How Would You Prove It?
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Transcript of How Would You Prove It?
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