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Broad Topics > Habits of Mind > Resilient

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Can You Make 100?

Stage: 3 Challenge Level: Challenge Level:1

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

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Tower of Hanoi

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

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Elevenses

Stage: 3 Challenge Level: Challenge Level:1

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

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M, M and M

Stage: 3 Challenge Level: Challenge Level:1

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

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Difference Sudoku

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use the differences to find the solution to this Sudoku.

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Factors and Multiples Game

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

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

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Factors and Multiples Puzzle

Stage: 3 Challenge Level: Challenge Level:1

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

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Substitution Cipher

Stage: 3 Challenge Level: Challenge Level:1

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

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Product Sudoku

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Squares in Rectangles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Odds and Evens

Stage: 3 Challenge Level: Challenge Level:1

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

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Isosceles Triangles

Stage: 3 Challenge Level: Challenge Level:1

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?

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Cuboids

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Reflecting Squarely

Stage: 3 Challenge Level: Challenge Level:1

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

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Estimating Angles

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

How good are you at estimating angles?

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Triangles to Tetrahedra

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Reach 100

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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In a Box

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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American Billions

Stage: 3 Challenge Level: Challenge Level:1

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...

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Number Daisy

Stage: 3 Challenge Level: Challenge Level:1

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?

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Two and Two

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Nine Colours

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Where Can We Visit?

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Funny Factorisation

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

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Overlaps

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Forwards Add Backwards

Stage: 3 Challenge Level: Challenge Level:1

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

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Add to 200

Stage: 3 Challenge Level: Challenge Level:1

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

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Wipeout

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Kite in a Square

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Charlie's Delightful Machine

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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A Little Light Thinking

Stage: 4 Challenge Level: Challenge Level:1

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

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Data Matching

Stage: 5 Challenge Level: Challenge Level:1

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

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Frogs

Stage: 3 Challenge Level: Challenge Level:1

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