This content was created by Rob Langman. This content was uploaded by Rob Langman. This is a YouTube video titled "Greater Depth in Fractions" (created 2024-04-04) — an instructional classroom resource presented by Zoe. The presenter explains activities to assess and extend pupils' understanding of fractions, including comparing 6/7 and 7/9 using fraction walls and lowest common multiples, and exploring multiplication by 1/2 (and generalizing to other unit fractions like 1/5) with pictorial and concrete representations. The content is aimed at primary teachers and Year 6 pupils working at greater depth, focusing on mastery, terminology (numerator/denominator), and extension tasks.
Chapters
Hi, I'm Zoe and in this video we're going to be looking at some activities that address greater depth with fractions. They're going to help us to assess the understanding and knowledge of pupils around fractions. Here's our first problem. Which is bigger, six, seven or seven, nine? Now, our pupils might look and say, well, seven, nine, both of those numbers are the same or larger than the numbers in our first fraction. That is a usual misconception. And so they'll say, no, 79 is bigger. What helps for pupils who may not be working at greater depth level is having our fraction walls back up there. So, 6, 7, what can we see? 1, 2, 3, 4, 5, 6, 6, 7 would take us to there 7/9. 1, 2, 3, 4,. 5, 6, 7. We can see the disparity. 6/7 is clearly bigger than 7/9. Now, for our pupils working at greater depth, we might ask them, is there another way that they can prove that these fractions that 6/7 is bigger? We're hoping here that they think of lowest common multiple and they look at the denominators and say I our lowest Common multiple of 7 and 9 is 63. So we can turn both of these fractions into 60 thirds. We can multiply our first fraction by 9, where 96 makes 54. We can multiply our second fraction by 7. Seven sevens gives our numerator 49. Again, getting them used to using the terms numerator and denominator is really crucial for this. So we can see our denominators are now the same. We can see clearly 54, 63 is greater than 49, 63. So 6/7 is indeed the bigger fraction. Getting them to use, though the pictorial as well as these more abstract ideas is really good practice. Moving on to our second problem. Now, this one is best suited for year six. Multiplying any number by a half will. Will give the same answer as dividing by two. Is this correct? This gives them lots of scope for practice, for trying things out. Pictorial representations and concrete representations are really good for this. So let's say we've got four, we're going to multiply four halves. So we've got four halves here. And what we can see clearly, two halves make a whole. So four lots of a half is two and four divided by two is indeed two. So we can see that we might be on the right lines. Again, using these halves we've got up here, we've got 12 halves. Connecting those together, we can see that we've got six wholes. So 12 lots of a half is indeed the same as 12 divided by two. Hopefully enough practice and they'll be able to get lots of examples of this moving them on. For those pupils really working at greater depth, we can extend this. So we're now just multiplying by a half. We're going to multiply by a fifth. Is this the same as dividing by 5? Again, pictorial representations would be really useful for this. Does this then work for any fraction? So, again, we're taking that generalization another step further. Can they write a rule that describes what they found? This is real mastery. So there we have it. Two activities that will help you assess fractions.
