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KenKen: Developing Number Sense for All Jackie Murawska, Ed.D. North Central College Naperville, Illinois jmurawska@noctrl.edu Illinois Council of Teachers of Mathematics Annual Meeting October 18, 2013

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Agenda 1.What is KenKen? 2.Let’s try some! 3.Why is KenKen good? (Common Core, of course) 4.When and how could I use this? 5.More KenKen!

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What is KenKen? KenKen is a puzzle similar to Sudoku Invented in 2003 by Tetsuya Miyamoto, a Japanese mathematics instructor, as a means to help his students improve their math and logic skills KenKen is Japanese for “square wisdom” or “cleverness squared”

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Let’s Try Some! How to play: 1.Fill in each square with a single number. In a 3x3 grid, use the numbers 1 through 3. In a 4x4 grid, use the numbers 1 through 4. In a 5x5 grid, use the numbers 1 through 5…and so on. 2.Do not repeat numbers in any individual row or column. For example, in a 3x3 grid, each column and each row should be filled in with the numbers 1, 2, and 3, with no duplication. 3.Each heavily outlined set of squares is called a “cage.” The numbers in each cage must combine (in any order) to produce the target number indicated in the top corner by using the mathematical operation next to the target number. 4.A number may be repeated within a cage as long as it is not in the same row or column. (http://www.kenken.com/)

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3x3 KenKen (+ −) Puzzle No. 37, http://www.kenken.com/

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3x3 KenKen (× ÷) Puzzle No. 442, http://www.kenken.com/

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3x3 KenKen (+ − × ÷) Puzzle No. 620, http://www.kenken.com/

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4x4 KenKen (+ − × ÷) Puzzle No. 4703, http://www.kenken.com/

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Why is KenKen Good? Fun! Fun! I mean - engaging Builds confidence Encourages positive attitudes Aligns with Common Core Standards for Mathematical Practice K-12 Content

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Mathematically proficient students: 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make sure of structure 8. Look for express regularity in repeated reasoning Standards for Mathematical Practice

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KenKen Promotes… Problem solving and perseverance MP. 1 Make sense of problems and persevere in solving them Reasoning MP. 2 Reason abstractly and quantitatively Communication and teamwork MP. 3 Construct viable arguments and critique the reasoning of others Argumentation and justification MP. 3 Construct viable arguments and critique the reasoning of others

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KenKen Helps Build Skills Required for Common Core Mathematics K-12… Basic math facts 2.OA.2Fluently add and subtract within 20 using mental strategies. 3.0A.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division Number theory topics: divisibility, factors, primes 4.OA.4Find all factor pairs for a whole number in the range 1–100…Determine whether a given whole number in the range 1–100 is prime or composite. Combinatorics K.OA.3Decompose numbers less than or equal to 10 into pairs in more than one way HS.F-IF.7c Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. HS.S-CP.9 Use permutations and combinations to compute probabilities of compound events and solve problems

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When and How Could I Use KenKen? Warm-up End of class activity for skills practice Focus for team problem solving Just-in-case box of problems Math club Competition Extra credit Teacher education Content course: factors and divisibility activity Methods course: games to facilitate engagement and understanding

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4x4 KenKen (+ − × ÷) Puzzle No. 4831, easy, http://www.kenken.com/

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4x4 KenKen (+ − × ÷) Puzzle No. 5284, medium, http://www.kenken.com/

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5x5 KenKen (+ − × ÷) Puzzle No. 10639, easiest, http://www.kenken.com/

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5x5 KenKen (+ − × ÷) Puzzle No. 10584, easiest, http://www.kenken.com/

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References KenKen main site: http://www.kenken.com/ Daily KenKen on NCTM’s Illuminations website: http://illuminations.nctm.org/ Advanced KenKen reasoning strategies: Reiter, H., Thorton, J., & Vennebush, P. (2011). Using KenKen to build reasoning skills. Retrieved from http://www.saylor.org/site/wp- content/uploads/2012/06/MA111_Kenken.pdfhttp://www.saylor.org/site/wp- content/uploads/2012/06/MA111_Kenken.pdf

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5x5 KenKen (+ − × ÷) medium, http://www.kenken.com/

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