1. Welcome to the KS2 Parents Maths Workshop

2. Thinking is at the heart of Mathematics and therefore should be at the heart of mathematical teaching and learning.

3. Aims of today
To get an insight into how Maths is taught at St Mary’s RC Primary School.
To take away some ideas to support your children at home.
To take part in a variety of maths activities.

4. Maths at St Mary’s Let’s start doing some Maths….
Add these numbers up:
What strategies did you use?

5. The New Maths Curriculum
Children should:
Become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations and developing an argument, justification or proof using mathematical language.
Solve problems by applying their mathematics to a variety of problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

6. Maths at St Mary’s RC Primary
more
subtract
product
factor
sum
add = + x %
Here is a receipt for some shopping. How much did I spend? How much change did I get from £20?

7. Maths at St Mary’s RC Primary
Number bonds are the window to success in KS2 and it is vital that your child knows these securely as they enter this phase.
By the end of Year 4, your child is expected to know all their times tables up to 12 x 12. To ensure this, we practice the tables daily and explore connections between the tables. e.g. to find 6 x 8, we know 5 x 8 is 40, so 6 x 8 is one more 8, so is 48.

8. Maths at St Mary’s
An App to download to help with times table learning:
100 Squares Calc.
My Maths also has a good bingo activity in the Games section.

9. Singapore Maths This term we introduced Singapore Maths from Y1 – Y3.
The teaching of maths in Singapore works on the premise of:
Early Success
Strong Basics
Steady Progress

10. Singapore Maths Children must know the following inside out:
Number bonds to 9 10 20
100
Multiplication tables

11. Singapore Maths

12. Use of appropriate strategies
Singapore Maths
Spiral approach
C P A
Use of appropriate strategies

13. The Spiral Approach
The Spiral Approach (Bruner 1977, 1996) is adopted to ensure that concepts and skills are sequenced appropriately across levels and in increasing depth. It allows for inter-relating of new learning with previous learning, thus building on from children’s understanding.

14. Singapore Maths
This is a short video showing how Singapore Maths works.

15. Singapore Maths Teaching is based on what they call the CPA process
Concrete  Pictorial  Abstract

16.  Singapore Maths Concrete The use of real life objects
Then moving on to Manipulatives or what we refer to as apparatus 

17.  Singapore Maths Pictorial Abstract
(In the in case of Singapore Maths this is the Bar Method)

18. Place Value
Place value is at the heart of the number system. All digits have a value and a secure understanding of this will enable children to use and understand different calculation methods.
As a school the children spend the first term each year concentrating on place value, number bonds and multiplication tables.

19. Place Value using CPA
Concrete (Apparatus) Pictorial Abstract

20. Dienes Equipment 1 2 3 9

21. Representing Numbers using Dienes

22. 4-Step Problem-Solving Strategies George Polya [1887-1985]
Devise A Plan
List & check
Model drawing
Look for pattern
Working backwards
Can you state the problem in your own words?
What are the unknowns?
Understand the
Problem
What information can you obtain from the problem?
What are you trying to find?
Carry out plan
Check each step
Look Back
Make Sense/Reasonable

23. Problem Solving Thinking skills Heuristics
The heuristics of problem solving are the strategies or tactics used in solving problems.
Thinking skills
Heuristics

24. Problem solving Heuristics Thinking Skills Act it out
Restate the problem in another way
Use a diagram/model
Use tabulation
Make a systematic list
Look for pattern(s)
Work backwards
Use before-after concept
Use open sentence
Make a supposition
Simplify the problem
Solve part of a problem
Thinking Skills
Classifying
Comparing
Sequencing
Analysing parts and whole
Identifying patterns and relationship
Induction
Deduction
Spatial Visualisation

25. Model drawing method Helps pupils visualise situations
Creates concrete pictures from abstract situations
Builds on the pupils’ learning through seeing and doing
Transforms words into recognisable pictures/illustrations

26. Model drawing method Primary 1 – 6 [years 2-7]
draw pictures to illustrate numbers (nos.  20)
introduce bar models (simple word problem – nos.< 100)
Part-Whole Model
Comparison Model (Fraction Model)
Before-after concept

27. Stages of Model Drawing
Pupils have been introduced this method as
early as Primary 1 [year 2]
STAGE 1: PICTORIAL REPRESENTATION
This is the introduction to the model- drawing method, or the bar method. + =

28. Stages of Model Drawing
STAGE 2: DRAW PICTURES INSIDE A BAR
This prepares pupils for the use of ‘bars’. It also helps them to be more focused and detailed in their representations. =

29. Stages of Model Drawing
STAGE 3: REPLACE PICTURES WITH DOTS AND DRAW ARROWS OUTSIDE THE BARS
The pictures are now represented using other symbols. This eases the drawing of complicated pictures. At this stage, the most important focus is on the arrows drawn outside the bar. ?

30. Stages of Model Drawing
STAGE 4: REPLACE DOTS WITH NUMBERS
A bar representing a bigger value should be such that it looks longer than a bar whose value is less. This helps in the visualization of the solution. 3 1 ?

31. Stages of Model Drawing
STAGE 5: USE NUMBERS OUTSIDE THE BARS
As problem-solving becomes more complex, numbers are written outside the bars. ?

32. Stages of Model Drawing
STAGE 6: LABEL THE BARS
At this stage, the pupils would have been quite comfortable with the use of models. Hence, we teach them to label the bars appropriately.
Example: Hani has 12 marbles. Ben has 4 more marbles than Hani. How many marbles does Ben have? 12
Hani 4
Ben ?

33. How Model Drawing or the Bar Method is used.

34. How Model Drawing is Used.
Part-Whole Model: For addition & subtraction
1. Finding the whole, given the parts. ?
2. Finding an unknown part, given the whole and vice versa a b ? ? a b b

35. Using Model Drawing

36. Using Model Drawing

37. Using Model Drawing

38. Comparison Method

39. Using Model Drawing
Comparison Model: For comparison Using two or more bars depending on the number of types items involved. Example : Ali has 10 marbles. Bob has 2 more marbles than Ali. How many marbles does Bob has? Ali Bob 10 2

40. Using Model Drawing Example: Mom is 28 years older than Joe.
Mom is 4 years younger than Dad.
Their total age is 84 years old.
What is Mom’s age?

41. Mom is 28 years older than Joe. Joe Mum
Example:
Mom is 28 years older than Joe.
Joe
Mum 28

42. Using Model Drawing
Example: Mom is 28 years older than Joe. Mom is 4 years younger than Dad. 4 28
Joe
Mum
Dad 84

43. Using Model Drawing Ali has £96 less than Ben.
Susan has £302 more than the total
amount that Ali and Ben have.
Susan has £623 more than Ali.
How much money does Susan have ?

44. Using Model Drawing
Ali Ben Susan ? = = 225 Susan has = 848 96
302
623

45. Using Model Drawing The Fraction Model
There are 3/5 as many boys as girls.
If there are 75 girls, how many boys are there?
Boys
Girls 75

46. Activity ideas
Draw a line. Mark 0 and 10 (or any number range needed). Roll a dice. Decide where that number would go and write it in. Repeat. This could also be played with playing cards. You can also start at any number and include whatever your child needs, eg decimals or fractions.
Inbetweenies
Start by asking for a 2 digit number. Place it at the start of the line. Now ask for a higher 2 digit number and place at the end of the line. Now keep asking for numbers in between until you start having to think about decimals and then the fun begins! 39
39.4 40 50 67

47. Fractions and decimals
Player 1 chooses 2 numbers to make into a fraction. Using a calculator divide these 2 numbers to convert to a decimal. Place them in roughly the right place along the line then cross off the 2 numbers used. Now player 2 chooses 2 other numbers. The winner is the first person to get 3 fractions/decimals in a row without the other player stopping them.

48. Activity ideas
Place Invaders! You can use a calculator if you like. Enter a 5 digit number into your calculator ensuring each digit is different. You may not use 0. When a number is called out, look to see if this digit appears in your number. If it does, you can change that digit to 0 by subtracting the appropriate number using the calculator keys. The first to reach exactly zero is the winner.

49. Nice or Nasty! Nice version!
This game can be played in a number of ways, including with decimals. Either play it by seeing who can end up with the highest (or lowest) number. You need to decide beforehand. Using a 1-9 dice, take turns to roll it. Whatever number you land on needs to be placed on one of your squares. If you are making a 3 digit number, for example, and you are seeing who gets the highest number then you would be hoping to place any larger numbers in the hundreds column and smaller ones in the ones column, but you never know what you will roll! You can also play a version where you add numbers and decide on your target total at the start of the game.
Nice version!
Have a target total and the winner is whoever gets closest to that target without going bust.
Nasty version!
You are allowed to place digits on your partner’s board to make it trickier for them.

50. Q & A with some of the Maths Team
MATHS PLAYTIME
Q & A with some of the Maths Team