Resources tagged with: Working systematically

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

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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.

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Sitting Round the Party Tables

Age 5 to 11 Challenge Level:

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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Counters

Age 7 to 11 Challenge Level:

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

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Number Daisy

Age 11 to 14 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?

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Button-up Some More

Age 7 to 11 Challenge Level:

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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Arrangements

Age 7 to 11 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....?

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One to Fifteen

Age 7 to 11 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?

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More Magic Potting Sheds

Age 11 to 14 Challenge Level:

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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Weights

Age 11 to 14 Challenge Level:

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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Magic Potting Sheds

Age 11 to 14 Challenge Level:

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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Teddy Town

Age 5 to 14 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?

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Window Frames

Age 5 to 14 Challenge Level:

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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Build it Up

Age 7 to 11 Challenge Level:

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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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.

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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?

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Team Scream

Age 7 to 11 Challenge Level:

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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How Long Does it Take?

Age 7 to 11 Challenge Level:

In this matching game, you have to decide how long different events take.

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Advent Sudoku

Age 11 to 14 Challenge Level:

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

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Map Folding

Age 7 to 11 Challenge Level:

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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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?

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A Right Charlie

Age 7 to 11 Challenge Level:

Can you use this information to work out Charlie's house number?

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Family Tree

Age 7 to 11 Challenge Level:

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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Plates of Biscuits

Age 7 to 11 Challenge Level:

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

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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?

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Creating Cubes

Age 7 to 11 Challenge Level:

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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Bunny Hop

Age 7 to 11 Challenge Level:

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

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Single Track

Age 7 to 11 Challenge Level:

What is the best way to shunt these carriages so that each train can continue its journey?

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Addition Equation Sudoku

Age 11 to 14 Challenge Level:

You need to find the values of the stars before you can apply normal Sudoku rules.

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Crack the Code

Age 7 to 11 Challenge Level:

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

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Waiting for Blast Off

Age 7 to 11 Challenge Level:

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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Shunting Puzzle

Age 7 to 11 Challenge Level:

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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Winning the Lottery

Age 7 to 11 Challenge Level:

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

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Knight's Swap

Age 7 to 11 Challenge Level:

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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Read This Page

Age 11 to 14 Challenge Level:

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

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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.

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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.

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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?

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Extra Challenges from Madras

Age 11 to 14 Challenge Level:

A few extra challenges set by some young NRICH members.

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Plate Spotting

Age 7 to 11 Challenge Level:

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

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The Pet Graph

Age 7 to 11 Challenge Level:

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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Product Sudoku

Age 11 to 14 Challenge Level:

The clues for this Sudoku are the product of the numbers in adjacent squares.

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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.

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A Bit of a Dicey Problem

Age 7 to 11 Challenge Level:

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

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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.

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Half Time

Age 5 to 11 Challenge Level:

What could the half time scores have been in these Olympic hockey matches?

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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?

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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?

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Rolling That Cube

Age 5 to 11 Challenge Level:

My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?

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Calendar Cubes

Age 7 to 11 Challenge Level:

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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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.