Fox Scales Tallest UK Building | Proportion and Scale Drawing Activity

1. A fox has been found eating scraps of food from builders at the top of the tallest building in the UK.

2. When it’s completed in 2012, the building will have 72 storeys and will stand 310 metres tall.

3. To give readers a sense of the height of the Shard, The Sun’s story about the fox included this graphic of well-known buildings. Spend a minute looking at The Sun’s graphic and the heights given. What do you notice?

4. These pictures are in the same proportion as the images in The Sun. The height of the Shard is 1 016 feet. If this were a scale drawing, how tall would The Angel of the North be? What would be its wingspan? 1016 984 771 591 443 66 0 Height in feet London Eye 443 ft Eiffel Tower 984 ft Canary Wharf 771ft The Gherkin 591 ft The Angelof the North 66ft The Shard 1 016 ft Which of the other buildings are shown to scale?

5. It’s in the News!Fox scales Shard Teacher Notes

6. Fox scales Shard Introduction: A fox has been found living off scraps of food left by builders at the top of the UK’s highest building! When completed, the Shard, near London Bridge, will be 1 016 feet high. The fox cub, named Romeo by workers, is thought to have climbed to the peak of the building using the central stairway. Fortunately the story has a happy ending. Romeo was given an all clear by the vet, a good feed, and was released back onto the streets of Bermondsey. This resource uses a graphic used by The Sun newspaper to illustrate this story as a context to explore proportion and scale drawing.. Content objectives: This context provides the opportunity for teachers and students to explore a number of objectives. Some that may be addressed are: • use proportional reasoning to solve problems, choosing the correct numbers to take as 100%, or as a whole; compare two ratios; interpret and use ratio in a range of contexts • check results using appropriate methods • 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:

7. ×? Angel’s actual height Shard’s actual height ×? ×? Angel’s measured height ? ×? Activity: Students are first asked to look at The Sun’s graphic and see what they notice. The scale of The Angel of the North is clearly incorrect, but the correctness or otherwise of the scales of the other illustrations is less obvious. Students are invited to consider what height The Angel of the North is shown at if the scale is correct. Students can then explore whether the remaining illustrations are accurate. Differentiation: To make the task easier you could consider: • provide measurements for the class of the heights (as measured on the printed handout of slide 4) • consider using a multiplier grid: More information and strategies for using this type of grid can be found in the Proportional Reasoning department workshop. To make the task more complex you could consider: • reducing the scaffolding so that students independently decide how to solve the problem • challenging students to write a letter to the newspaper explaining the error and offering a correction. Working in groups: This activity lends itself to paired discussion 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. 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 proportional reasoning to solve a problem, choosing the correct number to take as 100%, or as a whole (calculating level 7) • solve problems involving the conversion of units and make sensible estimates of a range of measures in relation to everyday situations (SSM level 5) • use their own strategies within mathematics and in applying mathematics to practical contexts (using and applying mathematics level 4)

8. Probing questions: These might include: • what other information do you need to solve this problem? • how many times taller is the Shard than The Angel of the North in real life? • how many times taller is the Shard than The Angel of the North in the graphic? • how many steps do you estimate you’d need to climb to reach the top of the Shard? • how long would the journey take in a lift? • how tall is 310m? Compare it to a tall building you know well. You will need: The PowerPoint (you will need to print Slide 4 as a handout). There are four slides: The first slide introduces the story about the fox climbing the Shard The second slide offers a few details about the Shard. More can be found on the Shard website. The third slide introduces the graphic from the newspaper (through the link) and invites students to spend a minute looking at the image and the heights given then asks, what do you notice? The final slide shows images of the buildings in the same proportion as The Sun’s graphic and asks whether the other buildings are drawn to scale. You might like to print The Sun’s graphic to support this work.