On March 10, 1876, Alexander Graham Bell finally got his invention working: the telephone. It worked nothing like our phones today: the very first phones were sold in pairs, where each phone could call only that one other phone (you had to pick that other person carefully). Then came the “switchboard,” which let you call any other phone, but the “operator,” a phone company person in the middle of town, had to plug in wires to connect your call for you. Now we can call anyone anywhere on our own within seconds, and through the air. But that first phone, that first time talking to someone through a wire, must have looked like magic.
Wee ones: If in your house you have 2 old-fashioned wired phones and 2 cellphones, how many phones do you have in total?
Little kids: Bell’s telephone was a big hit: by end of 1877 there were 3,000 phones in use, and by mid-1878 there were 10,000. How many new phones showed up in between? (Hint: Think in chunks of thousands.) Bonus: The first “phone directory” – list of people’s names and numbers – was in New Haven, Connecticut, with just 50 people for the whole town. If your parents’ cellphone contains 80 phone numbers, how many more numbers do they have?
Big kids: In 1989, over 3 million Americans had cellphones, which link phone calls through the air. Now the U.S. has over 300 million cellphones. How many times did that total multiply by 10? Bonus: The thing is, we still have old phone wires stretching across telephone poles. If your town has phone wire along 5 north-south streets and 5 east-west streets, and those streets are spaced 1/2 mile apart, how many miles of phone wire do those streets use? (Assume just one wire per street, and the 1st and 5th streets in each direction are the borders.)
The sky’s the limit: Back when phones were sold in pairs, a dozen people with phones could pair off in only 6 possible conversations. If suddenly a switchboard connected all 12 phones with each other, how many total pairs of callers did they suddenly have?
Wee ones: 4 phones.
Little kids: 7,000 more phones. Bonus: 30 more phone numbers.
Big kids: It grew tenfold twice (x10, and x10 again). Bonus: 20 miles: there are 10 wires in total, with each street only 4 blocks long, or 2 miles apiece.
The sky’s the limit: 66 pairs, which is 11+10+9+8…+2+1. The shortcut formula for connecting p people is p x (p-1) /2. It’s half because these are the pyramid-stacking numbers, or “triangle numbers” – they are each 1/2 a rectangle that’s p tall and p-1 wide.