Exploring and noticing

How many different number families can you find?

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

Who said that adding couldn't be fun?

How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

Dotty Six is a simple dice game that you can adapt in many ways.

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?