# 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.

### Reach 100

##### Age 7 to 11Challenge 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 14Challenge Level

How good are you at estimating angles?

### Number Lines in Disguise

##### Age 7 to 14Challenge 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 16Challenge Level

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

### Substitution Cipher

##### Age 11 to 14Challenge Level

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

##### Age 11 to 14Challenge Level

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

### Factors and Multiples Puzzle

##### Age 11 to 14Challenge Level

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

### Isosceles Triangles

##### Age 11 to 14Challenge 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 14Challenge Level

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

### Odds and Evens

##### Age 11 to 14Challenge Level

Are these games fair? How can you tell?

### Number Daisy

##### Age 11 to 14Challenge 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?

### Frogs

##### Age 11 to 14Challenge 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 14Challenge 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 14Challenge 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...

##### Age 11 to 14Challenge Level

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

### Reflecting Squarely

##### Age 11 to 14Challenge Level

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

### Elevenses

##### Age 11 to 14Challenge 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?

### Tower of Hanoi

##### Age 11 to 14Challenge 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 14Challenge 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 14Challenge Level

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

### Squares in Rectangles

##### Age 11 to 14Challenge 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 14Challenge 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 14Challenge 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 16Challenge 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 16Challenge 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 16Challenge 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 16Challenge Level

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

### Product Sudoku

##### Age 11 to 16Challenge Level

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

##### Age 11 to 16Challenge 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 16Challenge 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 16Challenge 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 18Challenge 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 16Challenge Level

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

##### Age 14 to 16Challenge 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 16Challenge Level

Use the differences to find the solution to this Sudoku.

### Data Matching

##### Age 14 to 18Challenge Level

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

### Kite in a Square

##### Age 14 to 18Challenge Level

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