For a few years, I’ve noticed that kids not only don’t know/struggle with their times tables, but also general ‘number sense’.
Mathematical Induction, topic 7.4 in the NSW Board of Studies Mathematics Extension 1 Syllabus, is difficult conceptual. I suspect students think there is a bit of smoke and mirrors happening. One introduction that I use, I first saw in a resource by Stuart Palmer. The same story appears in this article online: Mathematical Induction (PDF 92KB), Helen Bush, Reflections August 1992 sourced on NSW HSC Online.
For “Arts and Crafts Thursday”* we made a foldable to summarise the formula in the topic Series and Applications (Topic 7 in the NSW BOS Mathematics Syllabus).
I put up my first image on Dan Meyer’s 101 Questions yesterday, Kitchen Scale. Wander over there.
What’s the first question that comes to your mind?
Back in 2010, putting a piece of wall in our kitchen to attach a child gate to, a problem arose about evenly spacing screws.
This is part 2 of my electronic worksheets for Consumer Arithmetic. Part 2 focuses on Spending Money, in particular: profit and loss, discounts, purchasing, best buys and buying on terms (hire purchase). (Part 1 focused on earning money)
A couple of end-of-term/year activities…
Through the start of this term, I’ve been creating a series of electronic worksheets (in Excel) to cover the ‘earning money’ part of a Consumer Arithmetic topic.
It’s the last day of term here, so teachers might want to spend some time today fixing up their room. So, I brought my Made4Math Monday forward.
I needed some times table posters for my classroom, but the posters you can buy tend to be for younger students and I haven’t seen a grid version (rather than each table listed separately).
As I said in an earlier post...
2012 is looking like a year of quiet reflection (i.e. maybe not much on this blog), contemplation and trial and error.
Here is some recent thinking, please comment.
A foldable for reviewing the Rules of Differentiation. Click the preview to see the full version.
Year 11 Mathematics have one of their three periods a week, last period on Fridays. Of course, they’re not highly motivated at that time.
The other week, we folded parabolas, I called it “Arts and Craft Friday”.
The next week, they surprised me by asking what we were doing for “Arts and Craft Friday”… I had nothing!
I recently received an email from the AAMT:
National Mathematics Day is Friday 18 May and looks at codes and code-breaking — to celebrate the centenary of the birth of Alan Turing.
Each year I use the TV Show, The Biggest Loser, as an application of percentages – here is a worksheet for 2012 setting out the contestant data that your students can use to perform some calculations.
I’m completing this activity earlier than normal this year, so the data is from earlier in the competition.
I recently used the “Locker Problem” in a Year 7 Maths Enrichment class (mixed ability). Here are some resources I used:
Where do you go for maths lessons and good lesson ideas?
Here’s the start of my list, I’m not particularly recommending these sites, just listing them as places to look for ideas.
Whilst often used as a textbook example, I had never seen negative numbers used in a lift before.
A number plane drawing worksheet for making the Superman logo. Included in the file (see below) is a page with a suitable coordinate grid.
On MathsStarters, I have added a Frequency Distribution Table tool. The tool lets you have 3 to 10 scores, you tally as you go and the frequency and total are calculated.
You could use this on a projector/IWB (the buttons for incrementing the tally are sized for an IWB). Or, students could use this to record data on their own laptop as they collect it – paperless!
Smartie colours are not evenly distributed across the two bags of 11 fun size boxes I used with my class:
Playing with the kids' toys on the weekend, I came across this car and became interested by the relationship between pulling it back and how far it would travel.
Was it a linear relationship or something else?
Looking around, there are lots of activities for collecting and analysing data using small boxes of Smarties. Here is my version.
I’m not trying to present a view, either way, on the carbon tax being debated in Australia. But those against the carbon tax seem to be providing some good fodder for the maths classroom.
Last term I had Year 9 review and learn index notation and the index laws through some self-directed activities.
I know there are stacks of GeoGebra files available on the Internet, but I’ve started putting my own here on the site.
Some games, played with dice, for getting the hang of decimal place value.
Having made a Tables Spider this other day, I realised that I made myself a template for creating all sorts of “spiders”.
With Stu Hasic’s Student Response Network (SRN) virtual clicker software installed on the 2011 DER laptops that NSW public school students in Year 9 receive this year, I wanted to try it out.
In 2007, I wrote about a resource, a Number Spider, that I used as a lesson starter.
Each year I use the TV Show, The Biggest Loser, as an application of percentages.
Here are some resources for the new year…
When introducing the topic of ‘ratio’, I use the mixing of cordial as an illustration that most kids get.
The idea of using 1 part of cordial to 4 parts of water makes sense to them – and they get the idea of equivalence when you mix the cordial in a different sized container (I use the examples of using cups to fill a bottle for a picnic, and using buckets to mix a big batch for a party).
Tanya Duffy shared a great coordinate geometry activity on a private forum earlier in December.
You might have seen this map featured around the place recently:
I like teaching surface area, I think it’s an interesting topic. Yet, I find kids struggle with the concept. Not understanding the basics of area and then getting over the prior knowledge of solids meaning volume are two aspects that cause some difficulty.
This is a great interactive for representing simple inequalities on the number line: Inequalities with GeoGebra.
Returning from a few weeks leave, it wasn’t clear where my Year 8s were up to. I figured they had started looking at grouped data, but I didn’t want to repeat work they might have already seen.
I showed WCYDWT: Spacing Evenly to some of my classes this week. A couple of reflections…
A real-life version of this problem presented itself today.
(Source: Elementary Math Mastery, Rhonda Farkota)
Jeff of Webmaths points out a new Australian TV show, Letters and Numbers.
Things are tough at my school at the moment, tougher than normal. There are many reasons for that, this is not the post to discuss them though.
For Australian teachers with access to objects from The Le@rning Federation, the resource Bridge Builder is a nice way to deal with geometric patterns and finding the algebraic rule.
It’s that time of year again… that’s right… Year 8 solving equations.
Each year for the Term 3 SDD (Staff Development Day), the four schools (three 7-10 and one 11-12) in the collegiate I work in get together for a combined program.
In recent years, Sydney Water has been encouraging households to save water. “With limited and highly variable rainfall in the catchments, the community can no longer rely on water from the dams.” source
The end of term series of posts are some of the most popular on this site.
This is a resource for skills in working with time.
I’ve been trying to increase my use of the laptops with Year 9.
In the NSW Mathematics Syllabus students are to learn about “rounding numbers to a specified number of significant figures” [NS5.2.1].
This is a fairly simple activity that allows for something different in the teaching of Pythagoras’ Theorem.
Here’s a quick starter activity for rounding.
How do you make a unit on percentages richer / project-based / engaging / authentic?
Starting Algebra with Year 8, we spend a couple of lessons on various “algebraic techniques”. I’ve been trying to find some activities which provide a little more engagement. I created “The Land of Algerb“ to explain multiplying pronumerals.
In 2009, Year 9 got their DER netbooks and now they are in Year 10. This year’s Year 9 does not have their netbooks yet, and so this gives teachers a little time to get their heads around the inclusion of netbooks into the classroom. This year, I’m teaching a 5.2 pathway Year 10 class (and a Year 9 5.2 class).
Some chocolate discussion starters for looking at bar graphs: a series of chocolate bar graphs.
This week, my Year 8s have been looking at inequality signs, graphing inequalities and solving simple (one-step) inequalities. Today, after solving inequalities, we played a simple game. A simple, obvious game, that really doesn’t warrant a blog post.
The end of term/year often brings lots of disruptions. So, as much as I like to keep teaching till the end, some days require something a little different. I like hands-on quasi-mathematical activities that allow every student to engage with and complete. And on Thursday, just before having one of those disrupted days, I found this…
Despite every Year 9 student having a laptop for a few weeks, the topics we’ve been covering haven’t lent themselves to full laptop lessons. To end the term, though, we’re reviewing graphs.
A lesson for Year 9 students with DER laptops, or anyone really.
Here’s a great example of a graph that is just wrong, the data may be correct, but it has obviously been represented the wrong way. Watch the video…
I think that each student using a netbook/laptop in your class presents some slightly different issues in Maths.
I’m about to get into Surface Area with Year 8. Of course, there will be chocolate. But, since I last looked at Surface Area with Year 9 I’ve been thinking about Heat Sinks.
This is an amusing video to introduce probability… some of my Year 8s found it hilarious.
As I mentioned, the DER roll-out hit my classroom as we were in the midst of Algebra. Due to a tight program and exams shortly, I had to stick with a couple of topics which don’t really allow for “play” on the laptops as much as I would have liked.
A lot of the Algebra taught at the Stage 4 level is technique, and so matching activities work particularly well to practise and review skills.
Here’s a review of some of the ways I’ve found to make matching activities for use on the laptops.
A Digital Education Revolution (DER) laptop in the hands of all Year 9 students changes everything… or does it?
I’ve been meaning to try ClassTools.net for a while. With ClassTools.net you can make interactive Flash games, from a range of templates, then save and share them.
Tomorrow is the last day of term… hurray! Here’s another end of term activity for use with your maths class.
Last year, I posted the Melbourne Storm Number Plane Logo – and today, exactly one year later, purely by coincidence, I’ve made a Brisbane Broncos Number Place activity.
Year 8 were recently assessed on solving equations and I was a little perplexed by the results.
An excuse to use chocolate in a maths lesson…
This week, Year 9 were looking at finding the perimeter of shapes that include curves (parts of a circle).
Here’s a quirky little activity that uses the DER laptops.
Google Sketchup is one of the applications bundled on the DER netbooks being rolled out into NSW Public High Schools in Term 3. But as it’s free, you can download it now for Windows XP/Vista & Mac OS X.
What else could you do with capacity? As I was getting a glass of juice to have with my breakfast, I was thinking that I could use this image as a quick question at the start of a lesson.
With laptops rolling out shortly and projectors appearing in some classrooms, we should be thinking about collecting digital media for use as stimulus or investigation material. So, the other day when filling up my young daughter’s bottles, I took some pictures.
For a while I’ve been collecting and saving to a web-site maths objects to use with my classes. By objects I mean single activities, rather than a web-site of maths activities. I’ve been trying to take some of the many things I find and save to delicious and put a purpose to them – deciding that it’s something I could use with one of my classes.
I wanted to play a multiplication bingo type game with a class the other day, so I grabbed two 10 sided dice (apparently you don’t need to call a single dice a “die” anymore) out of the cupboard. Then I thought… hey I have a projector and a laptop.
Depending on what they’ve previously experienced, students struggle with the immense scale of the universe (mind you, so do I).
When starting “Volume” with Year 8, we start by looking at cubic units and isometric drawings. This year, with an interactive whiteboard (although, these resources are also suited for use with just a projector or in a computer lab), I was able to use a couple of excellent online resources.
I was preparing for part of a presentation to the staff at my school tomorrow, highlighting the importance of numeracy being included in all subject areas.
Here’s a PowerPoint file I made to quickly review transformations before getting into congruency.
I need to learn to use GeoGebra because it looks like a fantastic app, it’s free and shortly our students will have their own netbooks, itching to use them. I find the best way to learn new software is to do something with it that you need.
The Biggest Loser, the Australian version, is again on television. This year, Year 9 are looking at Percentages at the same time.
The last week of term begins next week…
I used to think that I knew what 1 billion was, i.e. 1 000 000 000 000. Then a couple of years ago, I looked on Wikipedia and found there were two defintions: Long and short scales.
As part of a unit on Trigonometry, we review compass and true bearings before working with bearings in Trigonometry problems.
To start this review lesson, we looked at some images from Google Earth.
A really easy way to create engagement when introducing a new topic is to explain some of it’s applications outside of the maths classroom. For Trigonometry, I use an explanation of how I used trigonometry in a previous career to find the height of trees.
In my fourth year of teaching, I’m finally happy with how teaching sector graphs went.
Recently Dan Meyer posted his thoughts on the ideal maths textbook, which would actually be a
digital archive of very interesting mathematical media. This is a great idea, and whilst I don’t have a projector in my classroom yet (although fingers-crossed), it would be something that I would buy/subscribe to. Anyway, there was a challenge in this for me: being mindful of the media I consume and the world around me to collect digital bits and pieces that might help explain a mathematical concept (I commented on Dan’s blog that I missed the opportunity to take a picture of 3m³ of dirt I had delivered). The second, to my mind harder, challenge is to take that item and make a meaningful and engaging connection with a concept being taught in class.
As I was putting together a lesson on using conversion graphs, I couldn’t find a nice temperature conversion graph - so I created one.
I’m currently sorting through the many teaching blogs I subscribe to, trying to cull the list. The thing about Maths related blogs that tends to keep them in the list is that Maths teachers generally write more practical posts.
Here’s a video about the history of number, in particular the numbers 0 and 1. Our Year 7 program begins the year looking at ancient number systems, so this video will fit in nicely.
The end of year activity of choice this year, will be making Zombies!
Trying to motivate Year 10 after the School Certificate Exams are completed is tough. I like to use geometric design activities. Whilst they seem like “fun”, or at least non-taxing on the brain – they get the students following a procedure, using geometric instruments and can be lead to a good discussion about the Mathematics of design.
Around this time each year, our programs have Year 8 and Year 10 looking at the Number Plane. For the end of the term, it’s nice timing, because it allows us to draw some pictures on the number plane. One favourite is the logos of various
Understanding the concept of a fraction by shading in a part of a shape is a fairly standard introductory activity. When I did a search on Flickr for fractions, I found this set of fraction shading diagrams*. What I liked about these diagrams is that you are required to represent two fractions on one diagram.
Building an Angle Wheel is a great way to consolidate an introduction to angles for Year 7.
When looking at measurement, year 7 measure “body units” and use them to measure things in the classroom, as an example of estimating. Then, when we move onto perimeter, we come back to one body unit, the pace.
‘The Biggest Loser’, the Australian version, is currently on Channel 10. Conveniently, it appears on TV the same time we’re looking at Percentages with Year 8 providing a great connection between popular culture and maths.
Google have added a nice little feature to their online spreadsheet – the ability to collect information via an online form.
It’s been two terms since my last post on this blog, End of term activities. So, as I return to this blog at the end of the year, here are some more “last day” type activities.
For the last day of term, lessons may not follow a normal program, however they can still be engaging and mathematics related.
An outdoors activity is always a welcome change to a maths lesson. To introduce rates, I take the class outdoors to measure their heart rate.
Simon Job — eighth year of teaching maths in a public high school in Western Sydney, Australia.
MathsClass is about teaching and learning in a maths classroom. more→
maths bookmarks on Pinboard