1. Bar models for problem-solving1

2. Lesson objective Use bar models to solve problems
Today we are going to learn to use bar models. This is an approach that you might want to use to solve some problems. We are going to work with lots of different problems and solve them always using bar models.

3. Bar models – what are they?
Picture of a problem using a bar or bars:
A bar model is just a rectangular bar that helps you to picture a problem and decide what to do to solve it.

4. Bar model – starter
So, if I was to teach a lesson dedicated to bar models, I might start like this…
Here’s a rectangular bar. How could you use a bar like this to model tenths?  

5. Bar model – starter
You could split the bar into ten sections and in each section, write 1/10
How could this same bar be used to model percentages? What would each section represent now?  

6. Bar model – starter How many sections would you shade to show 60%?
How many sections would you shade to show ¼ of the remainder of the bar?
What fraction is left?
Each section now represents 10%.
I might then ask these questions…
How many sections would you shade to show 60%? (answer: 6 sections)
How many sections would you shade to show 1/4 of the remainder of the bar? (answer: shade 1 more section)
What fraction is left? (answer: 3/10)
What fraction does each section represent? (answer: )
What percentage does each section represent? (answer: 20%)
How many sections would you shade to show 40%? (answer: 2 sections)
How many sections would you shade to show of the remainder of the bar? (answer: 2 more sections)
Tell students that 2 sections of the bar represent £5. Draw a bracket above 2 sections and write £5. Ask students to work out how much money the whole bar represents. When a student gives the correct answer, ask them to explain to the rest of the class how they got their answer.
Reinforce with working:

7. Bar models – example
Here’s a simple problem which could use a bar model. I might begin by showing students this problem, drawing a bar and asking them what the whole bar represents.

8. Bar models – example
Here we have drawn a bar to represent Isabel’s 2 shares and Freya’s 3 shares. And we know they have £20 in total.
What’s the value of each share? (Answer: £4)
How much do they each receive? (Answer: Isabel receives £8; Freya receives £12)
Students can try questions 1 and 2 on the worksheet.

9. Bar models – example
Sophie spends 40% of her birthday money on a necklace, and of the remainder on earrings. She is left with £ How much birthday money did Sophie receive?
We can also use bar models for more complex problems.
Difficult to get students to know where to start with a problem like this. However, using a bar model… building it up one phrase at a time, it is much clearer what you need to do.

10. Bar models – example
Now I am going to show you how we can use bar models for a harder problem.
Talk through the worked example, showing how you read one phrase at a time in the problem and add the information to the bar model.

11. Bar models – example Talk through the worked example.
Read the problem, represent one piece of information at a time on the model. Here Sophie spends 40% on a necklace.

12. Bar models – example
The next piece of information is that ½ of the remainder is spent on earrings. So now we can show that on the bar model.

13. Bar models – example
Continue talking through solving the problem using a bar model.

14. Bar models – example
Continue talking through solving the problem using a bar model.

15. Bar models – example
Continue talking through solving the problem using a bar model.
Emphasize showing working clearly. Encourage students to check back that they have provided an answer to the question they have been asked.
Students can try questions 3, 4 and 5 on the worksheet.
You could ask students to compare the bar models they drew to answer the problems.

16. Bar models – example There are 125 boys in year 7.
There are 25 more girls than boys.
How many girls are there in year 7?
Here is another problem that can be solved using bar models. You could do this without, but today we are practicing solving problems with bar models, so I want you to draw the models to help you solve all of these.

17. Bar models – example There are 125 boys in year 7.
There are 25 more girls than boys.
How many girls are there in year 7?
The first bar shows the 125 boys in year 7. Then because we are comparing the numbers of boys and girls, we draw the bars under each other. We mark that there are 25 more girls than boys. Now we can see clearly how we can work out how many girls there are. What is the answer? (Answer: 150)
Students can try questions 6, 7, 8 and 9 on the worksheet.

18. Bar models – question 9 SAMs Mathematics Paper 1 (Non-calculator)
– Q13 Foundation & Q1 Higher
This is question 9 on the worksheet. You could use the next slide to work through the answer with students.

19. Bar models – answer to question 9
Answer to question 9 on the worksheet.

20. Bar models – question 10 Flu is passed around an accounts department.
The clerk has   times the days off sick that the accountant has.
The accountant has   of the time off sick that the book-keeper has.
In total they take 10 sick days.
How many sick days do they each take?
This is question 10 on the worksheet. You could use the next slide to work through the answer with students.

21. Bar models – answer to question 10
10 days
Answer to question 10 on the worksheet.

22. Edexcel Autumn Mock 2016 H Q3
Can you use bar modelling to solve this?