The size of glasses used in pubs is set by law.

The consultation period about whether to update laws that have been in place for many years finishes this month.

Beer has been served in pints since 1698, when an Act of Parliament ruled ale and beer should be sold in pints or full quarts (two-pints). In the last century, half and third pints were also introduced as legal measures.

I went to Australia last year. They already serve drinks in two-thirds of a pint glasses. They call

them ‘schooners’.

The NHS says that men should not regularly

drink more than 3-4 units daily.

That’s about one and a half pints isn’t it?

If I had two schooners, would that be more than one and a half pints?

If this rectangle is

one… …which of these is

one and a half and

which is the same as

two lots of two thirds?

How do you know?

If I had two schooners, would that be more than one and a half pints?

1

1

3

2

3

2

3

1

2

1

2

1

2

Using only these rectangles, how many ways can you make one and a third?

What other amounts can you make that are less than one and a half?

Up2d8 mathsPints and Schooners

Teacher Notes

Pints and Schooners

Introduction: The National Weights and Measures Laboratory is just coming to the end of a consultation period which could see a new measure introduced topubs and licensed premises. It’s argued that the new two-thirds of a pint measure would provide customers with more choice, particularly whenordering drinks with a higher alcohol content. This resource encourages students to explore the safe drinking recommendations and, in doingso, develop their understanding of fractions.Content objectives: This context provides the opportunity for teachers and students to explore a number of objectives. Some that may be addressed are:• add and subtract fractions by writing them with a common denominator; calculate fractions of quantities (fraction answers); multiply and

divide an integer by a fraction• strengthen and extend mental methods of calculation to include decimals, fractions and percentages, accompanied where appropriate by

suitable jottings; solve simple problems mentally• identify the mathematical features of a context or problem; try out and compare mathematical representations; select appropriate

procedures and tools, including ICT.

Process objectives: These will depend on the amount of freedom you allow your class with the activity. It might be worth considering how you’re going to deliver theactivity and highlighting the processes that this will allow on the diagram below:

Activity: The activity explores adding fractions (halves and thirds) using the context of legal measures in UK pubs. The task is for students touse the images to explore ways in which they can make amounts equal to, or less than, one and a half (which represents approximately theGovernment’s advice for the maximum number of pints of 4% beer that can be consumed in an average day). Students are first asked to use adiagram with a rectangle labelled as ‘1’ and are asked to justify which of the other two rectangles is one and a half and which is the same as twolots of two thirds. Students are then given a sheet with rectangles of various sizes and asked to explore ways in which they can use the variousrectangles (representing the legal measures in UK pubs) to create totals less than or equal to one and a half. The activity is designed to be usedat the beginning of some work on fractions with the students experimenting and generating their own strategies for combining fractions.

Differentiation: You may decide to change the level of challenge for your group. To make the task easier you could:• reduce the number of fractions used to create a total less than one and a half• remove the constraint that the total has to be less than one and a half, instead asking the students what totals they can make using the

rectangles on the sheet• provide the students with some fraction circles as well as the rectangle images to help them make connections between the different images

of fractionsTo make the task more complex, you could consider:• insisting on more mathematical rigour when the students are justifying their solution – maybe asking for a written explanation• Reducing the scaffolding that you might give to structure the task, allowing the students more opportunity to develop their independenceThis resource is designed to be adapted to your requirements.

Outcomes: You may want to consider what the outcome of the task will be and share this with students according to their ability. This tasklends itself to a poster on which students are encouraged to explain their strategies – maybe putting down two different representations of oneand a half, and explaining how they know that they represent the same amount..

Working in groups: This activity lends itself to paired or small group work and, by encouraging students to work collaboratively, it is likely thatyou will allow them access to more of the key processes than if they were to work individually. You will need to think about how your class will work on this task. Will they work in pairs, threes or larger groups? If pupils are not used toworking in groups in mathematics, you may wish to spend some time talking about their rules and procedures to maximise the effectiveness andengagement of pupils in group work (You may wish to look at the SNS Pedagogy and practice pack Unit 10: Guidance for groupwork). You maywish to encourage the groups to delegate different areas of responsibility to specific group members.

Assessment: You may wish to consider how you will assess the task and how you will record your assessment. This could include developingthe assessment criteria with your class. You might choose to focus on the content objectives or on the process objectives. You might decide thatthis activity lends itself to comment only marking or to student self-assessment. If you decide that the outcome is to be a presentation or aposter, then you may find that this lends itself to peer assessment.If you use the APP model of assessment, then you might use this activity to help you in building a picture of your students’ understanding.Assessment criteria to focus on might be:• recognise approximate proportions of a whole, and use simple fractions and percentages to describe these (Numbers and the number

system level 4)• use equivalence between fractions and order fractions and decimals (Numbers and the number system level 5)• draw simple conclusions of their own and give an explanation of their reasoning (using and applying mathematics level 5)• present a concise, reasoned argument, using symbols, diagrams, graphs and related explanatory texts (using and applying mathematics

level 6).

Probing questions: You may wish to introduce some points into the discussion, which might include:• what’s the same and what’s different between two thirds and two lots of one third?• how do you know you’ve got all of the ways of making a total less than one and a half?• can you make exactly two using only the rectangles on the sheet? How many ways? How do you know?• how many halves are there in two thirds?• point to one of the other rectangles on the sheet (eg. the two thirds) and ask “If this rectangle represented one pint, how much would the

other rectangles represent?”

You will need:

The PowerPoint presentation, with the final two slides printed as worksheets. You might also like to have some scissors available to the

Students. There are five slides:

The first two slides set the scene and introduce the proposed two thirds measure.

The third slide introduces the recommended maximum average daily alcohol intake.

The fourth slide gives students an opportunity to explore which is larger, one and a half or two lots of two thirds. This also gives the teacher an opportunity to listen to any misconceptions that may arise. This slide could be printed as a worksheet.

The fifth slide sets the task. This slide could be printed as a worksheet.