Bar Model A visual model for helping to

Bar Model A visual model for helping to solve maths problems.

The bar model is used in Singapore and other countries, such as Japan and the USA, to support children in problem solving. It is not a method for solving problems, but it is a way of revealing the mathematical structure within a problem and gaining insight and clarity as to how to solve it. It supports the transformation of real life problems into a mathematical form and can bridge the gap between concrete mathematical experiences and abstract representations.

The bar model

The “basic” part-whole bar model In problems involving addition and subtraction, there are three possible unknowns… as illustrated here. Given the value of two, the third can be found.

The “basic” part-whole bar model This diagram encapsulates all of the following relationships: a=b+c; a=c+b; a–b=c; a–c=b

Understanding the basic part-whole model Addition and Subtraction

Solving problems using the part-whole model

Using the part-whole model to solve problems Addition and Subtraction

Using the part-whole model to solve problems Addition and Subtraction I have 12 sweets and my mum gives me 6 more. How many sweets do I have altogether?

Using the part-whole model to solve problems Addition and Subtraction

Using the part-whole model to solve problems Addition and Subtraction 582 children took part in a schools sports day. There are 214 girls. How many boys are there?

Using the part-whole model to solve problems Multiplication and Division

Introducing the comparison model

Using the comparison model to solve problems Addition and Subtraction

Using the comparison model to solve problems Addition and Subtraction There are only red and blue fish in an aquarium tank. There are 246 red fish, and there are 113 fewer blue fish. How many fish are there in the tank?

Using the comparison model to solve problems Addition and Subtraction John paid £ 4516 for his holiday and Sue paid £ 1259 for her holiday. How much more did Sue pay?

Using the comparison model to solve problems Multiplication and Division

Using the comparison model to solve problems Multiplication and Division There are 34 white cars in a car park. There are six times as many red cards as there are white. How many red cars are there?

Problem solving beyond the four operations

Using the bar model for… Fractions, Ratio and Percentage What might the question be?

And for solving problems of increasing complexity….

…the working backwards strategy! 16 m 22 s

Using the bar model to solve problems Try these for yourself. Can you use the bar model to help? There are 18 girls in a class. 25% of the class are boys. How many children are in the class? Is your bar model the same/different than other people’s?

Using the bar model to solve problems Try these for yourself. Can you use the bar model to help? Is your bar model the same/different than other people’s?

Using the bar model to solve problems Try these for yourself. Can you use the bar model to help? Lauren spent 20% of her money on a dress. She spent 2/5 on a book. She had £ 72 left. How much money did she have at first? Is your bar model the same/different than other people’s?

Using the bar model to solve problems Try these for yourself. Can you use the bar model to help? I cycled to Highfield Park. I completed 3/7 of the distance in the morning and half of the remaining distance in the afternoon. I still had 16 miles left to travel. What is the total distance to Highfield park? Is your bar model the same/different than other people’s?

Using the bar model to solve problems Try these for yourself. Can you use the bar model to help? A computer game was reduced in a sale by 20% and it now costs £ 48. What was the original price? Is your bar model the same/different than other people’s?

Using the bar model to solve problems Try these for yourself. Can you use the bar model to help? Is your bar model the same/different than other people’s?

Using the bar model to solve problems Try these for yourself. Can you use the bar model to help? The population of Atos is three times that of Bem, and 30 000 more than that of Cinder. The total population of these three towns is 390 000. Find the population of Atos and of Cinder. Is your bar model the same/different than other people’s?

Using the bar model to solve problems Try these for yourself. Can you use the bar model to help? • Link to NCETM’s word problems filtered by year group: • https: //www. ncetm. org. uk/resources/44569 Is your bar model the same/different than other people’s?

Some resources to get started…

Using the bar model to solve problems Try these for yourself. Can you use the bar model to help?

Understanding the basic part-whole model Addition and Subtraction Part, part, whole