A short instructional video by Felicity (uploaded by Rob Langman) introducing improper fractions. The presenter defines improper vs. proper fractions, demonstrates conversion of mixed numbers to improper fractions using pictorial models (e.g., 3 3/4 = 15/4) and shows how to represent improper fractions like 7/5 with bar models, and suggests classroom strategies to build conceptual understanding.
Chapters
Hi, I'm Felicity, and in this video we're going to be looking at ways in which we can build a conceptual understanding of improper fractions. Now, in our previous video, we've established that an improper fraction is a fraction that has a larger numerator than its denominator. Let's look at a couple of examples. So, first of all, we've got our proper fractions in which the numerator is smaller than the denominator. So we have 1 over 5, or 1/5, or 2 over 3 or 2/3. But an improper fraction, as I've said, is when the numerator is larger than the denominator. So here we've got five over two or five halves, or ten over six is another example. Or ten, six. So let's look at how we can represent these improper fractions pictorially. So here I've got three and three quarter cakes. Now, the denominator is four, so I need to divide each whole into four equal parts, as I've done already. Now, I need to shade in the quarters that we're concerned with. So the three wholes add up to 4, 8, 12 quarters. But then we still need to figure out what this equals when we add the remaining three quarters. And we can see this is 15. So as an improper fraction, three and three quarter cakes would be 15 over four. Once the children are confident using these pictorial representations, we can change the order around and give them an improper fraction to start off with. So, for example, we've got seven over five. We'd need to ask them to represent this pictorially. So let's use a bar model. Now, number five is the denominator. So we divide the bar into five equal parts, as I've done here, and I've shaded in these three fifths. But we've still got two fifths left over to make seven fifths. So what we'd need to do is make another bar, divide into five parts again, but then just shade in the two remaining fifths that we're concerned with. Finally, we can count up these shaded sections and we can see that we've got seven fifths or seven over five as an improper fraction. These are just some ways in which you can help develop a conceptual understanding of improper fractions.
