Resources tagged with: Working systematically

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Broad Topics > Thinking Mathematically > Working systematically

A First Product Sudoku

Age 7 to 14
Challenge Level

Given the products of adjacent cells, can you complete this Sudoku?

An Introduction to Magic Squares

Age 7 to 16

Find out about Magic Squares in this article written for students. Why are they magic?!

Take Three Numbers

Age 7 to 11
Challenge Level

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Multiplication Squares

Age 7 to 11
Challenge Level

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Making Maths: Double-sided Magic Square

Age 7 to 14
Challenge Level

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

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?

The Moons of Vuvv

Age 7 to 11
Challenge Level

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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?

Consecutive Numbers

Age 7 to 14
Challenge Level

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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?

One of Thirty-six

Age 5 to 7
Challenge Level

Can you find the chosen number from the grid using the clues?

Number Detective

Age 5 to 11
Challenge Level

Follow the clues to find the mystery number.

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.

Magic Vs

Age 7 to 11
Challenge Level

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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!

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.

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?

Twinkle Twinkle

Age 7 to 14
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.

Spell by Numbers

Age 7 to 11
Challenge Level

Can you substitute numbers for the letters in these sums?

The Puzzling Sweet Shop

Age 5 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?

Lots of Lollies

Age 5 to 7
Challenge Level

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Magnetic Personality

Age 7 to 16
Challenge Level

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

A Bag of Marbles

Age 5 to 7
Challenge Level

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Games Related to Nim

Age 5 to 16

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

Multiply Multiples 2

Age 7 to 11
Challenge Level

Can you work out some different ways to balance this equation?

Possible Pieces

Age 5 to 11
Challenge Level

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

Maths Trails

Age 7 to 14

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.

Centred Squares

Age 7 to 11
Challenge Level

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

How Many Times?

Age 7 to 11
Challenge Level

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

Seating Arrangements

Age 7 to 11
Challenge Level

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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?

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.

Crack the Code

Age 7 to 11
Challenge Level

The Zargoes use almost the same alphabet as English. What does this birthday message say?

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?

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?

Broken Toaster

Age 7 to 11 Short
Challenge Level

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Being Resourceful - Primary Number

Age 5 to 11
Challenge Level

Number problems at primary level that require careful consideration.

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?

Colour in the Square

Age 7 to 16
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?

All the Digits

Age 7 to 11
Challenge Level

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Seven Flipped

Age 7 to 11
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.

Whose Face?

Age 5 to 11
Challenge Level

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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.

Greater Than or Less Than?

Age 7 to 11
Challenge Level

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

Fake Gold

Age 7 to 11
Challenge Level

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

What Could it Be?

Age 5 to 7
Challenge Level

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Pasta Timing

Age 7 to 11
Challenge Level

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

Growing Garlic

Age 5 to 7
Challenge Level

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

Seven Pots of Plants

Age 7 to 11
Challenge Level

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

1 to 8

Age 7 to 11
Challenge Level

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