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 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.

Subtracting a Negative - The Third Umpire

My Lovely Year 7s are starting their topic on directed numbers/integers at the moment. Over the years we have had a lot of discussions about how to get them to really understand about adding a negative and especially subtracting a negative.

With some help from my lovely husband, it seems that sport or some kind of game is the way to go. He played a version of cricket where each batsman stays in for a fixed number of overs, but gets a negative score added if they get "out". I thought it was a great idea, and had lots of potential for negative numbers - what if the third umpire overturns an out?

Here's the game we played today:

Students came up in pairs, one pair at a time, to play. They had 30 seconds to throw a bean bag between them (from behind marked lines) as many times as they could.

Scoring:
1 point for each successful catch.
-1 points for each time the bean bag hit the ground but was picked up again in less than 2 seconds.
-5 points for each time the bean bag stays on the ground for 2 seconds or more.

Also I stopped them mid-game so we could discuss the scores on the board.

I considered the penalties for dropping as negative numbers, rather than subtractions, so that we could write our number statements that way. That also allowed us to subtract a negative score if a penalty was overturned.

For example:

A pair of students catch the bean bag 22 times, then drop it. I rule that it is on the ground for more than 2 seconds.

So I write 22 + (-5) =

Here we can talk about the use of brackets, how they may or may not appear and why we might use them. We can also talk about how we would say it. Do we say "22 plus minus 5" or "22 plus negative 5" or can we say "22 plus take-away 5"? Which ones make sense? Which is the most clear?

Now they know that the pair have lost points, because they did something wrong, so 22 + (-5) = 17.

But they did appeal that it was less than 2 seconds. We took a vote. My decision was overruled.

So I write 17 - (-5) =

I'm removing the negative score. They all know already that the result should be back at 22. So we can now discuss why that is.

In summary at the end of the games we talked about adding and subtracting positive numbers, and adding and subtracting negative numbers, since we had done a bit of all of these.

After we played that version a few times, we switched to a system where the scores started at -20. This allowed us to do the same types of calculations, but in the negative numbers and crossing zero. I have a number line across the front of my room which helps a lot in these situations.