## Free Parent Involvement Activity – "Brain Busters" – Ages 7 and Up

What is the Rule of 72?

Sock DrawerSo as not to wake up his brother, Mark leaves the light off while looking for a pair of socks. He knows he has twelve black socks and eight blue socks in the drawer. What is the minimum number of socks he will need to pick out in order to ensure that he has a matching pair? (Hint available*)

Generous Grandparents – Grandpa wants to help you save up for a new bike. he says that as long as you start with one penny in your piggy bank he will add enough money each day to your bank to double the amount already in there. After you put the penny in, Grandpa puts in one cent the first day, two cents the second day, four cents the third day, etc. On the twelfth day your piggy bank is full. On which day is your piggy bank half full?

Not to be outdone, your Grandma decides that she will also give you one cent on the first day, two cents on the second day, four cents on the third day, etc. With both grandparents now contributing, on which day would your piggy bank be half full? (Hint available*)

Age of Reason – If I add two times my age two years from now to three times my age three years from now, the result is six times my current age. How old will I be four years from now?

(Hint available*)

Source: Bright and Beyond, Smart & Simple Thinking Activities to do with your Child, Ages 7 and up. Available at Schoodoodle.com.

Hints:

Sock Drawer — Three socks. If Mark picks three socks the possibilities become black/black/black, blue/blue/blue, black/black/blue, or blue/blue/black. There is a pair in each possibility.

Generous Grandparents — When only Grandpa contributes, the piggy bank will be half full on the eleventh day (i.e., the day before the last day). Remember, the amount doubles each day! When Grandma chips in too, the piggy bank is half full a day earlier (Grandpa’s one quarter fill plus Grandma’s one quarter fill equals half full), so the piggy bank will be half full two days before the final day (day ten). (If a quantity doubles every day, then, today’s amount is half of tomorrow’s amount.)

Age of Reason — Seventeen years old. (Begin by figuring out his current age (x). 2(x+2) + 3(x+3) =6x, then add four.)

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