Reasoning in the classroom
Flying high
Year 9
Support materials for teachers
Year 9 Reasoning in the classroom – Flying high
These Year 9 activities focus on flying a small plane. Learners use real data to consider journeys
of different lengths.
Flying high
Learners use facts and figures to calculate
the fuel consumption of the small plane on
a journey of 450km.
Includes:
■■ Teachers’ script
■■ PowerPoint presentation
■■ Flying high question
■■ Markscheme
How high?
They work in groups to investigate both time and fuel consumption when the plane flies
at different heights.
Includes:
■■ Explain and question – instructions for teachers
■■ Resource sheet – Flying high, flying low
Reasoning skills required
Identify
Communicate
Review
Learners choose their own
methods.
They use compound measures
and decide how their work can be
presented clearly.
They draw conclusions from their
calculations and use checking
strategies to decide if their
answers are sensible.
Procedural skills
Numerical language
■■ Compound measures
■■ Horizontal, vertical
■■ Choosing the degree of accuracy when
presenting answers
Year 9 Reasoning in the classroom: Flying high
Introduction
Flying high
Activity 1 – Flying high
or
Outline
Learners use facts and figures about a small plane to work out
which of two flight patterns uses less fuel.
You will need
TS
Teachers’ script
PowerPoint presentation
Q
Flying high question
Two pages for each learner, must not be printed double-sided
M
Markscheme
Year 9 Reasoning in the classroom: Flying high
Activity 1 – Flying high – Outline
TS
Presentation to be shown to learners before they work on Flying high
Slide 1
Reasoning in the classroom
The text in the right-hand boxes (but not italics) should be read to learners. You can use your
own words, or provide additional explanation of contexts, if necessary. However, if you are using
this as an assessment item, no help must be given with the numeracy that is to be assessed.
Flying high
Slide 2
(Keep this slide on the screen until you are ready to
start the presentation.)
How many of you have flown in a plane? Do you
know how many passengers it could carry? So far,
the greatest number of passengers that a plane
can carry is 900!
The bigger the plane, the more fuel it uses − and
fuel is very expensive. If you were in charge of an
airline, you would want to save fuel because that
would save you money (and it saves the Earth’s
resources). But why might you also want to make
sure that the flight was as quick as possible?
(A speedier turnaround may allow more flights
which increases income.)
We can think of a flight in three stages: the plane
goes up, then it flies horizontally, then it goes
down.
(Mimic each stage with your hands.)
Which stage do you think uses the most fuel per
kilometre? (Going up) The higher the plane flies
the longer it takes to reach that height, and the
more fuel it uses. So you would think that pilots
may not want to fly very high. But . . .
. . . when the plane flies horizontally, the higher it
flies the less fuel per kilometre it uses because the
higher up you go, the less air resistance there is.
Year 9 Reasoning in the classroom: Flying high
Activity 1 – Flying high – Script
TS
Slide 3
Let’s see some facts and figures about this plane.
It’s quite a small plane, though it can travel fairly
long distances.
Let’s suppose the pilot wants to fly from A to B,
and has decided to climb to 7000m.
Slide 4
Flying the plane from A to B,
going up to 7000m
• it travels 92km closer to B
• it takes 9.8 minutes
• it uses 249kg of fuel
92km
Slide 5
Flying the plane from A to B,
horizontally
• every km takes 0.065 minutes
• every km uses 1.59kg of fuel
? km
In the time it takes the plane to climb to 7000m it
has travelled 92km closer to its destination. That’s
just a bit further than the distance from Cardiff
airport to Carmarthen.
How long does it take the plane to climb to
7000m? (9.8 minutes) And how much fuel does it
use in that time? (249kg)
Of course how far the plane flies horizontally
depends on how far away B is from A. It could be
a short distance, or a long distance, but every km
will take 0.065 minutes.
So how many minutes does it take for the plane
to fly 100km horizontally? Yes, 6.5 minutes
because 0.065 × 100 = 6.5
The plane uses 1.59kg of fuel for every km that it
flies. So how much fuel does it use when it flies
100km horizontally? (159kg)
Year 9 Reasoning in the classroom: Flying high
Activity 1 – Flying high – Script
TS
Slide 6
Flying the plane from A to B,
going down from 7000m
The plane starts descending when it is 88km
away from its destination – it takes 8.1 minutes to
fly those 88km and it uses 59kg of fuel.
• it starts to descend 88km from B
• it takes 8.1 minutes
• it uses 59kg of fuel
88km
Now you are going to answer some questions
about flying this plane. All the information you
need is on the question paper.
Remember to show your working so that
someone else can understand what you are doing
and why.
(If you are using this item for assessment purposes,
you may wish to limit the time available, e.g.
10 minutes.)
Year 9 Reasoning in the classroom: Flying high
Activity 1 – Flying high – Script
Q
Imagine that you are the pilot of this plane.
You need to choose whether to fly at 5000m or 10 000m.
For a flight of 450km, there is little difference in terms of time.
But which uses less fuel?
Use the information on the opposite page.
Remember to show calculations to explain your answer.
4m
Flying high
Activity 1 – Flying high – Question
Q
Flying at 5000m
Flying from A to B, going up:
• it travels 57 km closer to B
• it takes 7 minutes
• it uses 178 kg of fuel.
57km
Flying from A to B, horizontally:
• each km takes 0.072 minutes
• each km uses 1.82kg of fuel.
? km
Flying from A to B, going down:
• it starts to descend 59 km from B
• it takes 5.8 minutes
• it uses 43kg of fuel.
59km
Flying at 10 000m
Flying from A to B, going up:
• it travels 155 km closer to B
• it takes 14 minutes
• it uses 356 kg of fuel.
155km
Flying from A to B, horizontally:
• each km takes 0.067 minutes
• each km uses 1.14kg of fuel.
? km
Flying from A to B, going down:
• it starts to descend 135km from B
• it takes 11.6 minutes
• it uses 86kg of fuel.
Flying high
135km
Activity 1 – Flying high – Question
M
Activity 1 – Flying high – Markscheme
Marks
Answer
4m
Shows both 828.88 and 624.4 to justify the
decision to fly at 10 000m
(accept 828 to 829 inclusive and 624 to 625 inclusive)
Or 3m
Shows 828.88 or 624.4
(accept 828 to 829 inclusive or 624 to 625 inclusive)
Or 2m
Shows both 607.88 and 182.4
(accept 607 to 608 inclusive and 182 to 183 inclusive)
Or 1m
Shows 607.88 or 182.4
(accept 607 to 608 inclusive or 182 to 183 inclusive)
7
Total fuel used, in kg, at 5000m
and at 10 000m
7
Fuel used, in kg, when flying
horizontally
7
Number of km flown horizontally
Or
Shows 334 or 160
Year 9 Reasoning in the classroom: Flying high
Activity 1 – Flying high – Markscheme
M
Activity 1 – Flying high – Exemplars
5000m: 450 − 57 − 59 = 334
334km at 1.82 = 607.88kg
so altogether it does 607.88 + 178 + 43 = 828.88kg
10000m: 450 − 155 − 135 = 160
160km at 1.14 = 182.4kg
182.4 + 86 + 356 = 624.4kg
So it should go at 10000m because it uses loads less.
5000m
fuel use = 403kg 828.88kg
time = 36.848 minuets
10000m
fuel use = 624.4kg
time = 36.32
5000m
865.688
10000m
660.72
5000
334
450km:
Correct; 4 marks
●
This learner sets out their work clearly, showing correct figures
to justify their conclusion.
Correct; 4 marks
anser
100 00m is
cheaper because
when you add
the amount
of fule to
amount of mins
you get 10000m
as less
horizontally
828 kg of petrol
607.1
178
043
828
–
●
This learner needs prompting to read information given: in
addition to finding the number of kg they have calculated the
times taken, but these can be ignored. However, this learner
needs support to understand that adding fuel and time is
meaningless.
Shows 828; 3 marks
●
10,000 290 x 1.14 330.06 kg petrol
356
86
772
This learner shows some correct working but appears not to be
using a calculator which incurs a time penalty. Knowing when
and why to use a calculator is an important numerical skill.
772 kg of petrol
155 + 135 = 190 = 260km × 1.14 = 29640kg fuel
Flying 5000
57 + 59 = 116 = 334km × 1.82 = 60788kg fuel
so because the air is thinner I would rather
fly at 10,000
5000m
57 ÷ 178 = 0.3202247 km per kg
59 ÷ 43 = 1.37209302 km per kg
0.3202247 + 1.37209302 + 1.82 = 3.51209772,
so 1.17 (3 s.f.) km per kg on average
10000m
155 ÷ 356 = 0.43539326 km per kg
135 ÷ 86 = 1.5697644 km per kg
0.43539326 + 1.5697644 + 1.14 = 3.14516070,
so 1.05 (3 s.f.) km per kg on average
so the higher one is better
Year 9 Reasoning in the classroom: Flying high
Shows 334; 1 mark
●
There is an error in adding 155 and 135, and for both fuel
calculations the decimal point has been omitted. This learner
needs support to check their work and also to use the equals
sign correctly.
Incorrect; 0 marks
●
Although this learner communicates effectively, the calculations
are meaningless because the number of kilometres per stage
varies.
Activity 1 – Flying high – Exemplars
How high?
Activity 2 – How high?
or
Outline
Learners continue working with facts and figures about the small plane introduced
in Activity 1 – Flying high. They share the work within their group and make decisions together
about how to present their findings.
You will need
R
Resource sheet – Flying high, flying low
One for each learner
Access to a spreadsheet is recommended, but is not essential
Year 9 Reasoning in the classroom: Flying high
Activity 2 – How high? – Outline
Activity 2 – How high?
Give each learner a copy of the resource sheet Flying high,
flying low and explain that it shows more facts about the small
plane introduced previously.
Explain
Their task is to work in groups to investigate both time taken and fuel consumption at
different heights for a flight of 450km, or for any other distance that they choose. Which
height would they recommend the pilot to fly at, and why?
Within each group, they will need to apportion the calculations to be undertaken. They
will also need to agree how best to present their results, which could be displayed as
posters.
■■ How have you shared out the work? Are you checking each other, and if so, how?
■■ How could you use a spreadsheet to save doing lots of calculations by hand?
■■ What accuracy are you using, and why? (The idea of a three-stage journey − up, across,
Question
down – is a simplification, and the values within the table have been rounded, so too great
an accuracy would be unwise.)
■■ Why is flying at 10 000m not possible for a flight of 200km? (To reach that height the
plane flies 155km, but coming down the plane flies 135km. 155 + 135 > 200.) For your
chosen distance, what is the maximum height at which you could fly?
■■ How are you going to bring all the calculations together in a way that makes sense to
others? Have you thought about using graphs?
Year 9 Reasoning in the classroom: Flying high
Activity 2 – How high? – Explain and question
R
Flying from A to B, going up
Height
(m)
Flying from A to B, horizontally
Time
Distance Fuel used
(minutes)
(km)
(kg)
Height
(m)
Time per km Fuel per km
(minutes)
(kg)
Flying from A to B, going down
Height
(m)
Time
Distance Fuel used
(minutes)
(km)
(kg)
1000
1.4
8
36
1000
0.125
1.92
1000
1.2
10
14
2000
2.8
18
71
2000
0.102
1.97
2000
2.3
22
20
3000
4.2
30
107
3000
0.088
1.95
3000
3.5
33
27
4000
5.6
43
142
4000
0.078
1.90
4000
4.6
46
35
5000
7.0
57
178
5000
0.072
1.82
5000
5.8
59
43
6000
8.4
74
214
6000
0.068
1.72
6000
6.9
73
51
7000
9.8
92
249
7000
0.065
1.59
7000
8.1
88
59
8000
11.2
111
285
8000
0.063
1.43
8000
9.3
103
68
9000
12.6
132
320
9000
0.062
1.24
9000
10.4
119
76
10000
14.0
155
356
10000
0.067
1.14
10000
11.6
135
86
11000
15.4
180
392
11000
0.068
1.01
11000
12.7
153
95
12000
16.8
206
427
12000
0.068
0.91
12000
13.9
171
105
Flying high
Activity 2 – Flying high, flying low – Resource sheet