Conjecturing and generalising

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

An investigation that gives you the opportunity to make and justify predictions.

This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?

A point moves on a line segment. A function depends on the position of the point. Where do you expect the point to be for a minimum of this function to occur.

Can you tangle yourself up and reach any fraction?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?