From http://www.shoeguide.org/Shoe_Sizinghttp://www.shoeguide.org/Shoe_Sizing How long, in centimetres, do you think a size 21 shoe will be? Why?
Can you imagine the size of the person who could fit into them?
The tallest man ever to have lived is Robert Wadlow (1918 – 1940 ), pictured here with his father. He was 2.72 metres (8 ft 11 inches) tall and wore US size 25 shoes (pictured above next to US size 12). How tall might the wearer of the size 21 trainers be? What else can you predict about him?
Big foot Introduction: A pair of size 21 trainers has been found at a petrol station in Derbyshire! Police are hunting high and low (though maybe not too low!) for the owner of the enormous Nike basketball boots. Denise Bostock, who works in the lost property office for the police said, “You just can’t imagine the size of the person who could fit into them.” It’s this statement that this resource explores, using the context of the shoes to make predictions – firstly, in a number sequence, and then using survey data. Content objectives: This context provides the opportunity for teachers and students to explore a number of objectives. Some that may be addressed are: communicate own findings effectively, orally and in writing, and discuss and compare approaches and results with others generate terms of a linear sequence using term-to-term and position-to-term rules, on paper and using a spreadsheet or graphics calculator plan how to collect the data; construct frequency tables with equal class intervals for gathering continuous data and two-way tables for recording discrete data write about and discuss the results of a statistical enquiry using ICT as appropriate; justify the methods used. 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: There are two activities – both look at using mathematics to make predictions using the size 21 shoe as a context. The first activity shows the students conversion charts for different systems of measuring shoe sizes. Students are asked to predict how long, in centimetres, the size 21 shoe might be. The second activity looks at Robert Wadlow, the tallest man ever to have lived. He wore a US size 25 shoe and students are asked to predict how tall the person who wore the shoes might be. It is likely that students will want to carry out a survey to plot height against shoe size. Depending on the focus you want to put on this activity, you might like to encourage students to use data from CensusAtSchool to skip the collect data part of the data handling cycle and move straight to the represent and analyseCensusAtSchool part. One of the nice things about this activity is that there is no correct answer. Students might feel uncomfortable about this and want an answer – it is important that they are confident in their predictions and can justify their methods so, depending on your class, having a competition to see which pair or group can present the most convincing argument might be a nice extension to this activity. Differentiation: To make the task easier you could consider: using just one of the activities providing a small data set for students to analyse providing a plan for the way in which students are to collect data providing a graph (maybe using the CensusAtSchool website) showing a relationship between height and shoe size.CensusAtSchool website To make the task more complex you could consider: asking the students to offer a written justification of their prediction for the first or second activity challenging students to work out a range for their predictions rather than a single number. The challenge in both these activities is set more by the way of working than the content and it is the amount of scaffolding provided that is likely to have the greatest impact on the level of challenge. 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: present information and results in a clear and organised way (using and applying mathematics level 4) draw simple conclusions of their own and give an explanation of their reasoning (using and applying mathematics level 5) communicate interpretations and results of a statistical survey using selected tables, graphs and diagrams in support (handling data level 6) show understanding of situations by describing them mathematically using symbols, words and diagrams (using and applying mathematics level 5) appreciate the difference between mathematical explanation and experimental evidence (using and applying mathematics level 7).
Probing questions: These might include: what mathematical questions might the first slide raise? is a size 8 shoe double the size of a size 4 shoe? which system of shoe sizes makes the most sense? Which makes the least sense to you? how can you convert between different size systems? is it true that the tallest man in the world will have the largest feet in the world? the lady from the lost property thought the shoes might belong to a basketball player. Why do basketball players have big feet? is it true that tall people have bigger feet? if the size 21 shoes belonged to a woman, would you expect her to be taller or shorter than a man with size 21 feet? You will need: The PowerPoint (you might like to print Slide 2 as a handout). There are four slides: The first slide introduces the story and offers the opportunity for the teacher to ask students what mathematical questions they might ask about this context. (If a good one comes up, there might be no need to carry on with the rest of the slides!) The second slide gives a table showing different systems for sizing shoes around the world and asks the question, “How long, in centimetres, do you think a size 21 shoe will be? Why?” The third slide uses the quote, “You just can’t imagine the size of the person who could fit into them,” to encourage students to think about what someone with size 21 shoes might be like. The final slide introduces the tallest man ever to have lived (who wore US size 25 shoes) and poses the questions, How tall might the wearer of the size 21 trainers be? What else can you predict about him?