Greater Depth In Number And Place Value

Hi, I'm Zoe and in this video we're going to consider working at greater depth with number and place value. We're going to look at three example activities you could use with pupils and consider what we'd expect to see from pupils working at that level. This problem here is our first one and it's considered suitable for lower key stage two. We've got 2600s is less than 250 tens. True or false? Prove it. Now, using this activity, we're going to explore their place value. They could use a place value chart. They could of course use their base 10 blocks as well to support that learning those concrete representations for pupils who aren't quite at working at greater depth yet, we're going to use our place value chart to explore this. So 2600s, here's our hundreds column. We need 26 of them. Hopefully the pupils realize that 2600s is again the same as 2,600. And what are we missing? We're missing our placeholders in our tens and our ones column. So Our first number, 2600s is 2,600. Doing the same. 250 tens. Here's our tens column. We need 250 of them. Hopefully pupils using their place value. Look, 250 tens. What's missing? We need a place value holder. Here's our placeholder in our ones. We've got the number 2500. Going back to our question to see if they have got the answer is 2000-600- hundreds less than 250 tens. Looking at our place value board here? No. So this is false. We can use our place value to secure that. If pupils are struggling with this and they need a bit of support and again, we know that that is hundreds. How many hundreds make a thousand. There are 10 of them. We've got 20, so that's 2000 and then we've got 6 hundreds on top of that. Hopefully that will support those not quite working at greater depth and encourage that mastery in mathematics. Moving on to our second problem. This is designed for upper Key Stage 2, using these digits, what two numbers would give the greatest difference? What two numbers would give the smallest difference? One of your numbers must be negative and one must be positive. We can see this is now upper Key Stage 2. Really sound knowledge of place value and understanding of number sense needed here. So we've got our three number cards. If they need a bit of support, again, a number line would be really useful. And again reminding them that zero in the centre would help. They have to use our maths words difference to understand that that is how far is between them? 426. We're trying to make the greatest difference. Hopefully they realize they need to make the biggest number. So 642. They have to make the smallest number at that end. It's a negative number. Okay. So we're going to have to have exactly the same digits but with a minus sign. Hopefully pupils can get there themselves, but with a bit of support, maybe having these on cards and moving them around, that would help. So we've got our two biggest numbers and we can find the difference between them. When they come on to look at the smallest difference, hopefully what we can see is that they have to do minus 246 and 246 at this end. Again, a discussion around what happened to the digits. Oh, we've gone from biggest to smallest. Now we've gone from smallest to biggest. Does this always work? A bit of exploration for them. Again, giving them different number cards to practice. This would really help. Moving on to our last problem. Again, this is about number sense, but also about rounding. So them understanding the rules around rounding and how this can help solve this. Freddie's thinking of a number. He says that his number rounded to the nearest 10,000 is 50,000. Abdul is also thinking of a number. He says his number rounded to the nearest thousand is 48,000. Abdul says that Freddie's number must be greater than his. Is he right? Now, here, what we're wanting, we're wanting them to prove this, but it's proof by counterexample. So if they can find something that doesn't fit this, then actually they've proved by counterexample this isn't true. So they're looking at our limits. Nearest 10,000, 50,000. We're looking for the smallest number they can make. The smallest number that Freddy could have had was 45,000. Again, maybe a little reminder at the beginning that when it's four or below, we round down and when it's five or above, we round up, that would help. Abdul says his 90 to the nearest thousand is 48,000. So the smallest number he could have had was 47,500. Again, here, we've now proven by counterexample that he is not right. Freddy's smallest number could be 45,000. Abdul's smallest number could be 47,500. So actually, Abdul's number might be greater than Freddy's. You could then deepen their thinking by asking what. What examples could we give where Freddie's number is bigger? What conditions would that have to fit under and again, pupils could then come up with their own problems where they have to think about this, develop it and then share it with their friends. And that is working at greater depth with number and place value.