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:
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:
You can even use the empty number line to explore relationships between fractions, decimals and percentages:
What could A be?
After a frustrating literacy conference today I wanted to reassure myself that it is possible to promote literacy in maths. The ever-reliable Mr. Collins has this. Brilliant.
Teach Like a Champion Technique 49: Normalise error
Respond to the sequence ‘getting it wrong then getting it right’ as if it is completely normal.
- Expect both right and wrong answers to happen and don’t make a big deal of either.
Teach Like a Champion Technique 48: Explain Everything
Constantly remind students why you do what you do and ground explanations in a clear purpose
- Successful explaining occurs before or after poor behaviour, not during.
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.
Teach Like a Champion Technique 20: Exit ticket
Set a single question or short sequence of problems to solve at the end of the lesson, and analyse the results.
- Keep them simple – if students get them wrong you need to know why.
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