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Resources tagged with Working systematically similar to Exploring Wild & Wonderful Number Patterns:

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Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically

Age 7 to 11 Challenge Level:

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

A Square of Numbers

Age 7 to 11 Challenge Level:

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Six Is the Sum

Age 7 to 11 Challenge Level:

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

Dart Target

Age 7 to 11 Challenge Level:

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

Open Squares

Age 7 to 11 Challenge Level:

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Oh! Harry!

Age 7 to 11 Challenge Level:

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Magazines

Age 7 to 11 Challenge Level:

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

Forgot the Numbers

Age 7 to 11 Challenge Level:

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

Polo Square

Age 7 to 11 Challenge Level:

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Zargon Glasses

Age 7 to 11 Challenge Level:

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Spell by Numbers

Age 7 to 11 Challenge Level:

Can you substitute numbers for the letters in these sums?

How Much Did it Cost?

Age 7 to 11 Challenge Level:

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

The Dice Train

Age 7 to 11 Challenge Level:

This dice train has been made using specific rules. How many different trains can you make?

Age 7 to 11 Challenge Level:

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

A Mixed-up Clock

Age 7 to 11 Challenge Level:

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Arranging the Tables

Age 7 to 11 Challenge Level:

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Being Resourceful - Primary Number

Age 5 to 11 Challenge Level:

Number problems at primary level that require careful consideration.

Sums and Differences 2

Age 7 to 11 Challenge Level:

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Page Numbers

Age 7 to 11 Short Challenge Level:

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

Rabbits in the Pen

Age 7 to 11 Challenge Level:

Using the statements, can you work out how many of each type of rabbit there are in these pens?

A-magical Number Maze

Age 7 to 11 Challenge Level:

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

Bean Bags for Bernard's Bag

Age 7 to 11 Challenge Level:

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Sums and Differences 1

Age 7 to 11 Challenge Level:

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

A Shapely Network

Age 7 to 11 Challenge Level:

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

Pouring the Punch Drink

Age 7 to 11 Challenge Level:

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

The Pied Piper of Hamelin

Age 7 to 11 Challenge Level:

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Two Primes Make One Square

Age 7 to 11 Challenge Level:

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

Seven Square Numbers

Age 7 to 11 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.

Five Coins

Age 7 to 11 Challenge Level:

Ben has five coins in his pocket. How much money might he have?

Sticky Dice

Age 7 to 11 Challenge Level:

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

All Seated

Age 7 to 11 Challenge Level:

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Dice and Spinner Numbers

Age 7 to 11 Challenge Level:

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

How Old?

Age 7 to 11 Challenge Level:

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

Age 5 to 11 Challenge Level:

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Train Carriages

Age 5 to 11 Challenge Level:

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

Worms

Age 7 to 11 Challenge Level:

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

The Puzzling Sweet Shop

Age 7 to 11 Challenge Level:

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Twenty Divided Into Six

Age 7 to 11 Challenge Level:

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

X Is 5 Squares

Age 7 to 11 Challenge Level:

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

Today's Date - 01/06/2009

Age 5 to 11 Challenge Level:

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

Two Egg Timers

Age 7 to 11 Challenge Level:

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

On Target

Age 7 to 11 Challenge Level:

You have 5 darts and your target score is 44. How many different ways could you score 44?

Plants

Age 5 to 11 Challenge Level:

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Difference

Age 7 to 11 Challenge Level:

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Build it up More

Age 7 to 11 Challenge Level:

This task follows on from Build it Up and takes the ideas into three dimensions!

Prison Cells

Age 7 to 11 Challenge Level:

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Prompt Cards

Age 7 to 11 Challenge Level:

These two group activities use mathematical reasoning - one is numerical, one geometric.

Journeys in Numberland

Age 7 to 11 Challenge Level:

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Hubble, Bubble

Age 7 to 11 Challenge Level:

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

Mystery Matrix

Age 7 to 11 Challenge Level:

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.