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KenKen: Developing Number Sense for All. Illinois Council of Teachers of Mathematics Annual Meeting October 18, 2013. Jackie Murawska, Ed.D. North Central College Naperville, Illinois jmurawska@noctrl.edu. Agenda. What is KenKen? Let’s try some! Why is KenKen good?

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kenken developing number sense for all

KenKen: DevelopingNumber Sense for All

Illinois Council of Teachers of Mathematics

Annual Meeting

October 18, 2013

Jackie Murawska, Ed.D.

North Central College

Naperville, Illinois

jmurawska@noctrl.edu

slide2

Agenda

  • What is KenKen?
  • Let’s try some!
  • Why is KenKen good?
  • (Common Core, of course)
  • When and how could I use this?
  • More KenKen!
slide3

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”
slide4

Let’s Try Some!

  • How to play:
  • 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.
  • 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.
  • 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.
  • A number may be repeated within a cage as long as it is not in the same row or column. (http://www.kenken.com/)
slide5

3x3 KenKen (+ −)

Puzzle No. 37, http://www.kenken.com/

slide6

3x3 KenKen (× ÷)

Puzzle No. 442, http://www.kenken.com/

slide7

3x3 KenKen (+ − × ÷)

Puzzle No. 620, http://www.kenken.com/

slide8

4x4 KenKen (+ − × ÷)

Puzzle No. 4703, http://www.kenken.com/

slide9

Why is KenKen Good?

  • Fun!
  • I mean - engaging
  • Builds confidence
  • Encourages positive attitudes
  • Aligns with Common Core
    • Standards for Mathematical Practice
    • K-12 Content
slide10

Standards for Mathematical Practice

  • 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

slide11

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
slide12

KenKen Helps Build Skills Required for Common Core Mathematics K-12…

  • Basic math facts
  • 2.OA.2 Fluently 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.4 Find 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
slide13

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
slide14

4x4 KenKen (+ − × ÷)

Puzzle No. 4831, easy, http://www.kenken.com/

slide15

4x4 KenKen (+ − × ÷)

Puzzle No. 5284, medium, http://www.kenken.com/

slide16

5x5 KenKen (+ − × ÷)

Puzzle No. 10639, easiest, http://www.kenken.com/

slide17

5x5 KenKen (+ − × ÷)

Puzzle No. 10584, easiest, http://www.kenken.com/

slide18

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 fromhttp://www.saylor.org/site/wp-content/uploads/2012/06/MA111_Kenken.pdf
slide19

5x5 KenKen (+ − × ÷)

medium, http://www.kenken.com/