The ways to make 15

We are starting 1st grade.  Math expands this year.  We really begin to add, and by the end of the year we are doing some subtracting, or adding in the opposite direction.  We will talk more about that later, but today I want to talk about 15.  15 you ask, what is important about 15?  Well, if you are learning to play the card game Cribbage, every way you can make 15, using  2, 3, 4, or 5 cards is important.  More importantly, it gives us an insight to the adding of single digits into the teens.  Like adding to 10 in Kindergarten we start by looking at the combinations that make 15.
Have them tell you all the ways they can think of for 2 numbers to make 15.    14 + 1, 13 + 2, 8 + 7, 10 + 5, and all of the others.  Then ask them to put them in order so they display a pattern:
                                                       1 + 14 = 15
                                                       2 + 13 = 15
                                                       3 + 12 = 15
                                                       4 + 11 = 15
                                                       5 + 10 = 15
                                                       6 + 9 = 15
                                                       7 + 8 = 15
Now look at the pattern.  As numbers get bigger on the left the numbers decrease on the right.  This gives the student a look toward subtraction as they get the idea of decrease and increase at the same  time.  The big step is to go one better.  This may be a challenge for your 1st  graders, but with your encouragement I believe they can do it.  How many ways can I use three digits, the same or different,
to sum to 15?  For most 5 + 5 + 5 might be the first thought. Great! Have them write it down.  However, as they will see there are many more, like 4 + 5 + 6, and 1 + 1 + 13.  There are two major goals in this exercise. The first is of course is knowing your combinations of adding that will duplicate as the numbers get bigger.  By the way, using a large number line that is probably on your wall is a great visual  for them.   The second is recognizing that by starting small and using a PATTERN, we can form all the combinations possible.
This is not a small problem, I would contend, if you gave them this to work on it would be the largest problem they ever had.  Like rearranging letters to make words, they are rearranging numbers they know to make an equal total.  They are creating things that are equal:  4 + 5 + 6 = 1 + 3 + 11.
                                            1 + 1 + 13 = 15
                                            1 + 2 + 12 = 15
                                            1 + 3 + 11 = 15
                                            1 + 4 + 10 = 15
                                            1 + 5 + 9 = 15
                                            1 + 6 + 8 = 15
                                            1 + 7 + 7 = 15
 By starting with these your class has practiced their sums to 14 as well.  I believe that by there need to make 15 accurately they solidly place the values that sum to 14 in their minds.  Now we have run out of what we can do starting with 1 so:
                                           2 + 2 + 11 = 15      we cannot use 2 + 1 it is in our above list
                                           2 + 3 + 10 = 15
                                           2 + 4 + 9 = 15
                                           2 + 5 + 8 = 15
                                           2 + 6 + 7 = 15
We are now finished with the 2's, and have practiced our sums to 13.  I will let you finish the list on you own. I ends with 5 + 5 + 5.


Remember, it is the pattern that is significant, the concepts will be obvious from there.  Have a good time with your numbers.