Birth Date Values

One of the great things about my role(s) this year is that I have had the opportunity to meet some fantastic Maths teachers and educationalists and last week I hosted Mike Ollerton for two separate events.  Mike has made many significant contributions to Mathematics education over the years and he has kindly permitted me to write about the ideas he shared with us last week.

This is a simple activity that feels quite fun and personal but could lead to some rich discussions. Mike’s description of it is here:

After going round the class, asking several children for their BDVs, there are many questions which might present themselves. Can you ask children to work out someone else’s birthday given their BDV?  Mike suggests lots more questions:

• Which BDVs only have one birth date?
• What are the minimum and the maximum BDVs in a class?
• Which BDVs have the most dates?
• What is the smallest BDV which cannot be made?
• What is the largest unique BDV?
• Which dates are square BDVs?
• Which dates are triangular BDVs?
• In a group of people who has the average BDV?

What other problems can you devise based upon BDVs?

Place value game

I often play this simple game with younger pupils to help them build a stronger understanding of place value. It’s simple and requires no resources.

Start off by drawing a place value chart on the board.  Depending on where you are at, you could do just hundreds, tens, ones or you could include digits either side of the decimal point, e.g. tens, ones, tenths and hundredths.  Use this as an opportunity to target questions at students as you are drawing the table “if we are doing place value, which column is this?”

Each group then has a row on the place value chart.  You want to limit it to about 6-7 groups otherwise it takes too long to get round to your go again.  It works really well with small classes working in pairs or threes.

Then we start randomly generating digits.  You could just use a dice (it doesn’t matter if you only have digits up to six), or using something like this from Classtools.net

There are a couple of twists that I have added to this over the years.

1, You don’t just get to place the digits in your own row, you can also place them in someone else’s row. So if you get a low digit, you can scupper someone else’s chances by putting it in their thousands column. This depends very much on the culture within the classroom. If you think there might be existing friendship issues amongst the group then it may be best to avoid this twist.

2, You could add some extra options as shown above, e.g. multiply or divide by ten.  This can make it a bit more interesting.  Other options might be to be able to erase a digit.

It’s good fun, but to get the most out of it, it is good to discuss at various stages who will definitely have the highest number / lowest number, etc.  You don’t always need to fill the grid completely to determine the order of the numbers. Why is this?

If you have used this or have any ideas for other “twists”, please drop me a line in the comments.

The Wisdom of the Crowd

Look, stats isn’t boring! I love doing these Wisdom of the Crowd exercises when teaching averages. Another way of doing it is to display a random scattering of dots on the screen (about 40 or so). Get everyone individually to provide an estimate then calculate the mean.
A really interesting addition to this is to do it once getting everybody to call out their estimate. Then, before calculating the mean, give everyone the chance to change their estimate and record them all a second time.
This can lead to regression to the mean, and standard deviation if you like.
See – stats isn’t boring!

Sir Francis Galton was a statistician in the 19th century. Thanks to him we have concepts such as correlation and standard deviation.  Galton, it would seem, thought through the filter of statistics, a genius who produced hundreds of papers and books on fields as diverse as meteorology, historiometry and psychometrics and who pioneered the use of questionnaires to gather better information for his statistical analyses.

Last week, at my school’s Open Evening, we conducted a mathematical experiment based on one of Galton’s observations.

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nRich games to practice key skills

There is a range of “take turns” dice games like this one on nRich.

I see this activity as a way of practicing key skills (in this case column addition) but in a much deeper way than repeated practice as you are working backwards to achieve a result.  I would think of this as adding a significant degree of difficulty over simply doing a page of sums; it would be something you would only chose to do once the basic process of column addition is reasonably secure. However, because it is engaging (i.e. competitive) students are more likely to stick with it.

To avoid the need to provide students with 10-dice an interactive dice could be displayed on the board. nRich have this handy spinners tool here and there are lots of other options online.

All students would then have the same set of numbers and it would be a competition to get closest to 1000.  You might need to note down the numbers as you go to prevent cheating!

Again, of course, the value in the activity comes from the discussion, both in pairs and in whole class.  I like the idea of saying that the target is 1000 but actually rewarding good discussion and reasoning rather than just closest answer (i.e 5 points for a new “noticing”, 5 points for the closest answer)

Another way is to determine all the required random numbers at the outset and the students can fill in the grid with full knowledge of their options.  Less luck involved and so probably less fun!

I would do one game whole-class, where students are playing individually. Then a second game where students are to work together in pairs competing against another pair so they can compare strategies once they have a degree of familiarilty with the problem and get some good discussion going on strategy.

Eyes down for a full house!

Bingo is one of those simple ideas that works so well for certain topics so I thought I’d collate some resources.  I recently went to a parents social at my son’s school where we spent 2 hours playing “Rock ‘n’ Roll bingo” (whilst eating Fish and Chips and drinking beer). OK, so maybe Maths bingo isn’t quite as much fun as trying to spot 80s song titles, but it did inspire me to have a go as it is something I haven’t done much of lately.

It’s a format that works well for topics that students are familiar with but which need more practice.  They need to be able to get 90% plus of the questions correct first time and in about the same amount of time across the room.  Use it as a revision aid but not the first time you introduce a new topic.  It’s likely to get loud, so save it for the end of lessons, maybe those Friday afternoon lessons…

Here are some tips for how to run sessions:

1. Bingo cards.  Some resources come with bingo cards to print out.  This is good for longer games – say 20-25 minutes, maybe as an end-of-term “treat”. However, some resources are designed to do as “quick bingo” by putting up, say 16 answers on the board and then getting students to make their own cards by choosing a random 9.  Make sure they write these in pen and that everyone has all 9 clearly written down before starting. No cheating!
2. Keeping track and checking. Some of these resources have answers provided, but I think it is better if you do the questions as you go along, just write them down on a scrap of paper as you go and use this to check once a claimant has called out. Do make sure you check answers carefully.  It doesn’t matter if it takes a minute or two, it adds to the suspense!  As soon as kids get an inkling that you are not checking carefully they WILL cheat!
3. Prizes.  I have a natural aversion to extrinsic motivation, but hey, a prize just makes it more fun, no matter how cheap or naff! If you are using a bigger bingo card with, say 20 answers then you can also offer line prizes, i.e. a prize to whoever gets the first line, maybe a sticker.
4. Ham it up! OK, this is very much down to your personal style and relationship with the class but have some fun with it! Live your dream of being a gameshow host. Pretend like these prizes are the most exciting thing anyone has ever won!

Here are some Bingo resources which cover a decent range of topics.  There are various Powerpoint resources on TES too, but I like these sites because they are simple and don’t require log-ins.

There are lots of topics on this site and various options for displaying random-generated questions.  Many of the topics include bingo options, here is an example:

Once you are in, there are further options to cover exactly what type of questions you want to display, and whether you want a 4×4 or 3×3 bingo grid. You then display all the answers for your students to randomly pick 9 or 16 from.  I really like the way it gives you the option to keep track of the answers as you go which makes checking at the end a whole lot easier!

There are lots of topics on this site, handily listed in menus. Students make their own cards by choosing 9 out of 16.

3. WMNet

There are lots of basic number topics in this collection with an emphasis on place value. Students choose 5 out of 12.

4. Mathsbox

There are some provided for free on mathsbox.org.uk which are designed to have the bingo cards printed out. I’ve used the Simplifying Surds ones which worked very well. Each topic contains 30 questions, 16 per card so take about 15 minutes. Presumably if your school pays the £60 annual subscription you get a lot more topics.

Creating data by learning your prime numbers

Here’s a little idea for a team activity that could get quite competitive and hopefully “fun”. I haven’t tried it yet, and it might be a while before I use this. When I do, I’ll try to update this post with any tweaks depending on how it runs.

It’s based a on this really simple website Is This Prime created by@christianp which I saw on Jo Morgan’s MathsGems.

It presents you with numbers and you click YES (i.e. it is Prime) or NO.  It’s not an app so it can be used on a laptop / desktop although it works really well on browser on a tablet.  I’ll be doing this in a computer room as a group activity.

I reckon this could work with classes from Year 5 to Year 8, but most pupils in the class will need to have a reasonably good grasp on their times tables or it could be frustrating. It provides consolidation of times tables and primes but I think the real objective here is actually to use this as a lead in to various data and averages topics.  I always try to teach KS3 Statistics using data that the students have created themselves as they are far more engaged and care about what the data is telling them. This not only provides that meaningful data, but does so in a way which consolidates some fundamental number facts at the same time

I plan to use Google Sheets to collect the data which we will then analyse in a later lesson.  Google Docs in general is great for this type of collaboration.  I have created a template for a group.

Each group has a separate sheet that they fill in as they go.  Just duplicate the sheets for as many groups as you have, making sure that each group is working on their own sheet before you start.

Talking of groups, here are my general rules for planning any group activity:

1. I chose the groups.  I have nothing against pupils working in friendship groups but I know who to avoid putting together and the process of self-selecting can be painful for some.
2. Everyone has a role. Some pupils will see group work as a chance to sit back and some will naturally dominate.  Assigning specific roles reduces this.
3. Everyone contributes equally. By rotating the roles I will try as far as possible to make sure that everyone ends up doing the same activities by the end of the session.

To get some excitement going, I’ll keep a running commentary on the highest score.  I also plan to write up the “Errors” that the Error Recorders give me as we go. I want to make sure we have some time at the end for reflection on how it went, i.e.

• Did you work together as a team? How did you support each other?
• What was a good strategy for a high score? (When I play it, I rarely use all 60 seconds as I am trying to go too quickly and so I am often tempted to guess ones I don’t know)
• As a team what did you do to make sure your scores were improving (Write down the errors on a big piece of paper? – I didn’t say you couldn’t!)

I would definitely leave the data analysis part until the following lesson.  There is lots you can do with this and it could form the basis of a series of lessons on Averages, Data representation including Box plots. We can start with the question, “Who was the winning team?”,  which in itself is open to interpretation.

Learning times tables – Number Happy Families

Anyone looking for a simple maths game for end of term Year 7 lessons? Here’s one.

I’ve always felt that secure knowledge of times tables at Year 7 is so important simply because it gives kids the confidence to engage in so many maths topics covered in that year.  As such any opportunity to practice is good even when it is in a simple game like this.

A Simple Factors and Multiples Team Game for 3-4 players

I came up with this idea whilst playing the traditional Happy Families card game with my family when on holiday. Kids seem to love this game – could I create a maths game as engaging?

I’ve tried this several times with Year 7 classes, playing in teams of 3 or 4 and they love it.

It takes very little preparation or explanation – in fact the students make the resources themselves!

The Cards

You need a set of 36 blank cards for each team. Anything will do.  I spent…

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Learning times tables – Number Happy Families

I’ve always felt that secure knowledge of times tables at Year 7 is so important simply because it gives kids the confidence to engage in so many maths topics covered in that year.  As such any opportunity to practice is good even when it is in a simple game like this.

A Simple Factors and Multiples Team Game for 3-4 players

I came up with this idea whilst playing the traditional Happy Families card game with my family when on holiday. Kids seem to love this game – could I create a maths game as engaging?

I’ve tried this several times with Year 7 classes, playing in teams of 3 or 4 and they love it.

It takes very little preparation or explanation – in fact the students make the resources themselves!

The Cards

You need a set of 36 blank cards for each team. Anything will do.  I spent about 10 minutes furious chopping on the guillotine for 7 teams, getting 12 cards out of each A4 sheet, so 3 sheets per team, 21 sheets in all.

The learning starts by getting the teams to create their cards using the following instructions:

1, Arrange your cards into 4 columns by 9 rows

2, You need to write the first 4 multiples of each number 2 to 10 so that every card has a number on it.

I put the 36 blank cards and the above on a slip of paper in an envelope and gave an envelope to each team.  With a bit of discussion within the teams, they worked out what they needed to do, but if you feel the task needs a bit more scaffolding you could use this diagram:

The Game

Once each team has their cards laid out on the table, they can start playing.

1. Shuffle the cards and deal them all out.
2. The objective is to collect “families” of numbers, e.g. 3,6,9,12 is the 3 family. The player with the most families wins.
3. Play starts with the first player asking one of the other players (they decide who) for a particular card, e.g. “Natasha, do you have a 5?” If Natasha has that card, she must hand it over. The first player can ask again (again, they can chose any player). If the answer is no, play moves on to the next player.
4. When a player has a family they must lay it face up on the table.
5. Play continues until all the cards are gone – it’s that simple!