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Resources tagged with Working systematically similar to Two Numbers Under the Microscope:

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

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Nineteen Hexagons

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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An Introduction to Magic Squares

Stage: 1, 2, 3 and 4

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

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Broken Toaster

Stage: 2 Short Challenge Level: Challenge Level:1

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

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Button-up Some More

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

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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Lots of Lollies

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

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Arranging the Tables

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

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.

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Seven Flipped

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

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

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Rabbits in the Pen

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

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

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Growing Garlic

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Seven Pots of Plants

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

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

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Factor Lines

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

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

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One of Thirty-six

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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

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A-magical Number Maze

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

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!

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Pouring the Punch Drink

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

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.

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Build it Up

Stage: 2 Challenge Level: Challenge Level:1

Can you find all the ways to get 15 at the top of this triangle of numbers?

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A Bag of Marbles

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Home City

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

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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Team Scream

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

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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Games Related to Nim

Stage: 1, 2, 3 and 4

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.

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The Pied Piper of Hamelin

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

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!

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The Moons of Vuvv

Stage: 2 Challenge Level: Challenge Level:1

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

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Adding Plus

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

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?

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Here to There 1 2 3

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

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Prison Cells

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

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?

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Magic Vs

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

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

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Two Egg Timers

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

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?

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Curious Number

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

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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Sums and Differences 2

Stage: 2 Challenge Level: Challenge Level:1

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?

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What Could it Be?

Stage: 1 Challenge Level: Challenge Level:1

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

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Take Three Numbers

Stage: 2 Challenge Level: Challenge Level:1

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

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Tiling

Stage: 2 Challenge Level: Challenge Level:1

An investigation that gives you the opportunity to make and justify predictions.

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Centred Squares

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

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

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Elf Suits

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

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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Polo Square

Stage: 2 Challenge Level: Challenge Level:1

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

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Zargon Glasses

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

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?

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Build it up More

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

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

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Greater Than or Less Than?

Stage: 2 Challenge Level: Challenge Level:1

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

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Dart Target

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

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.

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Open Squares

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

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

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Sums and Differences 1

Stage: 2 Challenge Level: Challenge Level:1

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

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Calendar Cubes

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

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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On Target

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

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

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How Old?

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

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

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Hubble, Bubble

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

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?

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X Is 5 Squares

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

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

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Halloween Investigation

Stage: 2 Challenge Level: Challenge Level:1

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

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Let's Investigate Triangles

Stage: 1 Challenge Level: Challenge Level:1

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

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Robot Monsters

Stage: 1 Challenge Level: Challenge Level:1

Use these head, body and leg pieces to make Robot Monsters which are different heights.

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Train Routes

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?

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All Seated

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

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?