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# Being Resilient - Secondary Students

### Inside Triangles

### Robot Monsters

### Mixed-up Socks

### Find the Difference

### Rolling That Cube

### Four Triangles Puzzle

### Developing Students' Resilience

### How Many Times?

### Dicey Perimeter, Dicey Area

### Nine-pin Triangles

### Which Scripts?

### Maze 100

### Reach 100

### Make 37

### Got It

### Number Lines in Disguise

### Factor Lines

### Factors and Multiples Game

### Substitution Cipher

### M, M and M

### Frogs

### Factors and Multiples Puzzle

### Isosceles Triangles

### Elevenses

### Can You Make 100?

### Reflecting Squarely

### Add to 200

### Number Daisy

### Forwards Add Backwards

### American Billions

### Overlaps

### Where Can We Visit?

### Tower of Hanoi

### Squares in Rectangles

### Cuboids

### Triangles to Tetrahedra

### Charlie's Delightful Machine

### Same Length

### Wipeout

### Product Sudoku

### Funny Factorisation

### Nine Colours

### Shopping Basket

### Two and Two

### Last Biscuit

### A Little Light Thinking

### In a Box

### Partly Painted Cube

### Difference Sudoku

### Latin Numbers

### Data Matching

### Kite in a Square

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*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.*

Age 5 to 7

Challenge Level

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Age 5 to 7

Challenge Level

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Age 5 to 7

Challenge Level

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

Age 5 to 7

Challenge Level

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Age 5 to 11

Challenge Level

My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?

Age 5 to 11

Challenge Level

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Age 5 to 18

Resources to accompany the Being Resilience collections.

Age 7 to 11

Challenge Level

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

Age 7 to 11

Challenge Level

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

Age 7 to 11

Challenge Level

How many different triangles can you make on a circular pegboard that has nine pegs?

Age 7 to 11

Challenge Level

There are six numbers written in five different scripts. Can you sort out which is which?

Age 7 to 11

Challenge Level

Can you go through this maze so that the numbers you pass add to exactly 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.

Age 7 to 11

Challenge Level

Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

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.

Age 7 to 14

Challenge Level

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

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.

Age 7 to 16

Challenge Level

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

Age 11 to 14

Challenge Level

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

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?

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?

Age 11 to 14

Challenge Level

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

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?

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?

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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

Age 11 to 14

Challenge Level

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

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?

Age 11 to 14

Challenge Level

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

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...

Age 11 to 14

Challenge Level

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

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?

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.

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?

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?

Age 11 to 14

Challenge Level

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

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?

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?

Age 11 to 16

Challenge Level

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

Age 11 to 16

Challenge Level

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

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?

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?

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?

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.

Age 11 to 18

Challenge Level

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

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?

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?

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?

Age 14 to 16

Challenge Level

Use the differences to find the solution to this Sudoku.

Age 14 to 16

Challenge Level

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

Age 14 to 18

Challenge Level

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

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?