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Maths Without Realising

Maths detective: choosing a route home

A mini detective challenge where children spot distance and problem solving while choosing a route home.

Quick answer

Maths detective: choosing a route home is about using maths skills like measuring distance, comparing routes, and solving problems to find the best way home.

Learning outcome

By the end of this page, you will be able to choose the best route home by comparing distances, times, and safety, using maths skills like measuring, counting, and problem-solving. Success signs:
  • You can measure how far different routes are
  • You can compare which route is shorter or longer
  • You can explain why one route might be better than another
  • You can use clues to solve a route mystery

Why this matters

When you go home from school or a friend's house, you're using maths without even realising it! You're comparing distances, thinking about how long it takes, and choosing the safest path. This is like being a detective, solving puzzles about how to get home. These skills help you in games, sports, cooking, and even planning your day. The better you get at maths, the easier it is to make smart choices in life.

How it works

Choosing a route home uses many maths skills:
  1. Measuring distance – how far you walk or travel
  2. Comparing routes – which is shorter, longer, safer
  3. Problem-solving – using clues to find the best way
  4. Time estimation – how long it takes to walk or travel

Examples you can see

Let’s imagine you’re going home from school and have two choices: Route A: Walk 200 metres straight down the street. Route B: Walk 100 metres, turn right, then walk 150 metres to get home. Which route is shorter? Let’s count: Route A = 200 metres Route B = 100 + 150 = 250 metres So, Route A is shorter by 50 metres. Let’s try another example. You're walking home from the park and see two paths: Path 1: 50 metres, then 70 metres Path 2: 30 metres, then 100 metres Path 1 = 50 + 70 = 120 metres Path 2 = 30 + 100 = 130 metres Path 1 is shorter by 10 metres.

Try it as a mini adventure

Maths Detective Adventure: The Mystery of the Missing Route You are a maths detective on a mission to find the best way home from school. But there's a problem – you don’t know which route is the shortest, fastest, or safest. Here's your clue: You start at school and can take one of three paths: 1st path: Walk 100 metres, then turn left, then walk 120 metres. 2nd path: Walk 150 metres, then turn right, then walk 80 metres. 3rd path: Walk 200 metres straight. Which path is the shortest? Let’s solve it together. 1st path: 100 + 120 = 220 metres 2nd path: 150 + 80 = 230 metres 3rd path: 200 metres The shortest path is the 3rd one – 200 metres straight! Now, you can use your detective skills to solve this mystery:
  • What clues did you use to solve the mystery?
  • What would happen if it started raining?
  • Which route would be safest?

Common mistakes

  • Mistake: Thinking you can just add the first and last numbers without counting all the steps.
    Why it happens: Kids rush to find an answer and forget to add all the parts.
    Fix: Count each part of the route and add them up one by one.
  • Mistake: Choosing the route that looks "shorter" but isn’t actually shorter.
    Why it happens: Sometimes a longer path seems shorter because it’s straighter or easier to walk.
    Fix: Measure each part and add them up to compare.
  • Mistake: Not thinking about safety or time.
    Why it happens: Kids often focus only on distance, not other factors.
    Fix: Think about how long it takes and if it’s safe to walk that way.

Parent and carer guide

Parents and carers can help by:
  • Asking questions like: “Which way do you think is shorter?” or “Why did you choose that path?”
  • Using real routes from your own walks or journeys to practice
  • Encouraging children to draw or build a map of different routes
  • Letting them make their own detective clues or games
  • Not worrying if they make mistakes – it’s part of learning!
What to say: “Let’s look at the different paths and see which one is shorter. What do you notice about the distances?” What not to do: Don’t rush or tell them the answer too quickly. Let them think and explore.

Practice questions

  1. Route 1: Walk 50 metres, turn left, then walk 80 metres. Route 2: Walk 100 metres, turn right, then walk 40 metres. Which route is shorter?
  2. You walk 120 metres, turn right, then walk 90 metres. How far did you walk in total?
  3. Which is shorter: 150 + 100 metres or 200 + 70 metres?
  4. Route A: 250 metres straight. Route B: 100 + 150 metres. Are they the same distance?
  5. You walk 180 metres, then 120 metres. How far did you walk altogether?
Answers:
  1. Route 2 is shorter (140 metres vs 130 metres)
  2. You walked 210 metres
  3. 150 + 100 = 250 metres, 200 + 70 = 270 metres. First is shorter
  4. Yes, both are 250 metres
  5. You walked 300 metres

FAQ

What is maths detective: choosing a route home? It’s a fun way to learn how to use maths when deciding how to get home. You use measuring, comparing, and problem-solving skills.

Why do I need to know about routes and distances? Because it helps you make smart choices, like choosing the fastest or safest way home. It's like being a detective in your own life!

Can I use this at home? Yes! You can practice with the paths from your own house to school or a friend’s house.

How does this help with school maths? It helps with addition, measuring, and comparing numbers – all important skills in maths.

What if I’m not sure which route is better? That’s okay! You can measure each part, add them up, and compare. It’s like solving a puzzle.