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Hands on Math for Early Elementary

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This workshop is for the Barton County Early Childhood Fair

This workshop is for the Barton County Early Childhood Fair

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Hands on Math for Early Elementary Presentation Transcript

  • 1. Hands-On Math Barton County By Michelle Flaming ESSDACK
  • 2. Focus: Curriculum Focal Points (NCTM)
    • Kindergarten: Represent, compare, and order whole numbers and joining and separating sets.
    • Kindergarten: Identify, duplicate, and extend simple patterns.
  • 3. Different Manipulatives
    • Cheap Manipulatives
      • Foam Creatures
      • Beans
    • Manufactured Manipulatives
      • Pattern Blocks
      • Unifix Cubes
  • 4. Design of Session
    • Represent, compare, and order whole numbers and joining and separating sets.
      • Body Counts
      • Part/Whole BINGO
      • Two of the Same
    • Identify, duplicate, and extend simple patterns.
      • Snakes and Rocks
      • Pattern Round Robin
      • My Function Book
  • 5.  
  • 6. Part/Whole Relationships
    • Definition: The ability to reason with numbers and to work with numbers flexibly, to chose the most appropriate representation of a number for a given circumstance.
  • 7. Part/Whole Relationships
    • Example:
      • The number “seven” can be represented as: 5 + 2
        • 3 + 4
        • 7 + 0
        • 9 - 2
        • 1 + 6
        • Etc….
  • 8. Part-Whole BINGO
    • Gather markers to represent the sum.
    • You can either cover a single track or you can use 2 or more tracks.
    • Must cover the entire track.
    • Example: I roll 6 + 4 = 10
      • Cover the 10 track
      • 2 and 8 track
      • 1,2, and 7 track
      • 1,3, and 6 track
  • 9. Two of the Same
    • Build a tower that is 6 cubes high using no more than 3 colors of unifix cubes.
    • Think about a way you can describe your tower.
    • Is there math language to describe the tower?
  • 10. Unitizing/Place Value
    • Definition: Unitizing is the place value understanding that ten can be represented and thought of as one group of ten or ten individual units.
    • HUGE shift in thinking for children
  • 11. Unitizing/Place Value
    • The number 34 can be represented as:
      • 3 tens, 4 ones
      • 2 tens, 14 ones
      • 1 ten, 24 ones
      • 0 tens, 34 ones
      • Etc…
  • 12. Unitizing/Place Value
    • “Big Idea” in mathematics.
    • Shift in reasoning, perspective, logic, and in mathematical relationships.
    • Connected to part/whole relationships.
    • Important skill for all operations.
  • 13. Relationships
    • Definition: Repeated subtraction is the equivalent to division and repeated addition is equivalent to multiplication. The relationship between the operations is necessary before facts can be automatic.
  • 14. Relationships
    • Research-based Strategy:
      • Cognitively Guided Instruction (Thomas Carpenter)
  • 15. A Numerically Powerful Child:
    • Decompose of break apart numbers in different ways.
    • Knows how numbers are related to other numbers.
    • Understands how the operations are connected to each other.
    • Connects numerals with situations from life experiences.
    • Creates appropriate representation for numbers/operations.
  • 16. What is Algebra?
    • Patterns
      • Repeating
      • Growing
    • Variables and Equations
      • Variables as Unknowns
      • Variables that Vary
      • Equality (Thomas Carpenter and Linda Levi’s work)
    • Functions
      • Regular
      • Proportions
    • Models
  • 17. Patterns
    • Identify, duplicate, and extend simple patterns.
    • Activity: Card Patterns
      • Repeating and Growing Patterns
      • Color, shape, number, movement, and nature
    • As early as 3 1/2 years of age.
      • Songs, Rhythmic Chants, Nursery Rhymes
    • Pattern recognition and generalization are central components not only in algebraic concepts but in our base-ten system.
  • 18. Patterns
    • Activity: Snakes and Rocks
      • Make a snake pattern using unifix cubes:
        • ABC,ABC,ABC
        • ABABAB
        • AABAAB
      • Put a part of their snake under the rock
      • Record on grid paper.
  • 19. Pattern Terminology
    • Item (element) - Appear in the same order in each repetition.
      • A is an item or element
      • B is an item or element
    • Sequence - The pattern itself (used with repeating patterns)
      • A, B, B, A, B, B, A, B, B, A, B, B
      • The A,B, B sequence repeated 3 x
  • 20. Patterns
    • Activity: Pattern Round-Robin
      • Use the square, triangle, and hexagon.
      • Make a repeating pattern
      • Extend the pattern for at least 12 items
      • Place them on the recording sheet under:
        • Pattern Blocks
  • 21. More Advanced …
      • Generalize the relationship between elements and their locations in a sequence and use that information to continue and predict, what will the 30th item (element) be?
        • 1, 2, 3, 4, 5, 6
        • A, B, A, B, A, B (B’s are always even. The 20th position will be a B)
  • 22. Variables and Equations
    • Understanding the concept of variable is fundamental to algebra and, as noted by Schoenfeld and Arcavi (1988, pg. 420), “is necessary for the meaningful use of all advanced mathematics.”
    • Student learning is strongly linked to personal concrete experience. Students can only move toward an understanding of symbols, only after a strong foundation has been built on the concrete level.
  • 23. Functions
    • Definition: A relationship between two sets A and B, expressed as an unambiguous rule which tells how to associate each member of A with one member of B (Karush, 1989).
    • The function is considered by many to be the single most important idea in mathematics at all levels.
    • Functions are the central idea that ties algebra and calculus together.
  • 24. Functions
    • A special type of function - Proportional
    • Elements are related by multiplication. (Rule is In x 4 = Out)
      • Examples:
        • 1 table has 4 legs, 2 tables have 8 legs
        • 1 foot = 12 inches
        • 1 quart = 4 cups
        • 1 ten = 10 ones
        • 1 hundred = 10 tens
        • 1 dime = 2 nickels
  • 25. Functions
    • Activity: Animal Functions
    • Identify the relationship between pairs of data in a t-chart.
    • Use the relationship “rule” to find the missing inputs and outputs, continue the table.
    • Describe the rule that relates the pairs of data using words.
    • Represent the function using symbols.
  • 26.
    • Representation systems:
      • Equations
      • Tables
        • Function Tables (Input/Output Machines, T-tables)
      • Graphs
  • 27. Web Resources
    • http://www.lulu.com
      • Search “Hands on Algebra”
      • Search “Hands on Numbers”
      • Search “Hands on Geometry”
      • Search “Hands on Measurement”
    • http://nlvm.usu.edu/en/nav/category_g_1_t_2.html
    • http://www.bbc.co.uk/schools/laac/numbers/chi.shtml
    • http://pbskids.org/cyberchase/games/algebra/algebra.html
    • http://pbskids.org/cyberchase/games/patterns/patterns.html
    • http://pbskids.org/cyberchase/games/functions/functions.html
    • http://www.hbschool.com/activity/busy_bees/index.html
    • http://www.tvokids.com/framesets/nook_new.html?game=141&
    • http://www.kidsplaypark.com/games/jack/
    • http://www.sesameworkshop.org/sesamestreet/?scrollerId=games