Creating and Manipulating Linear and Quadratic Expressions - Stage 3

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?

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?

More Number Pyramids

Age 11 to 14 Challenge Level:

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

Your Number Is...

Age 11 to 14 Challenge Level:

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

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?

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...

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?

Reversals

Age 11 to 14 Challenge Level:

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

Fibonacci Surprises

Age 11 to 14 Challenge Level:

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

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?

Quadratic Patterns

Age 11 to 14 Challenge Level:

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

Grow up Fast

Age 11 to 14 Short Challenge Level:

How old will Julie be when her age is equal to the sum of her daughters' ages?

8 in a Row

Age 11 to 14 Short Challenge Level:

The sum of five consecutive integers is equal to the sum of the next three consecutive integers. Can you find the largest of these eight integers?

Brothers and Sisters

Age 11 to 14 Short Challenge Level:

Can you work out how many brothers and sisters are in the family?

Cuboid Perimeters

Age 11 to 14 Short Challenge Level:

Can you find the volume of a cuboid, given its perimeters?

Black and Gold Storeys

Age 11 to 14 Short Challenge Level:

25 of the storeys of a 50 storey building are painted gold, and the rest are painted black...

Adding and Multiplying

Age 11 to 14 Short Challenge Level:

Amy misread a question and got an incorrect answer. What should the answer have be?

The Simple Life

Age 11 to 14 Challenge Level:

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