# From Exploration to Consolidation

Below are two pairs of tasks. Each pair offers the opportunity to put into practice the model of 'exploration, codification, consolidation', which was first developed by Ruthven.

The first task in each pair encourages learners to be playful with the mathematics and make their own discoveries (exploration). The teacher's role is then to help children articulate what they have learnt, introduce new vocabulary where appropriate, and support children in deepening their understanding by helping them link the new learning to their existing knowledge (codification). The second task in each pair then gives a new context in which children can apply what they have learnt in a meaningful way (consolidation). As a group these problems will give you the chance to develop all five strands of the rope model (understanding, skills, problem solving, reasoning and attitude).

This first pair of tasks makes use of the structure of dominoes.

### Domino Sets

##### Age 7 to 11 Challenge Level:

How do you know if your set of dominoes is complete?

### Amy's Dominoes

##### Age 7 to 11 Challenge Level:

Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?

This second pair of tasks provides a geometrical context.

### Possible Pairs

##### Age 7 to 11 Challenge Level:

In this game, you turn over two cards and try to draw a triangle which has both properties.

### Name That Triangle!

##### Age 7 to 11 Challenge Level:

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?