With everyone staying up late during vacation, people might be yawning more than usual. On average a yawn takes 6 seconds, and some scientists think yawning gives us energy by putting more oxygen into our blood. The weirdest thing is that people’s yawns make OTHER people yawn. Really, next time you’re in a group, try yawning: there’s more than half a chance that someone else will yawn within 5 minutes. And even your dog might yawn with you!

*Wee ones:* What numbers would you say (in your head!) to count off your 6-second yawn?

*Little kids:* If you yawn 7 times and your friend yawns just 2 times, how many more times did you yawn? *Bonus:* If you yawn 5 times a day, how many times do you yawn in a week? See if you can count up by 5s!

*Big kids:* If your yawn makes 2 other kids yawn, and each of them makes 2 more kids yawn, and each of them makes another 2 more kids yawn, how many of you have yawned in total? *Bonus:* At least how many more rounds like that would you need to have 50 people all yawn at least once?

*The sky’s the limit:* If there are 30 yawns in a room, and 4 times as many yawns come from dogs as people, how many of each just yawned?

Answers:

*Wee ones:* 1, 2, 3, 4, 5, 6.

*Little kids:* 5 more times. *Bonus:* 35 times: 5, 10, 15, 20, 25, 30, 35.

*Big kids:* 15 kids, including you (1+2+4+8). *Bonus:* 2 more rounds. The next round will add 16, giving us just 31, so you’ll need that next round of 32 possible yawns to reach 50.

*The sky’s the limit:* 6 people and 24 dogs. If there are 4 dogs for each yawning person, the yawners come in sets of 5, and 30 would have 6 of those sets. If you want to show with algebra, for p people and d dogs we have:

p + d = 30

d = 4p

Substituting into the 1st equation, we get

p + 4p = 30

5p = 30

p = 6 = number of people, so that gives us 4 x 6 = 24 dogs.