Number patterns - what use are they anyway?

Maths in the early years is a lot of playing with numbers to discover what they do - turn them this way and that, add 10, take 5, make it as big as you can, what happens if... 

Essentially it's about patterns. Recognising number patterns is an important problem-solving skill. We want our children to see a pattern when they look at examples because they can then use that pattern to generalise and predict in another circumstance. Transferring the play to mathematical understanding is the goal.

Parents often ask how they can help their children with mathematical understanding. This is often prefaced with something along the lines of 'I couldn't do maths...' But everyone can play with patterns. They can be fun and creative and lead to every child finding mathematics accessible and enjoyable.

Here are some examples our Year 2s and Year 3s are playing with at the moment.

 Fluency, understanding, reasoning and problem solving with patterns like this is expected by mid Term 2 for all Year 3 students.

Our first Assembly of the year is always a great time to tell stories

I love numbers. They tell so many stories. And there are many stories that are important for our school - especially at the start of the year. This morning 1HJ helped me tell some stories at Assembly.
1120 - our total enrolments for 2019. We are a very big school!
1120 kids in 45 classes. When we opened in 2010 we had only 12 classes!
264 - the number of children we had on 27 January 2010
10 - we're 10 years old this year!
9 - we're not 10 yet but all nine year olds can't wait to get to double digits! We will be 10 in Term 4 and we'll be having a big party with many classes contributing something towards it
189 - our biggest year level is Year 4
143 - and our smallest is Year 3
158 - we have 158 Preps in seven classes. It's the most Preps ever!
4 - four students didn't have black shoes to complement their uniform this week. We're hoping parents will be able to sort this out this weekend! 4 is also the number of children not wearing a hat for outdoor play. A hat is a must and we encourage all children to personalise their hats so they are easy to recognise and find.
32 - the school's leaders have picked up 32 pieces of rubbish as we've walked around the school this this week. Much of this was plastic and straws. We would love all children to bring nude food lunches - and many are! I've seen some fabulous lunch boxes this week.
31 - being at school as much as possible is really important. Every day makes a difference! 31 children came to school late this week, 16 left early and 51 didn't come at all. That's too many for the first week.
25 - we are celebrating 100% attendance and 25 classes had every child at school every day.
7 - we've felt sad that 7 children have experienced mean moments. These were all swiftly dealt with by class teachers and staff on duty.
886 - in end of 2017 reports 886 children received the equivalent of an A or B for behaviour. This is amazing! When this many children are focused, polite, caring and considerate teachers can teach so much more and everyone learns better.

2019 is going to be a bright year and we've gotten off to a great start.

Number sense - what is it and how do we get it?

I've blogged about number sense before ( see The times they are changing - your times tables, that is.).  It's an area we have put a lot of emphasis on over the last 18 months. And we've seen that students with number sense approach maths with a 'can do' attitude (no political pun intended here), they enjoy maths more, they start problem solving tasks with purpose, and most simply, they just know what to do. (Hands up everyone who felt like this in a maths class at school!)

Last week a parent asked Kathleen Gordon, one of our Year 4 teachers, for some assistance in helping his child with maths. As luck would have it, Kathleen had spent the Friday before with some of our other teachers at the uni learning some new techniques and understandings for parent education in maths, and more specifically number sense.  Kathleen's reply is a 'must read' for every parent (edited below).

'There is a tension between wanting to reach year level benchmarks and making sure students have established a strong foundation in the basics first. For example, pushing students to memorise multiplication and division number facts before they have a sound understanding of addition and subtraction number facts will result in poor quality understanding of both concepts.

Research shows that rushing on leads to poor performance and anxiety about maths. In the words of a highly regarded maths educator - it's like building the roof of a house before the foundations are complete. You can do it but chances are it will fall over before too long.

This may not be what parents want to hear. There is no quick fix for any child. 

Research shows that both using timed practise drills and using strategies to learn number facts are effective. However, when students know and use the strategies, they can recall facts long after tests and use this information to work out extended facts (3 x 2 = 6 so 3 x 20 = 60) and approximation tasks, and hence problem solve effectively.

Our school program supports the learning of number facts in multiple ways including teaching strategies for learning particular number facts and doing regular timed practise drills. The strategies are taught at school and form part of the take home package to practise with as homework.

If students regularly use these strategies and repetitive drills at home and school (rather than just trying to rote learn and memorise the facts) they should in time develop the required fluency.

Some students prefer to learn with visual aids and others with auditory ones. We teach students to find their preferred approach and use it repeatedly. Repetitive activities will help students learn. The kind of repetitive activities you can try include:
- saying the strategy (when appropriate) when writing down the number fact e.g. 'I know that 5 + 5 is 10 so 5 + 6 is one more which is 11' and doing this repeatedly
- recording the strategies for particular number facts (see number 1) on a mobile device such as an iPod and listening to it repeatedly
- make a poster of the tricky facts and put them up where they will be seen (bedroom, on the back of the toilet door etc)
- playing with flash cards (you can make your own, download them from the Internet or buy them from the supermarket for about $10) or fact family cards (available from class teachers)
- playing ‘beat the timer’ games with a set of number facts (allow four seconds for each – ten number facts in forty seconds) play these on paper, on the Internet, CD Rom or iPod (or similar) device
- learning rhyming chants or listening to and signing along to multiplication songs (these can be purchased on the Internet)
 

Fact family cards which we use in the classroom are available from class teachers. You may like to use them too. They help students see the relationships between addition and subtraction and between multiplication and division. They are also useful because they appear to reduce the amount of number facts to learn - (learn one and get three more for free – i.e.. If I know 2 x 6 = 12, I also know 6 x 2 = 12 and 12 ÷ 6 = 2 and 12 ÷ 6 = 2 ).'
 
This is fantastic advice for any parent wanting to help their child 'know what to do' when faced with a mathematics problem - and these problems present themselves everywhere in life, too - at the supermarket (or anywhere money is used in a transaction), when calculating quantities of an item required for a project, when estimating time for bus timetables or the number of days until the holidays.  Maths is everywhere - and fluent number sense kids can navigate these situations with ease.

What to do in this weather...

If you are like me, you are probably quite affected by the weather. On a sunny day I feel optimistic and uplifted. Warm sunshine imparts a general feeling of wellbeing. Rain, clouds and cool weather leave me feeling somewhat deflated and at times, quite gloomy.

I have always found that connecting with others generates the same feelings as sunny days - I don't mean connecting on the Internet such as Facebook and email. I mean real connection involving a warm bodied person who laughs along with you, gossips and tells stories.

Games are often at the root of all connection between humans. As a youngster my Grandma taught me how to play 21; a little unorthodox - but my skills and fluency in adding and subtracting numbers to 21, remembering what was left in the deck, and strategising about what Grandma had in her hand was phenomenal. Games were played in our home a lot - Monopoly, Scrabble, draughts and chess were the order of the day. I also remember Boggle, Battleships (my brothers loved that), Mousetrap, Pictionary, Uno and Four in a Row. Playing games was great fun and it taught us kids a lot about cooperation, being a 'good' loser, and the place of competition. We would laugh a lot, look at each other's faces, practice 'give and take', use our manners, and would usually be sitting around a table talking about other things as we played.

On the weekend I read about some research into the educational power of parents*. A group of 125 parents were asked to play a board game one night a week for four weeks with their children. The results were stunning - parents and teachers reported improved concentration, social interaction, and cooperation with siblings. (Doesn't every parent want this last one!) Playing board games also boosted patience, teamwork, sharing, communication, sporting behaviour, critical thinking skills, and fluency in maths and spelling. Family relationships improved and parents were amazed that their children did not need to be glued to the TV or Nintendo.

Parent engagement in their child's learning and development takes many forms - and if you are interested in giving your child's learning, manners, compassion, play habits, kindness and thinking skills a boost, you can't go wrong with a deck of cards and a game of 21! (Perhaps draughts might be a bit more politically correct these days.) And let's face it - our current weather system is certainly giving us plenty of reasons to stay indoors and enjoy the company of our family.

These days I still play games; many on my iPad. These are often designed to play alone or against the machine itself. I still find a way to interact with someone else, even if it means posting a 'Help' on my Facebook page for a 4Pics 1Word puzzle.

* Herald Sun, Wednesday 19 August 2009, p 27