# Working Systematically - Upper Primary

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.

### Sitting Round the Party Tables

##### Age 5 to 11Challenge 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.

##### Age 5 to 11Challenge 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

##### Age 5 to 11Challenge Level

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

### School Fair Necklaces

##### Age 5 to 11Challenge Level

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

### Nine-pin Triangles

##### Age 7 to 11Challenge Level

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

### What Do You Need?

##### Age 7 to 11Challenge 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?

### A Mixed-up Clock

##### Age 7 to 11Challenge 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?

### Fifteen Cards

##### Age 7 to 11Challenge Level

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

### Plenty of Pens

##### Age 7 to 11Challenge Level

Amy's mum had given her Â£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?

### First Connect Three for Two

##### Age 7 to 11Challenge 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.

### Magic Vs

##### Age 7 to 11Challenge Level

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

##### Age 7 to 11Challenge 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?

### Trebling

##### Age 7 to 11Challenge Level

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

### A Square of Numbers

##### Age 7 to 11Challenge Level

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

### Cubes Here and There

##### Age 7 to 11Challenge 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?

### First Connect Three

##### Age 7 to 11Challenge Level

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

### Domino Sets

##### Age 7 to 11Challenge Level

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

### Finding Fifteen

##### Age 7 to 11Challenge 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?

### Maze 100

##### Age 7 to 11Challenge Level

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

### All the Digits

##### Age 7 to 11Challenge 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?

### Reach 100

##### Age 7 to 11Challenge 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.

### Light the Lights Again

##### Age 7 to 11Challenge 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?

### This Pied Piper of Hamelin

##### Age 7 to 11Challenge Level

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

### Two Primes Make One Square

##### Age 7 to 11Challenge Level

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

### Sealed Solution

##### Age 7 to 11Challenge 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?

### Six Ten Total

##### Age 7 to 11Challenge Level

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

### Prison Cells

##### Age 7 to 11Challenge 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?

### Button-up Some More

##### Age 7 to 11Challenge Level

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

### The Dice Train

##### Age 7 to 11Challenge Level

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

### Curious Number

##### Age 7 to 11Challenge 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?

### Counting Cards

##### Age 7 to 11Challenge 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?

### Dice in a Corner

##### Age 7 to 11Challenge Level

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

### Cover the Tray

##### Age 7 to 11Challenge Level

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

### 5 on the Clock

##### Age 7 to 11Challenge 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?

### Make 37

##### Age 7 to 14Challenge 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.

### Factor Lines

##### Age 7 to 14Challenge Level

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

### Tea Cups

##### Age 7 to 14Challenge 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

##### Age 7 to 14Challenge 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?