**This page has been superseded by our Working Systematically - Primary Teachers page**

Scroll down to see our complete collection of KS2 problems that require children to work systematically, or explore the two sub-collections focusing on important aspects of systematic working.

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

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### Finding all possibilities Upper Primary

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

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### Ordered Ways of Working Upper Primary

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

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### Sitting round the party tables

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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### Beads and bags

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?

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### School fair necklaces

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

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### Round the Dice Decimals 1

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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### Greater Than or Less Than?

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

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### A Square of Numbers

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

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### A Mixed-up Clock

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?

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### Nine-Pin Triangles

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

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### Five More Coins

Could Ben have any amount of money between 5p and £2 in his pocket if he has five coins?

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### First Connect Three

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?

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### What Do you Need?

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?

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### Cubes Here and There

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?

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### Magic Vs

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

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### Coded hundred square

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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### Guess the dominoes

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

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### Buying a Balloon

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?

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### Multiply Multiples 1

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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### Two Primes Make One Square

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

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### Sealed Solution

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?

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### Display Boards

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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### Make 37

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

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### Finding Fifteen

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?

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### Light the Lights Again

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?

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### Button-Up Some More

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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### This 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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### Prison Cells

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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### All the Digits

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?

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### Reach 100

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.

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### Through the Window

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

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### Factor Lines

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

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### Counting Cards

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?

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### 5 on the clock

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?

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### Curious number

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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### Inky Cube

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?

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### Tea Cups

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.

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### The Dice Train

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

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### Cover the tray

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

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### Ribbon Squares

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?