🚀 StudyNest is growing. New lessons and worksheets are added regularly.

GRAPHS · LESSON 03

Scales and Accurate Plotting

Choose sensible scales and build graphs that are clear, accurate and easy to read.

⏱️ 12–15 min 📘 Foundation ✏️ Worked examples included

Learning Objectives

Introduction

This lesson develops Scales and Accurate Plotting from meaning and patterns before moving to calculations. Look for what the quantities, shapes or symbols represent, then connect that idea to the method.

Key Notes

Read the definitions and key facts below carefully. Each rule is most useful when you can explain why it fits the situation, not simply recall it.

🤔 Think About This...

A graph must show values from 0 to 100, but the paper has only 10 large squares.

Should each large square represent 1, 5, 10 or 20?

A scale of 10 is convenient because 10 large squares will represent 100.

🇿🇼 Zimbabwe example: The same graph skills can model mobile-data use, ZESA electricity units, rainfall in Mutare, kombi journeys and school attendance.

What Is a Scale?

A scale tells us how much each division on an axis represents. The physical distance between marks may be the same even when the numerical jump is different.

Key idea: A good scale uses the available space, is easy to count and includes every value that must be plotted.

Useful scales

1, 2, 5, 10, 20, 50 and simple multiples of these are usually easy to use.

Awkward scales

Scales such as 3.7 per square often make plotting unnecessarily difficult.

Worked Example: Choosing a Scale

Plot x-values from 0 to 8 and y-values from 0 to 40.

1

For x, use 1 large square = 1 unit.

2

For y, use 1 large square = 5 units.

3

Label both axes and write the scale values at regular intervals.

Checklist for Drawing Axes

  1. Draw the axes using a ruler.
  2. Label the horizontal and vertical quantities.
  3. Include units where necessary.
  4. Use equal numerical jumps for equal physical distances.
  5. Write the scale clearly.
Never change the scale halfway along the same axis unless the graph clearly shows a break.

Plotting Accurately

Mark each point with a small cross or clear dot. A thick, vague mark may cover several possible values.

Use a sharp pencil, check each coordinate twice and label important points only after plotting them.

✅ Quick Check

Choose a scale for values from 0 to 60 across 12 squares.
Why must equal distances represent equal numerical jumps?
What information should appear beside an axis?

🧠 Let’s Think Together

Before calculating, identify the information given, the result required and the mathematical relationship that connects them. Predict whether the answer should be larger, smaller or unchanged, then use that prediction to check the result.

Practice Questions

Foundation
  1. Choose a scale for 0 to 50 using 10 large squares.
  2. Choose a scale for 0 to 24 using 12 large squares.
  3. Explain why 1 square = 7 units may be inconvenient.
Developing
  1. Draw axes suitable for x-values −5 to 5 and y-values 0 to 100.
  2. Plot (−4, 20), (0, 50), (3, 80) and (5, 100).
Challenge
  1. A student uses one square = 4 units but labels the axis 0, 4, 8, 16. Explain the error.

✅ Check Your Work

Attempt the questions before opening the solutions.

Show answers and working

Foundation

  1. 5 units per large square.
  2. 2 units per large square.
  3. Seven is awkward to count repeatedly and makes labels less convenient than 1, 2, 5 or 10.

Developing

  1. One suitable choice is 1 unit per large square on x and 10 units per large square on y.
  2. The points are (−4,20), (0,50), (3,80) and (5,100).

Challenge

  1. The sequence should be 0,4,8,12,16. The label 12 was skipped, so the scale became inconsistent.

Common Mistakes

Exam Focus

Show the mathematical relationship you are using, keep notation consistent and give a clear final answer. Use a quick estimate, diagram or inverse operation to check that the result is reasonable.

Summary