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
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!
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”
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/)
3x3 KenKen (+ −)
Puzzle No. 37, http://www.kenken.com/
3x3 KenKen (× ÷)
Puzzle No. 442, http://www.kenken.com/
3x3 KenKen (+ − × ÷)
Puzzle No. 620, http://www.kenken.com/
4x4 KenKen (+ − × ÷)
Puzzle No. 4703, http://www.kenken.com/
Why is KenKen Good?
• Fun!
I mean - engaging
•
Builds confidence
•
Encourages positive attitudes
•
Aligns with Common Core
• Standards for Mathematical Practice
• K-12 Content
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
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
KenKen Helps Build Skills Required for
Common Core Mathematics K-12…
•
Basic math facts
2.OA.2
3.0A.7
•
Number theory topics: divisibility, factors, primes
4.OA.4
•
Fluently add and subtract within 20 using mental strategies.
Fluently multiply and divide within 100, using strategies such as the
relationship between multiplication and division
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.3
Decompose 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
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
4x4 KenKen (+ − × ÷)
Puzzle No. 4831, easy, http://www.kenken.com/
4x4 KenKen (+ − × ÷)
Puzzle No. 5284, medium, http://www.kenken.com/
5x5 KenKen (+ − × ÷)
Puzzle No. 10639, easiest, http://www.kenken.com/
5x5 KenKen (+ − × ÷)
Puzzle No. 10584, easiest, http://www.kenken.com/
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/wpcontent/uploads/2012/06/MA111_Kenken.pdf
5x5 KenKen (+ − × ÷)
medium, http://www.kenken.com/