Reasoning Month: Problem Solving for Primary Age Children

Reasoning is the idea of teaching children how to come to conclusions on their own, by using the elements of the problem to show that they understand how they have come to an answer. Problem solving for primary age children is really important if they are to pass the 11+ exam. A big part of the exam is around reasoning, both verbal and non-verbal. So what can you do to improve your child’s problem solving skills?

Puzzles, Brain Teasers and Logic

Using fun puzzles with evocative imagery is a good place to start with helping a child develop their reasoning skills. A fun sounding riddle can often engage children into wanting to work out the answer.

A Picture of the Farmer and his Cargo

Let’s look at a common reasoning puzzle:


A farmer is travelling with a fox, a sheep and a small sack of hay. He comes to a river with a small boat in it. The boat can only support the farmer and one other animal/item. If the farmer leaves the fox alone with the sheep, the fox will eat the sheep. And if the farmer leaves the sheep alone with the hay, the sheep will eat the hay.

How can the farmer get all three as well as himself safely across the river?

This puzzle is a great example of how you can use objects that children are familiar with to teach reasoning skills. Solving the farmer’s problem is simple with a bit of logical thought. Did you get it?

The farmer must take 4 trips with his goods and returns 3 times to pick up the rest of his cargo.

  1. The farmer takes the sheep to the other side and returns alone.
  2. The farmer takes the fox to the other side and returns with the sheep.
  3. The farmer takes the hay to the other side, leaving the sheep. He then returns alone.
  4. The farmer then takes the sheep to the other side.

We’ll never know why the farmer was taking a fox with him!

As you can see, this simple fun riddle provides plenty of thought and calculation. It will test your child’s reasoning skills.

Adding Maths into the Equation

Once you’ve mastered word riddles, there are trickier riddles which will really test problem solving for primary age children. This one is a maths problem spelt out…

Three people check into a hotel room. The bill is £30 so they each pay £10. After they go to the room, the hotel’s cashier realizes that the bill should have only been £25. So he gives £5 to the porter and tells him to return the money to the guests. The porter notices that £5 can’t be split evenly between the three guests, so he keeps £2 for himself and then gives the other £3 to the guests.

Now the guests, with their pounds back, have each paid £9 for a total of £27. And the porter has pocketed £2. So there is £27 + £2 = £29 accounted for. But the guests originally paid £30. What happened to the other pound?

Did you get it?

The answer is of course that there isn’t a missing dollar. The way the puzzle has been written is designed to confuse and make the puzzler work backwards.

Had the mistake not been made the three guests would had to have paid different amounts to make the £25 since they were refunded even amounts and the porter kept their cash he has the “extra” pound

£25 + 2 + 1 + 1 + 1 = £30

It’s simple once you know how to do it!

Problem Solving for Primary Age Children

Keep your eye out for more blogs during reasoning month. Whilst our three centres, Smart 11+ Tuition Harborne, Smart 11+ Tuition Solihull and Smart 11+ Tuition Sutton Coldfield, are closed, we want to enable your child to continue learning. If you want to find out more about joining when we reopen, please contact us below.