Non routine(probem and how to solve it)

iii) Gather information and select three non-routine problem and solve using two ore more types of problem solving. Select one strategy that is deemed to be most efficient and justify selection.

Question 1 :

In a non-leap year, which day is exactly in the middle of the year and what time is it?

i) TABLE

a) Understand the problem

§ What is given : Non-leap year

§ What is needed : The day is exactly in the middle and time of the

year.

b) Plan a strategy

§ Construct a problem-solving table

c) Devising

Month	Days	Hour
January	31	744
February	28	672
March	31	744
April	30	720
May	31	744
June	30	720
July	31	744
August	31	744
September	30	720
October	31	744
November	30	720
December	31	744
Total	365 days

1 year = 365 days

6 Month = 365 ÷ 2

= 182.5

§ Assume that 182.5 = 183

§ Total the days start from January until 183 days:-

31 + 28 + 31 + 30 + 31 + 30

= 181 days (June)

§ 181 days (June) + 2 days in July = 183 days. The day that exactly in the middle of the year is = 2^nd July.

§ 1 days = 24 hours

§ 24 hours × 365 days = 8760 hours

§ 6 month =8760 ÷ 2

=4380 hours (Until 30^th June)

· Total the hours start from January until 4380 hours:-

744 + 672 + 744 + 720 + 744 + 720 = 4344 hours

4380 hours – 4344 hours = 36hours

36 hours = 1 ½ day (in July)

36 hours -24 hours = 12 hours

24 hours = 1 July

12 hours = 2 July ( 12.00 p.m)

ii) DIRECT REASONING

a) Understand the problem

What is given : Non-leap year.

What is needed : The day is exactly in the middle of the year and the time.

b) Plan a strategy

· Use direct reasoning

c) Devising

· Non-leap year = 365 days

· So the middle of the year = 365/2

= 18.5

= 183 days

· January = 31 day

· February = 28 day

· March = 31 day

· April = 30 day

· May = 31 day

· June = 30 day

Total = 181 day

· To get 183 days, so we need to sum 181 days with 2 day in July. Now, day is exactly in the middle of the year is 2^nd July.

· Now 1 day = 24 hour

· We need to times 24 hour with the y of every month

· January 31 × 24 = 744 hour

· February 28 × 24 = 672 hour

· March 31 × 24 = 744 hour

· April 30 × 24 = 720 hour

· May 31 × 24 = 744 hour

· June 30 × 24 = 720 hour

· So, we needed to sum January until June 744 + 672 + 744 + 720 + 744 + 720 = 4322 hour

· Here we get 4344 hour until 30 June. After this we need times 1 ½ with 24 hour

· 1 ½ × 24 = 36 hour

· 1 ½ day = 24 ½ hour

· The answer is 2^nd July, 12.00 p.m

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