Krypto Challenges and Krypto Homework? Parent Pointers!
What is Krypto, anyway?
Your upper elementary or middle school student has come home with an unusual challenge: solve this Krypto problem! What on earth is Krypto, how do we do this, and is there a quick way to get an answer? For an explanation of Krypto, I have a related hub, which might help you get an understanding of what this new thing is (it's not new, but it is probably new to you).
For some thoughts and strategies in helping your child to approach this new homework, I will continue in this hub to give some examples and strategies. One important thing to keep in mind, dear parent, is that solving the problems for your child will not improve their math abilities. Krypto is more than just a math problem; it truly is a simple, but fantastic, way to make your child think, to stretch his or her brain a bit. If we train our children to problem solve, we enable them to become the problem solvers of tomorrow. Oil spills and budget deficits and overcrowding of public schools, all issues of today, are challenging, and we need our best possible problem solvers to attack the issues of tomorrow.
In order to help...
You will need an understanding of what Krypto can accomplish, and what many math teachers' objectives are in assigning a Krypto problem or Krypto challenge. My goal, when I was in the classroom, was to encourage mental math, first and foremost. Secondly, I would emphasize strategies. Thirdly, I would present the difference between using order of operations to display a solution, verses the verbal explanation of the process...communication skills, in other words.
I cannot speak for each teacher, but I can guess that the mental math aspect is high on the list of objectives.
A Sample Problem
From my Krypto deck, I deal out 5 cards. The first 4 numbers represented must be used to obtain the 5th as a solution. Suppose I deal out 15, 2, 7, 4, and 9. I will use the numbers, 15, 2, 7, and 4, and I want 9 as a solution.
I will try some different approaches as I go. I might try adding everything. That won't work because my solution is less than the other four numbers combined. I might try subtracting. 15-2=13, 13-7=6, and 6-4=2...I didn't get to 9. However, I might back up and add in that last step...6+4=10...close.
I may try multiplication and division. 15x2=30...can't divide by any of the other numbers, so maybe I can subtract. 30-7 is 23. 23-4=19...not even close. I try again.
At this point, your child may get a little frustrated because there isn't a clear answer. That's the point. It requires a little work. It requires trying something different. It requires thinking, rearranging, and higher thinking skills. It's not drill and kill, where the child robotically fills in the blank with an answer, right or wrong, and moves on through the worksheet.
It's possible there is no solution, but we haven't even begun to try everything possible. We need some thoughts as to other ways to look at these numbers.
Work with a few of your numbers...
Since we are working with several numbers, aiming for our solution, it may help to look at particular numbers which will get us close to our answer. For example, 15 is the largest number in our hand above. If I can get the other 3 numbers to make a 6, that 6 will subtract from 15, and get us to our desired solution of 9.
7-4 = 3
Using that 3, 3x2 = 6
Aaaah! That 6, subtracted from 15, will get us to our target number of 9!!!
However, there's more to turning in a Krypto solution than just getting your solution. Representing it correctly, using order of operations, is probably key to getting credit in class.
There are various ways to remember order of operations: PEMDAS is the anacronym, and the memory tool many use is, "Please excuse my dear Aunt Sally". This reminds us that Parentheses and Exponents take priority, followed by multiplication and division in order from left to right, and finally, addition and subtraction in order from left to right. With seventh graders, I don't think I ever got Krypto solutions from my students with exponents. However, parentheses were often needed.
In our example, we are going to go back and build our equation, based on our work.
(7-4) gave us the 3, which we multiplied by 2: 2 x 3 is the same as 2(7-4).
2(7-4) gave us the value of 6, which we subtracted from 15: 15 - 2(7-4).
Remember that a number right next to parentheses means multiply.
Some of my favorite approaches are looking for "hidden" values such as 1's or 0's. Why? Using some basic properties, multiplying by 1 is a great way of keeping a value the same. Adding a zero is another. Multiplying by zero results in a zero. Thus, using 1's and 0's can work for us in a Krypto hand.
Create small problems within your problem. If you see a couple of numbers which will give you the desired solution, see if you can get the remaining numbers to make a 1 or 0. For example, if I deal out 8, 12, 6, 5, and 4, I notice that the difference between 8 and 12 is 4. The other two numbers, 6 and 5, have a difference of 1. (12-8)(6-5)=4
To be the best help possible to your child, ask good questions, and try a few of these problems yourself. You can even pick up your own set of Krypto cards, and do some problems in your spare time. I don't believe there's a fast online tool to solve, but that's a good thing, as this can be a lot of fun!