I just read this story-telling post by @billgx which inspired me to write this post; it’s’ been a while, I know!

Bill’s post has just highlighted the power of stories – something I’ve been tossing around in the old brain for a while.  I thought it best to capture just a few of these thoughts for future use in teaching and learning.

We are always telling stories. Stories don’t have to be oral or written narratives. Just yesterday in my digital photography workshop, I alluded to photos as telling (or capturing) stories. It is sometimes difficult to glean the story depending on the medium used but the story is definitely there.

We enjoy listening to stories. Stories can be affirming with a by-product of connecting the audience to the story-teller – or the content itself.  I still remember when I told a class about Descartes before launching into the Cartesian plane. As a teacher, listening to our students’ stories afford us a glimpse to who they are and knowing students is important for good teaching and learning to happen.  Ditto for students.Here is a story-writing exercise I once did with a class just to get the creative juices flowing:

  1. Give each student a piece of paper.
  2. Everyone starts off with the same line, e.g. “Today as I got to the school gates….
  3. Then, everyone passes the paper to the left (or right) and then write a sentence to continue on.
  4. Continue the round robin, with prompts for introducing the ‘problem’ or ‘resolution’ or ending. 

Make sure you make time to read a few out or perhaps publish the stories. Depending on the age group, it might be necessary to establish some ground rules as you would for anything ‘anonymous’.

This might even be useful in a maths class, e.g. get students to do round-robin solution – each one just does one step. This may drive home the point of the importance of reasoning and ability to follow someone else’s line of thought.

Spreadsheets, Budgets and Formals

I’m not a big fan of spreadsheets – prefer databases more – but it needs to be taught. It can be a useful tool in life. Engaging and motivating low-ability year 10 maths students can be challenging the best of times. Here is a lesson I prepared that would teach them a life skill of budgeting using spreadsheets.

Lesson Activity

Year 10 formals is months away but this is something most year 10 girls are excited about. So when I said we’ll create a budget for it, everyone was excited to talk about something interesting.  Motivation covered!

  1. Brainstorm budget items (“What do I need for the formals?”) – emphasise no right or wrong answer, if not personally relevant then just set the budget to $0. The point of this step is to engage.
  2. Create a new spreadsheet and enter all the items under the heading of “What I need”. Good opportunity to revise basics of file creation/saving, renaming worksheet (Budget), data entry and Format-ting text and columns
  3. Add new columns with headings of Min, Max, Range (excellent chance to revise these statistical concepts). Each student enters their own budget, again no right or wrong. Format columns to currency.
  4. Calculate Range (=Max -Min columns); revise/teach use of Excel functions and autoFill.
  5. Calculate minimum and maximum budget totals; use autoSum or use SUM function
  6. With 9 months to go, create a monthly savings budget (=total / 9); some students don’t know the division symbol in Excel
  7. What are your cheapest (use MIN function) and most expensive (use MAX function) items
  8. Email your spreadsheet (make sure they all know how to attach files to email)

Discussion points

  • Can you afford your monthly budget (minimum, maximum)?
  • What adjustments can you make to afford the items? Are you working?
  • Would you consider borrowing or even doing without?
  • Would you negotiate with your parents? Can your budget spreadsheet help you talk to them?


The girls enjoyed this lesson. The discussions were interesting and for my part, enlightening: truly amazing what teenagers deem they need and how different they all can be. They did not even mind the spreadsheet and statistics bit and were all keen to follow the flow of the lesson. They compared their results and even they were amazed at how different they all were.

I like this lesson because it was relevant, engaging and differentiated.

The Vitruvian Man – a context for learning

Finding a quantity given a percentage (or fraction) is a useful skill yet considered to be an extension topic for year 8. I thought I could give it a go but set the scene, so-to-speak, without the oft-used context of shopping and sales.

Enter the Vitruvian Man. Wikipedia has a good image and brief explanation of this drawing by Da Vinci interpreting ideal (hu)man proportions according to Vitruvius. Wikipedia also provides a list of these proportions.

Lesson Activity

My ‘hook’ question to the class was “How do forensic scientists figure out the height of victims given minimal data?”

I showed and explained the Vitruvian Man. We even managed to do a quick revision of properties of squares and how this was used in the drawing. Anyway, here’s how I used this “tool”.

  1. Divide the class into pairs (or small groups).
  2. For each pair, give a card which showed one of the proportions (e.g. 1/4 of height = shoulder width) as well as a measuring tape
  3. They take the fractional measurement of their partner, i.e. the item to the right of the equation, e.g. shoulder width
  4. Demonstrate how to calculate the height given a known percentage (or fraction); in my example, multiply each side of the equation by 4
  5. Finally, measure the actual height and compare to the calculated height

Discussion points

  • How do the actual and calculated height compare?
  • What are the reasons for differences?
  • Why multiply both sides (make a point to mention working with Algebra and equations)?


The class really enjoyed the activity and didn’t really mind the ‘maths’ at all. Given that this class is deemed below-average, the level of engagement was good. The students – all girls – already associate percentages with sales but, for most if not all of them, this is the first time they’ve associated it with the human body. I know that I will use the Vitruvian Man again.

This was a lively lesson with talking and standing up and discussing. This isn’t every teacher’s cup-of-tea but it suits me just fine.

Percentage Composition

I wanted to make this lesson a bit more interesting as well as incorporate opportunities for connections with other maths topics.

I knew my year 8 class students loved music so I devised a very simple poll on Rob Thomas (one of the students was going to his concert): like him, don’t like him, don’t know him. This was a good opportunity to revise Frequency Distribution.

Just by fluke, our 3 fractions turned out percentages of recurring decimals (another connection). In that sense, it’s really not a very good first example! Anyway, someone asked if the percentages will total a hundred (I love it when they think!). So, we added and of course it didn’t. We got a result of 99.8%.  This opened up a discussion on the consequences of rounding/truncating decimals.

I made a statement that the most accurate way to represent not whole (fractional) values is via fractions. Nods all around until I asked, “‘Do you believe me?” The consensus was yes because I was the teacher. I was quick to point out that they should not always believe everything teachers say – they have to think if it’s reasonable; teachers are humans, after all, and can make mistakes. Besides, I really wanted to challenge my students to develop their thinking and reasoning.

So, I went back to the Frequency Distribution Table and 3 fractions. Adding the fractions naturally gave a total of 1 and nearly everyone said that’s 100%, as expected. Joy!

Were it a more able class (we stream our Maths classes), I could have pursued more connectionist opportunities but I did sense I’ve pushed enough today. I know I’ll refer back to this lesson when we actually do Data later in the school year. The class was engaged because they knew the meaning behind the numbers.

By the way, the statement is a fact I had truly learned in my previous career in IT. Particularly when I worked for a bank calculating interests, calculations in programs (software rather than curricular) were designed to stick to fractions as much as possible to minimise rounding errors.

In summary (more for my future reference),

Learning strategies: connectionism, motivation and engagement via meaningful and relevant examples, question/reason validity, compare/contrast

Fractions, Decimals and Percentages – provide different ways to represent fractional values, of which fractions are the most accurate

Tangential Learning

I’ve always been fascinated how learning is facilitated through fun, play and games. We have all had personal experiences attesting to this.

Professionally, I first heard about this by reading Marc Prensky’s work. Since then, I’ve always sought ideas on injecting fun activities into my classroom.

More recently, I watched the following video and first heard about Tangential Learning.

This video defines Tangential learning as

what you learn when you’re exposed to things in the context you’re already engaged in…’s the idea that some portion of your audience will self-educate if you expose them to concepts in the context that they already find interesting….

I’m not really a video-gamer, much less an author of one, but I lived by these principles and have indeed found that students were most engaged in their learning in such cases. Here are some examples:

1. Decimals

Throughout this topic, the students had to work out how many jelly beans will fit across their desks.  I worked through how they would have solved this problem as they learned more maths from primary school. It started with counting (teacher lines up jelly beans, student lines up jelly beans) to estimating to measuring and calculating. I should add that I had to throw the jelly beans lined up as they ‘carried my germs’. The students were aghast at such waste but they soon figured out that by measuring just one – and learning operations with decimals – they can earn their jelly beans. And so they did!

2. Algebra

I introduced this with a personal experience of wanting to learn how to play Rihanna’s Unfaithful on the piano. Not having played for years, this was a real challenge particularly because the music sheets were several pages long! As if learning Rihanna wasn’t cool enough, the students were particularly impressed that I used YouTube, i.e. this videoshowing me how to do it. The main point was that the video highlighted that the song only really had 3 repeating sections. Learn the 3 and you learn the song. So, not only did I get to learn to play the song, I memorised it really quickly. Patterns are the crux of Algebra. This has set the tone for the students to see that Algebra can be used in something so seemingly far removed from mathematics. Some of them also felt affirmed that teachers use YouTube to learn.

3. Reading Tide Charts and Timetables

The class was told that they were to plan a group’s day out to Manly beach using a wiki.  This YouTube video on wikis was really helpful to enthuse the class. The activity included collecting shells on the beach, watching a movie, catching public transport and be home in time for a particular TV show. I gave them all the web links they needed and they really did not mind reading tide charts at all; they knew it had to be low tide when they go shell-collecting. Some even appreciated learning about Sydney’s Trip Planner. All that besides, they also learned about the challenges of planning and collaborating.

Tangential Learning works and I like it. The real challenge is finding that context that students will be engaged in.