Before I start on the theme of my blog I want to give you a maths problem to try. Here we go:
You start with $100 and it increases in value by 10%. Your amount then decreases by 10%. How much do you have?
I will give the solution in my next blog in a fortnight, along with another problem, but in the meantime if you are feeling courageous you could reply with your solution.
Right onto my soap box – justify yourself!
I have just gone through the stage 5 mathematics books and found many students writing answers only. When asked how they reached their answers, many couldn’t explain.
Maths is not about getting the correct answer, it is about justifying or explaining your solution. It is about interpreting what the problem is, asking and then applying a correct process in a logical and sequential order. This process needs to be written down but not as a bald answer or separate little number crunches written over the page with the answer somewhere in the middle. Rather, the solution should start with a mathematical statement or number sentence that is simplified sequentially, working down the page until an answer is reached. Sometimes the solution is as simple as writing down what will be typed into a calculator along with the answer. Other times it may be several lines of working with a necessary process happening each step. Each new line should relate entirely to what was written previously.
In solving an order of operation question, for example, one student could correctly identify what part of the problem to solve first and write this down separately. When they combined this answer with the original problem again, they mixed up the order of the numbers and ended up with an incorrect solution. At least this student had a written solution so I was able to identify what was going wrong, the student was able to learn from it and, hopefully, is less likely to make that mistake again.
Remember mistakes are encouraged in maths (see my last blog).
Don’t forget to have a go at the problem at the start.
Nathanael says
99
Maureen May says
100 + 10% = 110.
110 – 10% = 99.