One of the concepts that student find very difficult in Mathematics are word problems. Some students can do these sums easily but then there are others. It doesn't matter how you explain something or how easy you try to make it all they see is this.
I have recently started giving my students word problems on a daily basis to make them more familiar and to give them more confidence. These word problems are often difficult but with time they solve these. It often amazes me how they solve these problems. Just shows you, there are many ways to kill a cat and that there are many ways to solve certain problems.
I have recently given them this particular sum.
Pete can complete a job in four hours, and Matt can do the same job in six hours. How long will it take them if they both work together at the job?
Most of them just added the times together and divided the answer with two. This is incorrect of course.
Here is the solution.
Easy enough. This solution is the correct way to solve these work problems, but it often takes a while to figure it out and if they make a calculation mistake somewhere the answer will be wrong.
One of my students came up with a totally different, YET BRILLIANT solution. This method works on each and every sum similar to the above. It is a quick calculation and very easy to solve. I am now using HIS method to teach this to the students.
Here is the sum again. This time with a different way to solve (and much easier too)
Pete can complete a job in four hours, and Matt can do the same job in six hours. How long will it take them if they both work together at the job?
Look at the amount of hours.
Pete = 4 hours and Matt = 6 hours. Multiply these times: 4 x 6 =24
Look at the amount of hours.
Pete = 4 hours and Matt = 6 hours. Now add these times. 4 + 6 = 10
Now you divide the answer in step 1 into the answer in step 2.
24 divided by 10 = Hence 2.4 hours.
I thought this was a brilliant method and have tested this on many other sums and it works out every time. With this method there are way less calculations and it takes less than a minute to get to the answer.
This is definitely a method that all students should learn and I always say:
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