### Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

### It Figures

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

### Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

# Flashing Lights

## Flashing Lights

Norrie is watching the aircraft warning lights on the tops of some tall buildings in the city. He sees two lights flash at the same time, then one of them flashes every $4$th second, and the other flashes every $5$th second.
How many times do they flash together during a whole minute?

Norrie then watched a third light. He saw it flash at the same time as the other two, then flash every $7$th second. How many minutes before this light again flashes at exactly the same time as the other two?

### Why do this problem?

This problem is a good way of introducing children to common multiples and it is also a useful context for looking at different recording methods.

### Possible approach

As a starter, you could split the class into two groups. One group will clap every $3$ beats and the other every $6$ beats, while you count the beats. Ask them to predict on which beats they will all be clapping. Try other rhythms in the same way e.g. $3$ and $4$. Can they explain why everyone will be clapping on certain beats? How would they work out which beats these were without clapping?

Then you could introduce the flashing lights context and ask children to work in pairs on it. After a short time, stop them briefly to share some of the different ways they are working and, in particular, to look at what they are writing down to help them. For example, some might list multiples, some might list consecutive numbers but highlight multiples in some way, some might colour numbers in the $100$ square ... You could talk about the advantages of each method discussed. In this instance, the recording is only for them. What might they do differently if they were recording their work for someone else to understand?

In the plenary, you can specifically introduce the vocabulary of common multiples if you haven't done so already.

### Key questions

When will the first light flash?
When will the second light flash?
So when will they flash together?
What do you notice about the times when they flash together?
How would you predict when they will flash together next?

### Possible extension

Music to My Ears would be a good problem for children to try next as it places greater emphasis on predicting when common multiples occur.

### Possible support

Some learners might find Clapping Times a good problem to try before this one.