Problem Solving with

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• Problem Solving with
• Model Drawing
• NCCTMs 39th Annual State Conference
• October 30, 2009
• Greensboro, NC

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North Carolina Teacher Academy Mission Statement

• The North Carolina Teacher Academy enriches
  instruction and impacts student achievement by
  supporting the growth and retention of highly
  qualified teachers through research-based
  professional development in the areas of school
  leadership, instructional methodology, core
  content, and instructional technology.

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What is Singapore Math?

• The term Singapore Math refers to the
  mathematics curriculum in the country of
  Singapore, developed by the Curriculum Planning
  and Development Institute and approved by their
  Ministry of Education.
• In the US, the term generally refers to the
  Primary Mathematics Series, which is the textbook
  series for grades 1 through 6.

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What are the strengths of Singapores Primary
Math Curriculum?

• The curriculum is high coherent it is taught in
  a logical, step-by-step manner that builds on
  students prior knowledge and skills.
• The curriculum follows a concrete to pictorial to
  abstract approach, based on Jerome Bruners work
  in the 1960s.
• Fewer topics are taught in greater depth. The
  goal is conceptualization and mastery.
• Problem solving is the heart of the Singapore
  curriculum.
• Place value, mental math, and computation are
  reinforced through problem solving, particularly
  through the model drawing approach.

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What are the strengths of Singapores Primary
Math Curriculum?

• Singapores Primary Mathematics education culture
  is reflective and based on students developing
  the following core understanding
• Number Facts and Number Sense
• Patterns, Visualization, and Communication
• The term Singapore Math is sometimes used
  interchangeably with the key strategies. They
  are NOT the same. Singapore Math refers to the
  entire curriculum.
• Key instructional strategies used in Singapores
  Primary Mathematics curriculum relates to place
  value, computation, mental math, and model
  drawing.
• These strategies are applicable and highly
  effective when used to supplement US math program.

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Example of Look Talk
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Examples of Number Bond Stories
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Example of Word Problems, Using Actual Pictures
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Examples of Word Problems, Using Tiles or Other
Manipulatives
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Examples of Word Problems, Drawing Units,
Discrete Model
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Examples of Word Problems, Using a Continuous
Model
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Model Drawing is . . .

• A continuous model strategy designed to help
  students understand and solve word problems.
• The pictorial stage in the learning sequence to
  move student into more abstract thinking.
• A process to develop students visual thinking
  capabilities and algebraic thinking.

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Model Drawing Develops Problem Solving Skills

• The unit bars model the relationships among the
  components of each word problem.
• While building models, given information is
  identified as well as the unknown quantity, which
  is a key concept in algebraic thinking.
• Model drawing encourages students to look beyond
  the surface to discover the concepts and
  relationships at the core of every math problem.

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Model Drawing Steps

• Read the entire problem.
• Decide who is involved in the problem.
• Decide what is involved in the problem.
• Draw unit bars of equal length.
• Read each sentence carefully, one at a time.
• Put the question mark in place.
• Work computation to the side or underneath.
• Answer the question in a complete sentence.

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Sample Word Problem

• Kayla had 4 blocks in her toy box.
• She added 7 more. How many total blocks did
  Kayla have in her toy box?
• Kaylas
• blocks

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Problems That Dont Lend Themselves to Model
Drawing

• True Guess and Check Problems
• Find a number between 50 and 75 . . .
• More Than One Correct Answer Problems Make a
  list, Combination Problems Use
  each digit once to make 24 . . .

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Problems That Dont Lend Themselves to Model
Drawing

• Find a Pattern Problems
  Fill in the next three numbers of the
  pattern 1, 1, 2, 3, 5, 8, __, __, __, . . .
• Draw a Picture Problem
  Reflect this image over
  the line of symmetry.

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Subtraction Action Problem
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www.thinkingblocks.com
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For more information.

• North Carolina Teacher Academy
• Julia Kron, Executive Director
• 909 Aviation Parkway, Suite 700
• Morrisville, NC 27560
• 1.800.801.7983
• www.teacheracademy.org
• karen.kelley_at_teacheracademy.org