technifyed

Pure Mathematics + Geography

Investigate the four-colour theorem with maps

Colour maps of states and districts with as few colours as possible and link it to graph colouring.

  • DifficultyEasy
  • Estimated time1 day
  • BudgetUnder ₹250
  • ClassClass 7–10
  • TeamSolo or up to 2
  • You needHousehold materials

Prerequisites: None beyond your class work

Original · by TechnifyedArt ProjectInvestigationBeginner friendlyLow costResearch orientedTwo subjects

My projects

Overview

Colour maps of states and districts with as few colours as possible and link it to graph colouring.

Skills you will use

Converting maps to graphsSystematic colouring

Materials and tools

  • Outline maps of a country, a state and an invented map
  • Coloured pencils
Expected costUnder ₹250About ₹30 at most, less if you borrow parts
Estimated duration1 day5 build steps, plus the report

Step-by-step roadmap

  1. Start

    You will finish with: coloured maps, a graph version and a note on the theorem.

  2. 1

    Prerequisites

    Nothing special to know first. Then collect the 2 items in the materials list.

  3. 2

    Learn

    Read up on graph theory: graphs, map colouring, proof. Your textbook chapter and one short video are enough.

  4. 3

    Plan

    Write your question, your hypothesis and the one thing you will change. Draw the table you will fill in before you start.

  5. 4

    Build

    1. Colour a map of states so no neighbours match, using as few colours as you can.
    2. Repeat for a district map.
    3. Draw a map that needs four colours.
    4. Convert one map to a graph.
    5. Try to draw a map needing five colours and explain why you fail.
  6. 5

    Test

    Repeat every reading at least three times and check the result against what the science predicts.

  7. 6

    Document

    Record every reading with its unit, photograph the setup and draw a graph of the result. Report structure

  8. 7

    Present

    Explain the question, the method and the graph in two minutes; keep the setup ready to demonstrate. Presentation structure

  9. 8

    Publish

    Share the report and photos with your class, a science fair or your school magazine.

Expected outcome

Coloured maps, a graph version and a note on the theorem.

Other versions of this project

Advanced version

Write a greedy colouring program and count how many colours it uses.

Ways to do this project

Text marked "You write this" is a prompt for your own work; everything else is specific to this project.

Problem
You write thisWrite your question as: How does [what you change] affect [what you measure]?
Hypothesis
You write thisWrite it as: If [I change this], then [this will happen], because [reason].
Variables
You write thisName the one thing you change (independent), the thing you measure (dependent) and what you keep the same (controlled).

Observation table

You write thisDraw a table with one column for what you change, one for each repeat reading and one for the average.

Graph
You write thisPlot what you changed along the bottom and what you measured up the side; use a bar chart for categories and a line graph for numbers.
Results
You write thisState what the graph shows in one or two sentences, with numbers.
Conclusion
You write thisSay whether the result supports your hypothesis and why you think so.

Display board

  • Title and your name
  • Question
  • Hypothesis
  • Materials
  • Procedure (with photos)
  • Data table and graph
  • Conclusion
  • What you would do next

Questions judges ask

  • What would you change if you did this again?
  • What was your biggest source of error, and how did you reduce it?
  • Where is this idea used in real life?

Working as a team

Solo or up to 2. Suggested roles:

ResearchSetup and measurementData and graphsDocumentationPresentation

Report and presentation

Report structure

  1. Title and question
  2. Background: the science behind it
  3. Hypothesis
  4. Materials
  5. Method (steps, with a diagram or photo)
  6. Observations (table)
  7. Results (graph and calculation)
  8. Sources of error
  9. Conclusion
  10. What you would do next
  11. References

Presentation structure

  1. The question
  2. Why it matters
  3. The idea behind it
  4. Setup (photo)
  5. Method in three steps
  6. Results (one clear graph)
  7. What the result means
  8. Errors and limits
  9. Conclusion and next step

Viva questions

Prepare your own answers to these before you present.

  • What is the aim of your project, in one sentence?
  • What is the principle behind it?
  • Why did you choose these materials or tools?
  • What result did you get, and was it what you expected?
  • What went wrong and how did you fix it?
  • How could this be improved or used in real life?

Resources

Source and attribution

Original

Written by Technifyed. Free to use for your own school or college project; write the report in your own words. Added 1 Oct 2026.

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