A short instructional video (presented by Zoe) showing two greater-depth Year 6 mathematics problems on length, mass and volume. Problem 1: find integer cuboid dimensions whose product is 42 cm³ (examples: 2×3×7 and 1×6×7) and discuss how permuting or scaling factors yields different orientations. Problem 2: a bar-model weight problem where Farhad is 12 kg less than Zaheer, Daniel is 0.6 kg more than Zaheer, and their total is 118.2 kg; the video demonstrates solving via bar modelling to find individual weights (Farhad 31.2 kg, Zaheer 43.2 kg, Daniel 43.8 kg). Emphasises concrete resources, number sense and bar-model reasoning for deeper assessment.
Questions this video answers
42 cm³
2 cm × 3 cm × 7 cm
1 cm × 6 cm × 7 cm
Farhad is 12 kg less than Zaheer; Daniel is 0.6 kg more than Zaheer.
118.2 kg
Chapters
Hi, I'm Zoe and in this video we're going to be looking at examples of greater depth problems that can be used to assess pupils understanding of length, mass and volume. This can be quite a complex area for pupils to visualize, so having those concrete resources to hand will be really useful. Here's our first problem. The volume of a cuboid is 42cm cubed. What could the dimensions be? We're hoping they remember the volume of a cuboid is length times width times height. So what they're actually trying to find is three numbers that multiply to make 42. Hopefully with 42 being an even number, they spot that it can be divided by two. So the first thing they can do is do 42 divided by two, which gets them 21. So the first dimension they've got of our cuboid is 2cm. They now need to find two numbers to make 21. Hopefully their knowledge of times tables is superb and they'll know it's three and seven. So two times three times seven is one possibility for our cuboid. When they make this cuboid, it's really key that they understand that when they move these numbers around, they'll have the same cuboid just in a different orientation. It will still be 2 by 3 by 7. That can be a sticking point for some of our pupils. Again, hopefully their fluency and their number sense, they know that if they double one of these numbers, they can half one of the other numbers, so they get a different cuboid. So if they doubled three, for example, to make it six, they could half two to make one. So a cuboid one times six times seven will also have a volume of 42cm cubed. It will be a different cuboid and there we're exploring with greater depth what that could be. So that's our first problem. Let's have a look at another problem to do with weights, measures. And again, this is a really complex problem, one you'd want year six to look at. Again, we're going to use our bar model. I'm not going to go into how this works. There are plenty of our videos on bar modelling, if you want to have a look at that. But Farhad weighs 12 kg less than Zaheer. Daniel weighs 0.6 kg more than Zaheer. Their combined weight is 118.2 kg. What does each person weigh? Again, we're drawing bars to help us here. So we've got Farhad in first. If he's 12kg less than Zaheer, we. We can see that here. This must be 12 kg. He's 12 kg more than Farhad. Just changing that round we've then got Daniel, he weighs 0.6 kilograms more than Zaheer. So this little bit of our bar here, that is 0.6kg. So hopefully pupils can now see we can have three bars exactly the same but we've got 12, 12, 0.6 together. So that's 24.6kg is the first thing that we need to take away. Upon doing that we have 93.6kg left that we can now share between these three bars. So each bar will be 31.2. We can then add this in. Sulphar had is now 31.2kg. So here is our 31.2 plus our 12 which is 43.2kg. And Daniel is our 31.2 plus the 12 plus the 0.6 so he will be 43.8kg. So using our bar model in a way with a problem that relates to mass really gets pupils thinking in a very complex situation. And there we have it. Two problems you can use to assess pupils understanding of length, mass and volume.
