Secondary Maths KS3

The lesson we are deconstructing is a KS3 Maths lesson called Mayan Numbers

Mayan Numbers

Maths

For each of these questions, refer to the diagram below to help you. First, the number 6 00 000 in the Indian number system is called...

The number 6 00 000 in the standard short-scale system is called...

The standard short scale number Four million, five hundred thousand is written in the Indian system as...

The Indian number seventeen crore, twenty two lakh, four thousand is written in the standard short scale system as...

Numbers and Numerals Lesson 3:

﻿Hello, everyone. This is Mr. Miller here. In this lesson, we're going to be looking at the Mayan number system. So first of all, I hope that you're all doing well and that you're ready for the final lesson in this short series. And before we get into the maths, I'm just going to explain a little bit briefly about this, where this Mayan number system came from. So the Mayan people were a civilization in Central America, in countries we know today as Mexico and Guatemala and other countries. And they were around for a very long time, starting off at least 4,000 years ago, and the lost Mayan city was kind of destroyed in 1697 when the Spanish came over and colonised much of the Americans. And they're a very interesting culture. You might recognise some of the old Mayan ruins, the old Mayan cities, which are still some of them around today, but they also made a lot of important contributions across culture as well. So in politics and maths as well. And one of the contributions in maths was the number system that they came up with, which is what we're going to have a look at today. So without further ado, let's have a look at the try-this task. And for this task, we are grouping numbers in groups of 20. So at the example at the top, we are looking at the number 54, and we can see that there are 2 groups of 20, and then another 14. So we've got a 20 in this first group, a 20 in that group and then a 14 leftover. So 2 groups of 20 and 14. So 3 numbers for you to have a think about. 24, 106 and 241. How many groups of 20 are there in each of these numbers, and then what are you left over with at the end? Pause the video two or three minutes, have a go at these three questions. Great. Let's go through this. Hopefully, you at least got the first one. So 24, of course, is 1 group with 20 and 4 leftover. The next one, 106. Well, that is 5 groups of 20. Because 20 times by 5 is 100, and then you need to make 106. So you've got 6 leftover. Next one, at 241. Well, that is actually going to be 12 groups of 20. That gives you 240. So 12 groups of 20 and 1 left over. And this is important because the Mayan number system looked at groups of 20. So now let's have a look, and see how they did this. So here's how the Mayan people did their number system. So the first row here, we've got the numbers 1 to 5. So you can see that 1 is written as 1 dot, 2 as 2 dots, 3 is 3 dots, 4 is 4 dots, but when we got to 5, you can see that they didn't do 5 dots. They just did a single line. And then 6, they did a line and then a dot above that because that's 5 plus 1. So how do you think they did the numbers 7 through 10? Well, if this is what you were thinking, then really well done. 7 is the line, which is 5 and 2 dots. Similar thing with 8 and then 9. And then when they got to 10, they did 2 lines because that is 2 lots of 5. Pause the video, 60 seconds. How do you think they did the numbers 11 through to 15? Okay, well, 11 is going to be 2 lines and the dot, because it's 2 lots of 5 plus 1, and so on, and then when you get to 15, you, of course, get 3 lines. Now, a very similar thing for 16 to 19, like that, but they're slightly different when you get to 20. Because when you get to 20, you stop doing all these lines and dots. We have something different. So this is what 20 is. Now, let's explain, what do you think is going on here? Okay. Well. You can see that we have started a new row above here. So this new row here with 1 dot in it represents 1 lot of 20. And then this thing, which looks a bit like a shell, is essentially a placeholder. So it doesn't actually mean anything. So 20 is represented by 1 lot of 20, and that 1 dot is in the next row above. Okay. Let's have a look at 21 to 25. So there you can see in each case, on the top row, we have got 1 dot. So 20, I'm sorry, 21 would be 1 lot of 20 and 1 lot of 1. Together, we have got 21. Okay. What do you think the number 25 would be represented as? Well, if you're thinking you were going to have a 1 dot at the top, which is 1 lot of 20, and then 5, and we're going to write 5 as a single line below just as we did before. This would be 25. We've got 1 lot of 20, 1 lot of 5. Together, that would be 25. So this is how the Mayan number system works. Let's have a look at the next slide where we're going to look at some larger numbers. Okay, so here we have got five Maya numbers that we are going to convert into base 10. Base 10 being our number system. Let's do the first one together, and then you can have a go at the rest. So I first of all, need to have a look at the top row here. And remember that the top row represents lots of 20. So I've got 2 lots of 20 in the top row, and I've got 2 lots of 1 in the second row. So 2 lots of 20 is going to be a 40. And then 2 lots of 1 is just 2. So this number is 42. Okay. Now it's your turn. See if you can have a go at these remaining four, and then we'll go over them together. Okay, great. Let's go over them. So the next one, I've got 3 in the top. That's going to be 3 lots of 20, which is 60. And then in the bottom, we've got a single line, which means 5, and then 4 dots, so that is 4. Altogether, in the bottom row, we have got 9. So 60 plus 9 is 69. The next one, well, I got a single line at the top, which is 5, so that is 5 lots of 20, and then a place holder at the bottom. So that's nothing there. 5 times 20 is 100. Next one. Well, I've got a 4 lots of 20 at the top, which is 80, and then 2 lines at the bottom. So 2 lots of 5 to give me 10. Add them together, that's 90. Last one is the trickiest one. So well done if you got this one. On the top row, we have got 1 line, which is 5, and 4 dots. So I've got 9 lots of 20. And in the bottom row, I've got 2 lots of 5. And then 3 1s. 2 lots of 5 is 10, and the 3 1s is 13. So I got 180 plus 13. That is 193. So really well done if you got some of these going from the Mayan number to the base 10. Okay, for the final slide, the explore slide, we are going to go from base 10 numbers to Mayan numbers. So let's have a look and see how we do it. Okay. So four numbers, five numbers, sorry to do here. And let's do they first one together, and the key in this one here is to think how many groups of 20 do we have here? So 55, let's think about the first one. How many groups of 20 go into 55? Well, if you're thinking we're going to have 2 groups of 20, that's going to be 40, and then I have 15 leftover. That is how we should think about it. So let's have a think about how we would write this in the Mayan number system. So at the top I need 2 groups of 20. So I need to represent 2 here. And I represent 2 with 2 dots like that. So that's 2 lots of 20, and now I need to represent 15 here. And 15, I know that I can do that as 3 lots of 5. So that is going to be 1, 2, 3 lines like that. So that is 55. And then you have got four more to do. They get a little bit challenging. So best of luck. Pause the video and see if you can do the remaining four questions. Okay, great. So well done, having a go at it. On the next slide, I'm going to show you all of the answers. Okay, so here are the other answers, and really, really well done if you got these. We can just go through one or two of them very, very quickly. So 62, we represented that as 3 lots of 20 plus 2. Should have been pretty straightforward. 147, we did 7 lots of 20 plus 7. And so we needed to represent a 7 at the top and a 7 at the bottom. We do that with 1 5 and 2 1s. Also really interesting to note about 399, because that is actually the largest possible number that we can represent using just the 2 rows. How do you think we would represent the number 400? What do you think we would do? Well, in this case, we would need an additional row. So we would need three rows here. The top row is going to be a lot of 400. So that is going to be 1 lot of 400. And then we would need shells in the low 2 rows as place values. So that would be the number 400. And as you can see using this system, we can get some quite large numbers pretty quickly. So that is why this number system is very, very useful. You know, you can imagine if you're running this big civilization, you're going to need some pretty big numbers to help you out. So anyway, that is actually it for today's lesson. If you're interested in this, there's lots of different articles online that you can look at this in more detail. So yeah, that is it for today. Hope you've enjoyed it and hope you've enjoyed this mini series of four lessons. Really good to dealing with you. So thanks so much for watching and how they wonderful day. Bye bye.

Let finish off with a quiz to see what we can remember about Mayan numbers!!  Good luck!

What number does this Mayan number represent?

Which of these pictures represents the number 17?

Which of these pictures represents the number 114?

Mayan Numbers Quiz

In this lesson, we will discover the differences between our Base 10 number system, and the Mayan number system.

ITT: Mayan Numbers

Secondary Maths KS3

1. Original Oak Lesson