Creating and Manipulating Linear and Quadratic Expressions - Stage 4


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

Finding Factors

Age 14 to 16 Challenge Level:

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

Hollow Squares

Age 14 to 16 Challenge Level:

Which armies can be arranged in hollow square fighting formations?

Factorising with Multilink

Age 14 to 16 Challenge Level:

Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

Pair Products

Age 14 to 16 Challenge Level:

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

What's Possible?

Age 14 to 16 Challenge Level:

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

Puzzling Place Value

Age 14 to 16 Challenge Level:

Can you explain what is going on in these puzzling number tricks?

Why 24?

Age 14 to 16 Challenge Level:

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

Always Perfect

Age 14 to 16 Challenge Level:

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

Pythagoras Perimeters

Age 14 to 16 Challenge Level:

If you know the perimeter of a right angled triangle, what can you say about the area?

Perfectly Square

Age 14 to 16 Challenge Level:

The sums of the squares of three related numbers is also a perfect square - can you explain why?

Difference of Two Squares

Age 14 to 16 Challenge Level:

What is special about the difference between squares of numbers adjacent to multiples of three?

Multiplication Square

Age 14 to 16 Challenge Level:

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

Plus Minus

Age 14 to 16 Challenge Level:

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

Square Number Surprises

Age 14 to 16 Challenge Level:

There are unexpected discoveries to be made about square numbers...

Harmonic Triangle

Age 14 to 16 Challenge Level:

Can you see how to build a harmonic triangle? Can you work out the next two rows?

2-digit Square

Age 14 to 16 Challenge Level:

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

Creating and Manipulating Linear and Quadratic Expressions Stage 4 - Short Problems

Age 14 to 16

A collection of short Stage 4 problems on creating algebraic expressions.



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