Multiplying fractions | Classroom activity

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So you’re about to teach, multiplying, fractions and you’re looking for an activity which is engaging and conceptually make sense. Well, this activity is for you hi, my name’s Tom Moore, and if you haven’t yet watched the video on partitioning the hole using your eye well then I recommend you go back and watch that now, because we’re going to be using that skill a number of times Through today’s activity now, you’ve been given the challenge of teaching students how to multiply fractions, wouldn’t it be cool if we ran an activity where students were able to discover this for themselves and truly understand what it is it’s happening when we do multiply fractions well, we’re Going to go through exactly this in this activity, let’s check it out by starting off with two fifths, multiplied by three quarters. So, first of all, we need to know what three quarters looks like and we’re going to use the same strategy as what we did in the previous video. That is we’re going to break our piece of paper into half and then half again to represent the quarters, and I’m actually going to color in three of these quarters to really make it clear to students. What actually is three quarters, so you can see that there now. I need to find two fifths of those three quarters and if you remember back to the previous video to find first, we go half half again and a little bit less. So therefore, it’s going to be roughly here and then I simply break up what’s remaining into the quarters, so I’m going to go half of that and then break that into halves as well. Now we know that two fifths of the whole page – well, one-fifth – would be this row here, but two fifths would be these two rows, but I don’t want the whole page. I want just the three quarters, so you can see here the two fifths of the three quarters he’s actually this section here. So, therefore, we can see that two fifths of three quarters is actually equal to six twentieths, because I’ve got six pieces of 20 equal parts on the whole page. Now, if I think about that as well, I could move these two pieces down to here to really show that is actually three tenths and I’ll show you what I mean. Let’S move these ones down. Yes, I’ll do a little cross say like that and we’ll move them down to here, like you can see now, if I actually show this in another way, I’ve got one two three out of there would be ten of the exact same shaped piece. So therefore, I’ve got 3/10 o 620 s is equal to 3/10 and it’s worth getting students to go through and do a number of these and use the model when doing so once they’ve done that get them to come back and have a look at their final Answers that is, you can have them. Look at the 2/5 of 3/4 equals 6 20s, for example, and ask them the question: can they see a way where they could simply look at the numbers and come to an answer without possibly needing to use the model? Now, at this point, hopefully some students when they’ve, got lots of different examples in front of them. They may be able to recognize that, instead of writing off, we can simply write x. That is 2/5 times. 3/4 is equal to 6 xx and that actually makes sense, because there are other examples where we can say x instead of off. For example, 3 groups of 4. That means 3 times 4. Doesn’T it – and it’s the same with this if I’ve got two fifths of a group of 3/4 well, that just means two fifths times 3/4, so there you have it. By doing this, it actually gets students to think about what it is that they’re actually doing using a model, but then come up with a faster strategy by finding patterns. First now, this model actually works for multiplying improper fractions as well. Let’S use this piece of paper as an example, we have one piece of paper here now. If I wanted to multiply one and a half by one and a half well, I simply go there’s one and I’ll fold this here into half that way, so that would be one and a half and then I’m going to multiply it by one and a half As well the other way, so that’s one and a half pieces of paper and I’ve got to fill in this little spot here and to do that, I need to come up with something that is exactly the same height and width. So, of course, to do that, I’m simply going to go here and this here and that fits in rather nicely so one and a half multiplied by one and a half is actually all there’s one, and this is half, and this is half so. Therefore, it’s going to be 1 plus 1/2 plus 1/2 plus 1/4, so 1, plus 1/2, plus 1/2 plus 1/4. Well, that’s actually going to be 2 and 1/4 is equal to it’s one and a half times one and a half, and there you go. The model works for improper fractions as well. So, as you can see, this is a fantastic model which demonstrates the students how to multiply fractions. It’S also a brilliant opportunity for them to go through and explore mathematics and seek patterns so that they can come up with their own way of how to multiply fractions without you needing to tell them now. This can be quite intrinsically rewarding, because when students can come up with this for themselves, it gives them some sense of pride and ownership over what they’ve been able to do rather than you simply tell them, and then this coupled with extrinsic comments such as congratulations. That’S not an easy skill to be able to do, and you figure it out all on your own really emphasizes the student. What they’ve been out to do throughout the lesson now remember there is a free lesson plan with this video just check out the description. Also, don’t forget to like comment and subscribe. My name is Tom Moore, we’ll see you next time. You

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