Line plots with fractions
A line plot is a quick way to show a stack of measurements. Each × represents one measurement. Stacks of × marks show how often each value appears.
In Year 5 we work with line plots where the data is fractional — the number line is labelled with fractions like 0, 1/4, 1/2, 3/4, 1, … rather than whole numbers.
A typical example
Nine pencils were measured to the nearest quarter-inch. Lengths: 1/4, 1/2, 1/2, 1/2, 3/4, 3/4, 1, 1, 1¼ inches.
The line plot looks like this:
What can you tell from this picture?
- Most common length: 1/2 inch (3 pencils — the tallest stack).
- Smallest: 1/4 inch.
- Largest: 1¼ inches.
- Total pencils: 1 + 3 + 2 + 2 + 1 = 9.
The "range" question
The most common Year-5 question on a fraction line plot is the range — the difference between the largest and the smallest value.
Range = largest − smallest = 1¼ − 1/4 = 1 inch.
That's exactly what the exercise Line plot with fractions asks. Find the leftmost ×, find the rightmost ×, subtract.
Step-by-step: subtracting fractions
If the largest and smallest values are both fractions, you need to subtract them carefully. The trick: rewrite them with a common denominator.
Range = 1¼ − ¾ = ?
Convert 1¼ to quarters: 1¼ = 5/4. Convert ¾ to quarters: 3/4. Same denominator now.
5/4 − 3/4 = 2/4 = 1/2.
Range = 2 1/2 − 1/4 = ?
Convert: 2 1/2 = 10/4. 1/4 = 1/4. Subtract: 10/4 − 1/4 = 9/4 = 2 1/4.
This is one place where fraction arithmetic shows up in real statistics work.
Why fractions?
In Year 5, you've just become fluent at adding and subtracting fractions. Line plots give those skills a real-life setting:
- Measuring pencils to the nearest 1/4 inch.
- Recording rain in 1/8-inch increments.
- Tracking growth in 1/2-cm steps.
Without fraction line plots, the only data Year 5 could show would be whole numbers — and that's not how measurement really works.
Tips and common mistakes
- Stack the X marks neatly. Each × should sit exactly above the tick mark. A drifted × means you can't tell which value it represents.
- One × per measurement. Three pencils of the same length = three ×s in a stack. Not one big ×, not five.
- Use a ruler when drawing. The number line should be straight and the ticks evenly spaced.
- Don't confuse a line plot with a bar chart. Bars have width and represent a category (red, blue, green). Line plots have ×s above a number line, so the order is fixed by size.
A puzzle
Eight cherry tomatoes weigh: 1/4, 1/4, 1/2, 1/2, 3/4, 3/4, 1, 1¼ ounces. Draw a line plot in your head.
- What's the heaviest tomato?
- What's the lightest?
- What's the range?
Heaviest: 1¼. Lightest: 1/4. Range: 1¼ − 1/4 = 1 ounce.