Kakooma Addition with Many Combinations

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Kakooma is a game created by author, Greg Tang that compliments the concepts we have been learning over the last few weeks, namely: Adding by making 10, 20, 100, etc. and Converting Funny Numbers to Serious Numbers.

This is a highly addictive game that I cannot stop playing. The instructions are found on the first page of each of the pdf files attached here. I have organized the packets by K-1^st Grade (A_K-1st.pdf and B_K-1st.pdf) and 2-6^th Grade (IA_2-6th.pdf and IB_2-6th.pdf and IIA_2-6th.pdf and IIB_2-6th.pdf). Each grade level has two packets since they will have extra time over the holiday break.

Kakooma are organized with squares that contain 4 numbers each, pentagons that contain 5 numbers each, hexagons that contain 6 numbers each and so on. For each grouping of 4-9 numbers, your job is to find one number that is the sum of two other numbers and circle that one number. You should write that number in the corresponding box below on the page. You repeat these steps for each cell (square, pentagon, hexagon, and so on). Once you have all of the boxes filled in below, repeat these steps again: find the one number that is the sum of two other numbers and you have solved this puzzle.

The more numbers you have in a cell, the more difficult it is to find the sum. This is because you have to calculate more combinations of sums. I always try to get the children to find a systematic approach to any math challenge. Systematic opposed to a random approach. Here, I have found it advisable to start with the smallest number in a cell and add it to the next smallest number and look for the sum. If the sum is not in the cell add the original smallest number to the next smallest number until the sums are too big for the rest of the numbers in the cell. If you do not find the solution by first adding the smallest number, start a new sequence of adding the second smallest number by the one just bigger than it and so on.

For example, if a cell contains the numbers 1, 23, 21, 10, 4, 13, 15. First, I would reorder these numbers in my head to 1, 4, 10, 13, 15, 21, and 23.  First add 1+4, 1+10, 1+13, 1+15, 1+21. None of these solutions are in the cell. Next, start with the next smallest number 4 but you do not need to add 4+1 because you already did this in the first sequence. This teaches the children the property called commutative (a+b=b+a). We add 4+10, 4+13, 4+15, 4+21. Again, no solution. Finally, we add 10+13 and see that 23 is a solution. Here you found the solution on the 10^th combination. Most of the time, you will find the solution much earlier.

Another way to approach this puzzle is to look for differences. If you see that 13 and 23 have a difference of 10, the larger of the two numbers is your answer. One way to test differences is to look at the smallest number (in the example above, the number 1). Are any of the numbers consecutive (meaning, they have a difference of one)? Then look at the next smallest number (in the example above, do any of the numbers have a difference of 4, and so on).

Have fun with Kakooma. 

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