Numbers in Our World

The syllabus for year 7 includes work on the history of number, which is a great opportunity to talk about the properties of our number system and also have some cross-curricular fun. This opportunity, however, is usually lost as we try to quickly get through the easy stuff and get to the content we know they will struggle with. This year we decided to do things a bit differently. My way of getting through the content more effectively and interestingly was to link some of the different number skills into lessons about ancient number systems.

We started with Roman Numerals and putting numbers into ascending and descending order. After looking at the numerals (most of them knew them already) and practising converting some numbers back and forth, we put a list of Roman Numerals into ascending order. Then we put Hindu-Arabic numbers (with different numbers of digits) in ascending order. Why was that easier? Not just because we knew the numbers better, but also because you could instantly see that longer numbers were bigger, which was not the case with Roman Numerals. Then we practised with some more ascending and descending order questions. (All this stuff is on a Prezi but it's a bit chaotic and just follows my mental lesson plan)

With two concepts off the list in one lesson, I went all out wasting time on the next one: Egyptian Numerals. This took a long time largely because we made our own fake papyrus out of old yellowed butcher's paper, then painted numbers on them, as well as learning about powers of ten, talking about how long multiplication works, multiplying Egyptian numbers the Egyptian way, and learning about the distributive law. But making the paper was the best bit! "I never expected Maths to be like this". "This is gross, but in a good way."

With Mayan Numerals we talked about adding and subtracting and how to borrow and carry, and did some in Hindu-Arabic and Mayan Numerals, as well as doing some activities from the pbs online cracking the Maya code lesson (although the final step of the birthday worksheet was way too hard).

I don't think I've enjoyed the start of the year this much ever. And I have a beautiful display in my room:

Angry Birds

I stumbled upon nets that make up into Angry Birds and even though I've never played the game, I was pretty excited. There just isn't enough maths that is cute!

The program for my year 10 class included constructing solids from nets, so I figured it may as well be a bit more fun and interesting. Here are the cute little guys above my whiteboards:

 

I also challenged them to take a blank net and draw their own cute animal design on it. They seemed amused by my stance that the world needs more cute maths.

I was wondering whether I was going too far off course with this idea, and as I thought about it I decided it has a lot of merit. To design on the net something that will look correct when folded up requires a kind of visualisation and spacial reasoning, and even choosing what solid shape will best suit your design idea is significant. So that prepares me for a year 7 lesson for later in the year!

Pi Week

Pi day: so good you have to celebrate all week!

This is the first time we've celebrated pi day at my school and it seems to have been a big success. I made a video slideshow of various images from the internet (pies, PhotoShopped pi images, t-shirts etc) with some pi songs (including Mathematical Pi, Lose Yourself in the Digits, Pi by Kate Bush, and Pi Day). We played this to a few classes and asked them to brainstorm ideas. Here are my year 7s ideas:

In the end we had a couple of major events and lots of little things in-class. Classes used Pimon to memorise digits, made posters, and threw a fake plush pie and recorded the results in a table and graph (they were revising for a test on data). My year 7s also were given a homework to do something pi themed. Some solved this old Pi Day Sudoku, one student made a soft toy pi symbol (I made a couple too!), one wrote a rap, some did pictures which are now adorning the classroom wall, including one on canvas!

 The fake pie was thrown 3.14 metres in the playground at recess and lunch to win a prize. This is the pie, which we happened upon in a toy shop!

Two classes made and decorated pies with the help of the TAS faculty and on Friday we had a huge pie sale for charity (raising over $700). Our Statistician (thanks to the CSIRO and their "Mathematicians in Schools") and the manager of a local pie shop were guest judges along with the principal. Here are some pies in the making:

I tried to make pi-shaped cookies, with only mild success. Here they are in varied states of evolution:

Looking forward to even more chaos and fun next year!

Incursion to the Mural

Today year 7 were looking at various groups of special numbers. So I took the opportunity to take them to the corridor outside the Maths staffroom and show them the mural.

They moved in groups around in front of the columns to work out what the pattern or type of numbers was (odd, even, square, triangular, Fibonacci and prime)

 

I also pointed out the factor tree, since we had had a discussion the previous lesson about whether or not they actually looked anything like trees.

 
Then we went back to the classroom to write up some notes on the new ones they had worked out (Fibonacci and triangular) and learn some more (Pascal's triangle and Palindromic numbers). After all the time and effort that we spent on it was lovely to finally use it in a lesson!

Week 2 Challenge Review, and end of the stupid challenge idea

The Counting On activity went well, and we used blu-tac to create the giant graph on the wall. We did run out of room for the prime numbers column and had to overlap.

Edit: Here is a picture of the graph. In future I would consider using a large floor space instead of the wall, so that we could fit all the prime numbers in properly! And discuss what would happen to the graph if we did more numbers. And if I put it on the wall again I would include labelled axes.

They loved the active "yes or no" categorising game. Each student had a number, and two ends of the room had "Yes" and "No" up on the wall. I called out questions like "Are you a prime number?", "Are you an even number?", "Are you divisible by 3?", "If you add 5 to yourself, do you have 4 as a factor?" and so on. It provided a good opportunity when someone was unsure to ask the whole class relevant questions like "How can you tell if a number is divisible by 3". And they loved it.

I'm already over the challenge thing

 Not surprising, but with contributions from a personal situation, I lost a lot of motivation. Plus two of my classes annoy me. But Year 7 continue to be lovely, so I will keep doing my best for them at least.

Year 7: We're going to be looking at prime and composite numbers and factors. The main activity I want to use for primes and composites is one from the Counting On numeracy framework. Students draw rectangles to find the factors of numbers (a different number on each sheet) then lay them on the floor (or stick to the wall) to create a bar graph of how many factors they have. Then you can instantly see prime numbers, and how one is not a prime, but has a special column all to itself. It also separates square numbers from other composites. After they've got the general idea I want to try an idea from Brent Vasicek at Scholastic for an in-class assessment of their understanding. I think I will give each child a number and then get them to sort themselves according to different criteria, e.g. primes over here, composites over there, sit down if you have 4 as a factor etc.

Week 1 Challenge Review

As per my previous post, I tried a few new things!

Count to a billion with Year 10 was not a huge success. Probably a third of the class had both the curiosity and the good behaviour that was required to get something out of this idea. Others did some timing and some calculations but didn't engage much in the investigation aspects, others offered some suggestions but produced no work of their own.

Some good points:

• Everyone was involved in converting a large number of seconds into years, so at least some content was covered.
• We discussed
• the variation that would occur between different people and different estimation choices.
• finding the mean of numbers and found an average of two times.
• which large numbers would take the longest to say.
• how maths in the real world is more like this, gathering information however you can, making choices, estimating, rounding, approximating, and not coming up with one correct answer, but one answer justified by working.
• We practised saying large numbers.
• Some of us had some fun.

Based on all that, and the difference in behaviour between the classes, I think it would work nicely with my year 7 class, so I'll try that later in the term.

Year 9 enjoyed "4 strikes and you're out" a lot, with some students quickly volunteered to come up and write their own. I asked questions about which numbers they could tell without guessing as we went, and was very impressed with some of their answers.  We used addition questions to warm up to the idea, then multiplication of fractions afterwards (what we were working on). Doing this on the board didn't engage all the students, and getting them to work in pairs would probably have been worse, but it was a nice thing to try.  Difficult with a large and poorly-behaved class (what isn't?).

Zero to Five was also quite successful. Some kids seemed to engage more with the examples on the board when using this strategy, asking more questions as I explained so that they could hold up 5 fingers. It was good for me to see the lower numbers come up and know that I needed to explain more. I told them "if you don't understand because you weren't listening to me, keep your hand down", which was also helpful to see!

Year 7s Weekend Homework Menu was fun. They had a choice of a game, a worksheet or a Tarsia puzzle. It took a bit of time, more than setting regular homework, but students came in one Monday showing me the puzzles and talking about the game, so it was probably worth the time. I think I'll have to review it again after a few more weeks.