Thought for the day: Sometimes you can use a Creative Math Prompt to introduce a new puzzle or game without explaining it! Simply give students a prompt showing an example of the puzzle or game, and ask them to figure out as much as they can about how it works. Follow up with a discussion to clarify any doubts.
Concepts: addition and subtraction facts and strategies, properties of addition and subtraction, logical reasoning
I notice that 1, 2, 3, and 4 appear exactly once in each row and column. (It may remind some students of sudoku puzzles.)
I notice that the grid is divided into parts (they are sometimes called "cages") by bold segments.
I notice that every cage shows a small numeral with a + or – symbol after it.
I notice that the numbers in the cages with + signs have a sum equal to the value of the small numeral.
I notice you can subtract the numbers in the cages with – signs to get the value of the small numeral.
I wonder if I could have figured out where to put the 1s, 2s, 3s, and 4s if they had not been filled in.
I wonder if there is more than one way to fill in the 1s, 2s, 3s, and 4s.
I wonder if I can find other puzzles like this somewhere.
I wonder if I could make up my own puzzles like this.
I wonder if I could use multiplication and division in this kind of puzzle.
I wonder if I could make up or solve puzzles like this with larger grids (5 by 5, 6 by 6, etc.)
Once students have had some practice solving these types of puzzles, they can create their own and share them with others. This may be even harder than solving them!
Reflecting and Extending
I notice that I can fill in some cells easily.
I notice that it helps to start with cells that obviously have only one possible answer.
I notice that it helps to keep track of the things I have tried (so that I don’t keep trying things that didn’t work before).
I wonder if there is more than one solution to the puzzle.
I wonder how hard it would be to create my own KenKen puzzles.
I wonder if there is an easy way to tell how many solutions a KenKen puzzle has.
This Creative Math Prompt is an example of a KenKen puzzle, a type of mathematical puzzle invented by the Japanese math teacher, Tetsuya Miyamoto. The official website at kenkenpuzzle.com will produce KenKen puzzles according to your specifications. You simply choose the size of the puzzle, the operations to use, and the level of difficulty that you want. The puzzles vary in difficulty from very easy to extremely challenging!
Once students have practiced solving KenKen puzzles for quite a while, ask them to try creating their own!
You may find rules for KenKen at www.kenkenpuzzle.com/howto/solve.