Problems

Materials:

  • pencil
  • paper

When Jack was one year old his mother bought a package of candles for his birthday cake. The package had 24 candles.

That year she put 1 candle on Jack’s cake. When he was two he had 2 candles and when he was three he had 3 candles, and so on.

3 birthday cakes, one with one candle, one with two candles and one with three candles.

One day Jack’s little sister Kate was born. Jack’s Mom used candles from the same package for Kate’s birthday cakes.
She had 1 candle on her first birthday cake, 2 candles on her second birthday cake, and so on.

The candle package was empty after one of Jack’s birthdays with just enough for Jack’s cake.

How old were Jack and Kate when the candles finally ran out?
How old was Jack when Kate was born?

Helpful Hints/Questions

  • Your child might want to draw the candles for Jack’s first few birthdays to get started.
  • How many candles will have been used for Jack’s cakes by the time he has had his fourth birthday? Fifth birthday? . . .
  • How does this help us to decide when Kate could have been born?

Adapted from nrich.maths.org