There are 71 NRICH Mathematical resources connected to Posing questions and making conjectures, you may find related items under Thinking mathematically.
Broad Topics > Thinking mathematically > Posing questions and making conjectures
Can you find out which 3D shape your partner has chosen before they work out your shape?
This task combines spatial awareness with addition and multiplication.
This challenge combines addition, multiplication, perseverance and even proof.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
You'll need to work in a group on this problem. Use your sticky notes to show the answer to questions such as 'how many girls are there in your group?'.
The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?
This activity focuses on similarities and differences between shapes.
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?
This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.
This task requires learners to explain and help others, asking and answering questions.
This task requires learners to explain and help others, asking and answering questions.
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
What's the largest volume of box you can make from a square of paper?
Can you find rectangles where the value of the area is the same as the value of the perimeter?
If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Alf Coles writes about how he tries to create 'spaces for exploration' for the students in his classrooms.
Can you find the values at the vertices when you know the values on the edges?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
An investigation that gives you the opportunity to make and justify predictions.
What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?
A point moves on a line segment. A function depends on the position of the point. Where do you expect the point to be for a minimum of this function to occur.
Which of these triangular jigsaws are impossible to finish?
Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.
Change the squares in this diagram and spot the property that stays the same for the triangles. Explain...
In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?
A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers?
Follow the directions for circling numbers in the matrix. Add all the circled numbers together. Note your answer. Try again with a different starting number. What do you notice?
Exploring and predicting folding, cutting and punching holes and making spirals.
Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?
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?