# Being Determined

Being Determined is part of our Developing Mathematical Habits of Mind collection.

Good thinkers are determined and persistent. 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.

How do we encourage our students to become determined 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 Determined - Number

Number problems that may require determination.

### Being Determined - Algebra

Algebra problems that may require determination.

### Being Determined - Geometry

Geometry problems that may require determination.

### Being Determined - Statistics

Statistics problems that may require determination.

### Funny Factorisation

##### KS 3 Challenge Level:

Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can you find the factors?

### Where Can We Visit?

##### KS 3 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?

### Nine Colours

##### KS 3 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

##### KS 3 Challenge Level:

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

### Number Daisy

##### KS 3 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?

### American Billions

##### KS 3 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...

### In a Box

##### KS 4 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?

### Reach 100

##### KS 2 & 3 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.

### Triangles to Tetrahedra

##### KS 3 Challenge Level:

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

### Estimating Angles

##### KS 2, 3 & 4 Challenge Level:

How good are you at estimating angles?

### Frogs

##### KS 3 Challenge Level:

How many moves does it take to swap over some red and blue frogs? Do you have a method?

### Reflecting Squarely

##### KS 3 Challenge Level:

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

### Cuboids

##### KS 3 Challenge Level:

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

### Isosceles Triangles

##### KS 3 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?

### Odds and Evens

##### KS 3 Challenge Level:

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

### Squares in Rectangles

##### KS 3 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?

### Product Sudoku

##### KS 3 Challenge Level:

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

### Substitution Cipher

##### KS 3 Challenge Level:

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

### Factors and Multiples Puzzle

##### KS 3 Challenge Level:

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

### Factors and Multiples Game

##### KS 2, 3 & 4 Challenge Level:

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

### Difference Sudoku

##### KS 4 Challenge Level:

Use the differences to find the solution to this Sudoku.

### M, M and M

##### KS 3 Challenge Level:

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

### Elevenses

##### KS 3 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?

### Tower of Hanoi

##### KS 3 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.

### A Little Light Thinking

##### KS 4 Challenge Level:

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

### Charlie's Delightful Machine

##### KS 3 & 4 Challenge Level:

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

### Kite in a Square

##### KS 4 Challenge Level:

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

### Wipeout

##### KS 3 Challenge Level:

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

##### KS 3 Challenge Level:

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

##### KS 3 Challenge Level:

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

### Overlaps

##### KS 3 Challenge Level:

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

### Can You Make 100?

##### KS 3 Challenge Level:

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