Real World Examples For Teaching Fractions on a Number Line

Number lines go wrong in SO many ways. Let us count the ways:

  1. Students struggle to read number lines when labels are missing on the tick marks.
  2. When drawing number lines students do not evenly space the tick marks.
  3. Students count the tick marks instead of the spaces and are often off by one increment.
  4. When a number line is open (without labels or tick marks) it’s difficult for students to imagine a benchmark number.
  5. Not all number lines go up in increments of 1 like most students think.
  6. Number lines are so abstract that students are unsure of what they might represent.

So then for fun…let’s throw FRACTIONS on the number line, that won’t be difficult at all!

All kidding aside, number lines are incredibly important. We use number lines in our lives ALL the time. When we drive, a road is just a gigantic number line. We listen to our GPS and we know about how far 1/4 mile is to our next turn. We use number lines when we measure length, or even as we measure capacity in a liquid measuring cup. I use a mental number line when I’m trying to figure out how much sleep I’ve gotten the night before.  We use number lines in real life without thinking about their mathematical significance, and yet often in many books/math curriculum you will see a number line without any connection to real life with it. No connection whatsoever!

So maybe 4th graders aren’t old enough to drive, but they sure can pretend!  Since they could already identify benchmark fractions on a number line, could they use this idea to learn about equivalence? Could we find two points on the road that could be called two different things?

teaching-fractions-on-a-number-line

So we started our engines, the 4th graders quickly realized that our number lines represented a mile, and that a mile could be marked in different ways. They even talked about how they’ve seen signs for 1/2 mile or 1/4 mile on the highway.

fractions-on-a-number-line1

After working for a bit, they began to see that this mirrored the previous day’s lesson of fraction equivalence with fraction strips.  The connections were forming, and even better they were splitting number lines in two ways without us having to present it that way.  Best of all, they made connections to why 2/8 was the same as 1/4, they were just cut into twice the number of pieces.  This was an awesome link to why equivalent fractions are related to multiplication and division.

Don’t have toy cars to use? Here are some other ways to make number lines real life for kids (all of which can be so precise that fractions are useful when reading the line):

  1. A tiny number line: You are watching an ant crawling on the sidewalk. How far has it gotten?
  2. An eating number line: A snickers bar is being eaten, how much has been eaten if you start at one end and start chomping?
  3. A measurement number line: How tall is the doorway to the classroom?
  4. A time number line: How long can you hang from the playground bars?
  5. A reading number line: How many pages have been read of your book if you stop in the middle of page 39?

When number lines are playful, and connected to real life they are not nearly as scary. Give them a try!

Start driving!

fractions-on-a-number-line

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