Resources tagged with: Working systematically

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Broad Topics > Mathematical Thinking > Working systematically

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?

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?

Roll These Dice

Age 7 to 11 Challenge Level:

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

Multiples Grid

Age 7 to 11 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?

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.

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?

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.

Code Breaker

Age 7 to 11 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?

Ladybird Box

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.

First Connect Three for Two

Age 7 to 11 Challenge Level:

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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 ...?

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?

Crack the Code

Age 7 to 11 Challenge Level:

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

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?

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?

Jigsaw Pieces

Age 7 to 11 Challenge Level:

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Painting Possibilities

Age 7 to 11 Challenge Level:

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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?

Encouraging Primary Children to Work Systematically

Age 3 to 11

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

Palindromic Date

Age 7 to 11 Challenge Level:

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

Ancient Runes

Age 7 to 11 Challenge Level:

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Red Even

Age 7 to 11 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?

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?

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?

Sociable Cards

Age 11 to 14 Challenge Level:

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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?

Calendar Sorting

Age 7 to 11 Challenge Level:

The pages of my calendar have got mixed up. Can you sort them out?

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?

Dicey Perimeter, Dicey Area

Age 7 to 11 Challenge Level:

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

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?

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.

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?

Adding Plus

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?

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?

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.

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.

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?

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.

Counting on Letters

Age 11 to 14 Challenge Level:

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

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?

Wonky Watches

Age 7 to 11 Challenge Level:

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

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.

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?

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.

5 on the Clock

Age 7 to 11 Challenge Level:

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

Half Time

Age 5 to 11 Challenge Level:

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

Junior Frogs

Age 5 to 11 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?

Finding All Possibilities Upper Primary

Age 7 to 11 Challenge Level:

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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.