Student instructions Introduction Bob and Mary decide to have a family and friends party to celebrate their 1 month dating anniversary. They are organizing pieces of pie as a snack. They were going to buy the pies from Lee’s Bakery but Mary's brother offers to do all of the baking instead, saying that homemade pies would be much cheaper and a more personal touch. Task A Investigate the cost per pie for the homemade pies and decide whether they will be the cheaper option for the party, given the following information: It is proposed that 52 pies be ordered in the ratio Potato Top : Mince and cheese = 7:6. Mary's brother has offered to make the same type and number of pies. Lee’s Bakery’s pies cost $7.50 each. A Potato Top pie will need the following ingredients: pastry (1 sheet), mince (350g), carrot (200g), onion (3 small onion, about 50g each), and peas (100g), potato (300g) The Mince and Cheese pie has the following ingredients: Pastry (2 sheets), mince (400g), carrot (200g), cheese (100g), onion (1 small onion, about 50g each), and peas (100g). Here are the costs of the ingredients for homemade pies: • • • • • • • Pastry comes in packets of 5 sheets and cost $4.50 Mince costs $10.99/kg 1 Grated cheese costs $8.40 for a 600g packet but is on sale at 6 off Carrots cost $2.39/kg Onions cost $2.99/kg Peas cost $2.50 for a 500g packet but is on sale at a 40% discount Potato costs $2.99/kg Clearly state what you are calculating at each step. Task B Mary’s brother points out that her homemade pies are bigger than Lee’s Bakery pies and you would need 20% more Lee’s Bakery pies than homemade ones. This means she can make fewer than 52 pies. However, there may be some wastage with her ingredient purchases. While she can buy exact amounts of the ingredients that are sold by weight, she has to buy bags, trays, jars and boxes. Use this information to revise your decision about which option is cheaper. Clearly explain any decisions you have to make in your investigation process. Assessment Schedule for “Pie” Evidence/Judgments for achievement To “Achieve” students will be required to apply numeric reasoning in solving problems. Students select and use a range of methods in solving problems. Students communicate solutions which typically require one or two steps. Student selects and uses at least three different numeric methods in an attempt to solve the problem. Examples of methods • Percentage decrease (cost of carrot) • Percentage of (cost per pie of onion) • Fraction of (cost per pie of peas) • Splitting in a ratio (number of each type of pie) • Reversing a percentage change (number of pies in Task B) An achieved student may draw the wrong conclusion about which option is cheapest due to having made mistakes in some working steps. At least 3 of the above skills must be carried out correctly.. Evidence/Judgments for achievement with merit Evidence/Judgments for achievement with excellence To achieve with “Merit” students will be required to apply numeric reasoning with relational thinking in solving problems. To achieve with “Excellence” students will be required to apply numeric reasoning with extended abstract thinking in solving problems. Students need to clearly communicate what they are working out at each step. Students will complete Task A competently (they may make a minor error) and investigate the effects of the extra conditions given in Task B. This should involve • Calculating the new number of pies correctly • Recognising that the comparison is between xx homemade pies and xx Lee’s Bakery pies, not xx and xx. • Rounding up to whole numbers of pies, bags, tins, etc • Keeping the number of pies of each type in the correct proportion (y:z). Students calculate the total cost of the homemade pie option, potentially with one or two minor errors. They compare this to the Lee’s Bakery pie cost and draw a consistent conclusion Students’ answers may vary slightly from those given on the next page due to early or different rounding or an allowable error. Students must use correct mathematical statements and clearly communicate what they are calculating at each step. If students calculate the cost for xx pies without allowing for wastage and therefore discover that homemade is cheaper, this is only Merit. Final grades will be decided using professional judgement based on a holistic examination of the evidence provided against the criteria in the Achievement Standard. Sample Answers are provided on the next page. Cost of Lee’s Pies 52 pies from Lee’s will cost 52 × $7.50 = $390 Home-made: 7 + 6 = 13 52 x 7 ÷ 13 = 28 Potato Top 52 x 6 ÷ 13 = 24 Mince & Cheese a1 Potato Top - per pie Pastry $4.50 ÷ 5 Mince $10.99 × 0.35 Carrot $2.39 × 0.2 Onion $2.99 × 0.15 Peas $2.50 × 0.6 × 100 ÷ 500 Potato $2.99 × 0.3 = $0.90 = $3.85 = $0.48 = $0.45 = $0.30 = $0.90 a2 a2 a2 a3 a2 Adding these six together means that a home-made potato top pie will be $6.88 which is 62 cents cheaper than Lee’s For 28 the cost will be $192.64 Mince & Cheese - per pie Pastry $4.50 × 2 ÷ 5 Mince $10.99 × 0.4 Carrot $2.39 × 0.2 Onion $2.99 × 0.05 Peas $2.50 × 0.6 × 100 ÷ 500 Cheese $8.40 × 5/6 ÷ 6 = $1.80 = $4.40 = $0.48 = $0.15 = $0.30 = $1.17 a2 a2 a2 a3 a4 Adding these six together means that a home-made mince & cheese pie will be $8.30 which is 80 cents more than Lee’s For 24 the cost will be $199.20 So ignoring any wastage from buying packs of 5 or bags of 500g, the total cost for the home-made pies will be $391.84 compared to a total of $390 for Lee’s pies. It’s cheaper (by $1.84 - and easier) to buy them all from Lee’s. m1 However, it might be even better to buy the mince & cheese pies from Lee’s and to make the potato tops at home. e1 Task B 52 ÷ 1.20 gives 431/3 homemade pies (so 44 then) a5 44 in the ratio 7:6 24 potato top and 20 mince & cheese a1 Making all these would need Pastry 24 + 20 × 2 = 64 sheets thus 13 packs of 5 $4.50 × 13 = $58.50 Mince (0.35 × 24 + 0.4 × 20) kg × $10.99 = $180.24 Carrot (0.2 × 44) kg × $2.39 = $21.03 Onion (24 × 0.150 + 20 × 0.05)kg × $2.99 = $13.75 Peas (44 × 0.1) = 4.4kg and thus 9 bags at $2.50 × 0.6 = $13.50 Potato (24 × 0.3) kg × 2.99 = $21.53 Cheese (20 × 0.1) = 2 kg and thus 4 bags at $8.40 × 5/6 = $28.00 Total $336.55 a3 a4 So, although there’ll be one sheet of pastry left over and 400g of grated cheese, it’ll be $53.45 cheaper to have home-made pies rather than those bought from Lee’s. m2 Clearly set out m3 The problem with making them at home is that you have to find the time to shop for the ingredients, transport them home, find the time to make the pies and then store them. There might also be problems in having the correct baking trays to cook the pies and the cost of the fuel to cook has not been factored in. It might still be easier to buy all the pies from Lee’s. e2 Achieved – any three different from a1, a2, a3, a4 and a5 Merit – achieved plus any two from m1, m2 and m3 Excellence – merit plus e1 and e2 Part A 52 @ 7:6 Lee Homemade Cost per each Pastry Mince Grated Cheese $4.50/5 $10.99/kg Carrot Onion Peas Potato $2.39/kg $2.99/kg $1.50/500 $2.99/kg Pastry Mince Grated Cheese Carrot Onion Peas Potato 52@ $7.50 Potato Top per pie 1 350 $8.40/600 $4.50/5 $10.99/kg 200 150 100 300 Mince n Cheese per pie 2 400 total Number sold in price 5 4.50 1000 10.99 390.00 211.84 178.16 28 cost/pie 0.90 3.85 25.20 107.80 600 8.40 0.00 1000 1000 500 1000 2.39 2.99 1.50 2.99 Home Lee's 0.48 0.45 0.30 0.90 6.88 7.50 Number sold in price 5 4.50 1000 10.99 24 cost/pie 1.80 4.40 43.20 105.60 13.44 12.60 8.40 25.20 192.64 $8.40/600 100 600 7.00 1.17 28.08 $2.39/kg $2.99/kg $1.50/500 200 50 100 1000 1000 500 2.39 2.99 1.50 0.48 0.15 0.30 11.52 3.60 7.20 8.30 7.50 199.20 Home Lee's 192.64 210.00 -17.36 199.20 180.00 19.20