The School Fair

This unit could be run as a unit over the course of a week.  Alternatively, you may wish to use individual lessons as starters for a more comprehensive study of one area of mathematics.

Session 1

In this session we introduce the idea of helping to plan the school fair and discuss some of the activities that might be found at a school fair.  Then we vote to see what activities are the most popular.

1. Introduce the idea of a school fair, ask students to brainstorm activities that might be at a school fair.  Record their suggestions on the board.  Try to keep the list reasonably short by grouping similar responses, for example ‘Sweet Stall’ and ‘Cake Stall’ could be grouped.

2. Ask students which they think might be the most popular activities.  Discuss suggestions but do not record them for now.

3. Ask students how they could work out what might be the class’ favourite activities.  Hopefully someone will suggest voting.

4. Run through the activities listed, collecting a vote of the most popular – ensure that students each only have one vote.

5. Discuss the results with students.
   Which activity is most popular?
   How many students voted for that activity?
   How many students voted for …?
   How many more students voted for … than for …?
   For ‘How many more…?’ type questions, encourage students to explain how they worked out their answers, prompting them to use part-whole strategies where possible.

6. Ask students whether the activity they voted for is the only one they liked.  It almost certainly won’t be.  Suggest another vote, but this time students are allowed to vote for their three favourite activities from the list. 

7. Depending on whether you think your students will be able to keep track and only vote for three each you may want to distribute three ‘voting counters’ to each student which they hand in to make their votes. 

8. Count the piles of counters to see how many students voted for each activity.

9. Discuss the results with students.
   Which activity is most popular?
   How many students voted for that activity?
   How many students voted for …?
   How many more students voted for … than for …?
   Are there any differences if we each get three votes?
   For ‘How many more…?’ type questions, encourage students to explain how they worked out their answers, prompting them to use part-whole strategies where possible.

10. The opportunity is now available to produce a graph of the most popular activities, from either, or both of the two sets of data.  If you decide to use Excel or similar to produce graphs the spreadsheet tutorial may be of assistance to you.

Session 2

In this session students practice their skill at estimating, and discuss some ways to improve the accuracy of estimates.

1. Ask students if they have seen how candy floss is made.

2. Most will probably not have, so a brief explanation may be required.  Candy floss is made by putting sugar in a machine which spins very fast, forcing the sugar out through tiny holes so that it forms thin strands which can be caught on a stick.  The important point to make is that candy floss is just sugar (sometimes with colour added).

3. Ask students how much sugar they think they would need to buy to make candy floss for the fair.

4. Record estimates, encouraging students to explain how they made their predictions.

5. Show students a 1.5 kg bag of sugar and ask them if that changes their estimates.  Allow them to feel the weight of the bag.

6. Ask students to estimate how much a bag of candy floss might weigh.  (Around 50-100g is reasonable).  If possible provide them with some objects of known weight to judge by (packets of crisps would be ideal).

7. Ask students how many bags of candy floss they think will be sold at the fair.

8. Ask for suggestions as to how they could work out how many bags of candy floss might get sold.

9. Ask students how many people they think will be at the fair.
   How many people are there in the class?
   How many people are there in the school?
   How many people will be at the fair if each person in the school brings two other people? (Parents, or siblings, or grandparents etc.)

10. If one quarter of the people at the fair buy candy floss, how many bags will be sold?

11. Now see if students would like to change their estimates of how much sugar would be needed.
    If we sold 200 bags of candy floss and they weighed 50g each, how much sugar would we need?
    How did you work that out?
    Share some strategies for this calculation.  Advanced additive students are likely to group in 10s, that is, 200 x 50 = (200 x 10) + (200 x 10) + (200 x 10) + (200 x 10) + (200 x 10) = 2000, 4000, 6000, 8000, 10000g.  Students may or may not realise that 10000g is the same as 10kg.

12. How much would it cost to buy the sugar if 1.5 kilo bags of sugar costs $2.10 each?  Students must realise that you can not buy part of a bag so they will need to buy 7 bags of sugar.

13. How much money will the candy floss stall make if candy floss costs $1 per bag?
    Again share strategies for the calculation.

14. Now ask your students to follow the same process with other foods that might be at the fair:
    How many cups of popping corn would you need to buy if one out of every ten people at the fair buy popcorn?
    How much tomato sauce would you need to buy for the sausage sizzle if half the people buy sausages and want sauce?
    Students could work in groups and record their working, then report back to the class.

Session 3

In this session we work outside to plan where activities could go on the school field so that they all fit in.

1. Ask students to identify which of the activities that they had listed would be best run on the school field.  If necessary you may need to add or exclude activities to make the problem solvable, yet challenging.  Suggest that activities such as gumboot throw (with a triangle of area required) and three-legged race/sack racing (a long strip required) are included.

2. Once you have listed the activities, draw a rough picture of the field and ask students to suggest where they think each activity should go.  With a little luck not everything will fit first time.

3. As a class go out and measure the field using a tape measure.

4. Return to class and draw a scale picture of the field on an A4 piece of paper.  Ensure that students understand the concept of scale.  For example the scale might be 1 cm to 5m, meaning that every 1cm on the map represents 5m on the field.  Ask students to help you work out the measurements required for the map:
   If the field is 40m long, how long should the field in the map be?
   If the field is 25m wide, how long should the field in the map be?

5. Now, on a separate piece of paper, but in the same scale, draw the shape and size of area required for the gumboot throw.  This will be a triangle (or more accurately a segment of a circle) big enough that everyone’s throw will be contained within the area.  You will need to discuss how far people might be expected to throw a gumboot, and maybe a practical experiment might help.

6. Show students how the gumboot throw region could fit in many different places on the field.

7. Explain to the students that their task in small groups is to make pieces of paper to represent the different activities that would be on the field, and then to arrange them in what they think is the best way for a fair.

8. Stop students occasionally to discuss the size of their various pieces and other factors that they are taking into account in the arrangement of activities. (For example, the water bomb catching activity is near a tap to fill water bombs from.)

9. Bring students together to discuss their final maps and compare similarities and differences.

10. Location, Location is a Level 3 Geometry unit around drawing a scale map of the classroom.

Session 4

In this session students will design and make a box for fudge.

1. Explain to students that at the fair there might be a sweet stall (it is probably one of the activities they had listed anyway).

2. Ask students how many pieces of fudge they would expect to buy in a small packet.  Agree on a number around 5-10.

3. Explain that the pieces of fudge will be around the same size as multi-link cubes, and that their job for this maths class is to design and make a box for the fudge to go in.

4. Show students how to make a basic box, using a pattern like the one below and allow them to go and experiment.  Encourage them to try different sized bases and different depths to create a box that will hold the desired number of multi-link cubes (pieces of fudge).

   

5. This activity is a good opportunity to reinforce measurement skills, as well as geometry skills.  Ensure that students measure lines and keep angles consistent.  You may want to require that the boxes be constructed solely from rectangular panels as this will simplify the activity.  A variety of pre-drawn templates could be made available for less able students to copy.

6. Students should bring their best box back to share with the rest of the class at the end of the session.

Session 5

This session is devoted to finishing off work from the previous four sessions.

In this session students should be given time to complete their work from sessions 1-4.  Extra activities related to the topic of a school fair for early finishers can be found in the Level 2-3 Figure It Out Theme book - Gala.