is best to use manipulatives to introduce lesson and/or concept.

What grade should we start introducing manipulatives?

Why Use Manipulatives?Motivate students

Feel like they’re 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

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 lessonConsider the students when planning the lesson

and choosing the appropriate manipulativesEncourage the students to talk and write about

what they have learned.Help the students to move from manipulatives to

paper-and-pencil operationsDiscuss observations and to help students draw

connections

Center 1: Base 10 Blocks

Center 2: Geoboards

Center 3: Pattern Blocks

Stations (5-7 minutes each)Place Value Blocks Activity: Make a list of how these

can be used in the classroom and then show me how many ways you can represent the number 123 using base 10 blocks (thousands, hundreds, tens, ones)

Geoboard Activity: Make a list of the many things this can be used for, then using a geoboard, show me how you can teach congruent/similar figures and angles

Pattern Blocks: Make a list of ways pattern blocks can be used and then show me one equivalent fraction.

Geoboards

Aid in the teaching of basic geometric concepts and in developing conceptual understanding of area and perimeter

Improve communication skills, share ideas, and use mathematical vocabulary.

Pattern Blocks

A tool to learn and practice fractionsCan be used to familiarize oneself with the

different shapes, their relations, and their proportions

Base 10 Blocks

Aid to teach Base 10 place value Basic arithmetic operationsUsually the foundation for understanding of

number sense

Challenge (with prizes)

Choices of ManipulativesTangramsPattern BlocksCountersGeoboardBase 10 BlocksColor Tiles (square inch tiles)

Challenge3rd Grade: MA.3.G.3.2 Compose and Decompose

Polygons

What manipulative and how?

Challenge4th Grade: MA.4.G.3.3 Area of Composite Shapes

What manipulative and how?

Challenge

What manipulative and how?

5th Grade: MA.5.G.5.4 Derive and apply formulas for areas of parallelograms and trapezoids.

What do you notice about the formulas? How do you prove it?

Virtual ManipulativesNational Library of Virtual Manipulatives

Gizmos- www.explorelearning.com

Journal Reflection

How can we use concrete resources to move students to the understanding of representational and abstract math concepts.