To infinity and beyond (grade 4 students)

Hey Mom, look at this ball bounce
I’ll drop it from a height of 2 metres
How far will it travel
Before it stops bouncing?
Going up and Going down

Will it be 100 metres
or even a kilometre?
It keeps bouncing and bouncing
It must travel far
It’s closer to,  …….10 metres Mom.

Bounce, bounce, bounce
Each bounce smaller
Bounce, bounce, bounce
Than the one before
Bounce, bounce, bounce
Each bounce smaller
Bounce, bounce, bounce
Than the one before

Here’s another puzzle, Mom.
You’re 10 metres from the door.
You walk halfway there.
Then half the remaining distance
And again and again, forever.

How far will you travel?
An infinite number of steps
But not more than 10 metres.
Reminds me of the bouncing ball
Each bounce is a fraction ,of the bounce before.

Walk, walk, walk
Each step smaller
Walk, walk, walk
Than the one before
Walk, walk, walk
Each step smaller
Walk, walk, walk
Than the one before

The Math Performance Festival is funded by the Imperial Oil Foundation, the Fields Institute, Research Western, the Faculty of Education at UWO, and the Canadian Mathematical Society. A project by George Gadanidis (UWO), Susan Gerofsky (UBC), and Rick Jardine (UWO).