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# Hands on Math for Early Elementary

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This workshop is for the Barton County Early Childhood Fair

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• ### Hands on Math for Early Elementary

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