## Problems vs. Exercises

Inspired by a blogpost by David Cox (@dcox21), I decided to use the same problem and added an extra fraction. Anyone following me for some time would see that I value mathematical thinking and, as David said, this is a good one to show problem-solving skills. I think it’s also a good one to revise, reinforce and connect mathematical skills (or tools as David calls them).

Simplify:

I asked the class what their first thoughts were upon seeing this problem on the board:

*“It looks complicated”**“It’s hard”**“It looks like a big problem with lots of little problems”*

They were all correct, of course, and I told them so (affirmation is good). I then told them that, in fact, they already have all the skills to solve this problem and they looked at me to as if I’ve gone mad. I suggested that, because it did look complicated, we look at the little problems that make up the big problem to make it easier (note the use of their responses; affirmation is good – oops, said that already).

I then asked what the problem looked like, that is, what’s familiar about the problem.

*1. **Dividing fractions*

*2. **Adding fractions*

*3. **Algebra – use of pronumerals/letters*

Upon revising the above, we added 2 more:

*4. **Multiplying fractions (division of fractions as multiply by inverse/reciprocal)*

*5. **Order of Operations (fraction bar as a grouping symbol)*

And so we set off to solve the problem and they asked for more to practice on, an Exercise as David puts it. This was the desired and expected effect. I used a similar approach when I introduced Decimals to my year 7 class last year (note to self: must share/blog this resource).

I should have also pointed out that this sort of thinking/questioning/problem-solving approach can be applied in real life. **Sometimes problems we face in life can seem hard and complex yet often, with chunking (or breaking down into smaller bits), we find that we have the skills/tools to solve them.**