Problem solving in Mathematics

How to solve a math problem? There are various methods. Let’s look at three of them: Create a similar but simpler problem. Start from the end. Draw a picture.

One thing to always do is really understand what is being asked for. To do this, you must first read the entire text of the math problem carefully. In a bowl are 6 red caramels and 4 brown. You take a caramel without looking. How likely are you to get a brown one?

And figure out what they are really asking for. They are asking: What is the chance of getting a brown caramel - if you’re not looking. Ok, now you understand what they are really asking. Let’s try the first method. Create a similar problem, but with simpler numbers.

Like this! With one red and one brown caramel, there's a 50 percent chance of getting a brown one, right? Why? Well, you divide the number of brown caramels, ONE, by the total number of caramels, TWO! One divided by two is 0,5 or 50 percent.

Can we use this method here? Yes! In the first problem there were four brown caramels, and a total of four plus six, that is, ten caramels. Four divided by ten is 0,4 - 40 percent. The chance of getting a brown caramel is thus 40 percent.

Now it’s time to ask yourself if the answer seems reasonable. Yes, 40 percent is reasonable because there is almost an equal number of brown and red caramels. Let’s look at another problem. A roof needs new roof-tiles, which have a width of 30 centimetres and a length of 40 centimetres. How many roof-tiles are needed if the roof is 100 square metres in size.

That’s a lot of information. Let's figure it out. With this problem we’ll start from the end. What are we looking for? The number of roof-tiles.

What do we need to know to get the number of roof-tiles? We need to know the area of one roof-tile. So this is a sub-problem needed to solve the larger problem. What do we need to know to solve the sub-problem? The width and the length.

Is that information written in the question? Yes, the width is 30 centimetres and the length is 40 centimetres. To compare one roof-tile with the roof area we need to change the unit. 30 centimetres is 0,30 metres, 40 centimetres is 0,40 metres. The area is 0,30 times 0,40 which is 0,12 square metres.

Now the sub-problem is solved. Now let’s solve the larger problem by using the first method again: simplify it. The roof has an area of 100 square metres. If one roof-tile had an area of 50 square metres, 100 could be divided by 50, which equals 2. So two roof-tiles would be enough.

In reality, a roof-tile has an area of 0,12 square metres. Solve the larger problem in the same way: using division. One more problem: You have a chocolate bar with 24 pieces. Wow! Chocolate!

Leon gobbles up a quarter of them. After a while, you eat one-third of those left. How many pieces are left? Remember, read the problem carefully so you understand the question. This problem can be simply solved by using the ‘draw a picture’ method.

Since Leon ate a quarter of the chocolate bar, set out all the pieces in four equal rows. There are 6 pieces in each row. Now simply remove one quarter - Leon’s row. Three rows left. You eat a third of what’s left: One of the rows.

Now there are two rows left. Two rows times 6 pieces is 12 pieces. And that is the answer. When you have a math problem maybe it’s not immediately obvious how to solve it. Make sure you understand the problem.

Then try these various methods: Simplify Start from the end; break it into sub-problems Draw a picture And finally check: is the answer reasonable? Now you can finish the chocolate. Leon!