List

Year 2 Conjecturing and Generalising

Poly Plug Rectangles
problem
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Poly Plug Rectangles

Age
5 to 11
Challenge level
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The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
Poly Plug Pattern
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Poly Plug Pattern

Age
5 to 7
Challenge level
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Create a pattern on the small grid. How could you extend your pattern on the larger grid?

What was in the Box?
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What was in the Box?

Age
5 to 7
Challenge level
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This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?
Two numbers under the microscope
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Two numbers under the microscope

Age
5 to 7
Challenge level
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This investigates one particular property of number by looking closely at an example of adding two odd numbers together.
Two Spinners
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Two Spinners

Age
5 to 7
Challenge level
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What two-digit numbers can you make with these two dice? What can't you make?
Round the Two Dice
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Round the Two Dice

Age
5 to 7
Challenge level
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This activity focuses on rounding to the nearest 10.
Unit Differences
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Unit Differences

Age
5 to 7
Challenge level
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This challenge is about finding the difference between numbers which have the same tens digit.
Five Steps to 50
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Five Steps to 50

Age
5 to 7
Challenge level
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Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
Double or Halve?
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Double or Halve?

Age
5 to 7
Challenge level
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Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
Circles, Circles
problem
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Circles, Circles

Age
5 to 11
Challenge level
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Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

I'm Eight
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I'm Eight

Age
5 to 11
Challenge level
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Find a great variety of ways of asking questions which make 8.
Dicey Addition
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Dicey Addition

Age
5 to 11
Challenge level
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Who said that adding couldn't be fun?
What's in a Name?
problem
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What's in a Name?

Age
5 to 7
Challenge level
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What do you notice about these squares of numbers? What is the same? What is different?
Always, Sometimes or Never?
problem
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Always, Sometimes or Never?

Age
5 to 11
Challenge level
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Are these statements relating to odd and even numbers always true, sometimes true or never true?
Carroll Diagrams
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Carroll Diagrams

Age
5 to 11
Challenge level
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Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Break it up!
problem
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Break it up!

Age
5 to 11
Challenge level
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In how many different ways can you break up a stick of seven interlocking cubes? Now try with a stick of eight cubes and a stick of six cubes. What do you notice?

Digit Addition
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Digit Addition

Age
5 to 11
Challenge level
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Try out this number trick. What happens with different starting numbers? What do you notice?

Clapping Times
problem
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Clapping Times

Age
5 to 7
Challenge level
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If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?
Growing Garlic
problem
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Growing Garlic

Age
5 to 11
Challenge level
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Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

Strike it out
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Strike it Out

Age
5 to 11
Challenge level
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Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

I Like ...
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I Like ...

Age
5 to 7
Challenge level
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Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?
En-counters
problem
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En-counters

Age
5 to 7
Challenge level
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This task requires learners to explain and help others, asking and answering questions.
Our Numbers
problem
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Our Numbers

Age
5 to 7
Challenge level
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These spinners will give you the tens and unit digits of a number. Can you choose sets of numbers to collect so that you spin six numbers belonging to your sets in as few spins as possible?

Ip Dip
problem
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Ip Dip

Age
5 to 11
Challenge level
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"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

Sitting round the party tables
problem
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Sitting round the party tables

Age
5 to 11
Challenge level
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Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
The add and take-away path
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The add and take-away path

Age
5 to 7
Challenge level
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Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
Largest Even
problem
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Largest Even

Age
5 to 11
Challenge level
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How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?
Make 37 Poster
problem
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Make 37

Age
5 to 11
Challenge level
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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?

Hundred Square
problem
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Hundred Square

Age
5 to 11
Challenge level
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A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

Ring a Ring of Numbers
problem
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Ring a Ring of Numbers

Age
5 to 7
Challenge level
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Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
Light the Lights
problem
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Light the Lights

Age
5 to 7
Challenge level
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Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

How Odd
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How Odd

Age
5 to 7
Challenge level
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This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?
Odd times Even
problem
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Odd times Even

Age
5 to 7
Challenge level
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This problem looks at how one example of your choice can show something about the general structure of multiplication.
Lots of Lollies
problem
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Lots of Lollies

Age
5 to 7
Challenge level
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Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

More Numbers in the Ring
problem
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More Numbers in the Ring

Age
5 to 7
Challenge level
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If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Stop the Clock
problem
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Stop the Clock

Age
5 to 7
Challenge level
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This is a game for two players. Can you find out how to be the first to get to 12 o'clock?