Creating and manipulating expressions and formulae

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

Can you find the hidden factors which multiply together to produce each quadratic expression?

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?

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

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

Look at the times that Harry, Christine and Betty take to pack boxes when working in pairs, to find how fast Christine can pack boxes by herself.

How does the perimeter change when we fold this isosceles triangle in half?

What does the sum of these three numbers tell us about their product?

Using the new operator $\oplus$, can you solve this equation?

Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?