Being Resilient

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.

How do we encourage our students to become resilient mathematicians?

Here are some problems that may require some determination. If you warn your students that the solutions may not be immediately obvious, and encourage them to persevere, they may learn to appreciate that success can be sweeter after a struggle.

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.

Estimating Angles

Age 7 to 14 Challenge Level:

How good are you at estimating angles?

Reach 100

Age 7 to 14 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.

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?

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?

Can You Make 100?

Age 11 to 14 Challenge Level:

How many ways can you find to put in operation signs (+ - x ÷) to make 100?

Odds and Evens

Age 11 to 14 Challenge Level:

Are these games fair? How can you tell?

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?

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?

Add to 200

Age 11 to 14 Challenge Level:

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

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?

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?

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...

Substitution Cipher

Age 11 to 14 Challenge Level:

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

Forwards Add Backwards

Age 11 to 14 Challenge Level:

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

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?

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?

Overlaps

Age 11 to 14 Challenge Level:

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

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?

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?

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.

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?

Wipeout

Age 11 to 16 Challenge Level:

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

Product Sudoku

Age 11 to 16 Challenge Level:

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

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.

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?

Kite in a Square

Age 14 to 16 Challenge Level:

Can you make sense of the three methods to work out the area of the kite in the square?

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.

Data Matching

Age 14 to 18 Challenge Level:

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