1.1a numeric reasoning

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.

• 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.

• Great Britain pounds are used as currency in England.

• The Exchange rate is: 1 NZ Dollar = 0.4931 GB Pound (January 2011).

Total Cost

• This figure should be rounded sensibly

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.

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:

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: