Solving word problems using the bar model Materials

Solving word problems using the bar model Materials developed by Paul Dickinson, Steve Gough & Sue Hough at MMU

Thank you • Sue, Steve and Paul would like to thank all the teachers and students who have been involved in the trials of these materials • Some of the materials are closely linked to the ‘Making Sense of Maths’ series of books and are reproduced by the kind permission of Hodder Education

Note to teacher In this Algebra Power. Point, students consider ways of representing problems presented in words through the use of two or more bars. In the Number module students worked with a variety of contextual situations which when drawn were very ‘bar like’ in representation. The focus in Number was to use one bar as a means of representing, to scale, quantities such as percentage, fractions, money, lengths, ratios and so on. Sometimes the single bar was thought of as a ‘double number’ line where the top line of the bar represented say, a percentage scale and the bottom line represented say price of a car. The use of the bar (or more than one bar) in this session is as a ‘model for’ or a ‘method for’ solving lots of different problems. Although the problems refer to imaginable real world problems, they do not necessarily look ‘bar like’ when you draw them. Students will have their own ideas about how to represent these problems on a bar and part of the sessions will be about developing a common understanding of how the word information transfers onto the bar. So, for example strategies such as : • Precisely labelling lengths across the top of a bar to represent a specific amount • Using comparison and shading to identify blocks within a bar which represent the same amount • Making effective choices about what is the ‘unit block’ within a particular problem ……………will help students to become more effective in using the bars to solve a variety of problems.

Note to teacher. There are three worksheets linked to this Power. Point (A 5, A 6 & A 7). Worksheet A 7 gives students an opportunity to revisit the sorts of problem they tackled within the Number module. This session also develops ideas around comparison of quantities, which are inherent in the solving of equations. In other words this session subtly shows links between topics in Number and Algebra. As a result of working, on these problems, it is intended that students and their teachers will start to see how drawing bars is a way of approaching and thinking about many areas of GCSE mathematics

Ages problem Dad is 37 years older than his son Joel. Dad is 4 years younger than Mum. The total of their ages added together is 99. How old is Mum? Spend two minutes trying to solve this problem on your own. Share your ideas

Word problems in general Word problems like the age problem from the previous slide are known to be challenging to solve- for people of any age. We will work on a method which involves drawing bars which will make the problems much easier to see.

Comparing quantities – Crisp packets Aksa eats 6 packets of crisps a week Latifa eats 10 packets a week Which bar refers to Aksa ? Which bar refers to Latifa? Say how you know

Comparing quantities - Pets Zahra has 6 pets Libby has 4 pets Which is Zahra’s bar? Which is Libby’s bar?

Comparing quantities - Pets Zahra has 6 pets Libby has 4 pets Which is Zahra’s bar? Which is Libby’s bar?

Comparing quantities - Wages Niyal earns £ 8 more than Neha a week Which is Niyal’s bar? Which is Neha’s bar? How much does Niyal earn in a week?

Comparing quantities - Coats Jake has 3 fewer coats than Daniel. Which is Jake’s bar? Which is Daniel’s bar? Where could you show the ‘ 3’ coats?

Word problems – the swimming party There are 25 children at Lola’s swimming party, including Lola. There are 13 more girls than boys at the party. How many girls and how many boys are at the party? Look carefully at the bars drawn and say how they represent the information in the question Where are the 25? Where are the 13? Where is Lola? Where are the boys? Copy the bars and use them to find how many girls and how many boys are at the party.

Word problems – the swimming party There are 25 children at Lola’s swimming party, including Lola. There are 13 more girls than boys at the party. How many girls and how many boys are at the party? Describe exactly what has been written on these bars and why. Now try the problems on Worksheet A 5

Word problems – Pocket money Jack has £ 12 more money in his pocket than Bella. Together they have £ 30. How much money does Bella have? Hint: Start by drawing two bars one to represent Jack’s money and one to represent Bella’s money

Word problems – Mum’s age Dad is 37 years older than his son Joel. Dad is 4 years younger than Mum. The total of their ages added together is 99. How old is Mum? Hint: Start by drawing three bars one to represent Dad’s age, one to represent Mum’s age and one to represent Joel’s age. Try to make up a similar problem for your own family and give it to someone in your class to solve. Now try the problems on Worksheet A 6

Word problems – Summary You can now tackle a large number of problems by drawing a bar or more than one bar to help you think about the problem. Worksheet A 7 gives a wide selection of problems to try. These relate to topics such as ratio, percentage, fractions and others. If you become stuck on any problem it is always worth drawing something like a bar, as this can help you to think about a problem in clearer way. Now try the problems on Worksheet A 7

Blank template slide Information Question 1 Question 2