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Download From Buttons to Algebra: Learning the Ideas and Language
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Sorting to Algebra Developing Mathematical Thinkers Cross Number Puzzles Puzzles are not "dessert" for after the "real" work is done. Selected properly and introduced thoughtfully, they can be the real work. EDC What am I supposed to do? What CAN I do? Algebraic Ideas Breaking it up 59 4 40 45 19 40 121 11 What does the “thick line” do? 4 What does the “thick line” do? 4 21 What does the “thick line” do? 4 21 25 What about this way? 100 What about this way? 100 27 What about this way? 100 73 27 Kindergarten Sorters Addition and Subtraction From sorting to algebra 4+5=9 5x + 3y = 23 3+1=4 2x + 3y = 11 5 17 + 46 = 13 Challenge: can you find some that don’t work? Is there anything interesting about addition and subtraction sentences? Back to the very beginnings Picture a young child with a small pile of buttons. Natural to sort. We help children refine and extend what is already natural. Back to the very beginnings blue gray 6 small 4 large 7 3 10 Children can also summarize. “Data” from the buttons. Abstraction If we substitute numbers for the original objects… blue gray small 6 4 2 6 large 4 3 1 4 10 7 3 10 7 3 A Cross Number Puzzle Don’t always start with the question! 7 6 13 5 3 8 12 9 21 1st grade Building the addition algorithm Only multiples of 10 in yellow. Only less than 10 in blue. 20 5 25 30 8 38 50 13 63 2nd grade Relating addition and subtraction 2nd grade 4 10 2 3 6 7 3 4 1 1 4 3 7 6 3 2 10 4 The subtraction algorithm 20 5 25 60 3 63 30 8 38 30 8 38 50 13 63 30 -5 25 25 + 38 = 63 63 – 38 = 25 The subtraction algorithm 20 5 25 50 60 13 3 63 30 8 38 30 8 38 50 13 63 20 5 25 25 + 38 = 63 63 – 38 = 25 Place Value Bonus 235 + 597 Place Value Bonus 235 + 597 Place Value Bonus 235 + 597 Place Value Bonus 235 + 597 Place Value Bonus 235 + 597 Place Value Bonus 235 + 597 Place Value Bonus 235 + 597 Place Value Bonus 235 + 597 Place Value Bonus 235 + 597 = 832 Cross Number Puzzles and Multiplication Developing a familiar multiplication algorithm Developing a familiar multiplication algorithm Developing a familiar multiplication algorithm Developing a familiar multiplication algorithm Developing a familiar multiplication algorithm Developing a familiar multiplication algorithm Developing a familiar multiplication algorithm Developing a familiar multiplication algorithm Developing a familiar multiplication algorithm Developing a familiar multiplication algorithm Developing a familiar multiplication algorithm The algebra connection: adding 4 2 6 4+2=6 3 1 4 3+1=4 7 3 10 7 + 3 = 10 The algebra connection: subtracting 7 3 10 7 + 3 = 10 3 1 4 3+1= 4 4 2 6 4 +2 = 6 The eighth-grade look 5x 3y 23 5x + 3y = 23 2x 3y 11 2x + 3y = 11 3x 0 12 3x + 0 = 12 x=4 All from sorting buttons! Algebra At the Core Kindergarten – Grade 5 Focus on underlying principles allows “two for the price of one” subtraction is un-addition division is un-multiplication Mastery of traditional algorithms Easier and more exciting to learn and explore More competently used For more information about Cross Number Puzzles and Think Math! visit thinkmath.edc.org