1. Maths – Helping our children to achieve
DEBORAH HAWORTH
Assistant Head
Maths Lead across the Federation

2. Aims of the session
To outline some of the changes in the approach to maths teaching
To share some of the activities that we do in school
To provide ideas on how you can support your child at home

3. When you hear the word Maths what do you think?
My favourite subject!
I struggled with it at school.
PANIC!
I found it difficult at school and now so does my child.
A life skill!
I wish I was learning it how my child is.

4. Maths teaching – a new approach
Developments and changes
The expectations are that children will cover the maths objectives for their year – these expectations have been raised
However, decisions about when to progress are based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly will be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material will consolidate their understanding, including through additional practice, before moving on.
Using a concrete, pictorial, abstract (CPA) approach at all ages for all children
Fluency and rapid recall
Depth
Mastery

5. Concrete Concrete representation
This is a 'hands on' component using real objects and it is the foundation for conceptual understanding

6. Pictorial Pictorial representation
Using representations, such as a diagram or picture of the problem.

7. Bar modelling

8. Bar modelling

9. Bar modelling

10. Bar modelling

11. Regrouping in ones + 1 4 9 3 2 8 Add the ones Add the tens
Hundreds
Tens
Ones
9 ones + 2 ones = 11 ones
Regroup the ones + 1 4 9 3 2 8
Add the ones
Regrouping in ones
Add the tens
Add the hundreds

12. Abstract + 1 4 9 3 2 8

13. Abstract experiences Abstract representation
The abstract stage - a child is now capable of representing problems by using mathematical notation, for example: 12 ÷ 2 = 6

14. What are the characteristics of a child who is good at maths?
takes risks
asks questions and explores alternative solutions without fear of being wrong
enjoys exploring and applying mathematical concepts to understand and solve problems
explains their thinking and presenting their solutions to others in a variety of ways
reasons logically and creatively through discussion of mathematical ideas and concepts
becomes a fluent, flexible thinker able to see and make connections

15. Getting to know activities
Can you show me …?
What do you know about…?
Where have you seen …? 24
How many ways can you make…? (using the 4 operations)
What is special about the number…?

17. Welcome mistakes! They are learning opportunities!

18. The object of learning
What’s a dog?

20. To understand what something is we need to understand what it is not.
What’s the same?
What’s different?
If a person wants to teach a child what dogs are, then he or she will probably show it many different kinds of dogs. However, Variation Theory posits that one cannot discern through ‘sameness’ (Marton, 2009). For example, the child in question may think that anything with four legs and a tail is a dog. So, when it sees a cat it will think that the cat too is a dog. Difference or variation is required for the child to discern the defining features of a dog. In other words, we must also show the child what is not a dog. When it is able to differentiate other animals, such as cows, horses, cats and pigs, from dogs, we can say that it has gained a deeper understanding of ‘dog’. For this child, a dimension of variation (animals that have four legs and a tail) is open, and ‘dog’ becomes a value in the dimension of variation, and all of the other animals in this dimension constitute the external horizon of ‘dog’.

21. Will children understand what 1 5 is if I show them lots of examples of 1 5 ?

22. Are they all fifths? If not, why not?
Show representations that are not the fraction. Why not? (Either the parts are not equal or the number of parts is too many too few for that fraction.)
Move to definition that you need 5 equal parts.

23. To understand what something is we need to understand what it is not.
If a person wants to teach a child what dogs are, then he or she will probably show it many different kinds of dogs. However, Variation Theory posits that one cannot discern through ‘sameness’ (Marton, 2009). For example, the child in question may think that anything with four legs and a tail is a dog. So, when it sees a cat it will think that the cat too is a dog. Difference or variation is required for the child to discern the defining features of a dog. In other words, we must also show the child what is not a dog. When it is able to differentiate other animals, such as cows, horses, cats and pigs, from dogs, we can say that it has gained a deeper understanding of ‘dog’. For this child, a dimension of variation (animals that have four legs and a tail) is open, and ‘dog’ becomes a value in the dimension of variation, and all of the other animals in this dimension constitute the external horizon of ‘dog’.

24. How many groups are there? How many things in each group?
Key questions
How many groups are there?
How many things in each group?
Understanding multiplication strand
Key teaching points
[1] Answering the key questions. Eg There are 3 groups. Each group has 2 dogs.
[2] Expressing mathematically in different ways: = 6; 3 twos = 6; 3 groups of 2 = 6
[3] Devising a summative statement: There are six dogs altogether.

25. Teach what isn’t a multiplication sentence

26. Useful things to practise at home:
Doubles and halves
Number Bonds of 10, 20 and 100
Adding or subtracting 2 small numbers
Multiplication tables and division facts
Linking multiplication tables x8 is double x4, x6 and x3 etc.
Making links 7x10 is 70 so 7x20 is 140
Rounding and estimating – shopping, eating out

27. Helping at home Cook – measuring and weighing
Look at numbers in the environment e.g. telephone keys, number of plates, door numbers, book pages, sleeps until Christmas!
Telling the time
Money
Comparing heights
Birthdays, Months of the year, Days of the week

28. Images with mathematical potential
What is this?
Where would you see these?
How many do you think there are?
What shapes can you see?
Are there any lines of symmetry?
Is there a repeating pattern?
What else do you notice?
How many…..do you estimate there to be?
What other questions could we ask?

29. Calendar activities Mark off days
What day is it today? Yesterday was…. Tomorrow will be….
How many days until the weekend?
Who has a birthday this week? How many days until Jack’s birthday?
How many school days left this month?
What fraction of the month is either a Monday or Tuesday?
Include rhymes/songs about days of the week, months of the year, seasons, weather….

30. Props around the home
A prominent clock- digital and analogue is even better. Place it somewhere where you can talk about the time each day.
A traditional wall calendar-Calendars help with counting days, spotting number patterns and
Board games that involve dice or spinners-helps with counting and the idea of chance
A pack of playing cards- Card games can be adapted in many ways to learn about number bonds, chance, adding and subtracting, 13 times tables
Measuring Jug-Your child will use them in school, but seeing them used in real life is invaluable. Also useful for discussing converting from metric to imperial
Dried beans, Macaroni or Smarties- for counting and estimating
A tape measure and a ruler- Let your child help when measuring up for furniture, curtains etc
A large bar of chocolate (one divided into chunks)- a great motivator for fractions work
Fridge magnets with numbers on- can be used for a little practice of written methods
Indoor/outdoor Thermometer- especially useful in winter for teaching negative numbers when the temperature drops below freezing
Unusual dice- not all dice have faces 1-6, hexagonal dice, coloured dice, dice from board games all make talking about chance a little more interesting
A dartboard with velcro darts- Helps with doubling, trebling, adding and subtracting.
Shapes – 2-D and 3-D – a tin of beans is a cylinder

31. Developing Maths Prompting thinking & questioning
Providing opportunities to manipulate, experience and see (use of resources)
Develop thinking through investigation
Reasoning and making connections
Engaging in talk
Enabling learning through drawing attention to different possibilities
Encouraging children to make links and generalise
Maths is about spotting patterns, making links and understanding how pieces of knowledge fit together NOT purely memorising facts and procedures by rote – but this is VERY important

32. Finally... Don't tell them you are hopeless at maths
You may remember maths as being hard, but you were probably not hopeless, and even if you were, that implies to your child, “I was hopeless at maths, and I'm a successful adult, therefore maths is not important”
Do play (maths) with your child
There are opportunities for impromptu learning in games with real people that you can't get from a DS or Xbox
Remember to refer to the booklet on the website
Do get excited about maths!

33. “Arithmetic is being able to count up to 20 without taking off your shoes”.
Mickey Mouse