Unlocking Place Value Power

Andrew Pasterfield

Hi everyone it’s Mr. Pasterfield here, and welcome to Mastering Maths, a weekly podcast for Year Six children at eastbrook School in Dagenham. . Each week I will explain the key concepts I will cover in the maths lessons the following week. The podcast will be released each weekend. So let’s get on with the first show.I’ve been teaching maths for a long time, and I love the moment when the place value light bulb appears in my class - that magical moment when someone suddenly sees the beautiful simplicity behind our \base 10 number system. Well, today we’re diving right into something that unlocks the world of big numbers: place value. Sounds fancy, right? But really, it’s the idea that every digit in a number has its own special spot—its own power, if you like. If you look at numbers up to 10,000,000—and yes, you actually can do this in Year Six!—you’ll notice every single digit carries a different weight depending on where it sits. So you’ve got millions, hundred-thousands, ten-thousands, all the way down to hundreds, tens, and ones. Imagine it like a set of boxes, and each box only fits a certain type of thing. Ones can only go in the ‘ones’ box, tens in the ‘tens,’ you get the idea.

Andrew Pasterfield

One of my favourite tricks—and, yes, you might’ve seen me do this if you’ve been in my class—is what I call ‘exchanging’ with your fingers. This is where you physically model the idea that, for example, if you’ve got ten ones, you can swap them for a single ten. You just lock all ten of your fingers together, and as you say ‘I’m exchanging,’ you’re showing that swap. Or if you’re swapping one ten for ten ones, you unlock your fingers and fan them out. I know, it sounds almost too simple, but honestly, I’ve watched Year 6 students at Eastbrook pick this up so naturally—sometimes I’d see them at break time doing finger exchanges with each other, almost like it was some secret handshake! And let’s be real, once you’ve seen how numbers work this way, you start spotting these patterns everywhere, from the buttons on your calculator to the way you count money.

Andrew Pasterfield

I remember this one lesson where I had everyone make a giant place value chart out of paper tiles—those big tiles for millions, down to the ones. We’d call out a huge number, say six million, two hundred thirty-four thousand, one hundred and five. You’d see hands shoot up as kids raced to stick the digits in exactly the right spots. Not gonna lie, the energy gets a bit wild. But that’s when maths starts to feel truly alive. And, you know, even the students who say at the start, ‘I’m rubbish at big numbers,’ are suddenly building numbers bigger than the school register, just by following the place value. It's about making sense of the code, not just memorising it.

Andrew Pasterfield

Okay, now let’s step it up a gear. If place value is the code, then the place value chart is basically your decoder ring. Each column—whether it’s for millions, or tens, or ones—keeps your digits organised, and makes sure you never get sixes and sevens muddled up. It’s a lifesaver when you start working with those really big numbers, believe me. Now, there’s something called the Gattegno chart that’s a bit of a game-changer. You might not have seen one yet, but it’s a chart that helps you actually see, with your eyes, how numbers play out as you multiply or divide by powers of ten.

Andrew Pasterfield

The really neat thing about the Gattegno chart is watching what happens when you multiply or divide by ten—a digit moves left and boom, suddenly it’s ten times bigger. Or, you move it right and it’s ten times smaller. So if you multiply 23 by 10, every digit moves left one spot on the place value chart, just like a dance along the columns. The Gattegno chart just makes it super visual. It even helps you justify what’s really going on when a number ‘shifts’—something that’s really important as you practice multiplying or dividing by 100, 1,000, or bigger powers of ten like 10,000. Instead of just saying, ‘move the decimal,’ you can see and explain, ‘ah, shifting left by three columns is multiplying by a thousand.’

Andrew Pasterfield

In my lessons, I sometimes challenge students with a matching game—here’s a number written out, now put each digit on the place value chart. Or try the same thing but with the Gattegno chart: which box are those digits living in now? And there’s always that lightbulb moment for someone—the penny drops, and they realise why numbers grow or shrink depending on their place. It’s just digits dancing along their columns, no magic involved, though it definitely feels a bit magical when you suddenly understand it.

Andrew Pasterfield

So there we are—a bit of chart magic that’s honestly at the heart of every big maths move you’ll make in Year Six. The more you practise placing digits and shifting them around, the more natural it gets. And who knows, maybe soon you’ll find yourself teaching someone else how to exchange with their fingers or how to shift numbers like a pro. Anyway, I hope that’s helped clear things up about place value and the mysterious powers of the chart. Keep practising, keep asking why, and I’ll see you for the next episode, where we’ll go even deeper. But for now, thanks for listening—and keep unlocking those maths secrets!