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Resources tagged with Working systematically similar to Natural Born Mathematicians:

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

I've Submitted a Solution - What Next?

Stage: 1, 2, 3, 4 and 5

In this article, the NRICH team describe the process of selecting solutions for publication on the site.

Encouraging Primary Children to Work Systematically

Stage: Early years, 1 and 2

This article for primary teachers suggests ways in which to help children become better at working systematically.

Difference

Stage: 2 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.

Making Maths: Double-sided Magic Square

Stage: 2 and 3 Challenge Level:

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Find the Difference

Stage: 1 Challenge Level:

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Maths Trails

Stage: 2 and 3

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

Inside Triangles

Stage: 1 Challenge Level:

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Triangles All Around

Stage: 2 Challenge Level:

Can you find all the different triangles on these peg boards, and find their angles?

A Square of Numbers

Stage: 2 Challenge Level:

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

Colour in the Square

Stage: 2 Challenge Level:

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

Twinkle Twinkle

Stage: 2 Challenge Level:

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Are You Well Balanced?

Stage: 1 Challenge Level:

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Winning the Lottery

Stage: 2 Challenge Level:

Try out the lottery that is played in a far-away land. What is the chance of winning?

More Transformations on a Pegboard

Stage: 2 Challenge Level:

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

Jumping Squares

Stage: 1 Challenge Level:

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

First Connect Three

Stage: 2 and 3 Challenge Level:

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Tetrafit

Stage: 2 Challenge Level:

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

Diagonal Sums Sudoku

Stage: 2, 3 and 4 Challenge Level:

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

Inky Cube

Stage: 2 and 3 Challenge Level:

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

Fault-free Rectangles

Stage: 2 Challenge Level:

Find out what a "fault-free" rectangle is and try to make some of your own.

Red Even

Stage: 2 Challenge Level:

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Number Daisy

Stage: 2 and 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?

Two and Two

Stage: 2 and 3 Challenge Level:

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

Page Numbers

Stage: 2 Short Challenge Level:

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

Combining Cuisenaire

Stage: 2 Challenge Level:

Can you find all the different ways of lining up these Cuisenaire rods?

Tessellate the Triominoes

Stage: 1 Challenge Level:

What happens when you try and fit the triomino pieces into these two grids?

Factor Lines

Stage: 2 Challenge Level:

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Counting Cards

Stage: 2 Challenge Level:

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

Mrs Beeswax

Stage: 1 Challenge Level:

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

Cover the Camel

Stage: 1 Challenge Level:

Can you cover the camel with these pieces?

Seven Flipped

Stage: 2 Challenge Level:

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Growing Garlic

Stage: 1 Challenge Level:

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Teddy Town

Stage: 1 and 2 Challenge Level:

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Multiples Grid

Stage: 2 Challenge Level:

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Triangle Animals

Stage: 1 Challenge Level:

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Counters

Stage: 2 Challenge Level:

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Triangle Edges

Stage: 1 Challenge Level:

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Three Ball Line Up

Stage: 1 Challenge Level:

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

One to Fifteen

Stage: 2 Challenge Level:

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Code Breaker

Stage: 2 Challenge Level:

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Same Length Trains

Stage: 1 Challenge Level:

How many trains can you make which are the same length as Matt's, using rods that are identical?

More on Mazes

Stage: 2 and 3

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

Nine-pin Triangles

Stage: 2 Challenge Level:

How many different triangles can you make on a circular pegboard that has nine pegs?

1 to 8

Stage: 2 Challenge Level:

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

Arrangements

Stage: 2 Challenge Level:

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Cuisenaire Counting

Stage: 1 Challenge Level:

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

Masterclass Ideas: Working Systematically

Stage: 2 and 3 Challenge Level:

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

Junior Frogs

Stage: 2 Challenge Level:

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Neighbours

Stage: 2 Challenge Level:

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Crossing the Town Square

Stage: 2 and 3 Challenge Level:

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.