Being resilient - Secondary students

Being Resilient is part of our Developing Mathematical Habits of Mind collection.

Good thinkers are resilient. They don't give up easily, and are motivated to work hard and keep going when faced with challenges. They recognise that we all fail sometimes, and when this happens, they bounce back and try alternative approaches. Find out more in What Does it Feel Like to Do Maths, which includes a film of the mathematician Andrew Wiles talking about his personal experience of seeking a proof of Fermat's Last Theorem.

Want to become a more resilient mathematician?

These problems may require you to persevere when the solutions are not immediately obvious. Take a look, we hope you'll stick with them and feel a sense of achievement at the end!

You can browse through the Number, Algebra, Geometry or Statistics collections, or scroll down to see the full set of problems below.

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Being resilient - number

Challenge level

Number problems that may require resilience.

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Being resilient - algebra

Challenge level

Algebra problems that may require resilience.

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Being resilient - geometry

Challenge level

Geometry problems that may require resilience.

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Being resilient - statistics

Challenge level

Statistics problems that may require resilience.

game

Favourite

Estimating angles

Age

7 to 14

Challenge level

How good are you at estimating angles?

game

Favourite

Factors and multiples game

Age

7 to 16

Challenge level

A game in which players take it in turns to choose a number. Can you block your opponent?

problem

Number lines in disguise

Age

7 to 14

Challenge level

Some of the numbers have fallen off Becky's number line. Can you figure out what they were?

problem

Factor lines

Age

7 to 14

Challenge level

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

problem

Got it

Age

7 to 14

Challenge level

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

problem

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

Factors and multiples puzzle

Age

11 to 14

Challenge level

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

problem

M, M and M

Age

11 to 14

Challenge level

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

problem

Elevenses

Age

11 to 14

Challenge level

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

problem

Charlie's delightful machine

Age

11 to 16

Challenge level

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

problem

Add to 200

Age

11 to 14

Challenge level

By selecting digits for an addition grid, what targets can you make?

problem

Forwards add backwards

Age

11 to 14

Challenge level

What happens when you add a three digit number to its reverse?

problem

Can you make 100?

Age

11 to 14

Challenge level

How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?

problem

Number daisy

Age

11 to 14

Challenge level

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

problem

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

Frogs

Age

11 to 14

Challenge level

How many moves does it take to swap over some red and blue frogs? Do you have a method?

problem

Reflecting squarely

Age

11 to 14

Challenge level

In how many ways can you fit all three pieces together to make shapes with line symmetry?

problem

Isosceles triangles

Age

11 to 14

Challenge level

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

problem

Odds and evens

Age

11 to 14

Challenge level

Are these games fair? How can you tell?

problem

Substitution cipher

Age

11 to 14

Challenge level

Find the frequency distribution for ordinary English, and use it to help you crack the code.

problem

Tower of Hanoi

Age

11 to 14

Challenge level

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

game

Last biscuit

Age

11 to 18

Challenge level

Can you find a strategy that ensures you get to take the last biscuit in this game?

problem

Wipeout

Age

11 to 16

Challenge level

Can you do a little mathematical detective work to figure out which number has been wiped out?

problem

Funny factorisation

Age

11 to 16

Challenge level

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

problem

Overlaps

Age

11 to 14

Challenge level

Can you find ways to put numbers in the overlaps so the rings have equal totals?

problem

Where can we visit?

Age

11 to 14

Challenge level

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?

problem

Same length

Age

11 to 16

Challenge level

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

problem

Squares in rectangles

Age

11 to 14

Challenge level

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

problem

Product Sudoku

Age

11 to 16

Challenge level

The clues for this Sudoku are the product of the numbers in adjacent squares.

problem

Nine colours

Age

11 to 16

Challenge level

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

problem

Shopping basket

Age

11 to 16

Challenge level

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

problem

Triangles to tetrahedra

Age

11 to 14

Challenge level

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

problem

Cuboids

Age

11 to 14

Challenge level

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

problem

Data matching

Age

14 to 18

Challenge level

Use your skill and judgement to match the sets of random data.

problem

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?

problem

Partly painted cube

Age

14 to 16

Challenge level

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

problem

Kite in a square

Age

14 to 18

Challenge level

Can you make sense of the three methods to work out what fraction of the total area is shaded?

problem

In a box

Age

14 to 16

Challenge level

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?