1. Singapore Bar Method Modelling

2. Why was it needed? Innovation in pedagogy, developed by the Ministry of Education in Singapore in 1980’s Developed to address nationwide problem of mathematics incompetence and low problem solving abilities Distinctive feature of primary school mathematics in Singapore Aligned to C-P-A approach in primary teaching

3. Concrete – Pictorial – Abstract (C-P-A) Develops ; multiplicative reasoning, proportional reasoning pre-algebraic thinking. Dr. Yeap Ban Har

4. My Project focus To see the improvement in confidence of students tackling a worded question using the Bar-Method Modelling approach. Problem – When I asked about the approach at Bukit View Secondary, they said “oh we don’t use this here, we try to get them to use algebra” So I thought this approach is effectively dead in the water

5. Secondary focus However, upon reflection and after some research I realise that it could still have benefits to our students. After all it is often reported that; Literacy and numeracy standards in the UK have shown no improvement at all in the last three years with the result that our 15-year-olds are now three years behind those in the world’s best education system - Shanghai in China - in maths.

6. Secondary focus – problem solving Algebra – teachers will build on Bar Method Modelling to help students formulate equations Applied to problem solving by the encouragement of ‘draw a picture’ Understand the problem Devise a plan Carry out the plan Check and extend What is given? Need to find? DRAW A PICTURE DRAW A PICTURE Look for patterns Work backwards Simplify the problem Use the plan Change the plan Show work clearly Question answered? Make sense? Have you estimated?

7. Some Blogs

8. http://www.mathsnoproblem.co.uk/singapore-maths

9. Some Prominent Figures Model Method (The Singapore Bar Method) by Dr Yeap Ban Har https://youtu.be/Em2yERb3Kfs

10. Testimonials

11. How does it work? Students draw part-whole or comparison models to represent quantities Allows students to communicate their understanding of a problem using visual diagrams Students gain a clearer understanding of how ‘knowns’ and ‘unknowns’ in a worded question are related.

12. Part – Whole Model Q:Jane has 3 balloons, Ken has 8 balloons. How many altogether? Concrete Pictorial Bar Model

13. Comparison Model Q:Jane has 3 balloons, Ken has 8 balloons. How many more balloons does Ken have than Jane? [Concrete – Pictorial] [Bar Model – Pictorial] 3 8 ? (difference)

14. Imagine you have five oranges and three apples, how many more oranges than apples?

15. At first children model the problem with physical objects they can move around: like these cut-out pictures.

16. After a few months they start to draw pictures of the problem to help them think about it.

17. Over time children drop the pictures and just draw boxes. Then they start adding numbers as labels.

18. Once children are confident with the meaning of the number symbol they no longer need to draw all the boxes. However they know they can always draw the boxes in again if they need to convince themselves.

19. How much change if you pay for a £30 shirt with a £50 note? The model can be used to help visualise almost any maths problem.

20. Three people want to split a restaurant bill of £76. How much for a couple who want to pay together? The model helps break the problem down. First divide £76 by 3. Then times the answer by 2.

21. In a year group there are 50 children. There are 10 fewer girls than boys. How many boys? The model can help visualise the unknown quantity. You can see that x + x - 10 = 50. If you add the 10 you get x + x = 60. So x = 30.

22. Bar – Modelling Through the Topics

23. Fractions “Peter is selling pencils. He sold 3/5 of them in the morning and 1/4 of the remainder in the afternoon. If Peter sold 200 more pencils in the morning than in the afternoon, how many pencils did Peter have in the beginning?”

24. Fractions “Peter is selling pencils. He sold 3/5 of them in the morning and 1/4 of the remainder in the afternoon. If Peter sold 200 more pencils in the morning than in the afternoon, how many pencils did Peter have in the beginning?”

25. Fractions “Peter is selling pencils. He sold 3/5 of them in the morning and 1/4 of the remainder in the afternoon. If Peter sold 200 more pencils in the morning than in the afternoon, how many pencils did Peter have in the beginning?”

26. Fractions “Peter is selling pencils. He sold 3/5 of them in the morning and 1/4 of the remainder in the afternoon. If Peter sold 200 more pencils in the morning than in the afternoon, how many pencils did Peter have in the beginning?”

27. Fractions “Peter is selling pencils. He sold 3/5 of them in the morning and 1/4 of the remainder in the afternoon. If Peter sold 200 more pencils in the morning than in the afternoon, how many pencils did Peter have in the beginning?”

28. Ratios “The ratio of Amy and Karen’s money is 5:3. After Amy spent half of her money, she had $15 less than Karen. What was the total amount of money that both girls had in the beginning?”

29. Ratios “The ratio of Amy and Karen’s money is 5:3. After Amy spent half of her money, she had £15 less than Karen. What was the total amount of money that both girls had in the beginning?”

30. Ratios “The ratio of Amy and Karen’s money is 5:3. After Amy spent half of her money, she had £15 less than Karen. What was the total amount of money that both girls had in the beginning?”

31. Ratios “The ratio of Amy and Karen’s money is 5:3. After Amy spent half of her money, she had £15 less than Karen. What was the total amount of money that both girls had in the beginning?”

32. Decimals “Mary has $15 before shopping. After buying 5 identical pencil cases, she was left with $9. How much does each pencil case cost?”

33. Decimals “Mary has $15 before shopping. After buying 5 identical pencil cases, she was left with $9. How much does each pencil case cost?”

34. Decimals “Mary has $15 before shopping. After buying 5 identical pencil cases, she was left with $9. How much does each pencil case cost?”

35. More Bar-Modelling Through the topic levels

64. Next Steps Try the bar method in one lesson with one class or small group of students (preferably students of lower ability or lacking confidence). Bring to the next session the worded question that you tried out (can be a question from the Collins textbooks). Bring also an example of a students work where they have tried the method. We can collate the questions and put into one file on the shared area.

65. Bigger Picture The idea is that we will test to see the effect of using the bar-model method compared to conventional teaching methods Compare using a control group and an experimental group Either low ability or low confidence students Small groups or whole classes