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Lesson · Grade 9 · Mathematics

Discrete or Continuous: When to Join the Points

  • Grade 9
  • Mathematics
  • 1 min 57 s
  • British Columbia
  • BC9-MA-15

Two graphs side by side compare tickets at $5 each, where 2.5 tickets makes no sense so the points stay apart, with a tank filling at 5 L a minute, where 5 × 2.5 = 12.5 L after 2.5 minutes so the points join into a line. It then shows the common mistake of joining the ticket points and ends with a simple test: if a value in between makes sense, join the points, and if not, keep them apart.

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In one sentence

The question this lesson answers

When you plot points on a graph, should you join them with a line? It depends on the data.

First example: tickets cost 5 dollars each.

Transcript

What the lesson says

When you plot points on a graph, should you join them with a line? It depends on the data.

First example: tickets cost 5 dollars each.

1 ticket costs 5 dollars, 2 tickets cost 10 dollars, and 3 tickets cost 15 dollars.

But can you buy 2.5 tickets? No. You cannot buy half a ticket, so 2.5 tickets makes no sense.

This is called discrete data: only separate values make sense, like whole numbers of tickets. So the points stay apart.

Second example: a tank starts empty and fills with water at 5 litres a minute.

After 1 minute it holds 5 litres, after 2 minutes 10 litres, and after 3 minutes 15 litres.

What about after 2.5 minutes? 5 times 2.5 is 12.5, so the tank holds 12.5 litres.

Time and volume are continuous: any value in a range makes sense, not just whole numbers.

So we join the points with a line, starting from 0 because the tank starts empty.

Reading a value between plotted points, like 12.5 litres at 2.5 minutes, is called interpolation.

A common mistake is joining the dots when only whole numbers make sense.

This line says 2.5 tickets cost 12 dollars and 50 cents. That makes no sense.

So ask: does a value in between make sense? If it does, join the points. If not, keep them apart.

Discrete data keeps its points apart, and continuous data joins them into a line.

Curriculum

Where this fits

British Columbia, Grade 9

Mathematics, Patterns and algebra: two-variable linear relations, using graphing, interpolation, and extrapolationBC9-MA-15

Previous: Dividing a Polynomial by a MonomialNext: Graphing y = ½x + 2 and Reading Between the Points

The outcomes and strands follow the British Columbia curriculum.

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