Search by Topic

Resources tagged with Making and proving conjectures similar to Expanding Pattern:

Filter by: Content type:
Age range:
Challenge level:

There are 30 results

Broad Topics > Using, Applying and Reasoning about Mathematics > Making and proving conjectures

Triangles Within Triangles

Age 14 to 16 Challenge Level:

Can you find a rule which connects consecutive triangular numbers?

Triangles Within Squares

Age 14 to 16 Challenge Level:

Can you find a rule which relates triangular numbers to square numbers?

A Little Light Thinking

Age 14 to 16 Challenge Level:

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

Happy Numbers

Age 11 to 14 Challenge Level:

Take any whole number between 1 and 999, add the squares of the digits to get a new number. Make some conjectures about what happens in general.

Triangles Within Pentagons

Age 14 to 16 Challenge Level:

Show that all pentagonal numbers are one third of a triangular number.

Helen's Conjecture

Age 11 to 14 Challenge Level:

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

Dice, Routes and Pathways

Age 5 to 14

This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .

Problem Solving, Using and Applying and Functional Mathematics

Age 5 to 18 Challenge Level:

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

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...

Loopy

Age 14 to 16 Challenge Level:

Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture?

Consecutive Negative Numbers

Age 11 to 14 Challenge Level:

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Exploring Quadratic Mappings

Age 14 to 16 Challenge Level:

Explore the relationship between quadratic functions and their graphs.

Exploring Simple Mappings

Age 11 to 14 Challenge Level:

Explore the relationship between simple linear functions and their graphs.

Charlie's Mapping

Age 11 to 14 Challenge Level:

Charlie has created a mapping. Can you figure out what it does? What questions does it prompt you to ask?

Close to Triangular

Age 14 to 16 Challenge Level:

Drawing a triangle is not always as easy as you might think!

Polycircles

Age 14 to 16 Challenge Level:

Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?

Arrowhead

Age 14 to 16 Challenge Level:

The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?

Multiplication Arithmagons

Age 14 to 16 Challenge Level:

Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

An Introduction to Magic Squares

Age 7 to 16

Find out about Magic Squares in this article written for students. Why are they magic?!

Alison's Mapping

Age 14 to 16 Challenge Level:

Alison has created two mappings. Can you figure out what they do? What questions do they prompt you to ask?

Quad in Quad

Age 14 to 16 Challenge Level:

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

How Old Am I?

Age 14 to 16 Challenge Level:

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

To Prove or Not to Prove

Age 14 to 18

A serious but easily readable discussion of proof in mathematics with some amusing stories and some interesting examples.

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?

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?

DOTS Division

Age 14 to 16 Challenge Level:

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

Janine's Conjecture

Age 14 to 16 Challenge Level:

Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .

Curvy Areas

Age 14 to 16 Challenge Level:

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

Few and Far Between?

Age 14 to 18 Challenge Level:

Can you find some Pythagorean Triples where the two smaller numbers differ by 1?

Epidemic Modelling

Age 14 to 18 Challenge Level:

Use the computer to model an epidemic. Try out public health policies to control the spread of the epidemic, to minimise the number of sick days and deaths.