Merry Mathsmas

That's the end of the Mathsmas Advent Calendar for 2012. Tomorrow is the last day for students to attend for us, then two days of Staff Development then the holidays!!

Merry Mathsmas Everyone!

Day 24: Christmas origami

I've always done a bit of origami at the end of the year to decorate the classroom.

One of my favourites from other years has been this sweet little Santa. Unfortunately the instructions are not in English but most of it is pretty clear and a quick bit of translation is easy enough.

This year I tried a bunch from this extensive list.

This little bear is already off to carry a Christmas present. Each year some of the staff do "Christmas Angels",  which is like a secret Santa but you do little things for the person all week.

The poor snowman can't stand up with his heavy scarf on. He had to have a lie down for his photo shoot.

Day 23: Christmas Number Plane Pictures

I love number plane picture activities. Plotting coordinates and getting a cute little creature or scene to colour in. For a real challenge though, get them to make their own. Here are some from our students last year.

Day 22: Number Pattern Christmas Lights

Thanks to the excellent crew on the department's social network Maang (specifically the Maths group Axiom) once again for a brilliant idea. The original was Christmas trees that lit up. My version is strings of Christmas lights.

Each string represents a number pattern and each bulb is a term in the pattern. Type in the missing terms in the blank (white) bulbs. When you finish the last term, the whole string lights up! It's pretty funky!


The first sheet is addition and subtraction, staying in the positive numbers. The second is addition and subtraction including negatives. And the third is multiplication and division patterns.

Here's an idea of what they look like when complete.

Have fun! I hope you're all enjoying the last week of term. I know I am.

Day 21: Fraction Word Puzzle

One of the New Century books, the Year 7 Teacher Resource Pack, has a fraction puzzle where you take a specified fraction of each word and add those letters to the blanks to complete a riddle. I've used this sheet a lot and had lots of fun with it. So I made my own for Mathsmas.


Also, making the think up was a very demanding literacy task for me! Once your students have had a go at one of these types of puzzles, get them to make up their own. There's loads of quote sites around or they can use some favourite song lyrics or whatever else. Thinking of words that contain the letters you want can be quite tricky.

Day 20: More Nets

On Day 17 I mentioned PaperCritters and the idea of getting students to make Christmas characters. I tried this yesterday and it was lots of fun! Some cute reindeer and elves and the Grinch.

I thought I'd share a few of mine with you so that you can use them if you like. The reindeer don't have antlers, but I marked some slits on the top to insert some.

First, the colourful Rudolph.




Then I did the reindeer and a snowman in black and white, since most teachers are probably like me and don't have easy access to colour printing or photocopying. That way they can be coloured in before assembly instead.

Day 19: Open-Ended Questions for Mathsmas

I recently used a lot of open-ended questions when teaching measurement to year 7. My favourite question ideas were from "Open-ended Maths activities" by Sullivan and Lilburn and I reviewed a couple of those ideas in this post.

Some Mathsmas ideas:

• What gift could you fit in this box? This stocking?
• If this stocking contained 10 presents, what size might they be?
• Draw a (reindeer/santa/elf/present/stocking/wreath) with an (area/perimeter) of x units.
• Make a Christmas design that is three-quarters red and one quarter green (use grid or isometric paper or pattern blocks)
• My friend and I ate all of a Christmas cake which was cut into 8 equal pieces. What fraction of the cake might each of us have eaten?
• Advent number of the day - use today's date or 25 for Christmas and ask students to write as many questions as they can think of with that number as the answer
• Two presents have the same volume but different mass. What could they be?
• What methods could you use to try to determine what is in a present without opening it?
• I used 1 metre of ribbon to wrap a present in the shape of a rectangular prism. What might the dimensions of the present be?
• I have 1 square metre of wrapping paper. What size presents could I wrap with it?
• Draw a Christmas design that has four lines of symmetry.
• Draw a Christmas design that has rotational symmetry.

What else would you add to this list?

Day 18: Christmas Tarsia

You can turn ANYTHING into a Christmas activity or decoration, if you really want to.

I made some tarsias in the "rhombus" shape and with some green, red and white paper and some decorative cutting, they become Mathsmas decorations!

Now I've caught up!! Back to one a day. Not long to go now!

Day 17: Christmas nets

Nets are great fun, and this year I'm starting to discover the abundance that are out there in the papercraft world.

We start with the very simple at Kidzone (which also has a bunch of other Christmas worksheets). They have a cube, rectangular prisms and a triangular pyramid/tetrahedron. You can print them in colour or in black and white and let the students colour them.

Then we can move on in difficulty and prettiness, although these ones are all meant to be printed in colour. There's this adorable December 2012 snowman desk calendar (all of these calendars are incredibly awesome, I'll have to start keeping an eye on this site). I liked it so much I enlarged it (manually, which is why it sits all wonky). I'm crossing off the days until the last one!

I'd love to use some of their ideas to make a big calendar for each term next year. Their Nutcracker from last December is awesome too.

I haven't tried these ones yet but I'm keen to. There are some crazy Japanese monkey things complete with presents, sleigh and tree plus lots of elves plus Santa, reindeer, sleigh and tree at this site.

I also discovered a nice paper toy creator at PaperCritters where you can draw and add features to the different views of your creature then print out the net. Here's the test one I made. Maybe get kids to make a Christmas character.

Day 16: Christmas Mazes

A quick search will find you a LOT of Christmas Mazes and similar puzzles. Here are some highlights.

• The ones at Classroom Jr are straightforward and cute. These are the ones in my patented Mathsmas folder.

• Activity Village have a few, but this Christmas Tree one is just beautiful. Forget the maze, I just want to colour this in.

• In amongst a huge list of printable Christmas activities at Print Activities are some "Count by..." mazes, such as this count by twos maze. They also have some Christmas Cryptograms that are fun too.

Day 15: The Twelve Days of Christmas

The Twelve Days of Christmas. It's full of mathematical opportunities.

• For primary school kids, you can focus on the numbers - drawing pictures of the gifts, using either the original version or an Australian version. Maybe the kids could come up with twelve days of gifts on another theme and illustrate those.

• Find the total number of presents given over the twelve days. This opens up a lot of potential for strategies for adding lots of numbers and looking for patterns.

• Or, use it as an exercise to learn the basics of formulas in Excel.

• The daily gift totals are triangular numbers. I find students forget triangular numbers easily (even though... they make a triangle... seems straightforward to me) so another opportunity to discuss them is good. Since they make a triangle, they can become a Christmas tree, or a Santa hat... is there anything else triangular at Christmas?

• The presents also relate to the numbers in Pascal's triangle, as this exploration shows (and Pascal's triangle also makes a Christmas tree...). I imagine drawing up a big Pascal's triangle and putting it up somewhere, then moving on to a Twelve Days activity, working out the numbers. Then ask the kids if they can see those numbers anywhere in the room....

• Check out Vi Hart's Christmath Special video for some other funny and interesting ideas. You could put up the numbers from 1 to 12 and get your kids to come up with interesting things about that number and make their own song.

Day 14: Snowflakes

Paper snowflakes. A Mathsmas essential. My snowflake-making craft has improved significantly since the advent of Mathsmas. Largely through lessons learnt from "Make your own paper snowflakes", which I bought as a gift for a colleague then shamelessly borrowed and used extensively. Did you know they are supposed to be hexagon-based? You probably did. I didn't.

So I did a worksheet all those years ago with a cloze passage, some facts, symmetry, and folding based on working out the angle to fold it on. Here it is.

Of course there are other cool snowflakes to make, like these twisty paper ones. For me, the little snips and cuts and experimentation of the traditional ones has a certain feel to it.

Day 13: Christmas Enlargements

A couple of years in a row I had the lowest year 8 class, trying to do rates and ratios at the end of term 4. Not the easiest task. One thing I latched onto was enlargements using a grid.

Originally I was just taking images from the internet of popular animals and cartoon characters, but obviously to share here I'll stick to my own work. No new illustrations I'm afraid, but I've reused my reindeer and a penguin from the ratio pictures.

Grid Enlargement Reindeer Grid Enlargement Penguin

Here is the proforma to make some more (not that it's hard to make, but save yourself some time). All you need to do is insert the image.

Grid Enlargement Proforma

Day 12: Calculator Word Stories

These are from an Australian company called 10 Ticks that I signed up for a while ago. They have a whole bunch of worksheets with some very cool, different ideas, and they also have a whole pack of Christmas maths worksheets.

You have to sign up, and for a while they seemed to send a lot of emails, but I haven't noticed that recently.

These word stories are pretty cool. The idea is you answer the questions on the calculator and it makes a word which you then fill in to the story.

You could get a class to do this (Christmas or not) as an activity to write their own stories. On second thoughts, maybe they shouldn't write their own stories. They would all be about boobs.

Other sheets from the Christmas pack include permutating baubles (exploration of permutations using colours), Christmas symmetry, and some general puzzle-type things.

They also have a colour-by-solutions Christmas pack. This is an idea I've explored myself, a colour-by where the work is a little bit harder and the answers aren't necessarily numbers. Mine was a colour-by-like-terms. I'll have to find that. And make it Christmassy. I think it was a dinosaur.

Anyway these ones include simplifying fractions, colouring by rounding, by number properties and by substituting into an algebraic expression. Pretty cool.

Day 11: Oh Mathsmas Tree

My sister called me yesterday to give me the news story that mathematicians have worked on the calculations required for the perfect Christmas tree. Best made-up-headline-word ever: Treegonometry.

Not sure if my tree from previous years is going to cut it.

This was the year I made it. I cut into a whole lot of sheets of green (and brown) paper and assembled with lots of blutac and masking tape.

Then we decorated. With origami santas and presents and some other stuff. There's a bauble that says "I love octagons".

I took the tree down piece by piece and reassembled it last year.

This year I'm thinking of going three-dimensional, after seeing this tutorial linked on Pinterest. Drawing up a net for that would be a great maths activity.

After construction, I might refer to that article to calculate the required size for our tree topper. And I'm sure there are more ways to enrich decorating the Mathsmas tree. Maybe some baubles with problems on them to solve before using to decorate. Hmm....

The Decennial Dalek

There was a lot of procrastinating about the Dalek. The students voted to have a Dalek, and my year 10 class especially liked to ask where the Dalek was.

One of them in particular.

"Miss, look at the wall. What do you see?"
*I hang my head in mock shame*
"Because I'll tell you what I DON'T see! A Dalek!!!"

So I decided to name the Dalek in his honour.

We all agreed that "memorial" was inappropriate, but had trouble working out a better term. So since he was completing year 10, we went with "Decennial" for, I understand, a 10th anniversary. He was pretty happy with the honour.

Donald is now over beside the Pencil Pal, to make room for the Dalek.

And Stitch remains in his old spot, pretty much. One of my year 7 students wrote up that tip, and I had to ammend it on instruction from a year 11. Although he did say you only appear to have more mass, to an observer. And less height or something. "So travelling very fast in space you appear shorter and fatter?" "Yes." I'll take his word for it.

Day 10: Christmas Sudoku

Sudoku with Christmas symbols instead of numbers. Some kids ones here and here. Not a bad intro to sudoku for kids who aren't already familiar with it, but way too easy for those who are.

This one's a bit bigger and uses the words from "Merry Christmas and a Happy New Year" and "Seasons Greetings". Your handwriting sure deteriorates writing whole words. But it's very achievable for a learner too.

To teach kids the ideas of Sudoku, I also found this Christmas Sudoku to play online that takes you through filling in the gaps with increasing difficulty. It's a very short run through, but you could discuss it as a class as a starting point.

Day 9: Christmas Codes

Another one of Michael's recent teaching activities. Rather than just giving out notes or reminders, he's been encoding them using dingbat fonts and getting the students to work them out.

The first time you do this with a class, it's good to give them the first line or at least a word or two to get them started. After that, talk about the common letters and words that are most likely to appear, or look at double letters, so they can start working them out for themselves. The more you do this activity, the better at it they will get.




There's lots of great free fonts out there for this, although some cool ones don't have the whole alphabet, or don't include numbers. I tend to look at dafont and I used Xmas Dings for this one.

Use it to encode wordy definitions at the start of a topic, or a summary at the end (this is a good one because they should have some idea of what words will appear). Or for reminders about what to bring to class, what topics will be studied this term, or class rules.

Get students to write their own summary of a topic and encode it and swap with another student to crack the code. Or give pairs of students a topic each from the whole year to summarise, encode, then give out a copy of each to the whole class.

Since it's Mathsmas, make a series of encoded clues to solve a greater puzzle and give a prize for the first to piece all the clues together.

Need a clue? The title is Triangles.

Day 8: Christmas Civiballs

What is it about me making a commitment to regular blog posting. It's an instant "get sick now" instruction to my body! I'm only feeling a little sick, but it's enough of an excuse (plus it's Sunday) to focus on another game today.

I got addicted to Civiballs a couple of years ago. The Christmas version is equally good. Again it's reasoning and logic, and also I think these strategies games require perseverence, which is a useful academic virtue. And it's super fun.

Enjoy!

Day 7: Christmas Maths Worksheets Part 2

It was weird that when I searched recently for Christmas maths worksheets that this one didn't come up in the first couple of pages. I even tried searching for the specific topics I knew the sheets were on, but no result. I had to go to my hard-copy Mathsmas folder and find the URL there. They are from Maths-Worksheets who have a whole section on Christmas worksheets. How did this not come up??

Sheets include loads of topics, mainly worded problems based around a Christmas theme. They range from basic operations up to some difficult data, probability and measurement problems.

Favourites of mine include the ones about wrapping paper and ribbon required for wrapping different presents (perimeter and surface area), the temperature in different areas around Santa's workshop (negative numbers), and how likely you are to pick a present of a certain colour out of a stocking (probability).

Day 6: Circumference and Area of Christmas Baubles

Posting every day? Who's stupid idea was this?

Lucky I am vaguely prepared. Here's one from my first year of Maths teaching:

I'm sure this is a theme which could be expanded on too, but in it's current form at least we have a nice worksheet, some actual measurement in the topic of measurement, and another pretty thing to colour and put on the wall.

Have a good weekend everyone! I'm off to another Katoomba High Girls Night.

Day 5: Christmas Word Clouds

One of the new teaching ideas I tried this year was to use a word cloud to introduce a section of text. My colleague Michael introduced me to this idea from a professional learning course he did about student engagement. Rather than just reading an article or other text, you start with a word cloud created from it. The students have to try to use the words to figure out what the article is about.

I tried this with my year 7 class when we started looking at negative numbers. I'd previously told them about my upcoming holiday to Canada (when we were looking at time differences and planning an overseas holiday) so I thought we would continue that theme. The article for this word cloud is about the weather conditions during different seasons in the town of Banff in the Rocky Mountains.

Pretty quickly they could tell it was about temperatures and seasons and other weather conditions, but they didn't know what Banff was and were confused by some other obscure words that appear rarely, like Aspens. Importantly, they noticed the temperatures including negative numbers that appeared.

I put up the article on the projector and they were actually interested in reading it to find out where the unusual words fit in.

Then we looked at tables of high and low temperatures and talked about temperature difference and comparing the numbers.

Today I read this article about the relative green cred of artificial and real Christmas trees. It contains a few interesting but very specific statistics about carbon use making the trees and also energy use of regular and LED lights.

So I used Tagxedo to create a word cloud for this one. Some points about Tagxedo:

• I like to copy the text rather than just use the URL so that I can control the input more closely if I need to, and avoid the extra bits and pieces at the end of the article and focus on the central text.
• You can change the shape of your word cloud. Since my first one was about temperatures, I kept it as a cloud. This one is about Christmas trees, and conveniently that is an option!
• Colours are changeable too, although we can only print in black-and-white in our staffroom.
• Under Word/Layout options are some useful features. For articles relating to Maths, an important one is to change it to include numbers. It also includes how many words to use, whether to combine related words and exclude common words.

So first students need to work out what the article is about. From there I'd like to ask some questions like "What are some Maths words that appear in the article?" "What might those words relate to?" "What numbers appear?" "What might the numbers represent?"

They might be interested in some of the names that appear. "Why would a person's name appear a lot in an article?"  It could be a good lead-in to a discussion about acknowledging sources and plagiarism.

On reading the article, I had questions about the Maths. The article says "A study as recent as 2009 (Ellipsos) concluded that a 7-foot cut tree's impact on climate is 60 percent less than a 7-foot artificial tree used for six years. So while cut trees are not carbon-neutral, in terms of carbon-use, they are better than artificial trees."

My question was, why 6 years? And can we extrapolate from that information to work it out for a different number of years? How much might they have rounded the percentage and how will that affect our ability to use that percentage?

Maybe that's it, or maybe this can lead into some research and calculations about environmental issues and Christmas like energy use or wasted wrapping paper. Lots of mathematical potential, and in a very open-ended way.

Day 4: Christmas Colour-by-numbers

These worksheets are only very simply addition and subtraction but great fun and really cute pictures to have to put up around the room as the end of the year approaches.

This is the display from 2010. I remember being surprised at how much my students of all ages loved these! Also featured Christmas sudoku (which I'll mention later) and a turkey (which I won't).

Day 3: Christmas Maths Worksheets Part 1

A lot of "holiday themed" worksheets are just normal questions with a few themed images around the edges. Which is ok I guess, but I'm looking for my themes to be a little more integrated.

Maths-Drills have a bunch that can be found here, and they range in how genuinely Christmassy they are. They include a few of the lame kind, but they have made a genuine effort with the others, and in any case they are all pretty and well-presented. And free!

Problem contexts include adding presents on Santa's list, ordering numbered baubles, Christmas word problems, reading tables about Santa's route between different cities, number patterns about how many toys the elves make each day, and of course a number plane picture.

Oops! I failed primary school maths :(

Day 2: Christmas Tree Light Up

I love logic games. This one's a great one. Not maths as such I suppose but problem-solving and logic for sure. And a good one because kids can just play around and see what happens or try to strategise.

One way I judge the quality of a game is how much time I spend playing it. This rates pretty high.

Day 1: Ratio Pictures

Let's start with something I actually created myself. Ratios can be a tricky subject for some but concrete or visual things help and make it more fun. For the end of the year, sometimes you need everyone to chill out, relax, and do a small amount of maths mixed in with a large amount of colouring.

I've put the images in pretty massive so they can be downloaded and printed clearly.

 
Penguins! Drawn by me. Their hats need to be coloured in the ratio described on the sign. The rest of the colouring is free-style.

This one was made using a free gingerbread man font. 

A four-part ratio, but if you just colour in as you go along the chain it'll still be pretty easy. Drawn by me.

Ratios of candy canes, baubles, present tags and present colours! Drawn by me. The font I used for the text is called Santa's Sleigh, it's one of my Christmas favourites.

A Mathsmas Advent

Get ready for a Mathsmas Teaching Advent Calendar! Prepare for 24 days of maths teaching ideas for the holiday season. I'm starting before December so there's time to get in the 24 days before the end of the Australian school year.

Let me quickly tell you the story of Mathsmas.

Once upon a time, I graduated as a TAS (technology and applied studies) teacher, and accepted a temporary part-time position as a maths teacher instead. An old school friend and I started teaching together at the same school that year (she was a visual arts teacher and had just retrained as a maths teacher). Christmas started to come around and I naturally started to decorate and come up with Christmas ideas.

Mathsmas was born.

Then somehow the two of us ended up in a classroom decorating competition that led to all sorts of crazy goings-on and the use of a lot of coloured paper. In the following years we have stopped competing, but Mathsmas lives on in a variety of classroom activities and decorations.

Over the rest of the school year I'm going to share with you my Mathsmas resources and ideas, as well as links to my favourites from other places.

Classroom decoration updates and open-ended questions

I made a wall decal! Actually, I made a fabric first, then a decal. Spoonflower is awesome. I wish I could wallpaper my classroom, then I would make loads of awesome maths wallpapers. But this will have to do. Inspired by the pencil creature from Donald-in-Mathmagic-Land.

Our faculty recently bought some books on open-ended questions in Maths and I've been using the ideas a lot teaching measurement to year 7. My favourite activities so far involve perimeter and area of letters.

The first one begins by showing a letter drawn on cm grid paper. Telling the kids that the diagonal is approximately 1.4cm, we work out the perimeter of the letter. Then the challenge - write your name on cm grid paper with a perimeter between 98cm and 102cm. This was awfully fun.

It was great to have a project that involved a bit of planning, but lots of checking, trial-and-error, and editing. And looks cool on the wall!

I did one too. As you can see, I'm not shy about working out, unlike a lot of the kids!

Then we looked at area. We tried to make letters with an area of ten square centimetres.

I haven't been posting much, but this weekend I'm starting something special for the end of school year! It's going to be fun.