List

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.



Factors and Multiples Game
game
Favourite

Factors and Multiples Game

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

Factor Lines
problem
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Factor Lines

Age
7 to 14
Challenge level
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Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Got It
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Got It

Age
7 to 14
Challenge level
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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.

Number Lines in Disguise
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Number Lines in Disguise

Age
7 to 14
Challenge level
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Some of the numbers have fallen off Becky's number line. Can you figure out what they were?
Two and Two
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Two and Two

Age
7 to 16
Challenge level
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How many solutions can you find to this sum? Each of the different letters stands for a different number.

American Billions
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American Billions

Age
11 to 14
Challenge level
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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...
Frogs
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Frogs

Age
11 to 14
Challenge level
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How many moves does it take to swap over some red and blue frogs? Do you have a method?
Reflecting Squarely
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Reflecting Squarely

Age
11 to 14
Challenge level
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In how many ways can you fit all three pieces together to make shapes with line symmetry?

Isosceles Triangles
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Isosceles Triangles

Age
11 to 14
Challenge level
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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
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Odds and Evens

Age
11 to 14
Challenge level
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Are these games fair? How can you tell?
Substitution Cipher
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Substitution Cipher

Age
11 to 14
Challenge level
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Find the frequency distribution for ordinary English, and use it to help you crack the code.
Factors and Multiples Puzzle
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Factors and Multiples Puzzle

Age
11 to 14
Challenge level
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Using your knowledge of the properties of numbers, can you fill all the squares on the board?
m, m and m
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M, M and M

Age
11 to 14
Challenge level
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If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Elevenses
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Elevenses

Age
11 to 14
Challenge level
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How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Charlie's delightful machine
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Charlie's delightful machine

Age
11 to 16
Challenge level
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Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

Add to 200
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Add to 200

Age
11 to 14
Challenge level
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By selecting digits for an addition grid, what targets can you make?
Forwards Add Backwards
problem
Favourite

Forwards Add Backwards

Age
11 to 14
Challenge level
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What happens when you add a three digit number to its reverse?
Can you Make 100?
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Can you Make 100?

Age
11 to 14
Challenge level
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How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?
Number Daisy
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Number Daisy

Age
11 to 14
Challenge level
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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?
Squares in rectangles
problem
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Squares in rectangles

Age
11 to 14
Challenge level
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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?
Product Sudoku
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Product Sudoku

Age
11 to 16
Challenge level
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The clues for this Sudoku are the product of the numbers in adjacent squares.

Tower of Hanoi
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Tower of Hanoi

Age
11 to 14
Challenge level
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The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
Last Biscuit
game

Last Biscuit

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

Wipeout
problem
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Wipeout

Age
11 to 16
Challenge level
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Can you do a little mathematical detective work to figure out which number has been wiped out?
Funny Factorisation
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Funny Factorisation

Age
11 to 16
Challenge level
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Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
Overlaps
problem
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Overlaps

Age
11 to 14
Challenge level
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Can you find ways to put numbers in the overlaps so the rings have equal totals?
Where can we visit?
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Where can we visit?

Age
11 to 14
Challenge level
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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?
Same length
problem
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Same length

Age
11 to 16
Challenge level
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Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
Shopping Basket
problem
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Shopping Basket

Age
11 to 16
Challenge level
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The items in the shopping basket add and multiply to give the same amount. What could their prices be?
Triangles to Tetrahedra
problem
Favourite

Triangles to Tetrahedra

Age
11 to 14
Challenge level
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Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Cuboids
problem
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Cuboids

Age
11 to 14
Challenge level
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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?
Nine Colours
problem
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Nine Colours

Age
11 to 16
Challenge level
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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?
Data matching
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Data matching

Age
14 to 18
Challenge level
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Use your skill and judgement to match the sets of random data.
A little light thinking
problem
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A little light thinking

Age
14 to 16
Challenge level
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Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

In a box
problem
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In a box

Age
14 to 16
Challenge level
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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?
Partly Painted Cube
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Partly Painted Cube

Age
14 to 16
Challenge level
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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?
Kite in a Square
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Kite in a Square

Age
14 to 18
Challenge level
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Can you make sense of the three methods to work out what fraction of the total area is shaded?
Difference Sudoku
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Difference Sudoku

Age
14 to 16
Challenge level
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Use the differences to find the solution to this Sudoku.
Latin Numbers
problem
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Latin Numbers

Age
14 to 16
Challenge level
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Can you create a Latin Square from multiples of a six digit number?