How Would You Prove It?How Would You Prove It?

Using Models for Number SenseUsing Models for Number Sense

Presented by Presented by

Teresa Savage & Karen MirkovichTeresa Savage & Karen Mirkovich

Swans Creek ES Swans Creek ES

Prince William County Schools, VirginiaPrince William County Schools, Virginia

Focus for TodayFocus for Today Use of the NCTM Process Standards Use of the NCTM Process Standards

with young students to enhance their with young students to enhance their problem solving skills. problem solving skills.

Students’ use of mathematical tools to Students’ use of mathematical tools to represent their thinking and prove represent their thinking and prove their solutions. their solutions.

Use of a Math Workshop format to Use of a Math Workshop format to support problem solving.support problem solving.

Collaboration of classroom teachers Collaboration of classroom teachers with a Math Specialist.with a Math Specialist.

Teacher ReflectionTeacher Reflection

How does the process of communicating by How does the process of communicating by students benefit students benefit

themselvesthemselves their peerstheir peers teachersteachers What would you see and hear in a What would you see and hear in a

classroom where students communicate classroom where students communicate in mathematics? in mathematics?

Creating a Environment for Creating a Environment for CommunicationCommunication

Student Centered

Classroom

Ownershipof the work

Ownershipof

discussion

Ownership in

collaboration

Providing a Context for Math TalkProviding a Context for Math Talk

Worthwhile Tasks

On-going Investigations

Embedded in real-life contexts

Spark DiscussionGalley Walks

Components of a Math WorkshopComponents of a Math WorkshopWhy, When, Where, How?Why, When, Where, How?

Posing a ProblemPosing a Problem Constructing Constructing

Knowledge through Knowledge through small group, pairs, or small group, pairs, or individual work. individual work.

Writing solutions Writing solutions and proofs.and proofs.

Math CongressMath Congress

The Masloppy Family The Masloppy Family Goes to New YorkGoes to New York

Which coins will Nicholas Which coins will Nicholas put in each bag? put in each bag?

There are three bags: There are three bags: subway tripsubway trip museum trip museum trip boat trip.boat trip.

Each bag has an equivalent Each bag has an equivalent amount. amount.

From From Trades, Jumps and HopsTrades, Jumps and Hops Mathematics in Context SeriesMathematics in Context Series

Fosnot & Lent (2007) Fosnot & Lent (2007)

The Subway ProblemThe Subway Problem

How many people could have left the How many people could have left the subway train and how many could have subway train and how many could have boarded if there were ten and now there boarded if there were ten and now there are fifteen and I stayed on the train?are fifteen and I stayed on the train?

From From Trades, Jumps and HopsTrades, Jumps and Hops Mathematics in Context Series Mathematics in Context SeriesFosnot & Lent (2007) Fosnot & Lent (2007)

Math Tools Math Tools

Mathematics in the tools or Mathematics in the tools or mathematics supported by the mathematics supported by the

tools? tools?

Representations and Models used for Representations and Models used for Number SenseNumber Sense

Cuisenaire RodsCuisenaire Rods Cube LinesCube Lines Empty Number LinesEmpty Number Lines Hundreds ChartsHundreds Charts Number StringsNumber Strings Tens FramesTens Frames Rek and Reks Rek and Reks