The wonderful world of the empty number line

Screen Shot 2013-08-11 at 09.36.44

How interesting can an empty number line be? Not very, I assumed. I’d read before about teachers raving about the concept. I’d always thought they were a little funny in the head. I am now officially a convert.

It turns out the empty number line can be used in a whole range of ways. Most simply, it can be a great mental tool for students’ addition and subtraction, by using multiples of 10, counting on etc.

For example, 12+13 becomes:

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25-12 becomes:

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So far so good, but it was what Diana and Marcus did next that was so exciting…using empty number lines to visually represent linear equations. (I’m aware there are many other ways to represent linear equations – this just feels like a particularly powerful one)

For example, taking the equation 3x+8=23:

Screen Shot 2013-08-11 at 09.37.02


Screen Shot 2013-08-11 at 09.37.11

so x=5


You can even use the empty number line to explore relationships between fractions, decimals and percentages:

Screen Shot 2013-08-11 at 09.37.18

What could A be?


Cold Call

Teach Like a Champion Technique 22: Cold Call

In order to make engaged participation the expectation, call on students regardless of whether they have raised their hands.

  • This allows you to better check for understanding, increases pace, and distributes work more broadly and more authoritatively.
  • Make it predictable, systematic (with a chart?), positive (prepare questions in advance!), scaffolded (break questions into simpler and harder for the same student).
  • Using cold-call to follow-up on previous questions, another student’s comment or the student’s own earlier comment is particularly effective.
  • Explain cold call the first time you use it.

Check for understanding

Teach Like a Champion Technique 18: Check for understanding

Gather data constantly and act on them immediately (hard to do but important)

  • Consider answers to questions as data sets, and ask enough times to get a reasonable sample, across known skill levels.
  • Respond to right answers with how and why follow-ups to ensure you spot false positives.
  • Don’t rely on self-report
  • Use monitoring to assess the number and type of errors being made by students.
  • When errors are identified, you can respond in several ways:
    • Reteach using a different approach
    • Identify and reteach the problem step
    • Identify and reteach problem terms
    • Slow the pace and reteach
    • Reteach in a different order
    • Identify and reteach to specific students