Algebra PlayClass 8 Mathematics Case Study Questions

Rohan is setting up a 'Mind Reader' game stall for his school fair. The game involves a series of mathematical steps that a participant must follow. Rohan claims he can predict the final answer, no matter what number the participant starts with. He has designed a simple trick to attract the younger students. The instructions are:

Rohan confidently tells every participant that their final answer will be a specific number. He wants to analyze the trick using algebra to be sure it always works and to think about how to create new, more complex tricks for the fair.

A magician is hired for a birthday party. He performs a math trick to guess a guest's birth date. He asks a volunteer, Priya, to perform a series of calculations quietly and only tell him the final result. The instructions are as follows:

Priya follows the steps and tells the magician her final answer is 788. The magician correctly guesses her birthday. We can use algebra to understand how he did it.

A school's eco-club is designing a vegetable garden. The garden is laid out in a large grid, similar to a calendar month. To make planning easier, they are selecting square sections for different types of plants. A student, Aisha, observes a pattern. She considers a $2 \times 2$ square of dates from a calendar page. Let's say the top-left date in this square is represented by the variable $a$. The numbers in a calendar grid increase by 1 as you move to the right and by 7 as you move down a row. Aisha tells her teacher that if she knows the sum of the four numbers in any $2 \times 2$ square, she can identify all the dates in it. For example, she is told the sum of four dates in a square plot is 60.