Welcome to the KS2 Parents Maths Workshop

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

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.

Maths at St Mary’s Let’s start doing some Maths…. Add these numbers up: 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 What strategies did you use?

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.

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?

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.

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.

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

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

Singapore Maths

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

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.

Singapore Maths This is a short video showing how Singapore Maths works. https://youtu.be/PfPcn3SohrI

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

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

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

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.

Place Value using CPA Concrete (Apparatus) Pictorial Abstract

Dienes Equipment 1 2 3 9

Representing Numbers using Dienes

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

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

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

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

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

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. + =

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. =

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. ?

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 ?

Stages of Model Drawing STAGE 5: USE NUMBERS OUTSIDE THE BARS As problem-solving becomes more complex, numbers are written outside the bars. 3 1 ?

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 ?

How Model Drawing or the Bar Method is used.

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

Using Model Drawing

Using Model Drawing

Using Model Drawing

Comparison Method

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

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?

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

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

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 ?

Using Model Drawing Ali Ben Susan ? = 623- 96 -302 = 225 Susan has 623 + 225 = 848 96 302 623

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

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

Fractions and decimals 1 2 3 4 5 6 7 8 9 10 11 12 0 1 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.

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.

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.

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