To celebrate the Queen's 90 decades last week, our school had a 'Decades Challenge'. Each class was given it's own decade to learn about, and we then spent our week learning about different aspects of our given time frame.
In P3, we got the 1970's - how fun! And since we were doing fractions in maths
Since we are P3, my class hadn't had much exposure to fractions (other than halving and quartering) before we started, so my 'learning intention' for this activity was to reinforce the meaning of the numerator and denominator. So we looked at how we 'name' fractions (this is the role of the denominator) and then how we count how many of that size piece we have (the numerator).
For example, if we cut our banana up into 6 equal pieces, we name those pieces 'sixths'. If we cut our apple up into 4 equal pieces, we name those pieces 'fourths' (or 'quarters', which my kids have been told over and over is just a fancy name for 'fourths'). If our strawberry is cut up into 2 equal pieces, both pieces are called a 'half' (and that is the tricky one, since it means the denominator is two, even though half doesn't sound anything LIKE 'two'!).
Then, once we know what to call each piece (based on how many pieces we cut one whole piece of fruit up into), we can count how many pieces we have - this is our numerator. So if our banana is cut into 6 pieces (sixths), and I take 3 of those pieces, I've taken three sixths of the banana (which is also one half, of course - a connection a few of my kids did manage to make).
We had apples, bananas, strawberries and grapes to cut up. The kids at each table took turns cutting up their fruit. First, we cut up on the banana into 6 equal parts, and everyone got a chance to name the fraction. Each table had 2 bananas - so we 12 sixths. We did look at that fraction, and talked about the fact that the denominator is how many pieces we cut ONE thing up into (and we had 2 bananas, which is why we had more than 6 'sixths'). Some of my kids got this, although it was tricky for others. We also divided our 12 banana pieces out evenly, and that was more straightforward - everyone got three sixths of a banana.
Our apple was quartered and our strawberries and grapes were halved. We did the cutting all together, and then we made sure we could name the fractional pieces we had made (based on how many pieces ONE whole was cut up into). Then we counted how many of those size pieces we had.
Once all the cutting up was done, my lovely PSA and I went around with a bowl of chocolate for everyone to dip their fruit pieces into. The kids might or might not have to have named their fractional piece before being given access to the chocolate!
It was quite a fun maths lesson, and I felt like it reinforced the idea of 'naming the pieces' (denominator) vs. 'counting how many pieces we have' (numerator) quite well.
If kids really understand what the denominator tells you (and that is naming the fraction), it's much easier for them to understand later on why you don't add the denominators together when you are adding fractions.