Creating and manipulating expressions and formulae

problem
Seven squares

Age

11 to 14

Challenge level

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

Age

14 to 16

Challenge level

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

Age

14 to 16

Challenge level

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?
problem
Perimeter expressions

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

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?
problem
Packing boxes

Age

14 to 16

Challenge level

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.
problem
Folding in half

Age

14 to 16

Challenge level

How does the perimeter change when we fold this isosceles triangle in half?
problem
In sum-mary

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

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

Age

14 to 16

Challenge level

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