Prime retail space on London’s New Bond Street is now the most expensive in Europe, with the best shops costing up to £925 per square foot per year.

A retailer hopes to set up a store on New Bond Street. They need 50m of clothes rails. These can be either against the wall or free standing. They come in 1m lengths. They also need 20m 2 of shelving which must be against the wall. Shelves cannot be stacked more than two high. Clothes rails can be attached end to end to create rows. Each row of rails must be at least 2m apart to provide access.

Imagine you’re building a retail space on New Bond Street. What shape and size of retail space will meet these requirements at the lowest cost? How will you fit the rails and shelving into the space? At £925 per square foot, what will the annual rent be? Requirements: 50m of clothes rails. These can be either against the wall or free standing. They come in 1m lengths. 20m 2 of shelving which must be against the wall. Shelves cannot be stacked more than two high. Clothes rails can be attached end to end to create rows. Each row of rails must be at least 2m apart to provide access.

It’s in the News! Store wars Teacher Notes

Store wars Introduction: A recent study has found that retail rents on London’s New Bond Street are the highest in Europe, with a prime location costing £925 per square foot per year. This resource uses the context of a retail space to give students the opportunity to develop work on length and area, as well as develop problem solving skills. Students are challenged to create a space to contain 50m of clothes rails and 20m 2 of shelving, leaving space for access, but with the smallest footprint and, therefore, smallest annual rent. Content objectives: This context provides the opportunity for teachers and students to explore a number of objectives. Some that may be addressed are: know and use the formula for the area of a rectangle; calculate the perimeter and area of shapes made from rectangles choose and use units of measurement to measure, estimate, calculate and solve problems in a range of contexts communicate own findings effectively, orally and in writing, and discuss and compare approaches and results with others; recognise equivalent approaches 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 the activity and highlighting the processes that this will allow on the diagram below:

Activity: The activity provides a context for students to work with measures of length and area as well as working on mathematical processes and applications. Students are challenged to find the minimum area which will fit the constraints given. These constraints are flexible and have been left deliberately open to interpretation to allow you to tailor the activity to your group (for example, no mention is made of the need for doors or windows!). The competitive element of this activity could be enhanced by offering a reward to the group who successfully fulfil the constraints in the smallest area. Differentiation: The content of this task is relatively low, the organisation and logic of the task can, however, end up being quite challenging. You may decide to change the level of challenge for your group. To make the task easier you could consider: fixing the shape of the space as, for example, a rectangle, maybe providing several different sizes of rectangles for them to work with removing the shelving or giving the shelving requirement as a length rather than an area ignoring the question about the rental cost or provide a method for converting from square metres to square feet. To make the task more complex you could consider: suggesting that the students move beyond polygons in their design – does this result in cheaper rent? allowing the students to attach rails at angles to create more complex rail shapes. This resource is designed to be adapted to your requirements. Working in groups: This activity lends itself to paired work and small group work and, by encouraging students to work collaboratively, it is likely that you 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 to working in groups in mathematics you may wish to spend some time talking about their rules and procedures to maximise the effectiveness and engagement of pupils in group work (You may wish to look at the SNS Pedagogy and practice pack Unit 10: Guidance for groupwork). You may wish 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 developing the assessment criteria with your class. You might choose to focus on the content objectives or on the process objectives. You might decide that this activity lends itself to comment only marking or to student self-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: use and interpret mathematical symbols and diagrams (Using and applying mathematics level 3) find perimeters of simple shapes and find areas by counting squares (shape, space and measure level 4) understand and use the formula for the area of a rectangle and distinguish area from perimeter (shape, space and measure level 5) identify and obtain necessary information to carry through a task and solve mathematical problems (using and applying mathematics level 5).

Probing questions: These might include: is it better to make the walls flat or to have indented sections? which shape gives the biggest space inside for the smallest wall space? what’s the best shape to make the shelves so that they take up the smallest amount of space? how much space might you need around the door? if you have enough clothes to fill 50m of rails, how much space might you need as a stock room? You will need: The PowerPoint presentation: there are three slides: The first slide introduces the story. The second slide sets the context and gives the constraints. The final slide sets the task and lists the constraints that students must stick to.