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1.1A Numeric Reasoning
Read and highlight
• Mike and Huia are planning to travel to
England for a holiday. They plan to be in
England for 3 months, and during that time
take a 3 week bus tour through France and
Spain.
Read and highlight
• Mike and Huia are planning to travel to
England for a holiday. They plan to be in
England for 3 months, and during that time
take a 3 week bus tour through France and
Spain.
• This assessment activity requires you to
calculate the amount of money they will need
to save for their trip, and how long it will take
for them to save it.
• This assessment activity requires you to
calculate the amount of money they will need
to save for their trip, and how long it will take
for them to save it.
• Use the following information to find out
how much money they will need to save, and
how long it will take them to save this
amount.
• In the solution of this problem you should:
• Show calculations, as appropriate, that you
have used in the solution of the problem;
• Use mathematical statements;
• Explain what you are calculating at each stage
of the solution.
• The quality of your discussion and reasoning
and how well you link this to the context will
determine the overall grade.
Do the expenses first
• They estimate for each day they are in
England, between them they will need on
average NZ$240 (to the nearest $20) when
they are not on the bus trip.
Number of days
• They estimate for each day they are in England,
between them they will need on average NZ$240
(to the nearest $20) when they are not on the
bus trip.
•
•
•
•
3 months estimate 92 days
Minus bus trip (21 days)
Total number of days = 71
Cost = 240 x 71 = $17,040
• The cost for the return air tickets is $2500,
plus GST (15%), each.
• The cost for the return air tickets is $2500,
plus GST (15%), each.
Cost (airfares) = 2 ´ 2500 ´1.15 = $5750
• The 3 week bus trip costs 2000 Great Britain
pounds per person.
• Great Britain pounds are used as currency in
England.
• The Exchange rate is: 1 NZ Dollar = 0.4931 GB
Pound (January 2011).
• The 3 week bus trip costs 2000 Great Britain
pounds per person.
2 ´ 2000
bus trip
= are used=as$8111.95
• Cost
Greatfor
Britain
pounds
currency in
0.4931
England.
• The Exchange rate is: 1 NZ Dollar = 0.4931 GB
Pound (January 2011).
Total Cost
• This figure should be rounded sensibly
17040 + 5750 + 8112 = $30902
Now work on ‘how long’
• Huia earns $850 each week. Mike earns $790
each week. Huia is able to save 2/5 of her
income, and Mike 35% of his income to put
towards their saving for the trip.
Savings per week
• Huia earns $850 each week. Mike earns $790
each week. Huia is able to save 2/5 of her
income, and Mike 35% of his income to put
towards their saving for the trip.
2
850 ´ + 0.35 ´ 790 = $616.50
5
Make a comment that some weeks they may be able
to save more than this and other weeks less than this.
Estimate of the number of weeks to
save for the trip
• Rough calculation:
30902
= 50.12
616.5
Conclusion
• It will take over a year to save for this trip as
they will need money for insurance and
spending money as well.
Points to think about and discuss
•
•
•
•
Rounding sensibly - to the nearest $20
Additional spending on the bus trip
Variation in the exchange rate
The variation in the number of days in three
months
• The fairness of them contributing different
amounts to the saving for the trip
• The interpretation of this question is ‘open’.
Students may provide a solution that involves
Huia and Mike saving for their holiday
separately.
• Huia saves $340
• Mike saves $276.50
• It will take Mike longer if they are covering
their own costs: 15450
276.5
= 56