### Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

### Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

### Rolling Around

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

# Measured Upside Down

##### Stage: 3 Short Challenge Level:
See all short problems arranged by curriculum topic in the short problems collection

Baby's nearly one year old now.

We've worked out how to weigh her but nurse and I still have trouble measuring her height. She just will not stand up straight against our measuring chart. In fact she can't stand up at all yet!

So we measure her upside down.
Last year nurse held Baby's feet, keeping them level with the $140 \; \text{cm}$ mark, while I read off the mark level with the top of Baby's head: $97 \; \text{cm}$.

This year it was my turn to hold the feet. Being taller than nurse, I held them against the $150 \; \text{cm}$ mark, while the nurse crawled on the floor to read the mark level with the top of Baby's head: $84 \; \text{cm}$.

How many centimetres has Baby grown in her first year?

If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.