Category: Numbersense

Pennies to Heaven

Pennies to Heaven is a Fermi Problem, basically a “headmath” experiment. Fermi Problems, originally developed by Enrico Fermi, one of the greatest experimental and theoretical physicists of the 20th century, are real-world estimation problems. So we ask, “If we had a stack of pennies as tall as the Empire State Building, how big a room would we need to hold them?” Like most Fermi problems the answer to this one is a delightful surprise and requires us to think out-of-the-box. Always ask, “What do you guess?” “Would you need a whole house or something bigger, just your bedroom, or a closet, or something even smaller?”

Magic Rectangle

Multiplication tables have some wonderful and quite surprising patterns. This is one of them. Draw any rectangle in a multiplication table and you will find that the products of opposite corners are equal. For example a rectangle around a full 12 by 12 table will be 1144 and 1212. Try it, is it always true? Why?

Products as Areas

Using the times table, students can see that products are always rectangles, and that they represent the area of that rectangle. They should explore the times table by playing with these rectangles whose sides are the factor of the products.

Place Value

Our number system inherited from India and from the Medieval Arab world enables us to use just 10 symbols to write any number we can imagine. Students learn in this spreadsheet to enter numbers, to compare compact and expanded forms of those symbols and to add units to any number. Students who like to explore further can extend the place values from 3 digits to more and learn the trick that lets them include any kind of text with numbers they can change.