X Tables
Problem Solving

Non-routine problems

Build resilience with unfamiliar problems that need strategy.

Quick answer

Non-routine problems are puzzles or challenges that don’t have a clear method or step-by-step solution. You need to think creatively and try different strategies to solve them.

Learning outcome

By the end of this page, you will be able to solve unfamiliar problems by using different strategies like drawing pictures, making a list, working backwards, or trying a simpler version. Success signs:
  • You can identify when a problem is non-routine.
  • You can choose a strategy to start solving a new problem.
  • You can explain your thinking when solving a puzzle.
  • You feel more confident when facing a problem you haven’t seen before.

Why this matters

Non-routine problems help you become a better thinker and problem solver. In school, you might face word problems or puzzles that don’t follow a usual pattern. In real life, you often need to think outside the box to solve everyday challenges like planning a party, sharing toys fairly, or finding the quickest way to get to school. These problems are not just for school – they help you in games, sports, cooking, and even building with LEGO. Learning to solve non-routine problems builds your confidence and makes you more flexible in how you think.

How it works

Solving non-routine problems is like being a detective. You don’t know what the answer is from the start, so you need to:
  1. Read the problem carefully
  2. Think about what you know and what you need to find
  3. Try a strategy, like drawing a picture or making a list
  4. Check if your answer makes sense
  5. Try again if it doesn’t work
This process takes time and patience, but it’s okay to make mistakes. The goal is to learn how to think through new problems.

Examples you can see

Let’s look at a few examples of non-routine problems and how to solve them. Example 1: The Magic Square You have a 3x3 grid (like a tic-tac-toe board). You must place the numbers 1 to 9 in the squares so that every row, column, and diagonal adds up to the same number. This is a classic non-routine problem because there’s no formula. You need to try different combinations and use logic to find the right arrangement. Example 2: The Missing Numbers There are 5 apples in a basket. You take out 3 apples. Then you put back 2 apples. How many apples are in the basket now? This is tricky because it’s not just addition or subtraction. You need to think step-by-step and keep track of what happens to the apples. Example 3: The Party Planner You are planning a party for 12 friends. You want to make sure everyone gets 2 cookies. Cookies come in packs of 4. How many packs do you need? This problem has more than one step. You need to multiply, divide, and think about how many packs are needed.

Try it as a mini adventure

Adventure: The Treasure Hunt You are going on a treasure hunt in the garden. Here’s your clue: You start at the big oak tree. You walk 5 steps forward, then turn left and walk 3 steps. Then you turn right and walk 2 steps. You stop and dig. Where did you dig? To solve this:
  1. Start at the oak tree
  2. Walk 5 steps forward
  3. Turn left and walk 3 steps
  4. Turn right and walk 2 steps
  5. Dig at the final spot
You can act out this adventure with your family or draw a map to help you solve it. This kind of problem helps you think about direction and distance.

Common mistakes

  • Mistake: Jumping straight into solving without reading the problem carefully.
    Why it happens: You might be excited to start or think you already know the answer.
    Fix: Read the problem at least twice. Ask yourself, "What do I need to find?" and "What do I know?"
  • Mistake: Giving up too quickly if the first method doesn’t work.
    Why it happens: You might feel frustrated or think you're not smart enough.
    Fix: Remember that solving hard problems takes time. Try a different strategy or break the problem into smaller parts.
  • Mistake: Not checking your answer.
    Why it happens: You might be in a hurry or think you’re done.
    Fix: Always ask, "Does this make sense?" or "Can I check this another way?"
  • Mistake: Thinking that non-routine problems are always hard or impossible.
    Why it happens: You may have heard that only smart people can solve them.
    Fix: Everyone can solve non-routine problems with practice and the right strategies. It’s about thinking, not being perfect.

Parent and carer guide

Parents and carers can support children by:
  • Encouraging children to read the problem slowly and think about what it’s asking.
  • Helping them choose a strategy like drawing a picture or making a list.
  • Letting them make mistakes and try again – this is part of learning.
  • Asking questions like, "What do you know?" or "Can you try a different way?"
  • Practising with puzzles or games that require thinking and planning.
It’s important not to rush or give answers. Instead, guide your child to think through the problem step by step. If they get stuck, suggest they take a break or try a simpler version of the problem.

Practice questions

  1. There are 10 birds on a tree. 3 fly away, then 2 more come. How many birds are on the tree now?
  2. You have 15 sweets. You eat 5, then share the rest equally between 2 friends. How many sweets does each friend get?
  3. There are 4 boxes. Each box has 6 toys. You take 2 toys from each box. How many toys are left?
  4. Tom has 12 stickers. He gives 3 to his sister, then gets 5 more from his friend. How many stickers does he have now?
  5. There are 8 people at a party. Each person shakes hands with every other person once. How many handshakes are there?
Answers:
  1. 10 – 3 + 2 = 9 birds
  2. 15 – 5 = 10 sweets, then 10 ÷ 2 = 5 sweets each
  3. 4 boxes × 6 toys = 24 toys. 24 – (2 × 4) = 24 – 8 = 16 toys
  4. 12 – 3 + 5 = 14 stickers
  5. Each person shakes hands with 7 others. 8 × 7 = 56. But each handshake is counted twice, so 56 ÷ 2 = 28 handshakes

FAQ

What is the difference between routine and non-routine problems?

Routine problems are ones you can solve with a known method, like 5 + 3 = 8. Non-routine problems don’t have a clear method and need creative thinking to solve.

Why are non-routine problems important?

They help you think more deeply, become more flexible in your thinking, and prepare you for real-life challenges that don’t have simple answers.

How can I get better at solving non-routine problems?

Practice with puzzles, play games that involve logic, and try to solve problems in different ways. Don’t be afraid to try, fail, and try again!

Are non-routine problems only for older children?

No! Even young children can try simple non-routine problems, like puzzles or pattern challenges. The more you practice, the better you get.

Can I use a calculator for non-routine problems?

Yes, you can use a calculator for the math, but you still need to think about what the problem is asking and how to solve it.