List

Creating and manipulating linear and quadratic expressions: Age 11-14

This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.

Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.

problem

Your number is...

Age

7 to 14

Challenge level

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?

problem

The Number Jumbler

Age

7 to 14

Challenge level

The Number Jumbler can always work out your chosen symbol. Can you work out how?

problem

Special numbers

Age

11 to 14

Challenge level

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

problem

Number pyramids

Age

11 to 14

Challenge level

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

problem

Crossed ends

Age

11 to 14

Challenge level

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

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

Think of two numbers

Age

11 to 14

Challenge level

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

problem

More number pyramids

Age

11 to 14

Challenge level

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

problem

Always a multiple?

Age

11 to 14

Challenge level

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

problem

Reversals

Age

11 to 14

Challenge level

Where should you start, if you want to finish back where you started?

problem

Fibonacci surprises

Age

11 to 14

Challenge level

Play around with the Fibonacci sequence and discover some surprising results!

problem

The simple life

Age

11 to 14

Challenge level

The answer is $5x+8y$... What was the question?

problem

Quadratic patterns

Age

14 to 16

Challenge level

Surprising numerical patterns can be explained using algebra and diagrams...

Creating and Manipulating Linear and Quadratic Expressions - Stage 3 STEM footer

You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.