This is an optional task. This is the take-home test which will be taken into consideration in the event that you did not do well on the Final Problem Solving Test. Each task is valued at 10 points.

Your submission is graded as Exceeding Expectations (good solutions in all tasks), Meeting Expectations (ggod solution in at least one task) or Approaching Expectations (some attempt at the problem s but without success).

Problem A

Jon has a set of cards, numbered 1 to 100.

He removed some cards with consecutive numbers and found that the total of these numbers are 50.

What are these cards?

Write an explanation to show how you arrive at the solution.

Show that you engage in the look back stage of Polya's model.

Problem B

Find the largest rectangular box (by capacity) that can be made using a sheet of A5 paper.

Explain the steps that you take to make sure this is the largest capacity possible i.e. how do you know this is the largest possible value?

Provide an explanation if a container with a larger capacity floats better.

Problem C

The Door Bell Rang

Ma makes some freshly baked chocolate chip cookies, and her two kids sit down to eat the when ding dong! the doorbell rings! More kids arrive to share the cookies, but just when they sit down, ding dong! Finally, when there is only one cookie for each child, the doorbell rings again. Who is it? Grandma with a new tray of fresh baked cookies! And no one bakes cookies as good as Grandma's! Hutchins sneaks a bit of math into this funny tale.

In the original story, Ma baked 12 cookies. This is my version. Needs to have basic literacy in Singlish.

Cookies, cookies, there's chocolate chip and durian bits too.

One cookie left when put in twos.

Cookies, cookies, enough for you, you, you and me.

One cookie left when put in threes.

Cookies, cookies, good to eat with Milo and Kopi-O.

One cookie left when put in fours.

Cookies, cookies, come, come, die, die must try.

One cookie left when put in fives.

Cookies, cookies, baked from nenek's secret mix.

One cookie left when put in six.

Cookies, cookies, more sedap than the ones you bought in London.

No cookie left when put in sevens.

Give one, or better, two, method(s) to find the number of possible cookies in the given story. Originality is valued.

Footnotes (in case you are not literate in Singlish and local dialects): durian = a type of fruit, Milo = brand of a chocolate drink, Kopi-O = black coffee with sugar, die, die must try = definitely must give it a try, nenek = grandmother, sedap = delicious.

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