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