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Magic Squares for Special Occasions

Stage: 3 and 4

This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.

Eleven

Stage: 3 Challenge Level:

Replace each letter with a digit to make this addition correct.

Tis Unique

Stage: 3 Challenge Level:

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

Largest Number

Stage: 3 Challenge Level:

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

Crossed Ends

Stage: 3 Challenge Level:

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

I'm Eight

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

Find a great variety of ways of asking questions which make 8.

Always the Same

Stage: 3 Challenge Level:

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

The Patent Solution

Stage: 3 Challenge Level:

A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?

Diagonal Sums

Stage: 2 Challenge Level:

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Hot Pursuit

Stage: 3 Challenge Level:

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

Cows and Sheep

Stage: 2 Challenge Level:

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

Digit Sum

Stage: 3 Challenge Level:

What is the sum of all the digits in all the integers from one to one million?

Stage: 2, 3 and 4 Challenge Level:

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .

Adding and Subtracting Positive and Negative Numbers

Stage: 2, 3 and 4

How can we help students make sense of addition and subtraction of negative numbers?

Consecutive Negative Numbers

Stage: 3 Challenge Level:

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Score

Stage: 3 Challenge Level:

There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about. . . .

Aba

Stage: 3 Challenge Level:

In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.

Pyramids

Stage: 3 Challenge Level:

What are the missing numbers in the pyramids?

One Wasn't Square

Stage: 2 Challenge Level:

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

Kids

Stage: 3 Challenge Level:

Find the numbers in this sum

And So on and So On

Stage: 3 Challenge Level:

If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?

Numbered Cars

Stage: 2 Challenge Level:

I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

Stage: 1 and 2 Challenge Level:

Who said that adding couldn't be fun?

Clocked

Stage: 3 Challenge Level:

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

Like Powers

Stage: 3 Challenge Level:

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n$ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

Spell by Numbers

Stage: 2 Challenge Level:

Can you substitute numbers for the letters in these sums?

Card Trick 2

Stage: 3 Challenge Level:

Can you explain how this card trick works?

Making Sense of Positives and Negatives

Stage: 3

This article suggests some ways of making sense of calculations involving positive and negative numbers.

Super Value Shapes

Stage: 2 Challenge Level:

If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

Cunning Card Trick

Stage: 3 Challenge Level:

Delight your friends with this cunning trick! Can you explain how it works?

Calendar Capers

Stage: 3 Challenge Level:

Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat. . . .

Top-heavy Pyramids

Stage: 3 Challenge Level:

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

Jugs of Wine

Stage: 3 Challenge Level:

You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?

Arrange the Digits

Stage: 3 Challenge Level:

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

Dividing a Cake

Stage: 2 Challenge Level:

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

GOT IT Now

Stage: 2 and 3 Challenge Level:

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

Make 37

Stage: 2 and 3 Challenge Level:

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

Machines

Stage: 2 Challenge Level:

What is happening at each box in these machines?

The Deca Tree

Stage: 2 Challenge Level:

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Seven Square Numbers

Stage: 2 Challenge Level:

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Rod Measures

Stage: 2 Challenge Level:

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

1, 2, 3 Magic Square

Stage: 2 Challenge Level:

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

A Rod and a Pole

Stage: 2 Challenge Level:

A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?

Two Primes Make One Square

Stage: 2 Challenge Level:

Can you make square numbers by adding two prime numbers together?

The Clockmaker's Birthday Cake

Stage: 2 Challenge Level:

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Cuisenaire Environment

Stage: 1 and 2 Challenge Level:

An environment which simulates working with Cuisenaire rods.

Reverse Trick

Stage: 2 Challenge Level:

Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?

Magic Triangle

Stage: 2 Challenge Level:

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

Brothers and Sisters

Stage: 2 Challenge Level:

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

Sometimes We Lose Things

Stage: 2 Challenge Level:

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.