Bar Method at Belmont School Thursday 16th November Numicon Counters Footballs Strip of paper Paper clip NCETM videos? – strip of paper Planning from Mathematics mastery and Caroline to be shared as well. http://downloads.bbc.co.uk/skillswise/maths/singapore-model/singapore-model-cutout-pictures.pdf  In Singapore, children are encouraged to use visual models such as ‘bar models’, ‘ten frames’, arrays and place value charts. We are going to focus on the ‘bar model’ which is specifically used to help children make sense of word problems. The approach is meant to reveal the structure of the mathematics in the problem. It is not a tool for performing a calculation. In Singapore, children begin to solve multi-step word problems from the equivalent of our Year 4 using this technique. This is applied to solve increasingly more difficult problems. Some schools in England are now beginning to apply this approach and are finding it really helpful. Deconstructing the Singapore Model Method 1. It’s a problem-solving strategy—a subset of the “Draw a diagram” strategy. 2. It’s a hybrid of China’s line method and Russia’s box method. 3. It’s the an acceptable way of showing your working s out in SATS 4. It’s a problem-solving method that isn’t recommended for visually challenged or impaired learners. 5. It allows questions traditionally set at higher grades (using algebra) to be posed at lower grades (using bars). The model diagram is actually an algebraic method of using boxes to represent unknown variables. With the model diagram therefore, a student can understand algebraic concepts more visually snd concretely. Going to be taking this up to Year 6 – need to now the impact of what you are doing lower down the school – has on further up the school – always good to have a year 6 teacher here – classes say – they know that – when get to year 6 ch. Struggle – needs to be a whole school policy to follow it – very positive feedback from schools who have introduced it.

Our Year of Maths Why is Maths a focus at Belmont? What do we know about Maths achievement at Belmont? What do we intend to achieve?

How do we teach Maths at Belmont? Concrete – Picture – Abstract Calculation Policy ..\Maths\Calculation Policy.pdf

What is the Singapore Bar? The bar model method is a strategy used by children to visualise mathematical concepts and solve problems. The method is a way to represent a situation in a word problem, usually using rectangles. Whole Part Part

Why is the Singapore Bar being promoted? Adaptable across many mathematical topics Helps pupils develop a deep, long-term and adaptable understanding of maths Uses concrete, pictorial and abstract approach

Pictorial Concrete Abstract ? 8 + 2 = 10 8 2

How do we use it across the school The bar model is introduced in EYFS and continued and developed throughout the year groups. Use of CPA approach is used alongside the bar model. It models the question to aid understanding – it doesn’t give the answer!

1. Lining up objects in a row Helping your child develop conceptual understanding 1. Lining up objects in a row Children start by counting familiar things using blocks or cut-out pictures they can physically line up in a row. For instance counting pieces of fruit, their own ages, or people in the room. With one block or cut-out picture for each orange, or year, or person. They can learn most basic maths concepts with these objects. For instance add objects to the row, or take them away, to understand adding and subtraction. Or split a row in the middle to understand halving.

2. Drawing boxes around pictures Then children start to draw pictures on paper of the things they are counting, with a box around each picture. So there's one box for each thing they are counting. Over time they drop the pictures and just draw the boxes. They learn the concept of addition first and then they introduce the bar method to solve problems.

3. Labelling the boxes 3 Gradually, once they are confident with drawing boxes to count objects, children start to write the number of boxes as a figure above the drawing. Eventually they no longer need to draw all the boxes. They just draw one long box or bar and label it with the number. This step away from one-to-one representations to symbols is crucial and it may take a year or more for some children to become confident with it. But the benefits later on are worth it. This model of numbers as labelled bars is known as the Singapore model, and it's a tool children can use to understand almost any concept in maths, including multiplication and division and even algebra. Professor Lianghuo Fan, former editor-in-chief of Singapore's maths textbooks, has researched the reasons for Singapore's success in maths. As he puts it: "People have different views about the reasons for Singapore students' performance, but one thing that is universally agreed is that the Singapore model method is key."

The 4 operations 4 + 5 = 5 + 4 = 9 – 5 = 9 – 4 = 4 + ? = 9 ? + 5 = 9 Part-part-whole Addition and subtraction 9 4 5 4 + 5 = 5 + 4 = 9 – 5 = 9 – 4 = 4 + ? = 9 ? + 5 = 9 9 - ? = 4 ? – 4 = 5

Comparison Fred has 7 pairs of shoes. Mark has 2 more pairs of shoes. How many pairs does Mark have? 7 F 7 2 M

Finding the difference A lolly costs 6p. Sally paid with a 10p coin. How much change does she get? 10p 6p ?

Problems involving totals Bob and William have 19 Christmas presents altogether. William has 5 more than Bob. How many presents does William have? B 19 Find the cost of the pink bars? 19 – 5 = 14 One pink bar? 14 divided by 2 = 7 Williams? 7 + 5 = 12 W 5 How can we find the cost of the pink bars?

Multiplication and division Ms Childs puts four 5p coins into her purse. How much is in her purse altogether? ? 5p 5p 5p 5p

I have 36 cars shared into 4 equal piles. How many in each pile? Division (sharing) I have 36 cars shared into 4 equal piles. How many in each pile? Division (grouping) I have 36 cars in groups of 4. How many groups can I make? 36 ? 36 4 4 ?

Scaling as multiplication John has six marbles. Alex has five times as many marbles. How many marbles does Alex have? 6 J 6 6 6 6 6 A

Problems involving totals William have two times more pears then Ben. They have 24 pears. How many pears does William have? B 24 W Find the cost of the pink bars? 3 bars = 24 One pink bar? 24 divided by 3 = 8 Williams? 8 x 2 = 16 Two times more, not twice as amany. How can we find the cost of one pink bars?

How can you help at home? Rock Star Times Tables Mathletics Useful resources and websites BBC - KS2 Bitesize - Maths Encourage the use of concrete objects and move into pictorial and abstract