Answer to Year 5 Maths Problem

The answers are 44cm for both shapes & 65 people.

How would GradeBusters have taught the techniques for these exam questions?

Problem Solving at GradeBusters teaches children how to use the maths to help solve the problem, but it also teaches them to see the problem.

In the article use of words like “Hard” & “Impossible” prevent the person trying to solve the problem from even attempting to solve it, as those words are so final.

We like to say that things are either tricky or straightforward, this means the student is already in a more positive frame of mind- ready to “have a go” as they are empowered to think.

In an exam or test you are given all the information you need to solve the problem. Here at GradeBusters we are consistent with our language and approach allowing the student to get on with solving the problem.

In our Problem Solving sessions we teach how to identify both the “Implicit” and the “Explicit” information. What are the given  “Facts of the Matter”? What are the hidden “Facts to be worked out”?

Considering the Train Problem:

You need to make a scary step because you do not know how many people are on the train to begin with.  The scary step is to say “Let X be the number of people on the train to begin with.”

Once you have made this step we can deduce the following;

In the problem what is the Explicit Information?
19 people got off.  This means Implicitly that you need to takeaway 19.

17 people got on.  This means Implicitly that you need to add 17.

There are 63 people on the train after the first stop.  This means Implicitly that the total number now on the train is 63.

You had X people on the train to begin with, as a result of deducing the Implicit meaning from the Explicit facts, the following Maths Statement describes what has happened:


What is the value of X to make this true?

X = 65

In GradeBusters the Maths sessions from our very first course recommended for Year 1 teaches children Algebra.