www.tie.net. use relational thinking with properties and strategies to learn the basic math facts
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Good Morning and Welcome!BLt Collaborative staff training
Dec. 16, 2009
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Developing Fluency with the Basic Math Facts
Use relational thinking with properties and strategies to learn the Basic Math Facts
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Using Flashcards
Assumea = b = c = d =
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How do we want students to know their
Basic Facts?
Memorization vs.
Internalization
Think about it
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Apply the properties with understanding
• Cross off the facts on the table as you apply the properties and strategies.
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1- Constructing meaning
I can---• Build it• See it• Count it• Put it
together• Take it apart
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Constructing meaning with numbers 1-10
• +1, -1• Part-Part Whole• Anchors of 5 and 10• Visual patterns
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Visual Patterns- Quick Images
• ‘Instantly’ see how many
• Recognize a number pattern as a whole
• Recognize a number as having parts
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2- Making Number Relationships
• Connecting a quantity to numbers, symbols
• Using strategies -making a ten-doubles ,+1, -1-ten and some more• Applying properties
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Develop Fluency with Word Problems
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3-Working towards recall“I just know it.”
• Quick Recall of math facts• Maintenance of Facts• Use Mental Computation to
reinforce basic number combinations
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Playing the Games
• With a partner play one or more of the following games
• Compare, Double Compare• Five in a Row, Roll and Record• How many are Hiding, Make 10, Tens Go
Fish
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Strategy Card Sort
• To build number relationships, students sort cards into strategy categories.
• Individually put the addition expressions into similar categories, then check with a partner in your group.
• How can this help you remember math facts?
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Addition Card Categories
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Role of Math Games
Support •Fluency•Strategic Thinking•Range of Learners•Families
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Sequence of learning Addition and Subtraction
Grade Investigations1st grade
• Combinations that make 10
2nd grade
• Addition combinations to 10 + 10•Practice related Subtraction combinations
3rd grade
• Subtraction combinations to 20
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Assessment of the Facts
K-2 •Individual interviews
•Individual observation•Small Group observation
How many am I hiding?
Games, word problems
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Playing the Games 10-20Play one or more of the games to
practice fact fluency with the combinations to 20.• Chips• Plus 9 or 10• War• Double it Arrays
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10 Minute Break
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Multiplication and DivisionRead Multiplication and Division
Look for evidence of:1- Constructing Meaning2- Reasoning Strategies3-Working towards Recall
Discuss with your group what activities students would be doing in each of
these phases.
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Apply the properties with understanding
• Cross off the facts on the table as you apply the properties and strategies.
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Multiplication Quick Images
• ‘Instantly’ see how many
• Recognize a number pattern as a whole
• Recognize a number as having groups of, sets of
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Multiplication Quick Image Activity
• One person flashes a x quick image card for 3 seconds.
• How did you see it? Share with the group.• Take a quick image card and rewrite it,
using its parts.5 x 6 = (3 x 5) + (3 x 5)
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Array Cards-visual image
Read- Array
Cards InInvestigations
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Playing the Games-Arrays
Play one or more of the array games
• Count and Compare• Missing Factors• Small Array/Big Array
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Sequence of Learning Grades 3-5
Grade Investigations3rd grade Multiplication combinations with
products to 504th grade Multiplication with products to 12 x 125th grade related Division combinations to 12 x
12
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Suggested Sequence of Learning- Multiplication• Read the Multiplication Combinations
sequence of learning.• How can this sequence support relational
thinking?• Discuss ways you have sequenced
learning the multiplication facts?
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Assessment of the Facts in Investigations Gr. 3-5
Group Assessments
•Addition•Subtraction•Multiplication•Division
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Playing the Games-Multiplications
Play one or more of the multiplication games.• How many rows, stacks, cups?• How many rows? In each row?• Circles and Stars?
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Students taking ownership
Students engaged together in ‘doing math’• Sharing strategies• Listening• Working collaboratively• Talking
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Many opportunities to PRACTICE
Day-to-day teaching of curriculum
• focused mini-lesson, numbertalks• games and activities• homework, practice pages• word problems
Make learning meaningful and engaging
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Developing Fluency with the Facts
Memorization Internalization