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Being Resilient is part of our Developing Mathematical Habits of Mind collection.
In Developing Students' Resilience, we offer you support and advice on how to encourage your students to become resilient mathematicians.
We know that good thinkers are resilient, they don't give up easily, and are motivated to work hard and keep going when faced with challenges. Here are some problems that may require similar determination from your students. You could warn your students that the solutions may not be immediately obvious, and they may need to persevere. We hope that they will have the opportunity 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.
How good are you at estimating angles?
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.
Some of the numbers have fallen off Becky's number line. Can you figure out what they were?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
A game in which players take it in turns to choose a number. Can you block your opponent?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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 find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Are these games fair? How can you tell?
How many moves does it take to swap over some red and blue frogs? Do you have a method?
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...
How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
In how many ways can you fit all three pieces together to make shapes with line symmetry?
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
By selecting digits for an addition grid, what targets can you make?
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
What happens when you add a three digit number to its reverse?
Can you find ways to put numbers in the overlaps so the rings have equal totals?
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?
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?
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
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?
Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?
Can you do a little mathematical detective work to figure out which number has been wiped out?
The items in the shopping basket add and multiply to give the same amount. What could their prices be?
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?
Can you find a strategy that ensures you get to take the last biscuit in this game?
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
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?
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?
Use the differences to find the solution to this Sudoku.
Can you create a Latin Square from multiples of a six digit number?
Use your skill and judgement to match the sets of random data.
Can you make sense of the three methods to work out what fraction of the total area is shaded?