Report

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