This post will be short and a little surprising (I hope). As you remember from some of my old posts (Games, Tutoring & Multiplication Table) I am tutoring a lot in this period and just a couple of days ago I got stuck at explaining something not extremely hard or complicated, and this is what happened:
We were doing surds and operations with them, everything was ok if the question had only surds in it. But when whole numbers appeared, for some reason the child (we will call her Carla for convenience) found it impossible to do. She had no problems before with order of operations and understood things quickly and nicely, also she was fine with negative numbers and fractions. So I thought she will understand easily, but I was mistaken. Here is where the problem came:
The above exercises have the solutions nicely done, but she got stuck at things like: in the 1st example from above Carla just continued doing 4+5=9 and then her answer would be 9 square root of 7. I tried explaining her they were different types of numbers and that 5 square root of 7 was in fact a multiplication between 2 different numbers. I’ve spent a couple of goood minutes trying to get her understand the thing, but I could not. I was kind of desperate, so I asked for a 5 minutes break. Carla looked strange at me, but she was ok with this and started telling me random things from school which was relaxing. During our conversation we started talking about what fruits we like and she told me she loves grapes and apples and then my brain exploded….. What I did next is extremely funny (for me and Carla): I started calling the square roots – apples and the whole numbers – grapes, telling her that there is no way to take 4 grapes and add them to 5 apples (she will always have 4 grapes and 5 apples because they cannot be added). And I think I have amused her at first a lot, but she got it immediately. And she has done all the questions with apples and grapes. At the end of the day we had a good laugh about it ^_^
The extremely nice thing happened yesterday, when I had another session with her. She told me she had explained my technique to one of her friends (important: Carla never considered herself good at maths, thus she never tried to explain things to her friends; normally it was her that needed help). And she said she has used it every time in the exercises. We even did a system with different types of apples for different square roots.
I hope you liked my small story about my tutoring experience. Let me know if you want to see more of these. Also tell me how would you explain this type of exercise to your students? I would love to hear new and funny techniques from you.