Mathematicians often explore structures, notice patterns, find rules and make generalisations. Once they feel they understand a structure, they then push at the boundaries, change the problem, and explore the new structures that emerge.
The Freedom and Constraints pathway on wild.maths.org offers students some situations which may initially seem constrained, but on closer inspection they may find there is more room to manoeuvre than they imagined.
The collection of related NRICH tasks below are ideal for teachers who want to promote creativity in the classroom. They are designed for classroom use, with accompanying Teachers' Notes and Resources.
The Freedom and Constraints pathway on wild.maths.org offers students some situations which may initially seem constrained, but on closer inspection they may find there is more room to manoeuvre than they imagined.
The collection of related NRICH tasks below are ideal for teachers who want to promote creativity in the classroom. They are designed for classroom use, with accompanying Teachers' Notes and Resources.
problem
Favourite
Dozens
Age
7 to 14
Challenge level
Can you select the missing digit(s) to find the largest multiple?
problem
Favourite
Two and Two
Age
7 to 16
Challenge level
How many solutions can you find to this sum? Each of the different letters stands for a different number.
problem
Favourite
American Billions
Age
11 to 14
Challenge level
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
problem
Favourite
Largest product
Age
11 to 14
Challenge level
Which set of numbers that add to 100 have the largest product?
problem
Favourite
Cinema Problem
Age
11 to 14
Challenge level
A cinema has 100 seats. How can ticket sales make £100 for these different combinations of ticket prices?
problem
Favourite
Odds and Evens
Age
11 to 14
Challenge level
Are these games fair? How can you tell?
problem
Favourite
How much can we spend?
Age
11 to 14
Challenge level
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?
problem
Favourite
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
Favourite
What numbers can we make?
Age
11 to 14
Challenge level
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
problem
Favourite
Gabriel's Problem
Age
11 to 14
Challenge level
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
problem
Favourite
1 Step 2 Step
Age
11 to 14
Challenge level
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
problem
Favourite
Take Three From Five
Age
11 to 16
Challenge level
Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?
problem
Favourite
Peaches today, Peaches tomorrow...
Age
11 to 14
Challenge level
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
problem
Favourite
Weights
Age
11 to 14
Challenge level
Different combinations of the weights available allow you to make different totals. Which totals can you make?
problem
Favourite
What numbers can we make now?
Age
11 to 14
Challenge level
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?