Task: sort the statements according to whether they are always, sometimes or never true.
This was the first time for this routine with my class (I included an example for each statement to help my EAL students with the language). Here is how we tackled it:
1. We started with a quick sorting activity with groups creating 3 piles of statements
2. I took one example from a group and asked the students to explain why they had placed it in that pile. At this point it became clear that we needed to breakdown what it means to prove if something is true or not. We discussed:
- examples and counterexamples
- how many examples you need to prove something is true
- convince yourself – convince others
- justifying reasoning
- using precise language
- ways of showing eg numbers, symbols, words, pictures, manipulatives
3. We created a shared proof on the board
4. Groups then were given materials to record their proofs for each statement
5. We paused periodically to share ideas, give feedback, go on gallery walks etc
There were some great questions raised and subsequent discussions:
- when you add numbers you get a bigger answer – Does zero count as a number?
- adding two 2-digit numbers results in a 3-digit number – What’s the difference between a digit and number?What about with decimals – is 6.3 a 2-digit number?
- when you subtract numbers you get a smaller answer – How do you subtract a negative number? (lots of number line work here to get our heads round subtracting negative numbers for those who were ready)
- How can we change the words so an always statement becomes a never statement?