We all know how important it is to show each line of working in a mathematics problem, both for the student in closing the learning/feedback loop, and for the teacher in being able to identify mathematical thinking (both the correct and incorrect types!).

Sometimes though, it's difficult for students to be encouraged to get the yellow ticks in their working out in Mathspace.  So here is one introductory way to promote the fact that yellow ticks are good.

## Play an equivalence game

From the eBook, navigate students to an algebraic subtopic like adding and subtracting algebraic terms, then navigate to the bank of questions for that subtopic.  {or for more junior students go to a number subtopic like adding and subtracting whole numbers}  Choose an appropriate question like 4x + 3x

Now we know that if a student answers the question correctly in this case 7x, they will get a green tick and the question is over. So for this first activity we want to try and enter AS MANY equivalent statements as we can, that is other statements equivalent to 4x + 3x, that is not the final answer.

Here is an example of many types of equivalent statements

• So set a timer on your projector for 1 minute and tell your kids to go for it!
• You can run this activity individually or in a group.
• When the timer goes off have them enter the the final step and get the green tick - but don't leave the page.
• Turn on the pencil tool (top right of your page)

and now we play ...

## Equivalence bingo

• Who has an expression using 3 terms? Give yourself 1 point for each one.
• Who has an expression using a subtraction?  Give yourself 1 point for each subtraction
• Who has an expression using a multiplication?  Give yourself 3 points for each multiplication
• Who has a really unique expression?  (duck around to the students and award 5 points for creative thinking!)

etc..

Each time you call out an example, you can collate ideas on the white board, discuss why they are equivalent and students can give themselves the points you allocate.  You may even choose to highlight commutative statements.

#### WHY?

This activity is great because it shows students the flexibility that they have in working out answers, they can indeed show all their thinking - each line will be marked correct and they never lose points for any correct line.