Being Resilient - Secondary

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.

Being Resilient - Number

Number problems that may require resilience.

Being Resilient - Algebra

Algebra problems that may require resilience.

Being Resilient - Geometry

Geometry problems that may require resilience.

Being Resilient - Statistics

Statistics problems that may require resilience.



Developing Students' Resilience

Age 5 to 18

Resources to accompany the Being Resilience collections.

Reach 100

Age 7 to 11
Challenge Level

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Estimating Angles

Age 7 to 14
Challenge Level

How good are you at estimating angles?

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?

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?

Add to 200

Age 11 to 14
Challenge Level

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

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?

Forwards Add Backwards

Age 11 to 14
Challenge Level

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

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?

Odds and Evens

Age 11 to 14
Challenge Level

Are these games fair? How can you tell?

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?

Can You Make 100?

Age 11 to 14
Challenge Level

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

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?

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?

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...

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?

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?

Substitution Cipher

Age 11 to 14
Challenge Level

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

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.

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?

Overlaps

Age 11 to 14
Challenge Level

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

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?

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?

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?

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?

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?

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?

Product Sudoku

Age 11 to 16
Challenge Level

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

Wipeout

Age 11 to 16
Challenge Level

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

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?

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?

Two and Two

Age 11 to 16
Challenge Level

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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?

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?

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?

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?

Difference Sudoku

Age 14 to 16
Challenge Level

Use the differences to find the solution to this Sudoku.

Latin Numbers

Age 14 to 16
Challenge Level

Can you create a Latin Square from multiples of a six digit number?

Data Matching

Age 14 to 18
Challenge Level

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

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?