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Mr G Online

Archive for Mathematics

Jun 09

In my role as Maths Leader in Grades 5/6, I have many opportunities to work with groups of children in both Grade levels. Sometimes I find it hard to report back to the classroom teachers what learning took place during my lessons with their students. This year I have increasingly turned to Padlet, a collaborative, interactive Online Board, to record the teaching and learning experiences I facilitate. Here I share my lesson documentation through an embedded link to my Volume Padlet (note: Padlet needs the latest version of IE, Chrome, Firefox or Safari to view and use)

My basic use of Padlet follows this structure:

  • I post the outline of Tasks to be attempted during the lesson.
  • I add the initial image resources and models/examples that are needed for the task.
  • Students scan the Padlet-created QR Code to quickly open up the Padlet on their iPads.
  • The students start working on the task as outlined by the instructions on the Padlet and begin recording their responses. With the online Padlet wall visible to everyone on the iWB, students can start responding to what others are recording and as a teacher I can monitor from anywhere in the room or on my iPad and identify students to support or extend.
  • I pause during and after each task and invite students to share their responses. As they are already recorded on the shared Padlet, no time is wasted waiting for them to rewrite their work. As a class we can utilise all the time on collaborating, sharing, discussing and questioning.
  • If tasks involve using physical or digital resources, the students can quickly post screenshots, photos or images straight onto the Padlet wall on their iPads or laptops. Using a range of familiar iPad apps, children can record and/or annotate their working out and post it straight to the wall.
  • At ant time during the lesson, with constant access to all of the work being done by the students through the visible workspace on the iWB, I can reconnect with the students and offer feedback, teaching support or ask questions to call on children to explain their learning.
  • When the students leave me, I can immediately post the Padlet wall with all of the students’ learning documented onto their class blogs for their teachers and parents to view.

This particular lesson, embedded below, began with students viewing four rectangular prisms of varying dimensions. The students were asked to order the objects from largest to smallest and justify their decisions. In a traditional classroom setting, a teacher may call on 3-4 students to share their opinions and move on without having a true indication of the other students’ understanding. In using Padlet, I have an easily accessible, permanent record of all of the students’ understanding of volume concepts.

TASK 1

TASK 1

The next task was to verify their conjectures by calculating the volumes of each prism. This particular group of students were high achievers and needed little assistance in calculating the volumes ( the LxWxH formula was not the focus of the lesson, anyway but with a second group of students, I needed to do some revision and monitor progress). They were asked to record their working out directly to Padlet, with the option of recording the detailed calculations on Explain Everything and posting screenshots of the work. This group were able to simply write their calculations directly into Padlet. This provided a record of their work for their teachers to see later and was also a way for me to view their capabilities on screen in case I needed to assist. This was not needed with this group, but with the second group I was able to identify students with gaps in their learning simply by viewing their work on the Padlet wall.( At no stage did any student notice what others were doing – they were engaged in their own work.) What was also good to see was the variety of ways students calculated the volumes in terms of selecting which numbers to multiply first. This initiated a discussion about factors and the commutative/associative laws for multiplication. With all possible combinations visible rather than the 3-4 examples that would have been shared in a traditional setting, we were able to enhance the understanding of the range of dimensions that can result in the same volume. This also allowed them to refer back to their initial misconceptions of volume ( taller is bigger, etc) and led to a quicker transition into the final task.

TASK 2

TASK 2

Now that they had come to the realisation that there are many ways to construct a box of the same volume, we moved onto the final task which was constructing prisms of varying dimensions that would make a volume of 72 cubic units. At this point, they were introduced to an already completed example of the final product I was expecting of them ( which was already embedded on the Padlet wall, but out of view until needed) and the iPad apps available for the task – Think 3D and Skitch. They were also given the option of using physical blocks if they preferred a more tactile method. The simplicity of the apps required little instruction and the students were quick to start experimenting, further developing their understanding of the Volume formula by constructing rather than just calculating. The idea of factors were utlilised as they constructed layers based on the factors of 72. Again, with the use of the Padlet wall, students were able to post their annotated ( using Skitch)  constructions directly on to the wall, providing a record of their work that can be accessed in the future. Seeing other students’ constructions on the wall enabled students to consider other possibilities and further built on their understanding of different dimensions, same volume, which they were then able to reflect on later when the wall was embedded on their class blog. Having the lesson documented on line means that students also have the opportunity to add to the wall later on at home and explain their work to their parents.

TASK 3

TASK 3

I see many benefits in this process of documenting the learning and not just in Mathematics.

  • In this new era of collaborative teaching, it’s a great way of recording a lesson for other members of the team to view.
  • As a Maths leader/mentor, it’s a useful way of modelling a lesson for teams to discuss.
  • For students, it gives them access to previous learning that they can revisit at different times of the year to review/revise and support their learning
  • For assessment purposes, it can provide a record of the different stages of learning that took place during a lesson or series of lessons.
  • the use of Padlet itself opens up personalised access for students to work at their own pace ( not evident in this lesson as it was more of a guided lesson rather than an independent task)

This week, I was involved in a school based ICT Conference at my own school, during which several teachers led workshops on various ICT tools and practices. I presented this lesson structure and use of Padlet to the staff and they saw great possibilities. I am going to continue to develop a range of learning experiences using this documenting method. I see it having great benefits in enhancing the learning at our school.

Below is the whole Padlet wall as developed during this lesson. (If it is not displaying, it is likely you are running an old version of IE, as mentioned above)

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Apr 13

It’s been around for a few years now and had plenty of interest from around the world already, but Mr G Online has only just discovered Maths Maps. From first impressions, I am absolutely blown away by the idea. The brainchild of leading UK educator Tom Barrett, (now based in Australia), Maths Maps uses Google Maps as the launching pad for Maths Investigations.

Barrett’s vision was for teachers around the world to collaborate on building Maths Maps, examples of some seen in the screenshots on the left. Here is a brief description of how it works from the Maths Maps website.

Elevator Pitch

  • Using Google Maps.
  • Maths activities in different places around the world.
  • One location, one maths topic, one map.
  • Activities explained in placemarks in Google Maps.
  • Placemarks geotagged to the maths it refers to. “How wide is this swimming pool?”
  • Teachers to contribute and share ideas.
  • Maps can be used as independent tasks or group activities in class.
  • Maps can be embedded on websites, blogs or wikis.
  • Tasks to be completed by students and recorded online or offline.

The collaboration aspect worked like this: ( again from the website)

How can you contribute?

  1. Explore the maps below for the ideas already added, follow the links to open them in a new window.
  2. Send me details of which map you want to edit and your Google email address and I will add you as an editor, follow the link from the email invite.
  3. Click on EDIT in the left panel.
  4. Zoom close to the city and it’s surroundings. (Don’t forget Streetview)
  5. Find some TOPIC ideas you can see.
  6. Add a placemark (use the right colour for the age group it is best for – see purple pin)
  7. Explain the activity in the description.
  8. Change the title to show how many ideas there are.
  9. Send out a Tweet or write a blog post to highlight this resource andencourage others to contribute.

For those of you who have never edited a Google Map before, you need a Google account to do so. Here is an annotated screenshot that shows the basic layout of the Edit stage. I know I say it a lot to colleagues who don’t believe me, but it is very easy to do, like most Web 2.0 tools.

I’m not sure I could handle the world wide collaboration long term but I think this would be very manageable at a school level if you could get together a team of teachers willing to contribute. To me, it is a great way of presenting worded problems in real life contexts. On one level, with the emphasis on teaching children how to analyse questions for standardised tests, this would be a more engaging way of presenting the problems to the children. On a more creative, engaging level, it provides opportunities for linking Maths to real problems, not just questions out of a textbook or practice test sheets.

Beyond the question level, it provides opportunities to investigate all Maths concepts as you can see from the screenshots above. Adding the investigations to an always available Google map means students can access the problems anytime, anywhere and can work at their own pace. I always see tech solutions for recording work for students to complete as a benefit, not extra work. Instead of photocopying or getting children to copy down unfinished problems in a rush before leaving, the work is stored online. It means it can be shared with other classes as well.

The image here shows how Maths Maps was set up to add problems and investigations for all grade levels so collaboration can take place across levels, allowing for differentiation possibilities. Barrett just colour coded the placemarks to match a grade level.

If students have access to Google accounts, it is a great opportunity for them to create their own investigations, taking it to a higher thinking level for them. Students in higher grades could create maps for lower grades to investigate or for their fellow classmates. If nearby schools wanted to join in, they could and, of course, you could go the Maths Maps website route and find some schools outside your area to collaborate with and learn so much more about the world.

Of course, there is no reason why it has to be limited to Maths. You could do the same investigations with geography heavy novels, historical events, geography investigations, anything you can link to real locations. It’s certainly open to a lot of possibilities and, while I know it’s easy for me to say, it doesn’t have a huge learning curve and, with collaboration, shouldn’t take too much time to create. If you are going to type out some questions and print out on paper anyway, it will not take much more effort to create this far more engaging option instead.

Here’s a direct link to one of Barrett’s embedded Maths Maps, 27 Measures Activities in Madrid. You can explore this in detail and get a greater sense of the range of real world Maths you can find in real geographic locations.


View 27 Measures Activities in Madrid in a larger map

And, since I’m one teacher who always has to practise what I preach rather than just post ideas from others, here’s my first attempt at starting a Maths Map around Melbourne – unfinished and early days but might test it out with a few of my colleagues and the Grade 5/6 students.

View Measuring Melbourne in a larger map

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Apr 01

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Around this time last year, I wrote a post about the lack of engaging Maths apps on the iPad that went beyond “skill and drill” number activities. Since then, developers have introduced a greater range of apps across all areas of the Maths curriculum that can be used to enhance the Maths teaching and learning in your classroom. Here’s a selection of 20 apps that cover Number and Algebra, Measurement and Geometry, and Statistics and Probability ( these are the Content strands (CS) Australia’s Mathematics curriculum has been categorized under ). They also cover the proficiency strands (PS) of Understanding, Fluency, Problem Solving and Reasoning. I’m sure other countries’ curricula are similar in many regards and you will be able to make the connections.

Undecided (free at time of writing)

A handy tool for probability experiments, Undecided comes with customisable dice ( up to six) with number of rolls, last roll and sum of rolls data, Heads/tails coin toss with cumulative tallies, a 1-10 spinner ( wish it was customisable) , Rock/Scissors/Paper and Short Straw simulations and a random number generator with customisable maximum number beyond thousands (although it’s time consuming to go beyond 1000).

CS  -Statistics and Probability  PS – Reasoning

Decide Now! ($0.99)

Does what Undecided doesn’t with spinner. You can create/edit unlimited numbers of spinners with any types of categories and combinations of categories. Minimum number of sections is 10. If you add less than that, it intelligently uses ratio to created the segments. Great for probability experiments, especially for increasing and decreasing chance of random events to occur.

CS  -Statistics and Probability  PS – Reasoning

DragonBox+ ($6.49 – expensive for multiple copies)

Despite the cost, which would be prohibitive for some schools with limited budgets, this is a clever app for building conceptual understanding of the principles for balancing algebraic equations. Presented in a game format, it builds up from simple to complex as you play through 5 levels and 300 individual puzzles. The object is to be left with a single object on one side by applying inverse operations to object on both sides. The final level introduces the alphanumerical symbols associated with algebra.

CS – Number and Algebra       PS – Understanding, Problem Solving, Reasoning

Dartfish EasyTag (free)

This app allows you to create data collection tools using panels as recording buttons for categories and and subcategories you create. Each time you touch a panel, it begins tallying results. It collects category totals and tracks the elapsed time by whole seconds, minutes and hours. Not only useful for data collection and statistics, but can be used as a simple timer as well. Results can be exported by email as a csv file which can be opened in Excel (not  iPad spreadsheet programs), although it records labels rather than numbers so editing the spreadsheet is necessary for tallying results.

CS – Measurement and Geometry, Number and Algebra  PS – Fluency, Reasoning

Pattern Blocks ($0.99)

A simple app that can be used for many purposes. The drag and drop geometric shapes can overlay translucently to create fraction models, supported by the grids. Tessellations can be created effortlessly and rotations can also be done. At junior levels, shape patterns can easily be created and continued. Relationships between different shapes can also be explored.

CS – Measurement and Geometry, Number and Algebra   PS – Problem Solving, Reasoning and Understanding

Room Planner (free)

Created with House planning in mind but can be applied for many measurement tasks. This app allows you to create and edit individual rooms or entire house plans. Each element ( room, architectural element or furniture) can have its dimensions adjusts though simple touch and drag, elements can be freely rotated and final plans can be viewed from all angles and views in 2D and 3D. Area and Perimeter investigations can be implemented and concepts of space can be explored through placing objects within the rooms. Text can be added and in 3D mode, creativity is encouraged though applying colours and textures for realism. Scale can be explored by creating models of actual rooms.

CS – Measurement and Geometry  PS – Problem Solving, Understanding and Reasoning

5 Dice Order of Operations (free)

A simple but engaging equation building game that builds understanding of order of operations rules. A target number is randomly selected and 5 dice are provided to use as the values to generate equations to reach the target. IT provides a whiteboard for experimenting with possibilities before dragging the numerals and operation symbols into place. There are options for using some or all operations and brackets to allow for different ability levels.

CS – Number and Algebra PS – Fluency, Problem Solving, Understanding and Reasoning

Foldify ($2.99)

Its whimsical nature and cost makes it appear superficial use of technology but it allows for an engaging exploration of 3D objects and nets. Can also be used to create patterns on dice faces that can encourage logical reasoning in building patterns.

CS – Measurement and Geometry PS – Reasoning and Problem Solving

Geoboard  (free)

Simply put, it is a Tech based Geoboard that allows for wide ranging angle and shape explorations as well as quick creations of arrays to build understanding of multiplication and division. Can also support fraction and decimal exploration with careful manipulation. Shapes can be rendered transparent or translucent for easier viewing and comparison.

CS -Measurement and Geometry, Number and Algebra   PS – Problem Solving, Understanding and Reasoning

Geometry Pad (free; $6.49 full features)

This app allows for exploration of shape, angles, co-ordinates, area, perimeter, circle properties,algebraic expressions on graphs and linear graphs ( functions in the paid version ). Free version is still quite functional but paid version has some compelling upgrade features for higher level mathematics.

CS – Measurement and Geometry, Number and Algebra    PS – Understanding, Reasoning

MyScript Calculator (free)

A screenshot doesn’t do this app justice. In a nutshell, this app converts your handwritten scrawlings into equations and calculates the answers. Recognises indices/roots, trigonometric functions, percentages and fractions as well as basic operations. YOu can edit equations on the spot by crossing out and replacing numbers and symbols and equations automatically update as you increase and decrease values on either side. Blank spaces are replaced with calculated values. A great app for exploring equations as well as a very functional calculator. Does have limits, which you will find as you explore but its free so explore at will.

CS – Number and Algebra    PS - Fluency, Problem Solving, Understanding and Reasoning

Friends of Ten  ($0.99)

A handy app for exploring subitising and the visual conceptualisation of 1-10, important number skills to develop in younger students. This app has six activities using Tens Frames to develop build to ten, how many and more than/less than.

CS – Number and Algebra   PS – Fluency and Understanding

Tens Frame Snap Lite (free)

This game based app consolidates the skills developed in Friends of Ten above using a 2 player Snap game.

CS – Number and Algebra   PS – Fluency and Understanding

Routes ($1.99) (My Maps – linked to Google Maps account – free but harder to use)

Using Google Maps as its base, this app allows students to build routes along maps by dropping waypoints along the way. It generates distances and estimated times along the route and between points and you can compare bicycle, car and walking routes to the same locations. It also creates instructions which can be tested by actually going out and following the routes created. The distances and times can also be tested by actually going along the route as well. Routes can be shared via email, Twitter/Facebook and printed.

CS – Measurement and Geometry, Number and Algebra     PS – Problem Solving, Reasoning and Understanding

Virtual Manipulatives! (free)

An app that provides manipulatives to explore the relationships between fractions, decimals and percentages. Limited to values from 1/2 to 1/12s ( no 1/7s or 1/9s)

CS – Number and Algebra    PS – Fluency and Understanding

Counting Board (free)

A simple but effective counting aid. Either show or hide numbers. Create visual number patterns. Use to develop count on/count to/ count backward strategies for counting, addition and subtraction. Has an option to say numbers as they are tapped.

CS – Number and Algebra    PS – Fluency and Understanding

Fraction Division ($0.99)

A very specific skill set for an app but great to see a conceptually difficult operation ( division of fractions) explained in a concrete way. I know teachers who don’t understand how to divide fractions or explore the rote learnt reciprocal concept. This app definitely helps

CS -Number and Algebra   PS - Fluency, Problem Solving, Understanding and Reasoning

Numbler Free (Free! – paid app $0.99)

A fun way to explore equations and practise calculations. Basically, this is a number based version of Scrabble. YOu are given a selection of tiles with numerals, operation symbols and an equality sign. The object is to make equations with the tiles you have and/or the tiles already on the board.  Easy to play, challenging to finish. Encourages experimentation by trying to score the highest possible score. Free version only allows for one player versus computer. Paid version allows two player game.

CS – Number and Algebra PS - Fluency, Problem Solving, Understanding and Reasoning

Logic Puzzles HD ($2.99)

I love Logic Puzzles. This app provides are large selection of puzzles to complete. While not easy to categorise under COntent strands, the logical reasoning developed throough these puzzles is essential for higher order thinking. I have successfully taught 7 year olds how to solve ( and create ) these types of puzzles which has encouraged thinking, problem solving, creativity and logic.

PS – Problem Solving and Reasoning

PollDaddy (free)

Others prefer SurveyMonkey but PollDaddy has its own iPad app that gives you a simple way to COLLECT data based on surveys created online. All you have to do is link the app to an account, download the survey and it creates an easy to use, question by question survey on the iPad. You can review the results and upload the surveys once done.

CS – Statistics and Probability

As you can see, most of these apps are free so you can easily try them out to see what you can do in your classrooms with them. The paid apps won’t exactly break the budget if you download one copy to try. While many have physical, old school versions that can be used instead ( just like they were pre-iPad), I am of the opinion that the iPad version are more user friendly are allow for more possibilities and instant, repetitive use.

Let me know what you think about these apps or maybe suggest some other apps I have left out.

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Mar 26
The World as 100 People

I want to share this infographic today. Its an effective representation of a lot of data on a familiar topic. Many have seen this information presented before. This website gives the statistics in a simple list. It also provides links to earlier reports and origins.

This site provides a series of posters that present the same information and extra data in a graphical way.


And there’s always a YouTube video out there covering the same topic. This one is based on older data

Data like this can generate a lot of opportunities for Maths lessons.

  • Investigation and Generation of different graphs to represent the data in different ways
  • Conversion of data into raw numbers – what is 33% of 7 billion?
  • Compare the data from different eras – what has increased/decreased? By how much? What is the % increase/decrease?
  • How many more/less between different groupings within categories?

We need to work with data more and more. It surrounds us in today’s media. Getting children to understand it should be a major part of our Maths curriculum. Infographics like this one are a good start.

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Mar 17

Algebra gets a ‘bum rap’. Then again, it has a lousy public relations manager. Whoever came up with the whole ‘letters and symbols’ campaign should be sacked. Yes, opening up to Exercise 7D and solving 50 variations of 2x + y = -7 is n0t anyone’s idea of fun. But as I said, Algebra needs a new PR campaign.

DISCLAIMER: I’m just a Primary/Elementary teacher without any official qualifications in High Level Mathematics – No Masters, no Ph.D, just an A+ Average in High School/College Maths and 25+ years teaching kids to enjoy,not stress about, Maths. I may be completely off base with the great mathematical minds out there in what I’m about to describe regarding Algebra but I make no apologies. my students get it this way – including the Year 7-11 students I’ve tutored at home to relieve the confusion caused at their schools. (WARNING: Bear with me, I’ll take a while to get to the point of this post’s title – skip ahead if you want to ignore my Algebra rant!)

Now we have that out of the way, back to my message for today. I have a certain belief about Algebra. I define it as a systematic way of organising, recording and explaining your mathematical thinking using numbers and symbols/letters instead of words and pictures. Where we seem to get lost is that we go straight to the symbol without developing the thinking through the words and pictures/objects. We provide no context or purpose; just a meaningless string of equations with Xs and Ys that need to be solved. I see Algebra as problem solving support, not equation solving.

Last week, I was called in to take a Grade 6 class to release a teacher for planning ( the usual release teachers were unavailable). Maths was on the agenda for the day and I had worked with some of the other Grade 6 students on a similar lesson earlier in the week as a support for some of the high achievers. This time, though, I was on my own and in control so I applied my full tech+Maths kit to the group of students I had for that session.

The lesson/task that preceded this actually had fractions as its focus. One of the teachers had introduced a task involving a a building pattern for shading in grids to make fractions.

The lesson was differentiated to allow for a range of responses. Some needed to build the patterns with counters to discover anything. And then there was “Sheldon” ( not the boy’s real name) whom I walked in on to find him showing his mate the formula for the relationship between square and triangular numbers! When I confronted “Sheldon” to explain his formula and why it worked, he didn’t know how. So began my challenge and the rationale behind the lesson I’m about to recount. In the end, Sheldon actually discovered the key to this lesson I led in the class I took later in the week.

SO…this fraction lesson turned into a pattern and algebra exploration. All the children were able to discover the growing patterns in both number sequences and could describe the change. Square number differences increased by +2, the triangular number differences increased by +1. But that additive thinking was as far as they got. They needed more support to think multiplicatively, to think ‘Algebra’.

Enter (finally we get to the title of this blogpost!) the iPad and AirServer. Yes, I could have done all of this without the technology. I had done so earlier in the week with my small group of advanced students. But the engagement and ease of use was no comparison between the ‘sheets of paper and coloured marker’ group and the iPad and AirServer. If you are unaware of AirServer, I explained its significance in a recent post. Basically it projects multiple iPad screens onto a computer connected to a projector/iWB.

We started with creating the fraction grids using the iPad App Hands On Maths Color  Tiles ( I reviewed this and others in the Hands On Maths collection last year ). Again, we could have hand drawn grids or made them with counters but I had the students more engaged by getting them to make 1 grid each using Color Tiles and getting multiple students to project their grid onto the whiteboard using AirServer. This took 1 minute instead of 10 and allowed us to move straight into discussion with all the visuals needed on the screen – created by students, not me.

We then discussed the three properties visible in these tiles – side length, square size and the shaded (red here) area ( they hadn’t recognised them as triangles yet). I introduced the problem solving strategy of ‘Make a table’ – a strategy that should be embedded in their thinking by now, but it wasn’t. I created the table on my iPad and projected it on the screen. The students then created their own tables, using Numbers, on their iPads and filled in the side lengths, square sizes and shaded areas. Once they had the numbers in tables, they could start looking for relationships in numbers across the properties, rather than just look at the isolated number sequences. It was at this point that some students were able to recgognise that the shaded area numbers increased by adding on the next side length.

From that discovery, some children then saw that by adding the side length e.g. 4 to the square number 16 ( by this time we had recognised these as square numbers, not just square size), 20 the shaded area was half the size – 10. Here we talked about the importance of proving our theory by testing with other numbers. EVERY child in the class then tested this out with the other numbers, using Explain Everything as a whiteboard to quickly write out equations and project them on the screen to show their proof. Again, this could have been done on paper but by spotlighting everyone through the AirServer iPad mirroring it engaged those children who more often than not pretend to do the work and then let the teacher pleasers to put their hands up and call out the answers. This process really had everyone involved at all times. Some of the less than stellar mathematicians were excited about this discovery. But we were not finished.

I wanted them to see what type of numbers they were creating with the shaded areas – most still didn’t realise. This time I went back to old school methods -

counters. AirServer and my iPad still played a role. I asked the group to use the counters to create the sequence of numbers in the shaded area column in rows. As they began, some weren’t sure what to do. Instead of telling them what to do, I used my iPad’s camera to spotlight pairs who were building triangles onto the screen, thus giving support to others who needed a hint. Every group then wanted their triangles on the screen as well! This idea of spotlighting using iPad and AirServer can work in many ways to maintain engagement – kids like to be on show and recognised .

Once this was done, the students realised they were creating square and triangular numbers and that there was a relationship between them. Children started to recall the rule we had discovered – square the side plus the side then half it gave us the triangular number. But I posed one final challenge – why does this work and how can we show it with our tiles to explain the relationship? Back to Color Tiles we went. We recreated our two coloured square tile pattern. Then we added an extra column/side length. Bingo! The students recognised that this created two equal halfs, a red and yellow half- two triangular numbers!

4×4 Square with extra column of 4 results in two equal shaded areas- triangular numbers!

The final step in the process now was to put all of these theories into one explanation and come up with a formula – finally Algebra was coming into play. The important thing here is that they were thinking algebraically all along – I just didn’t tell them because Algebra is such a dirty word. Now they were quite excited that they were doing algebra.

I asked them to take screenshots of the tiles and the table and import them into Explain Everything. Then we looked at the table again. I explained that the only difference between what we had been doing and algebra was that we needed to replace our words and ideas with letters and symbols. What was the starting point? The side lengths. What will we call them – we decided on s ( could have been x,y, l etc). What is the square number? s x s or s^2. What did we do next? +s. Finally we halved the total ÷2 . With all these symbolic represenations students were able to create a formula for finding a triangular number: (s^2 +s)/2

Now thinking they were expert mathematicians, the students were able to record their understandings in Explain Everything AND find any square and triangular number without creating a long sequence. And they got it because we started with the thinking and investigating, not the formula that “Sheldon’ told us about. By the way, he worked this out independently and actually helped out my thinking with the idea of adding the extra side to the square grid – that’s the first time I had visualised the two triangular halves. This shows that our high achieving students can support the learning in the class – they just need a biy of guidance in their thinking, He was happy with knowing the formula. Now he UNDERSTANDS the formula and why it works. His discovery helped the less able students to also understand the thinking behind it all. And the iPad, the apps  and AirServer kept them engaged long enough to get there.

Oh, one more thing. I mentioned earlier context and purpose. I put this whole task in the context of a tile designing company. I talked about how the construction of Federation Square ( a modern structure in the City of Melbourne laden with geometric designs ) was not a random design. It was very mathematical. I put to them the scenario of customers wanting a design like the one we investigated created at a size of their own choosing. As employees of the company, we needed a method for quickly calculating how many of each tile we would need – the formula we discovered would get the job done.

Algebra need not be hard. It’s just logical thinking written down in an organised, symbolic way. Taking students through the right process can demystify it all. And it doesn’t hurt to use a bit of tech like my good friends the iPad and AirServer to help them along the way.

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Nov 28

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This week, Grade 5 began a unit on Volume, Capacity and Surface Area. On a weekly basis, I take combined groups from the 4 grades consisting of the higher achievers, while the classroom teachers concentrate on the mainstream group and students needing more individual instruction to achieve success. I made a conscious decision this week to focus on using iPads with my group to explore both volume/capacity as well as surface area.

I chose 3 apps to assist me in this learning experience – Think 3D ( free version) and Skitch, which are both free apps and Numbers ($9.99- $4.50 through the Volume Purchasing Program if 20 or more bought). Note: you could substitute the currently free CloudOn app, which is basically a server based Office app, or Google Spreadsheets, a free component of Google Docs/Google Apps for Education.

In the past I would have run this lesson using a limited number of connecting blocks and would have asked the students to record their observations in their exercise books. In using the iPads and the selected apps, I wanted to trial how this type of investigation could be enhanced and improved upon by using technology rather than traditional tools.

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The lesson began with the following premise. Each pair of students ( didn’t have enough iPads for 1:1; would probably work in pairs regardless to encourage collaboration and discussion) was to create a cuboid or rectangular prism with a volume of 72 cubes using Think 3D. In the past, students would have used a limited supply of blocks and would only have had enough to make one model. Using the iPad app, they were able to explore multiple ways of making a 72 cube prism with a limitless supply of cubes with a simple touch of the screen adding or deleting  a cube to the prism each time.

Another advantage is that, while there are many benefits in physically seeing and touching a real 3D object rather than a 2D representation of one on a screen, the ability to rotate the prisms on the iPad to view the different surfaces with a simple swipe made for easy investigation and no chance of the object falling apart and needing to rebuild, thus saving time for more analysis.

Using Reflection on my Macbook ( also available for PCs), the children were able to mirror their iPad screens on our interactive whiteboard and share all of the possible prisms and cuboids. This allowed for easy comparison and discussion without having to move our models around as we would have in the past.

The next step was to save the models as images in the Photo library on the iPad so that we could import them into Skitch, (an annotation app linked to Evernote.) As you can see from the image below, the students were able to clearly label the dimensions of their prisms and record surface area measurements as well. The use of this app enables easy collection of data for assessment rather than the rather difficult alternative of taking photos with a camera and writing notes about each photo. It also makes it easy for the children themselves to keep records of their work and thinking, an improvement on the lesson for both teacher and student. They were also able to swipe back to Think 3D to manipulate the prism to investigate the dimensions closely during the annotation stage.

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We then opened up Numbers to systematically record and calculate the measurements using spreadsheet formulas. Being capable students, they already knew how to use the L X W for area and L X W X H for volume formulas. I wanted to skill them up in using spreadsheet formulas to make quick calculations so that more time could be used for analysing the measurement data and the 3D models.

The spreadsheet was laid out so all possible dimension combinations discovered by the students were recorded. We then inputted a volume formula to verify each prism had a volume of 72 cubes. We then used formulas of our own creation to calculate the surface area of each prism. Once one formula was created, we were able to copy and paste that formula for each prism to calculate each prism’s surface area. Once we had all of the volumes and surface areas, combined with the 3D models, students were then able to make informed conjectures, observations and proofs about why certain prisms of the  same volume had varying surface areas.

While I am not saying I haven’t taught this lesson successfully in the past, using these apps and the iPad allowed for more direct and focused engagement from all students. Previously, the recording of data would have been a whole class event, which I always feel has the potential for disengagement as children watch others do the work. Having limited resources in terms of blocks, early problem solvers are left waiting for others. With the use of Think 3D, they were able to continue on with their own investigations rather than waiting for another pair to make an alternative model.

With today’s lesson, the children were actively involved in all aspects. They had opportunities to explore as many options as they had time for, they inputted all mesurement data, they annotated all of their images, which enabled them to consolidate and record their thinking more efficiently. The technology used also enabled them to save a permanent record of all the work they did today, whereas in the past, it was lost once the cubes were packed up. I  think this is a good example of how technology, and the iPad in particular, can be used for greater engagement and deeper thinking in Mathematics. Yes, all of the steps in the lessons could have been done without tech or iPad specifically, but I don’t think it is as effective.

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Oct 06

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Mathematics – you either love it or you hate it. There seems to be very little middle ground in this area of thinking. The lovers can find something fascinating in any challenge involving the world of numbers, statistics, shapes and measuring. The haters switch off as soon as you announce ” Please get out your maths books” and go into a quivering near foetal position at the mere mention of the word ‘algebra’.

So where have we gone wrong? Is it just that Maths is too hard for some people? Or have we failed to make it relevant so the doubters just switch off? If we did a better job at showing how important Maths is to real life – that it doesn’t just exist within the confines of a lifeless text book divided into 12 chapters and 120 Exercises of mind numbing practice drills –  would we, along with an injection of teachers who truly love and understand Maths, finally produce a generation of mathophiles (if thats even a word)?

What are you doing to make Maths real in the classroom ( and beyond where it should be)?

  • Are you taking advantage of the simple beauty of Lego blocks to teach arrays, number patterns, counting and  visualization?
  • Do you rely on all those exercises in the textbook or do you show how Trigonometry and functions can be used  to build ramps, staircases, find out slopes;Test and adjust the water flow of a slope on a roof or a pipe; discover The effect of a ramp’s slope on the distance of a jump; work out whether throwing a ball on a steeper angle increases the distance it travels; test the physics of Angry Birds and other similar games?
  • Are you using ratio to alter recipes to cook for more or less people or for changing the taste of a sauce?
  • Do you just learn about the properties of different shapes or do you explore how different shapes fit into a space more efficiently and how this can impact design?
  • Are you buying all of your class/school supplies or getting students to organise surveys to find out parent/their preferences, do research on costing of supplies, table or graph results, compare costs of home purchases versus school purchases, investigate savings and what money could be used for instead?
  • Do you organise school events or have you thought about students working together to organise the costing of events like graduation parties, excursions, transport options, fundraising events?
  • Does your school block or encourage free fantasy sport online competitions which develop money management skills?
  • Do you go on excursions to local shopping centres to buy resources and look for the best prices and possible discounts?
  • Do you use worksheets about statistics and percentages or do you keep statistics about school sports events as real data to monitor performances?
  • Do you use Maths text books for examples or do you collect infographics from newspapers, news programs and websites so children have relevant, recent data to analyse?
  • Do you just serve up pages of algebra exercises to complete or do you demonstrate how algebra can be used as an efficient way to solve real problems, create formulas for simplifying work practices or show the usefulness of algebraic formulas in spreadsheets?
  • Are you still making graphs about favorite colors in the junior grades or are you teaching them that graphs can represent information from questions that make a difference to their lives ( that doesn’t have to be as deep as it sounds)?
  • Are you teaching students how to manage budgets, are you showing them how interest rates impact on their spending? Do they understand credit card debt?
  • Are you involving them in every mathematical possibility in a school day from helping out in the canteen, collecting and counting fundraising money, being timekeepers, sorting out notes in the office, conducting daily surveys of relevance, cataloging books, tallying fines or costs of replacing lost books in the library, helping the PE teacher measure results in athletics carnivals or repaint the lines on sports and games fields out in the playground?
  • Are your students building resources that involve accurate measurements like puppet theaters, book boxes and doll houses for the junior grades? Do you just draw plans to scale or let the children build scale models of real objects they measured?
  • Do you let your students take control of the layout of your room so that they can apply location strategies learnt in class?
  • When considering guest speakers to come to your classroom, do you just think authors and campaigners or do you think about builders, engineers, businessmen or others that can share Maths in the real world?
  • Do you see that organising collaborative discussions with classrooms around the world provides an opportunity for teaching time concepts?

The list can go on forever. I would love to hear from you about what you are doing in your classrooms to make Maths real, relevant and exciting. One idea would be sufficient or more if you want. I’ll add your ideas to my list ( and give you credit of course). Maths is too important to be feared. We have to show our students its worth. Join the conversation.

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Sep 28

Earlier in the year I wrote a post titled “Maths Extension/Enrichment with Edmodo“, outlining my plans for an enrichment/extension program for high achievers in Maths at school. It took longer than anticipated to get started but from the start of Term 3 (July), I met with 5 Grade 6 students, 8 Grade 5 students and a couple of very bright Grade 4 boys on a weekly basis for an hour. ( Another teacher does the same with Grade 3 and 4 students ).While we can argue that research suggests mixed ability groupings are more beneficial ( for the rest of the week, these children work in that environment), I am in no doubt that the program has been a resounding success and a great sense of engagement and enjoyment has been felt by all involved, including the Maths teacher!

Whether it is enrichment, extension or a mix of both, which was a point of contention with some readers back in the original post, I am not sure. Regardless, some great mathematical thinking is taking place every week between an enthusiastic, engaged group of students.

The weekly lesson itself takes no time to plan. I simply upload a problem to the MEP (Math Extension Program) Edmodo group at the start of the week so the students can check in for some preparation time before we meet. Don’t get me wrong, I know exactly what I want out of the lesson when I select the problem and I send a post lesson report to the classroom teachers outlining what we did. The beauty of what we do, though, is that we don’t know what will result from the lesson until it is over. There is no chalk and talk, no pre-task explanation of what to do, no expectations that we have to solve it at the end of the hour. What you will see is a group of mathematicians sitting around together, sharing strategies, discoveries, questions verbally, through demonstrations on the whiteboard or via iPads or by posting on Edmodo.

What has improved throughout the term has been their problem solving skills, collaborative discussions, use of technology aids to organise and simplify the process ( Numbers on the iPad  has been a real winner, using formulas to test and monitor conjectures, as has Explain Everything to record ideas and share via the whiteboard) and most importantly, their ability to articulate their thinking and learning, both their successes and failures ( something they haven’t experienced much beforehand).

A great example of the whole process is our last learning experience, which lasted over two weeks. Most of our problems have come from the well established Maths Enrichment website, nrich. ( another worthwhile site is New Zealand Maths ). The beauty of nrich is the incentive to have your solutions published on their website, giving bragging rights to those who succeed, either partially or fully ( more on that later) Our last problem before the holiday was Summing Consecutive Numbers. The problem is presented via an introductory video that explained the nature of the  task. Each student had their own iPad ( its only a small group – we could have used the laptops) so watched it independently. After a two minute debrief to make sure everyone understood the task, we went straight into solving the problem. Beforehand, though, we made a pact that we would publish our solution on nrich, which always had to be posted by the 21st of each month, which just happened to be the last day of Term 3 ( we had previously missed deadlines or solved old problems, so this was our first chance.)

What was great about this particular problem was that the task itself was simple to start with – just adding numbers – but discovering and proving patterns and formulas was a real challenge that need real arguing and collaboration. During the first hour, the students were so focused on discovering patterns. Every idea they had, no matter how small, was posted on Edmodo. This proved to be an important step as the following week we were able to refer back to all of our discoveries. LEt me interject here and state that I was an active part of this as well. Before the lesson started, I was none the wiser about the solutions so I became an authentic learner with my group, making conjectures and testing theories side by side with them. (I talked about the importance of being a learning role model in a previous post). Some children used Numbers spreadsheets to arrrange the numbers into common sets as we investigated, others jsut used pen and paper while others used Explain Everything to brainstorm every idea they had. At the end of the sessions, we had over 60 posts on Edmodo and had made some amazing progress and they continued on over the weekend and into the following week determined to meet our deadline.

The following week, we met with all of our discoveries articulated on Edmodo and we were ready to write our Proof of the Summing of Consecutive Numbers. The final result was exceptional and is published below for your viewing pleasure.
Consecutive Numbers Proof
I showed their classroom teachers and my fellow MEP teacher and they were blown away by the depth of articulation and understanding in the submission. I merely guided them through the process of writing the proof but it is all their work (some sentence structures needed some modelling). To a person, they all requested a copy to put in their blogs and digital portfolios and now wait excitedly for the news it is posted on nrich’s website next month. Regardless, I am going to showcase their effort at the School Assembly, much to their satisfaction of being recognised for being mathematicians.

Being such a successful and rewarding experience, I then started thinking – should this just be the domain of the MEP group? Why can’t the other students in their grade follow the same process? It’s not as if they don’t do problem solving based tasks. This task in particular could have been entered into by ALL the students at different levels and the MEP students could have worked with the others to extend their thinking. The more I work with my group, the more I realise this model of collaborative problem solving should be done more at school. Sure, some of the less able students would not have arrived at the sophistication of thinking these high achievers attained but they could have contriubted to the adding and would have discovered some of the lower level patterns.

I think we have to stop thinking that not all students can enter into these tasks. Nrich is full of problems for all ability levels. Its my new goal to attack at school. I still think these MEP students deserve their time together to work with like minds. But I also think everyone deserves the experience they are getting. It’s what a differentiated curriculum is all about.

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Jun 09

Earlier in the year, I wrote a couple of posts on the iPad and Maths Apps. I questioned whether there were apps out there that went beyond number facts drills and calculation games. One of my readers of those posts, Melissa,  let me know about a group of apps called Hands on Maths. This set of apps provide a range of digital versions of hands on manipulative tools that are needed to develop important Mathematics concepts and skills. I am in no way suggesting that they replace the physical tools entirely but they do provide always available, easy to manipulate tools that are linked to independent investigations generated by the app itself.

These apps include digital versions of geoboards, counting charts, Base 10 blocks, attribute blocks, fraction strips, grids, coloured tiles, abacuses and other maniuatives that support the development of basic number and spatial concepts.They would be particularly useful in supporting individual and small group learning plans for students who need visual aids and teacher aide intervention. Each app is customisable and allows for different skill levels and different types of tasks within the same app through a simple user interface. The settings are changed through the “cog” icon, the activities are accessed via the arrow icon and there is a home button to return to the beginning. There is also a tutorial included to explain the use of each app.

What follows is a brief overview of some of the Hands On MAths apps available on the iPad used on how I have used them. For a more expensive look at the apps before purchasing them ( each app is $1.99 AU or the equivalent in your country) the company Ventura Educational Systems has an excellent website providing detailed information about all their apps, including downloadable PDF instruction guides. I wish other app creators would provide this much information about their apps so that you could make informed decisions about purchasing.

BASE 10 BLOCKS

 Hands On Maths:Base 10 Blocks is a virtual mamipuative app that allows you to explore both whole number and decimal place value using the familiar base ten blocks, known in some countries as MAB. It also allows for addition and subtraction of numbers with and without regrouping. It is limited to 3 digit numbers from 100s through to hundredths. It works through simple dragging and dropping of block into a work space and the values are automatically generated as you build the numbers. A useful feature is built in that allows for groups of smaller values to automatically transfer into the higher value accompanied by an arrow that shows where the values transfer to. ( e.g when you make 12 tens in the tens place, it will change 10 tens into a hundred and leave the remaining 2 tens intact). this works in the decimal format as well. As I said in the introduction, I’m not suggesting we do away with the physical block usage as many younger mathematicians in training need to manipulate physical models. Where digital virtual manipulative excel is in instant feedback, quick turnaround of use, instant access and reuse and unlimited resources ( we often run short of blocks in whole class settings). Together with discussion with a teacher on a one to one or small group basis while manipulating the virtual blocks, I see this as a good tool for working with at risk students. I like that the app allows for the use of decimal place value as well, even though here is a school of thought that we should use different models for decimal place value. Me personally, I like to maintain the link between the base 10 system across whole and decimal numbers to show the consistent relationship.

INTERACTIVE HUNDREDS  CHART

The Hands On Maths Interactive Hundreds Chart is a counting board which you can set up starting from 0 or 1 and use to investigate, explore and discover number patterns and sequences. Users can mark out multiple counting sequences using different tools including crosses, ticks, circles and squares( transparent, opaque and solid) of different colours. Using these tools, students can discover patterns, common factors and multiples, predict the next few numbers in the sequence by studying the pattern show so far. They can create their own or follow sequences given by the teacher or other students. Used effectively, much discussion can be generated about number sequences as a precursor  to Algebraic patterns through visual representation. Again the advantage of the digital tool is the quick turnaround in exploring patterns and the instant reuse of the board.

INTERACTIVE COLOUR TILES

Hands On Maths Color Tiles has a huge range of options for developing important Mathematical concepts. The tiles can be used to create arrays for exploring multiplication and division. Addition and subtraction can be explored by adding or subtracting tiles by dragging on or off the workspace. These operations mentioned are supported by a built in pad that supports the calculations being done with the tiles. This pad can be customised to show fractional. decimal and percentage proportions of tiles on the workspace as well. There are also built in grids that can be used to support calculations or be used as graphs or co-ordinates. Symmetry can also be explored through symmetrical grids that create duplicate reflections vertically, horizontally or both as you place tiles on the grid. By exploring this app you will find more and more applications for the range of tools it provides. Read the PDF guide that is available on the website listed above. It gives further ideas. The moe I explore it the better opinion I form on this app. Check it out.

OTHER NUMBER BASED APPS AVAILABLE IN THE RANGE

There are a number of other apps in the Hands On Maths Range that address number concepts. I’ll provide the links here and direct you again to the company’s website so you can check out for yourself what these apps offer.

Number Sense provides ways for exploring whole numbers, fractions and decimals

Number Balance can support the introduction and development of equality, equations and algebraic thinking by providing a balance tool that enables you to crate equations that equal different value combinations on either side.

Tangle Tables and Multiplication Toolkit both give many opportunities to explore basic multiplication concepts in a hands on, concrete way.

Hands On Maths also has a number of apps that support the teaching of geometry and other spatial concepts. I’ll discuss them in a later post.

When I first discovered these apps, I thought they were nice little activities for the juniors to explore. As I explore them deeper, though I can see their applications in higher grades as well, used creatively and in context. In tutoring middle/high school children on the side, I get frustrated by the lack of hands on explorations of concepts by teachers in these schools. I can see a place for some of these apps in the right  context.  I recommend that certainly elementary/primary school teachers give these apps a go. Even if you don’t buy them, check out the company’s website ( I have absolutely no affiliation with them – I just discovered the site today file researching for this post). You might find some great applications for using the real versions of these virtual manipulatives that you can use to improve your maths teaching.

 

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May 26

Back in the 90s, as a young teacher known for his knowledge in Maths, I developed a comprehensive Maths program based on the curriculum of the time. I personally had great success with the program, which I dubbed “Household Maths”, and with my support several teachers I worked with also followed the program enthusiastically. With little co-ordination or entrepreneurial skills, I even managed to sell a few copies of it. For various reasons I don’t ant to get into here, I was drawn away from using the program for many years, even though I still had a strong belief in its purpose and results. Now with a renewed push for purposeful Maths, I want to bring “Household Maths” back again.

I think the basic premise of the program and the majority of its content and curriculum base is still sound, 20 years after I first created it. However, to get it adopted today, I’ll need to link it to current curriculum documents. Before I do that though, I’d like to throw it out there to the teaching community and gauge whether it is worth the effort. As I have said already, I really have faith in this program but I’m not going to spend months rewriting it for the 21st century curriculum if others don’t share my enthusiasm.

What follows is the original introduction and program summary ( with some comments about how I would integrate new technologies, as is my want). I would really appreciate some critical feedback on what you think. Attached at the end is the PDF version of the whole program so that you can view it in its entirety.

 During my years involved in education, whether as a student or teacher, many teachers have made Maths such a boring subject. In turn, their classes have responded by being bored. Sheets and sheets of repetitive sums have done nothing other than keep the bright child occupied and the struggler frustrated. I have been guilty of this myself. The struggler learnt to hate Maths and the bright child just did the sums because they were easy.

I have always looked for programs that made Maths interesting for the children. Many books and programs have been released under the heading of “Real Maths”. Too many, though, are just a book of activities that are not related to each other and could be dealt with in a single session ,are part of a program that still had too many worksheets filled with monotonous equations or aren’t that real to the children, anyway.

Finally I’ve decided to do something myself . I thought to myself – When is Maths most useful and meaningful? The simple answer was in daily life at home. Maths is all around us in our house. Paying bills, going shopping, looking for bargains, building a house, developing the garden, planning holidays -  all of these tasks are Maths at work.

I wanted more than a book of activities to keep the children busy once or twice a week, though. I wanted my entire Maths program for the year to be a rewarding, interesting and entertaining learning experience based on Maths at home. Children love pretending to be adults. So this program was going to treat them like adults.

The key to it all was always going to be making it interesting and fun. When faced with a policy that says Maths must be taught for one hour a day, so many teachers decide to make a worksheet of equations with as many sums as they can fit on it to keep the children working for the hour. Of course what happens is that the bright children barely have to think and finish within twenty minutes while the strugglers get stuck on the first sum for twenty minutes and just know they’ll never finish in time. This only builds up their frustration and hatred towards maths while the bright sparks just confirm what they already know – they’re good calculators. But can they think? Have they been taught to think?

The Household Maths Program aims to teach the children to think about Maths, to use Maths and to realise Maths is a vital part of life. It is aimed at Upper Primary/Junior Secondary/Middle School classes because of the processes involved. If used by an enthusiastic teacher willing to be challenged by the work the children will produce, it will send out into the world students who enjoy Maths and are able to use it effectively. The teacher will have a lot of fun too.

SUMMARY OF PROGRAM

The Household Maths program is made up of  two components.

- Weekly activities including shopping for essentials, receiving pay, paying Bills and rent / loan instalments, petrol, Life’s Little Surprises and other weekly expenses decided upon by the “family” of the household.

- Major tasks incorporating many maths skills and running concurrently with the weekly tasks. These tasks can last from 1 – 2 days to 4 – 5 weeks or more .

The weekly activities are set out as follows:

A description of the household is given to each child. Six different households are included  in this  program to  provide  a  variety  of  environments in the classroom.( you can create more if you wish. )  The description covers the weekly / fortnightly pays  ( or unemployment benefits ) received by spouses, the number of children in the family, house payment situation ( rent, loan or fully owned ), bank balance, credit card allowance, number of cars and something the household is saving for. The children fill in the blank lines with the names, ages and birthdays of their “children”.

Each child is given an exercise book or something similar. Each page in the book is to be divided up into four columns: income, expenditure, savings and balance. The children record all transactions in this book. An example of this transaction record is provided.

Provide each child with enough shopping lists to last the year out. ( master copy provided ). Each week the children will fill the list in and look through catalogues and dockets for prices to complete their weekly groceries. Get the children to plan a weekly menu to give them an idea of how much food they will need to buy their family.

A checklist of bills is provided to remind the children when they need to pay their bills. Set months for gas, electricity, water, council rates and phone bills are given by teacher. All other dates for bills are decided by children. Teacher gives bill totals to children. ( copies of services bills are provided in program. )

A record of credit card transactions is given to the children to allow them to keep  a record of what they have spent on their cards. Payment ( or part payment ) will take place at the end of each month.

A checklist of weekly expenses will be given to each child so that they can make sure they aren’t forgetting to do anything.

Each week the children will choose at random from a collection of cards called Life’s Little Surprises. On these cards are a selection of unplanned expenses and incomes such as fines, repairs, presents, updating, competition prizes, debts etc. Draw up a chart to record when these expenses will be paid.

The weekly tasks generally provide opportunities to use the four basic operations of addition,subtraction, multiplication and division and are fun and useful alternatives to pages and pages of drill worksheets.

NOTE: When I originally ran this program, all of these resources involved a lot of paper use. Today, with the advent of 1:1 laptop/iPad programs, all of these components could be implemented more effectively with technology. Google Calendar, the iPad Calendar or Edmodo’s calendar could be used to deliver or remind the students of all their bills and expenses. Databases, spreadsheet programs or iPad/iPod finance apps could be used to send scheduled bills or track expenses. Excel/Numbers/Google Spreadsheets could be used to record/check the weekly cash and credit card transactions. Users of interactive Whiteboards could hide the Life’s Little Surprises cards behind a graphic and the students could drag random expenses or incomes out on the board. 

New skills are taught and, more importantly, used through the Major tasks or integrated activities. It is important that new skills are taught in the context of how they can be used. There is no point teaching something like percentages as just a whole lot of unrelated numbers on a blackboard or worksheet. Children, especially those with a dislike for Maths, will see no use for them. Therefore, even at the teaching stage, the skills must be related to a useful purpose.

Just as important is to show how a variety of skills are needed to complete real life tasks. The integrated activities in this program involve the use of a number of skills. The age group this program is aimed at have many of these skills already so it isn’t that big a task to have the children working through these tasks. It is also easier teaching the new skills because the nature of the tasks gains and maintains the children’s full attention.

There are thirteen integrated activities in the program. Combined, they cover all the requirements of a Maths curriculum and will easily make up a year’s program.( Note: operations involving fractions may be found lacking in this program, mainly because it is hard to find a real life purpose for adding, subtracting and dividing fractions for the average person. They will have to be taught in a different context. )

Each activity is outlined in detail and the skills covered by it are included. Worksheets are occasionally included but the beauty of this program is that most of the resources are accessible to the children already and worksheets aren’t always needed. The materials required for each task are listed and most will be found in the home. Detailed lesson plans are also provided. Included is a checklist of skills that are taught through the program. You should find that everything in your school’s Grade 6 syllabus is included ( with the possible exception of some fraction work ). Use the checklist to record your students’ progress by ticking the box each time evidence of the skill being used is found. Space for comments is also provided.

TIMETABLING THE PROGRAM

 The general practice in schools is to allow approximately one hour a day for Maths. In doing so I would allow about 40 minutes for the main activity (10 minutes teaching and 30 minutes working on the task ) and the remainder of the time on individual household finance organisation.

I would begin most days with a few minutes for the children to carry out essential transactions , such as bill or loan payments and entering their pays into their accounts. Life’s Little Surprises is an activity the children looked forward to at the start of the week to see what was going to happen to them this time so I always timetabled it for Mondays. By the time they all chose the cards it took about 5-10 minutes . If they had the money, or it was a straightforward transaction such as a speeding fine, they often completed the transaction at this time. But often it required shopping around so having LLS on Monday gave them time for this.

After this brief activity , I would go straight into the main activity – the integrated tasks on the following pages. It is important not to spend too much time at the beginning teaching because the children will lose interest. Plan carefully which skills you want to focus on and what that will allow the children to complete. Remember the tasks are not one day activities so the children don’t have to be finished. Once the children are engaged in the activity, you are now free to concentrate on the children who need extra teaching.

Allow about ten minutes at the end of each lesson for the children to use their checklists to see what weekly transactions they must complete. (e.g. petrol, newspaper, bill due,etc.) If they don’t have much to do, allow them to browse through catalogues to find bargains, extra items they have to buy because of Life’s Little Surprises or to start filling in their shopping list. This time may also be used by the slower children to complete work on the main activity without being seen not to have finished as much as the other children.

At times, you may feel that the children are not doing enough Maths. They may spend ten minutes looking through a catalogue and complete two equations. The thinking you have to develop is : have they successfully used maths skills in this situation? Yes! And that is what is important. A child who completes 25 equations on a worksheet and the child who has bought a lounge suite, paid a bill and put her pay into an account are doing the same thing. Except the second child knows why she is doing those sums and is using Maths.

This program is about quality learning not filling in the time with lots of irrelevant equations.
( Of course you should still allow time for drills / games in basic number facts such as times tables.)

INTEGRATED ACTIVITIES
The 13 tasks I planned are;
BUILD YOUR OWN HOME
DESIGN YOUR GARDEN / ENTERTAINMENT AREA
PLANNING A HOLIDAY
GET THE MET / UP,UP AND AWAY
THIS IS AUSTRALIA CALLING
ON SALE NOW
FAMILY FUN
PARTY TIME
I’M BROKE
COOKING UP A STORM
CLASSIFIED INFORMATION
ODDS ON
ELECTION TIME
Check out the PDF below for more detail.
Each task is outlined as follows:
PURPOSE OF TASK
MATHS SKILLS TAUGHT/DEVELOPED THROUGH THIS UNIT
PREPARATION / RESOURCES
TECHNOLOGY COMPONENT
WHAT TO LOOK FOR WHEN ASSESSING
DEVELOPMENT OF SKILLS THROUGH ACTIVITIES

With greater access to websites, programs and apps, many of the tasks would be easier to complete while still requiring the same level of mathematics skill. Online shopping and auction/advertising websites, measurement and money converters, recipe sites and apps, travel websites and apps, websites for utility companies, on line maps and world time clocks….. the list goes on… provide a wealth of content to be used in real life situations.

 

Would appreciate feedback on whether the program still has merit today. Here is the PDF of the whole program     householdmath

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