# Working Systematically

Mathematicians try to work systematically so they can see how they worked something out, and see patterns which messy work might not reveal. Scroll down to see our complete collection of upper primary problems that require you to work systematically, or explore the two sub-collections.

### Finding All Possibilities Upper Primary

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

### Ordered Ways of Working Upper Primary

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

##### KS 1 & 2 Challenge Level:

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

### Half Time

##### KS 1 & 2 Challenge Level:

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

### Sitting Round the Party Tables

##### KS 1 & 2 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.

### School Fair Necklaces

##### KS 1 & 2 Challenge Level:

How many possible necklaces can you find? And how do you know you've found them all?

### Trebling

##### KS 2 Challenge Level:

Can you replace the letters with numbers? Is there only one solution in each case?

### Cubes Here and There

##### KS 2 Challenge Level:

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

### A Square of Numbers

##### KS 2 Challenge Level:

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

##### KS 2 Challenge Level:

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

### A Mixed-up Clock

##### KS 2 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?

### Domino Sets

##### KS 2 Challenge Level:

How do you know if your set of dominoes is complete?

### Fifteen Cards

##### KS 2 Challenge Level:

Can you use the information to find out which cards I have used?

### Plenty of Pens

##### KS 2 Challenge Level:

Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?

### What Do You Need?

##### KS 2 Challenge Level:

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

### Button-up Some More

##### KS 2 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 ...?

### Factor Lines

##### KS 2 Challenge Level:

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

### Maze 100

##### KS 2 Challenge Level:

Can you go through this maze so that the numbers you pass add to exactly 100?

### Two Primes Make One Square

##### KS 2 Challenge Level:

Can you make square numbers by adding two prime numbers together?

### Magic Vs

##### KS 2 Challenge Level:

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

### Sealed Solution

##### KS 2 Challenge Level:

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

### Light the Lights Again

##### KS 2 Challenge Level:

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

### Prison Cells

##### KS 2 Challenge Level:

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?

### Finding Fifteen

##### KS 2 Challenge Level:

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

### This Pied Piper of Hamelin

##### KS 2 Challenge Level:

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

### All the Digits

##### KS 2 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?

### Six Ten Total

##### KS 2 Challenge Level:

This challenge combines addition, multiplication, perseverance and even proof.

### The Dice Train

##### KS 2 Challenge Level:

This dice train has been made using specific rules. How many different trains can you make?

### Cover the Tray

##### KS 2 Challenge Level:

These practical challenges are all about making a 'tray' and covering it with paper.

### Counting Cards

##### KS 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?

### Curious Number

##### KS 2 Challenge Level:

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?

### Nine-pin Triangles

##### KS 2 Challenge Level:

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

### Dice in a Corner

##### KS 2 Challenge Level:

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?

### 5 on the Clock

##### KS 2 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?

### Reach 100live

##### KS 2 Challenge Level:

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

### First Connect Three for Two

##### KS 2 & 3 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.

### Make 37live

##### KS 2 & 3 Challenge Level:

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

### Tea Cups

##### KS 2 & 3 Challenge Level:

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

### Inky Cube

##### KS 2 & 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?

### First Connect Three

##### KS 2, 3 & 4 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?