The Mathemagician's Seven Spells

"Tell me the next two numbers in each of these seven minor spells", chanted the Mathemagician, "And the great spell will crumble away!" Can you help Anna and David break the spell?

Folding, Cutting and Punching

Exploring and predicting folding, cutting and punching holes and making spirals.

Seven Pots of Plants

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Locate the Lion's Lair

Why do this problem?

This problem allows learners to identify different patterns and then to try to refine their understanding of these patterns. It will help children grasp the idea of making a hypothesis and then amending it in light of new evidence.

Possible approach

It would be useful for the class to have access to a suite of computers for this activity. You could introduce the problem by displaying the interactivity for everyone to see and clicking on the sighting button just once. Invite pupils to talk in pairs about where the lair could be and allow the group to discuss the value of having several sightings before being more confident of locating it.

Continue clicking on the sighting button until someone is reasonably confident they can locate the lair. Ask this pupil to explain where they think it is and why before seeing whether they are right. Describing the chosen square is a challenge in itself and the group may develop ways of coding the grid to help. Once the lair has been located, you can draw the children's attention to the scoring system and they can try to beat the score in pairs.

After a while, bring them together to talk about the patterns they notice in the lion's behaviour and how this helps locate the lair. Pupils could then investigate the second type of behaviour in a similar way.

Key questions

How would you describe where the sightings are on the map?
If you're trying to get as high a score as possible, what are you looking for before you take a guess?

Possible extension

Learners could try this much trickier version of the problem where there are more hunting behaviours to explore.

Possible support

The best way to get into this problem is by having lots of tries. By asking children to describe the pattern made by the sightings on the map, you will help them to begin to suggest where the lair might be.