Skip to 0 minutes and 7 seconds PAULA KELLY: OK, so let’s come back to our idea of equivalent fractions. Again, we’ve got our chocolate bar. I’m going to have 2/5. So this section is the bit we’re going to eat, same as we had before. OK, now, I have another diagram here. What do you need to know about this diagram to compare to this one?

Skip to 0 minutes and 26 seconds MICHAEL ANDERSON: Well, they’re the same size, so they’ve both got the same height and the same width. But in this one, we split it into more smaller sections. And I think just from looking at it, just like the last time, we’ve taken each individual fifth and we’ve halved them again. So when we half that, we’ll have two here, two here, two here, two here, two here, two here. So 5 lots of 2, so there seems to be in tenths.

Skip to 0 minutes and 50 seconds PAULA KELLY: Perfect, yeah. OK, so we can write this, if we have our fraction, as tenths. And as we said earlier, we’ve doubled. So each one of these has been cut in half, so we’ve doubled.

Skip to 1 minute and 2 seconds MICHAEL ANDERSON: We’ve doubled the number of slices.

Skip to 1 minute and 5 seconds PAULA KELLY: Same again– the ones I’m going to actually eat, and have twice as many slices.

Skip to 1 minute and 9 seconds MICHAEL ANDERSON: Ah, because we had two parts, and they’ve been split into two each. So we’re going to now have four parts.

Skip to 1 minute and 15 seconds PAULA KELLY: Absolutely. OK, so if I shade in the same amount that we’ve eaten, again, it should be the same area. So if we come across– although we have our equivalent fraction of 4/10, it looks– or you may think you’re having more. We can see from my diagram it’s just the same.

Skip to 1 minute and 34 seconds MICHAEL ANDERSON: So in the previous examples, the numerators and the denominators– they went up by different amounts, but they went up by the same amounts each time.

Skip to 1 minute and 42 seconds PAULA KELLY: Yeah, there’s a pattern.

Skip to 1 minute and 43 seconds MICHAEL ANDERSON: So is there a better way, or a different way of creating equivalent fractions?

Skip to 1 minute and 48 seconds PAULA KELLY: So far we’ve had our chain, which helps us to see all of the equivalent fractions in order. We could continue our pattern of doubling, similar to here when we have our 10 equal slices. Here, each slice has been halved again.

Skip to 2 minutes and 4 seconds MICHAEL ANDERSON: Right, I see, yeah.

Skip to 2 minutes and 6 seconds PAULA KELLY: So this time we have 20 equal slices.

Skip to 2 minutes and 8 seconds MICHAEL ANDERSON: Oh, so I can put 20 in here, because we’ve taken the 10 pieces here and split them in half again, and we’re halving and halving and halving each time. And that gives us 20 pieces here. So with the four slices that we have highlighted, we’re going to half each of those. So that should give us 8.

Skip to 2 minutes and 25 seconds PAULA KELLY: OK, let’s see what happens. So again, we keep our area exactly the same. We haven’t changed how much we’ve had.

Skip to 2 minutes and 36 seconds There should be 8. Do some counting.

Skip to 2 minutes and 38 seconds MICHAEL ANDERSON: OK– 1, 2, 3, 4, 5, 6, 7, 8. So that pattern seems to hold.

Skip to 2 minutes and 44 seconds PAULA KELLY: Fantastic, OK. So again, [INAUDIBLE] between the 2 and the 4. We doubled. Between the 4 and the 8–

Skip to 2 minutes and 50 seconds MICHAEL ANDERSON: Doubled again.

Skip to 2 minutes and 51 seconds PAULA KELLY: Absolutely.

Skip to 2 minutes and 52 seconds MICHAEL ANDERSON: Oh, so I can put in a multiplied by 2 here.

Skip to 2 minutes and 55 seconds PAULA KELLY: And then because they’re equivalent fractions, whatever we do to our numerator, do the same thing to our denominator.

Skip to 3 minutes and 2 seconds MICHAEL ANDERSON: So I’m going to multiply this by 2 as well.

Skip to 3 minutes and 5 seconds PAULA KELLY: And we know that will work, because if we double 10, we get 20. If we double 4, we get 8.

Skip to 3 minutes and 10 seconds MICHAEL ANDERSON: OK. So in this last diagram, we’re repeating this process again. So I suppose I can make a prediction with this one. If we were halving each of these individual slices again, instead of 20, well, I can multiply that by 2 to get 40. So I don’t need to count them. And I think, again, with our equivalent fractions, multiply this by 2. I think we’re going to end up, when we shade the same amount in, as having a fraction, which is equal to 16 over 40.

Skip to 3 minutes and 39 seconds PAULA KELLY: OK. So for this one, again, if you try and keep it the same, [INAUDIBLE] this could be interesting. If we go across, let’s try there. Am I in the right place, there, do you think?

Skip to 3 minutes and 49 seconds MICHAEL ANDERSON: Well, let’s see. So I think there’ll be 16. So 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.

Skip to 3 minutes and 58 seconds PAULA KELLY: Not bad, not bad. OK, now we could, if we’re being very clever– as we see here, we’ve doubled and doubled again. I’ve also noticed if we multiply by 4–

Skip to 4 minutes and 11 seconds MICHAEL ANDERSON: Ah, so we can skip this middle step out and go straight from 2 over 5 to 8 over 20 by doubling and then doubling again, which is the same as multiplying by 4.

Skip to 4 minutes and 21 seconds PAULA KELLY: Perfect.

Skip to 4 minutes and 22 seconds MICHAEL ANDERSON: OK, so we’ve halved each of our blocks this time, and that’s produced this chain where we’ve been doubling both the numerators and the denominators. Did we have to halve? Can we may be cut them into thirds or fourths– quarters– or fifths or tenths?

Skip to 4 minutes and 38 seconds PAULA KELLY: Yes, any of those would work. So we could either halve each one, and we double. We could put each one to five and multiply by 5. As long as we keep those two things the same proportion, we’d have equivalent fractions.

Skip to 4 minutes and 51 seconds MICHAEL ANDERSON: So this is another way of creating a string of equivalent fractions.

Skip to 4 minutes and 55 seconds PAULA KELLY: Absolutely.

# Equivalent fractions: proportional reasoning

We continue to explore how to create strings of equivalent fractions.

In this video we consider a method to create equivalent fractions without the need to write down a string containing consecutive equivalent fractions.

The method considers what happens when the numerator and denominator are multiplied by the same amount each time.

## Practice: poster challenge

This task uses Padlet. Padlet is a virtual pin-board and allows you to share text, images and other files. You do not need a Padlet account to post. We recommend you post images or upload PDF files (if you create your recognition board in another format, Save As… PDF to upload). Guidance on using Padlet.

You’ll create a simple poster which you’ll upload to the Poster Challenge Padlet.

- Either by hand or using a program of your choice, create a quick poster showing at least 5 equivalent fractions and how you’ve reached each equivalent fraction (using one of the two methods we’ve shown you in this step and the previous step).
- Pick any fraction you like as your starting point, for example \(\frac{2}{3}\), \(\frac{5}{7}\), \(\frac{3}{13}\), \(\frac{5}{15}\), or \(\frac{11}{20}\).
- Upload images (from your mobile phone) or a PDF of a Word doc to the Poster Challenge Padlet.

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