After a mathematician friend of mine mentioned perfect numbers, I could not resist turning it into an investigative lesson! Turns out, a number is perfect if it is the sum of its factors (excluding itself). So many questions spring to mind to investigate! What numbers are perfect? Is there a pattern? Can we predict if a number is likely to be perfect? If the sum of the factors is greater than the number, it is known as an abundant number, if less, then a deficient number. So, I made a couple of investigation sheets (inspired by some questions I found on nrich.com), some with suggestions and some just asking them to sort numbers. I did ask them to have a theory or question in mind, though. I also added a Lightbulb Moments area for when they say things like 'Oh! A prime number couldn't ever be perfect because...'. (I am also going to do a display of this next year - all of our lightbulb moments. I have to include Gru from Despicable Me!). There was lots of opportunity for using mathematical vocabulary and even some English links when talking about abundant and deficient. Anyway, enjoy!
Recently, I held a Maths workshop. I like it best when the children both design and run something like this. It gives them a sense of pride to show-off what they are learning and to be able to lead their family members in activities. I usually run these things as a 'drop-in', with no formal introduction or anything. The parents come in when they collect their children at the end of the day and their child leads them around.
All of the activities here also make good warm-up activities for your Maths lessons.
Here are some snaps from my most recent Year 5 Maths workshop:
Show me your way
This station shows different calculations for people to write how they would work it out. I use this as a starter activity quite regularly. It's a good way to get children to think about different strategies and how they suit different questions and to think about how to present their working out so someone else can see their method.
Use what you know to find out what you don't know
Here, we were making a mindmap of derived facts. We worded this as 'Because I know 4 x 3 = 12, I also know...'. Some examples for this fact were 0.4 x 3 = 1.2, 40 x 30 = 1200, 8 x 6 = 24 (doubling all), 4/5 x 3 = 12/5=2 2/5, 12=4+4+4
We play this game a lot! When I use it as a starter, I give them a minute to think of as many as they can, either by themselves or using a Kagan structure, such as Rally Robin. All they have to do is put things of the same value between the equals signs. I give them a starting value, such as 2/5 and encourage them to think of different forms, e.g. equivalent fractions, calculations, decimals, words.
e.g. 2/5 = 0.4 = 1/5 + 1/5 = 1/5 x 2 = 1 - 0.6 = 1 - 6/10 = 1 - 3/5 = 2 fifths
You get the idea. It's a great way to get them thinking about equivalences and to reinforce the fact that the equals sign means just that - equal to and does NOT mean the answer is. Right from Reception, we move the equals sign around to try to avoid this misconception in the first place.
Some Foundation Stage-style practical learning here - very simply, pin the dates onto the timeline. A chance to practice using a scale and estimating. This also happens to fit in beautifully with our World War 2 topic.
What can you tell?
I LOVE this way of approaching data. In the past, I have seen my most able mathematicians rush straight to the question, take a quick glance at the graph or chart then write an incorrect answer before giving any time to looking at the graph and trying to work out what it is showing them.
The way I am teaching it is to give them graphs, charts and tables with no questions. The task is merely to look at it and write down everything they can work out from it. This open-ended task self-differentiates and takes very little preparation. The speech-bubble post-its seem to make the world of difference to the children's enjoyment!
One of the children's favourites! I challenge my top group to write their working out in one calculation. As a starter, I use the IWB. For this workshop, I put out laptops.
Although it's easy to make yourself, there's a super version on the NRICH website here, which is great, albeit very strangely organised. There's a fractions version, too!
Speaks for itself. Fun though!
I try not to use this blog as a soapbox, but I am on a mission to try to STOP teachers insisting on showing young children regular shapes first. In my opinion, this is the reason that my YEAR 5 children think that something is a pentagon because it 'looks like a house' or that something must be a triangle because it is 'pointy'. These are children who can tell you beyond all doubt how many sides a pentagon or triangle has, yet when you show them a pointy shape, their first, instinctive response is that it is a triangle. ARGH!!!!! So, I am all about irregular polygons at the moment. Anyway, rant over. ish.
So, we played a game. I gave each team of 4 a loop of string. I then challenged them to make different polygons in different ways. For example, in the picture above, I asked them to make a hexagon using all 4 children. I then asked them to make a different one or to just use 3 of the children.
The challenge really came when I asked then to use 3 children to make a decagon. Whoooooo! What a lot of debate and reasoning this took! I had to stop them in the end when I realised that the reason they were struggling was because not a single team had considered making a concave shape, which is far easier to hold. Concave shapes just don't come naturally into their heads as they are not shown these when they learn about shape.
I will definitely play this game again. It made a fun, hands-on warm-up and the kids loved it!
Happy New Year! Well, after an eventful Christmas and New Year, it's been full steam ahead this term. Our new topic is all about Holidays. Yes, I know that this is a common Foundation Stage and KS1 topic, but I've amped it up to KS2! There is so much learning to be done!! The children are loving this topic already. Anyway, I should start at the beginning...
To hook them into the topic, I allowed each team of 4 to come up with a 'tour group', who could be travelling together. We had pensioners, 2 couples, a single mum with 3 children, a family with 2 adults and 2 children, a swimming team on a social holiday and a group of university students. They thought of likes, dislikes, considerations (such as disabilities or allergies) and group dynamics. I then took them and redistributed them to different groups, along with a suitable budget and 2 holiday destination options.
Opening their envelopes was the funniest experience! The 'swimming team' squealed with excitement, the 'pensioners' groaned and laughed and the single mother declared that 'they'd better have a kids club because she's stuck on her own with them all year - this is her break', meanwhile a 'teenage daughter' was sulking about not being able to charge her iPhone in a tent! Talk about getting into character!!
In Maths, we decided to try to figure out how Trip Advisor rank attractions after realising that the top attraction often had a lower rating than those further down. I took screen shots of some of the top attractions in our local area (Manchester), and we had a look at the bars and numbers to check what each represented. After a quick recap of finding percentages using a calculator, the children explored possibilities. Some tried finding the percentage of 'excellent' reviews, some wondered if it was based on the percentage at 'average' or above (thus moving themselves on to a 2-step problem, having to total the categories they were including).
Okay, I know that this is nothing new, but we had a lot of fun measuring distances with maps, scales and pieces of string! We then extended this a bit to calculating how long a journey would take at a given speed. The maps we used were just simple Google maps of Greater Manchester, allowing us to find the distances between our school and local attractions. Later in the week, we converted these from metric to imperial, because let's be honest - who measures distances in kilometres?!
Check back next week for details about the walking tour we are designing for our parents and the fantastic speaking and listening that has come out of it! Sorry for the short post but, as you can see, we've been very busy! More to come soon, promise!
More real-life Maths! One of my children has a brother recently diagnosed with type 1 diabetes. She was been telling me all about his diet and that she has been helping her mum to work out what he has eaten and what he can have. Ping! Light-bulb moment! (We have those in our class, too!) So, our next real-life Maths challenge was to plan his meals.
We started off by looking at what nutritional information is available and what it means, recapped units of measure quickly and reading tables.
As usual in these challenges, I encouraged the children to make their own choices about presentation. Most of them went with a table.
As a plenary, the children thought about what skills they had used and noted them below their work. It was a nice way for them to see how their Maths skills overlap in real-life situations. (It was PJ day for Children In Need - hence the dressing-gown!)
I love teaching Maths. More than any other subject, learning is tangible - you can so often do something by the end of the lesson that you couldn't at the beginning. I have a real drive at the moment to give children the chance to apply their Maths in real-life contexts. I don't mean giving them word problems describing real-life situations, but actually doing a practical activity .
So, here's Friday's challenge:
Download the (slightly differentiated) letter:
I gave each pair an iPad and showed them some recipe and grocery shopping websites. We chatted a little about what we would need to find out and then off they went! Asda & Ocado were great, because you can add to your online basket without registering.
I like real-life, open-ended tasks like this one. There are so many directions to take it in - cost per person, scheduling the timings of the preparation and dinner, using ratio to calculate how much they would need for their guests. As I went around the classroom, I could guide and challenge each pair appropriately, letting their learning be guided by their experience on the day and questions they raised. While they may never be contestants on Come Dine With Me, they will inevitably have to budget, plan meals and do their grocery shopping at some point in their lives.
I've started making a note in the back of my diary every time I use Maths in my life. I'm quickly building a bank of lesson ideas that can be stretched, differentiated and explored in a multitude of ways: planning a trip (timetables, costs, data analysis of how popular a place is), sorting out bills & energy savings, buying Christmas gifts & calculating how much gift-wrap to buy & the net of the boxes... the list goes on and on!
Alright, I have never been one for boring displays, but recently I have become tired of bordered rectangles! Don't get me wrong, I have one or two, but I have been experimenting with different styles.
For my Writing and Maths walls, I just used big sugar paper sheets, wrote the headers on in felt-tip pen, then stuck them on the wall at a jaunty angle! We use Maths Makes Sense, so my Maths wall is split into Arithmetic, Geometry, Data & Measure and Reasoning. I just stick and scribble on it when I have something to remind them of!
For writing, I have broken the writing process down into 4 phases: researching the genre (deconstruction, pulling out the features, reading activities to explore), making a plan, writing, editing.
I've also been playing with my new window pens! Take a look on my lotus flower post.
Hi! I'm Mrs P: passionate primary school teacher!