Carving pumpkins for Halloween is a tradition that started in America in the 1800s

The world record for the largest pumpkin has been broken by a maths teacher in America!

Christy Harp grew a pumpkin that weighed 1 725 pounds, beating the previous world record of 1 689 pounds (766Kg)

Jamie Oliver says that a pumpkin that weighs 600g will feed 6 people.

How many people would Christy Harp’s pumpkin feed?

What would be its volume? How about its circumference? Its diameter?

Up2d8 mathsA Big Squash!

Teacher Notes

A Big Squash!

Introduction: Wikipedia says ‘A jack-o'-lantern is typically a carved pumpkin. It is associated chiefly with the holiday Halloween, and was named after thephenomenon of strange light flickering over peat bogs, called ignis fatuus or jack-o'-lantern. In a jack-o'-lantern, typically the top is cut off, andthe inside flesh then scooped out; an image, usually a monstrous face, is carved onto the outside surface, and the lid replaced. At night a light isplaced inside to illuminate the effect. The term is not particularly common outside North America, although the practice of carving lanterns forHalloween is.’ Giant pumpkin-growing competitions are common in the USA with some competitions awarding up to $6 per pound for thewinning pumpkin!.

Content objectives: This context provides the opportunity for teachers and students to explore a number of objectives. Some that may be addressed are:• solve problems involving measurements in a variety of contexts; convert between area measures (e.g. mm2 to cm2, cm2 to m2, and vice versa) and

between volume measures (e.g. mm3 to cm3, cm3 to m3, and vice versa);• choose and use units of measurement to measure, estimate, calculate and solve problems in a range of contexts; know rough metric equivalents of

imperial measures in common use, such as miles, pounds, and pints;• 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 the impact of enlargement on volume. Students are introduced to a pumpkin which broke theworld record and are then shown a recipe from Jamie Oliver which feeds six people. Students will firstly need to decide whether to work inimperial or metric units (depending on the level of your group you may ask them to calculate the conversion from lbs to kgs using theinformation on slide two) and are then asked to consider how big the world record pumpkin might be. If possible it would be useful to have anormal-sized pumpkin to hand to allow them to measure circumference and diameter etc.Initially students are likely to expect a linear relationship (that as the weight doubles, so the diameter and circumference will double) and theteacher’s role in this is to engage students in considering how reasonable this is without giving away the rule.

Differentiation: You may decide to change the level of challenge for your group. To make the task easier you could consider:• drawing a conversion graph to change pounds into kilograms (kgs)• providing them with information about metric and imperial conversions or changing the PowerPoint so that the weights are already in kgs• writing a recipe to use with the pumpkin you have in the classroom.To make the task more complex, you could consider:• insisting on more mathematical rigour when the students are justifying their estimated measurements• challenging them to refine their model to make it more realistic.This 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 in which students are encouraged to briefly justify their estimated measurements. You might also ask each group topresent their findings to the rest of the class.

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

Probing questions: Initially students could brainstorm issues to consider. You may wish to introduce some points into the discussion, which

might include:• what’s the same and what’s different about Christy Harp’s pumpkin and the one in the classroom?• is it always, sometimes or never true that when you double the circumference of a circle you double the area?• is it always, sometimes or never true that when you double the diameter of a circle you double the circumference?.• what measures of volume do we use regularly? Which is appropriate in this situation?• how might we measure the volume of a pumpkin?• how many square centimetres are there in a square metre? In a cubic metre?• how many small pumpkins would you need to feed the same number of people as Steve Connolly’s pumpkin? How much space would

they take up if you had to transport them?

You will need: • A pumpkin and tools to measure the radius, circumference and volume. • The PowerPoint presentation. There are three slides:

The first slide sets the mood and links the activity with Halloween.

The second slide gives data about the world record pumpkin attempt, giving the weight of the pumpkins in pounds.

The final slide gives details of a Jamie Oliver recipe and poses the questions, How many people would the record breaking pumpkin feed? What would be its volume? How about its circumference? Its diameter?