## Thursday, 12 November 2015

### Visual & Numerical Add/Subtract Fractions Strategies

Being able to visualise what we are doing when manipulating fractions is key to student understanding.

So today, we looked at visual and numerical strategies we can use when adding or subtracting fractions.  (Having a class with some students who are showing advanced understandings and others with beginning understandings, I was hoping this would cater to all those different levels and needs for moving forward)

We began with this question:   1/2 + 2/3

Students thought of different strategies they could use to work it out.  It was interesting to see which students chose visual and those that chose numerical strategies. Having them think of more than one strategy helped deepen their thinking. Some challenged themselves by trying to visualise the fractions on a number line.

Students were invited to share strategies they had come up with and we discussed these as a class.  We discussed how visualising fractions is important to understand what we are really doing when we add or subtract fractions.

Shared strategies:

After this sharing, we repeated for this subtraction question:

1 1/4 - 1/2

This time the children were encouraged to try to use both visual and numerical strategies.  It was interesting to notice those with more advanced understandings actually struggling a bit when visually representing the subtraction.  It challenged their thinking quite a lot and it reminded me that even when a student shows they know HOW to solve a maths problem, it doesn't necessarily mean they understand the WHY behind it.

We then shared and discussed some really fascinating strategies we came up with for the subtraction question both visually and numerically.

We then looked at some addition/subtraction word problems of various levels.  Partners chose a question they felt was at their level and then they both visualised the sum and shared what they had created.  They really enjoyed seeing how their partner saw fractions happening in their mind compared to themselves.

Samples: