Examining a Half

Today we built upon our number sense as a lead into our unit on fractions, decimals and percentages.

As we are often looking at mathematical thinking as creative thinking. We began by using the think-pair-share thinking routine by seeing how many different ways we could represent a half.

When it was time to share our ideas with our partner, we then published some of the ideas we particular liked on our shared recording paper (see below).



I was part of a PD with Martin last week and he shared his thumbs up, sideways and thumbs down strategy to help have children build their number sense in a non-threatening and engaging way.




I thought of how we could use this strategy for fractions and made some slides up to have children think about whether the things shown are greater than, equivalent to or less than a half.

The strategy is pretty simple. When you have an idea, show with you thump what you think. We would then discuss our reasons.  I designed some of them so that there are more than one possible answer based upon the way we perceive it to generate some interesting discussions. 

We looked at the first slide:



Everyone showed a sideways thumb indicating they thought it was equivalent to a half.

So far, so good, but also so easy.





This one took a bit longer to think about:



Get us thinking about decimals.




This one had different thoughts. Most of us saw it as the amount of cake there is and therefore had their thumbs up to indicate it is greater than a half.  A few of us saw it as the amount of cake missing and so had their thumbs down to indicate it is less than a half. 

We thought it interesting how mathematical thinking can involve different perceptions. 






After, we discussed by how much is is greater than a half.














Lots of interesting estimating strategies were shared for this graph:














Looking at real life examples we use halves:






This one also had different points of view.
Most, interestingly, saw this has equivalent to a half. Students explained how they saw it as half a whole franc.
A few saw it has greater than a half because it is simply 50 centime. 50 being greater than a half. 
We appreciated the different ways we could look at it.






This one also generated an interesting discussion. same of us looked at the ones and therefore saw it as greater than a half. Others saw the inner grams measurement and so saw it as equivalent to half (a kg). Others still saw it as 500 grams and therefore greater than a half:







Students were invited to peer teach the class of strategies they used to work this one out:
























A few shared how visualising is a useful strategy with these types of questions:



So many different perspectives - half a year, number of highlighted days, 3 months out of 6 months etc:









A lot of us got tricked by this one. The answer is 12 which is greater than a half:





















We love how it doesn't matter how many zero place values we add to a decimal, so I included this one to end:



With these understandings of how many ways we can look at a half, we then thought about the following with our partners:


We showed with our fingers how many we thought.  Students shared how 75 - 25 equals 25; not a half. But a lot of us were tricked by that which we wondered why now that we can see it that way. Some then shared how 2 1/2 - 1 1/2 equals one whole.

In partners, we then did the following:




Here are some of our ideas. Inside the circle were our ideas of how we can represent a half.

To reflect, we thought about some of the big ideas this learning helped us to understand. Here were our ideas:

° There are many different ways to represent a half.

° Fractions can be converted into decimals and percentages.

° There is more than one answer in maths.

° Maths is about creative thinking.

° Maths is about experimenting (I love this one!)

° Visualising is an important strategy in maths.

° When we challenge our thinking, we can make new discoveries. 

° We can a half as an important comparison of numbers and things. 

I think the thumb strategy was an engaging, enjoyable and informative way to help introduce children to our new unit. It did feel non-threatening and importantly, I think, reinforced the idea that mathematical thinking really is about creative thinking rather than right-wrong answers that traditional 'school maths' can be like. 

Here is a link to the slideshow: Feel free to copy, change and use :)  Slideshow Link