Primary Curriculum Map

The problems below have been selected because they are closely linked to the curriculum, while providing opportunities for all students to work and think like mathematicians. They have detailed Teachers' Resources offering guidance on how they can be used in the classroom.

Please email any comments to primary.nrich@maths.org.

Looking for secondary problems? See the NRICH Secondary Curriculum Map.

Key

Articles are indicated by an 'A'.

Tasks badged filled star are suitable for the whole class;
Tasks badged are suitable for the majority;
Tasks badged are for those who like a serious challenge.

Highlight problems

Thinking mathematically

Exploring and noticing
Working systematically
Conjecturing and generalising
Visualising and representing
Explaining, convincing and proving

Mathematical mindsets

Being curious
Being collaborative
Being resourceful
Being resilient

Number - Number and Place Value

EYFS	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Post-Primary
Counting
Say one number for each item in order: 1, 2, 3, 4, 5 Know that the last number reached when counting a small set of objects tells you how many there are in total ('cardinal principle') Count objects, actions and sounds ELG - Verbally count beyond 20, recognising the pattern of the counting system Beat the Clock Beat the Clock Children use everyday language to talk about time, to compare quantities and to solve problems Tidying Tidying When tidying away toys in this activity, children will use their counting skills to check that all the toys are in the box. Number Book Number Book Creating a 'Book of Four' is an opportunity for children to collect groups of four objects and consider how the groups are similar. Counting Collections Counting Collections In this activity, children choose collections of items to count and are supported as they find ways to keep track of, and record, their counting. Counting Collections in the Early Years Counting Collections in the Early Years In this article for practitioners, Cath Gripton and Deliah Pawluch explore the 'counting collections' approach, which encourages children to spend time playing and experimenting with counting. A Incey Wincey Incey Wincey In this game, children roll the dice and count how many steps to move the spider up or down the drainpipe.	Count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number			Count backwards through zero to include negative numbers	Interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero Swimming Pool Swimming Pool In this problem, we're investigating the number of steps we would climb up or down to get out of or into the swimming pool. How could you number the steps below the water? Sea Level Sea Level What numbers would you put on this number line as it goes under the sea level? More Tug of War More Tug of war In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?	Use negative numbers in context, and calculate intervals across zero First Connect Three 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?	Place Value, Integers, Ordering and Rounding
	Count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens Writing Digits Writing Digits Lee was writing all the counting numbers from 1 to 20. She stopped for a rest after writing seventeen digits. What was the last number she wrote? Grouping Goodies Grouping Goodies Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had? Same Length Trains Same Length Trains How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical? Biscuit Decorations Biscuit Decorations Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated? Number Match Number match Can you work as a group to match these numbers? Shut the Box Shut the box An old game with lots of arithmetic!	Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward or backward Buzzy Bee Buzzy Bee Buzzy Bee was building a honeycomb. She decorated the honeycomb with a pattern using numbers. Can you discover Buzzy's pattern and fill in the empty cells for her? Five Steps to 50 Five Steps to 50 Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?	Count from 0 in multiples of 4, 8, 50 and 100	Count in multiples of 6, 7, 9, 25 and 1000 Count Me In Count Me In How do you know whether you will reach these numbers when you count in steps of six from zero?	Count forwards or backwards in steps of powers of 10 for any given number up to 1000000
	Given a number, identify one more and one less		Find 10 or 100 more or less than a given number	Find 1000 more or less than a given number
Comparing Numbers
Compare quantities using language: 'more than', 'fewer than' ELG - Compare quantities up to 10 in different contexts, recognising when one quantity is greater than, less than or the same as the other quantity Estimation Station Estimation Station This activity involves filling a jar with small objects to encourage estimation and counting skills. The Voting Station The Voting Station This task encourages children to count and compare numbers when using 'voting bricks' to vote for a book at story time.	Use the language of: equal to, more than, less than (fewer), most, least All Change All Change There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice? Dotty Six Dotty Six Dotty Six is a simple dice game that you can adapt in many ways. Making Sticks Making Sticks Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines? Robot Monsters Robot Monsters Use these head, body and leg pieces to make Robot Monsters which are different heights.	Compare and order numbers from 0 up to 100; use <, > and = signs Next Domino Next Domino Which comes next in each pattern of dominoes? That Number Square That number square Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid? 100 Square Jigsaw 100 Square Jigsaw Can you complete this jigsaw of the 100 square?	Compare and order numbers up to 1000	Order and compare numbers beyond 1000	Read, write, order and compare numbers to at least 1000000 and determine the value of each digit (appears also in Reading and Writing Numbers)	Read, write, order and compare numbers up to 10000000 and determine the value of each digit (appears also in Reading and Writing Numbers)	Place Value, Integers, Ordering and Rounding
Understand the 'one more than/one less than' relationship between consecutive numbers Number Rhymes Number Rhymes In this activity, the rhyme 'Ten Green Bottles' is used to encourage children to count backwards to work out how many bottles are left. Using Books: Maisy Goes Camping Using books: Maisy Goes Camping The book 'Maisy Goes Camping' introduces children to the idea of using the size and number of objects to work out how many will fit in a 'tent'.							Place Value, Integers, Ordering and Rounding
Identifying, Representing and Estimating Numbers
ELG - Have a deep understanding of number to 10, including the composition of each number ELG - Subitise (recognise quantities without counting) up to 5 Hidden Jewels Hidden Jewels In this 'hide and reveal' game, children are encouraged to say the number of gems without counting them. Number Talks Number Talks In this task, children have the opportunity to talk about what they see when they look at a number representation. Subitising Subitising In this article for EY practitioners, Dr Sue Gifford outlines what we mean by subitising and how we can teach it. A	Identify and represent numbers using objects and pictorial representations including the number line All Change All Change There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice? Dotty Six Dotty Six Dotty Six is a simple dice game that you can adapt in many ways. Eightness of Eight Eightness of Eight What do you see as you watch this video? Can you create a similar video for the number 12?	Identify, represent and estimate numbers using different representations, including the number line How Would We Count? How would we count? An activity centred around observations of dots and how we visualise number arrangement patterns. Count the Crayons Count the Crayons How could you estimate the number of pencils/pens in these pictures? Tug of War Tug of War Can you use the numbers on the dice to reach your end of the number line before your partner beats you? How Many? How Many? Have a look at these photos of different fruit. How many do you see? How did you count?	Identify, represent and estimate numbers using different representations	Identify, represent and estimate numbers using different representations Representing Numbers Representing Numbers Find as many different ways of representing this number of dots as you can.			Place Value, Integers, Ordering and Rounding
Reading and Writing Numbers (including Roman Numerals)
Experiment with their own symbols and marks as well as numerals Link the number symbol (numeral) with its cardinal number value Dice Dice This dice activity encourages children to relate the number on the dice to the number of teddies they need to choose. Show Me Show Me In this task, children will learn different ways of representing the same number. Owl's Packing List Owl's Packing List In this activity, children can practise reading numbers and counting items in order to help Owl pack for his holiday. Golden Beans Golden Beans This task provides children with an opportunity to count 'golden beans' and find a number card to represent how many they have.	Read and write numbers from 1 to 20 in numerals and words	Read and write numbers to at least 100 in numerals and in words	Read and write numbers up to 1000 in numerals and in words		Read, write, order and compare numbers to at least 1000000 and determine the value of each digit (appears also in Comparing Numbers)	Read, write, order and compare numbers up to 10000000 and determine the value of each digit (appears also in Understanding Place Value)	Place Value, Integers, Ordering and Rounding
				Read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of zero and place value	Read Roman numerals to 1000 (M) and recognise years written in Roman numerals Roman Numerals Roman Numerals Can you find some examples when the number of Roman numerals is fewer than the number of Arabic numerals for the same number?		Place Value, Integers, Ordering and Rounding
Understanding Place Value
		Recognise the place value of each digit in a two-digit number (tens, ones) 6 Beads 6 Beads If you put three beads onto a tens/ones abacus you can make the numbers 3, 30, 12 or 21. What numbers can be made with six beads? Two-Digit Targets Two-digit targets You have a set of the digits from 0 to 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible? Digit Addition Digit Addition Try out this number trick. What happens with different starting numbers? What do you notice? Snail One Hundred Snail One Hundred In this game, you throw a dice and move counters along the snail's body and in a spiral around the snail's shell. It is about understanding tens and ones. Number Detective Number Detective Follow the clues to find the mystery number.	Recognise the place value of each digit in a three-digit number (hundreds, tens, ones) Which Scripts? Which Scripts? There are six numbers written in five different scripts. Can you sort out which is which? Coded Hundred Square Coded hundred square This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?	Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones) Four-Digit Targets Four-digit targets You have two sets of the digits 0-9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible? Nice or Nasty Nice or Nasty There are nasty versions of this dice game but we'll start with the nice ones... The Thousands Game The Thousands Game Each child in Class 3 took four numbers out of the bag. Who had made the highest even number? The Deca Tree The Deca Tree Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.	Read, write, order and compare numbers to at least 1000000 and determine the value of each digit	Read, write, order and compare numbers up to 10000000 and determine the value of each digit	Place Value, Integers, Ordering and Rounding
Rounding
				Round any number to the nearest 10, 100 or 1000 Reasoned Rounding Reasoned Rounding Four strategy dice games to consolidate pupils' understanding of rounding.	Round any number up to 1000000 to the nearest 10, 100, 1000, 10000 and 100000	Round any whole number to a required degree of accuracy Round the Three Dice Round the Three Dice What happens when you round these three-digit numbers to the nearest 100?	Place Value, Integers, Ordering and Rounding
Problem Solving
Solve real world mathematical problems with numbers up to 5 Mathematical Problem Solving in the Early Years: Developing Opportunities, Strategies and Confidence Mathematical problem solving in the early years: developing opportunities, strategies and confidence In this article for Early Years practitioners, Dr Sue Gifford outlines ways to develop children's problem-solving strategies and confidence in problem solving. A Mathematical Problem Solving in the Early Years Mathematical Problem Solving in the Early Years This article describes how the NRICH Early Years resources aim to further develop young children's natural problem-solving abilities in the context of mathematics. A The Box Game The Box Game In this game, children will use their addition and subtraction skills to keep track of the number of toys hidden inside a box.		Use place value and number facts to solve problems Round the Two Dice Round the Two Dice This activity focuses on rounding to the nearest 10. I Like ... I Like ... Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea? Light the Lights Light the Lights Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights? Largest Even Largest Even How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?	Solve number problems and practical problems involving these ideas Number Differences Number Differences Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this? Magic Vs Magic Vs Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?	Solve number and practical problems that involve all of the above and with increasingly large positive numbers	Solve number problems and practical problems that involve all of the above Less is More Less is More Use your knowledge of place value to try to win this game. How will you maximise your score?	Solve number and practical problems that involve all of the above Number Lines in Disguise Number Lines in Disguise Some of the numbers have fallen off Becky's number line. Can you figure out what they were? Round the Four Dice Round the Four Dice This activity involves rounding four-digit numbers to the nearest thousand.	Place Value, Integers, Ordering and Rounding

Number - Addition and Subtraction

EYFS	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Post-Primary
Number Bonds
ELG - Automatically recall (without reference to rhymes, counting or other aids) number bonds up to 5 (including subtraction facts) and some number bonds to 10, including double facts Shopping - Pirate Poundland Shopping - Pirate Poundland In the pirate pound shop, children can practise their counting skills by choosing ten items to spend their ten pounds on. Double Trouble Double Trouble This story about some troublesome dogs encourages children to find and model doubles of different numbers.	Represent and use number bonds and related subtraction facts within 20 Domino Sorting Domino Sorting Try grouping the dominoes in the ways described. Are there any left over each time? Can you explain why? One Big Triangle One Big Triangle Make one big triangle so the numbers that touch on the small triangles add to 10. Butterfly Flowers Butterfly Flowers Can you find two butterflies to go on each flower so that the numbers on each pair of butterflies adds to the number on their flower? Ladybirds in the Garden Ladybirds in the Garden In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make? Number Lines Number Lines Leah and Tom each have a number line. Can you work out where their counters will land? Pairs of Numbers Pairs of Numbers If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?	Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100 Number Round Up Number Round Up Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre. Strike it Out Strike it Out Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Mental Calculation
	Add and subtract one-digit and two-digit numbers to 20, including zero Sort Them Out (1) Sort them out (1) Can you each work out the number on your card? What do you notice? How could you sort the cards? Two Dice Two Dice Find all the numbers that can be made by adding the dots on two dice. Number Balance Number Balance Can you hang weights in the right place to make the the number balance balanced? Find the Difference Find the Difference Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.	Add and subtract numbers using concrete objects, pictorial representations, and mentally, including: - a two-digit number and ones - a two-digit number and tens - two two-digit numbers - adding three one-digit numbers Jumping Squares Jumping squares In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible. Dicey Addition Dicey Addition In these addition games, you'll need to think strategically to get closest to the target. Arranging Additions and Sorting Subtractions Arranging Additions and Sorting Subtractions Order these four calculations from easiest to hardest. How did you decide? Subtraction Slip Subtraction Slip Can you spot the mistake in this video? How would you work out the answer to this calculation? Unit Differences Unit Differences This challenge is about finding the difference between numbers which have the same tens digit.	Add and subtract numbers mentally, including: - a three-digit number and ones - a three-digit number and tens - a three-digit number and hundreds		Add and subtract numbers mentally with increasingly large numbers	Perform mental calculations, including with mixed operations and large numbers Dicey Operations Dicey Operations In these addition and subtraction games, you'll need to think strategically to get closest to the target.	Number Operations and Calculation Methods
	Read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs (appears also in Written Methods) 2, 4, 6, 8 2, 4, 6, 8 Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make? How Do You See It? How do you see it? Here are some short problems for you to try. Talk to your friends about how you work them out. What Could It Be? What Could It Be? In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case? Equivalent Pairs Equivalent Pairs Can you match pairs of cards which show the same amount?	Show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot				Use their knowledge of the order of operations to carry out calculations involving the four operations	Number Operations and Calculation Methods
Written Methods
	Read, write and interpret mathematical statements involving addition (+), subtraction (-) and equals (=) signs 2, 4, 6, 8 2, 4, 6, 8 Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make? How Do You See It? How do you see it? Here are some short problems for you to try. Talk to your friends about how you work them out. What Could It Be? What Could It Be? In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case? Equivalent Pairs Equivalent Pairs Can you match pairs of cards which show the same amount?		Add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction	Add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate	Add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction)		Number Operations and Calculation Methods
Inverse Operations, Estimating and Checking Answers
		Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems How Many? How Many? This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask? The Add and Take-Away Path The add and take-away path 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? What Was in the Box? What was in the Box? This box does something to the numbers that go into it. If you know the numbers that come out, what might be going on inside the box? Doing and Undoing Doing and undoing An investigation looking at doing and undoing mathematical operations focusing on doubling, halving, adding and subtracting. Secret Number Secret Number Annie and Ben are playing a game with a calculator. What was Annie's secret number?	Estimate the answer to a calculation and use inverse operations to check answers	Estimate and use inverse operations to check answers to a calculation	Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy	Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy Four Go Four Go This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?	Number Operations and Calculation Methods
Problem Solving
	Solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = ? - 9 The Tall Tower The Tall Tower As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?	Solve problems with addition and subtraction: - using concrete objects and pictorial representations, including those involving numbers, quantities and measures - applying their increasing knowledge of mental and written methods Eggs in Baskets Eggs in Baskets There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. How many eggs are in each basket? What's in a Name? What's in a Name? What do you notice about these squares of numbers? What is the same? What is different? Cuisenaire Counting Cuisenaire Counting Here are some rods that are different colours. How could I make a yellow rod using white and red rods? Sitting Round the Party Tables 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. Half Time Half Time What could the half time scores have been in these Olympic hockey matches? Two Spinners Two Spinners What two-digit numbers can you make with these two dice? What can't you make? Heads and Feet Heads and Feet On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there? Noah Noah Noah saw 12 legs walk by into the Ark. How many creatures did he see? The Brown Family The Brown family Use the information about Sally and her brother to find out how many children there are in the Brown family. Birthday Cakes Birthday Cakes Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?	Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction Domino Square Domino Square Use the 'double-3 down' dominoes to make a square so that each side has eight dots. Consecutive Numbers Consecutive Numbers An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore. 4 Dom 4 Dom Use these four dominoes to make a square that has the same number of dots on each side. Buying a Balloon 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? Super Shapes Super Shapes The value of the circle changes in each of the following problems. Can you discover its value in each problem? Finding Fifteen 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? A Mixed-up Clock 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? Dice in a Corner Dice in a Corner How could you arrange at least two dice in a stack so that the total of the visible spots is 18? Build It Up Build it up Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways. Play to 37 Play to 37 In this game the winner is the first to make the total 37. Is this a fair game? Strike It Out Strike it Out Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game. Got It Got It A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.	Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why Roll These Dice Roll these Dice 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? Amy's Dominoes Amy's Dominoes Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing? Fifteen Cards Fifteen cards Can you use the information to find out which cards I have used? Sealed Solution 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?	Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why Twenty Divided Into Six Twenty Divided into Six Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done? Reach 100 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. Six Numbered Cubes Six Numbered Cubes This task combines spatial awareness with addition and multiplication. Six Ten Total Six Ten Total This challenge combines addition, multiplication, perseverance and even proof. Maze 100 Maze 100 Can you go through this maze so that the numbers you pass add to exactly 100? Subtraction Surprise Subtraction Surprise Try out these calculations. Are you surprised by the results?	Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why	Number Operations and Calculation Methods
						Solve problems involving addition, subtraction, multiplication and division Planning a School Trip Planning a School Trip You are organising a school trip and you need to write a letter to parents to let them know about the day. Use the cards to gather all the information you need. Two and Two Two and Two How many solutions can you find to this sum? Each of the different letters stands for a different number. Three Neighbours Three neighbours Take three consecutive numbers and add them together. What do you notice? Always, Sometimes or Never? Number Always, sometimes or never? Number Are these statements always true, sometimes true or never true? 4 by 4 Mathdokus 4 by 4 Mathdokus Can you use the clues to complete these 4 by 4 Mathematical Sudokus?	Number Operations and Calculation Methods

Number - Multiplication, Division and Ratio

EYFS	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Post-Primary
Multiplication and Division Facts
ELG - Explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally Maths Story Time Maths Story Time This story provides an engaging context for children to share out the treasure fairly among the characters. Baskets Baskets This activity encourages children to practise their sharing and counting skills by putting small objects into some baskets. Using Books: The Doorbell Rang Using books: The Doorbell Rang In this activity, the book 'The Doorbell Rang' by Pat Hutchins provides an engaging context in which children can explore sharing. Two Halves Two Halves This task provides children with the opportunity to investigate halving different shapes and check that they have made two halves.							Number Operations and Calculation Methods
		Recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers Two Numbers Under the Microscope Two numbers under the microscope This investigates one particular property of number by looking closely at an example of adding two odd numbers together. More Numbers in the Ring More Numbers in the Ring 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? Always, Sometimes or Never? Always, Sometimes or Never? Are these statements relating to odd and even numbers always true, sometimes true or never true? Clapping Times Clapping Times 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? Double or Halve? Double or Halve? Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target? Ring a Ring of Numbers Ring a Ring of Numbers Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd. Make 37 Make 37 Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick ten numbers from the bags so that their total is 37? Even and Odd Even and odd This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together? How Odd How Odd 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? Pairs of Legs Pairs of legs How many legs do each of these creatures have? How many pairs is that? Take Three Numbers Take three numbers What happens when you add three numbers together? Will your answer be odd or even? How do you know? Odd Times Even Odd times Even This problem looks at how one example of your choice can show something about the general structure of multiplication. Tables Teaser Tables Teaser How will you work out which numbers have been used to create this multiplication square?	Recall and use multiplication and division facts for the 3, 4 and 8 multiplication tables Ordering Cards Ordering cards This problem is designed to help children to learn, and to use, the two and three times tables. Music to My Ears Music to my Ears Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?	Recall multiplication and division facts for multiplication tables up to 12×12 Carrying Cards Carrying Cards These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers? Table Patterns Go Wild! Table patterns go wild! Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids. Multiples Grid Multiples Grid 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? Multiplication Square Jigsaw Multiplication Square Jigsaw Can you complete this jigsaw of the multiplication square? Times Tables Shifts Times Tables Shifts In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time? Light the Lights Again Light the Lights Again Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you work out the rule for each light? Let Us Divide! Let us divide! Look at different ways of dividing things. What do they mean? How might you show them in a picture, with things, with numbers and symbols? Remainders Remainders I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be? The Remainders Game The Remainders Game Play this game and see if you can figure out the computer's chosen number. Shape Times Shape Shape Times Shape These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are? Zias and Zepts Zias and Zepts On the planet Vuv there are two sorts of creatures. The Zias have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zias and how many Zepts were there?			Number Operations and Calculation Methods
Mental Calculation
			Write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods (appears also in Written Methods) Which Symbol? Which symbol? Choose a symbol to put into the number sentence.	Use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers Digit Discovery Digit Discovery Here is an interesting property about two sets of digits. Can you work out what the digits might be? Climbing Conundrum Climbing Conundrum Five children are taking part in a climbing competition with three parts, where their score for each part will be multiplied together. Can you see how the leaderboard will change depending on what happens in the final climb of the competition? Four Go Four Go This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?	Multiply and divide numbers mentally drawing upon known facts Picture Your Method Picture Your Method Can you match these calculation methods to their visual representations? Compare the Calculations Compare the Calculations Can you put these four calculations into order of difficulty? How did you decide?	Perform mental calculations, including with mixed operations and large numbers More Dicey Operations More Dicey Operations In these multiplication and division games, you'll need to think strategically to get closest to the target.	Number Operations and Calculation Methods
		Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot		Recognise and use factor pairs and commutativity in mental calculations
					Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 Multiply Multiples 1 Multiply Multiples 1 Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it? Multiply Multiples 2 Multiply Multiples 2 Can you work out some different ways to balance this equation? Multiply Multiples 3 Multiply Multiples 3 Have a go at balancing this equation. Can you find different ways of doing it? An Easy Way to Multiply by 10? An Easy Way to Multiply by 10? Do you agree with Badger's statements? Is Badger's reasoning 'watertight'? Why or why not?
Written Calculation
		Calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs I'm Eight I'm Eight Find a great variety of ways of asking questions which make 8.	Write and calculate mathematical statements for multiplication and division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written methods (appears also in Mental Methods)	Multiply two-digit and three-digit numbers by a one-digit number using formal written layout	Multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers All the Digits 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? Trebling Trebling Can you replace the letters with numbers? Is there only one solution in each case?	Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication	Number Operations and Calculation Methods
					Divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context Division Rules Division Rules This challenge encourages you to explore dividing a three-digit number by a single-digit number.	Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context Divide numbers up to 4 digits by a two-digit whole number using the formal written method of short division where appropriate, interpreting remainders according to the context	Number Operations and Calculation Methods
Properties of Numbers: Multiples, Factors, Primes, Square and Cube Numbers
				Recognise and use factor pairs and commutativity in mental calculations (appears also in Mental Calculation)	Identify multiples and factors, including finding all factor pairs of a number, and common factors of two numbers Sweets in a box Sweets in a box How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction? Three Dice Three Dice Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice? Abundant Numbers Abundant Numbers 48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers? Flashing Lights Flashing Lights Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute? Multiplication Squares Multiplication Squares Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only. Which is Quicker? Which is quicker? Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why? Factor Track Factor track Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules. Factors and Multiples Game Factors and Multiples Game A game in which players take it in turns to choose a number. Can you block your opponent? Satisfying Four Statements Satisfying Four Statements Can you find any two-digit numbers that satisfy all of these statements?	Identify common factors, common multiples and prime numbers Factor Lines Factor Lines Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line. Round and Round the Circle Round and round the circle What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen. Factor-Multiple Chains Factor-Multiple Chains Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers? Counting Cogs Counting Cogs Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why? The Moons of Vuvv The moons of Vuvv The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse? Mystery Matrix Mystery Matrix Can you fill in this table square? The numbers 2-12 were used to generate it with just one number used twice.	Factors, Multiples and Primes
					Know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers Two Primes Make One Square Two Primes Make One Square Can you make square numbers by adding two prime numbers together? Xavi's T-Shirt Xavi's T-shirt How much can you read into a T-shirt?
					Establish whether a number up to 100 is prime and recall prime numbers up to 19 Dicey Array Dicey Array Watch the video of this game being played. Can you work out the rules? Which dice totals are good to get, and why?
					Recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³) One Wasn't Square One Wasn't Square Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were. Cycling Squares Cycling Squares Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only? Up and Down Staircases Up and Down Staircases One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down? Square Subtraction Square subtraction Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
Order of Operations
						Use their knowledge of the order of operations to carry out calculations involving the four operations	Number Operations and Calculation Methods
Inverse Operations, Estimating and Checking Answers
		Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems How Many? How Many? This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask? The Add and Take-Away Path The add and take-away path 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? What Was in the Box? What was in the Box? This box does something to the numbers that go into it. If you know the numbers that come out, what might be going on inside the box? Doing and Undoing Doing and undoing An investigation looking at doing and undoing mathematical operations focusing on doubling, halving, adding and subtracting. Secret Number Secret Number Annie and Ben are playing a game with a calculator. What was Annie's secret number?	Estimate the answer to a calculation and use inverse operations to check answers	Estimate and use inverse operations to check answers to a calculation	Use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy	Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy Four Go Four Go This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?	Number Operations and Calculation Methods
Problem Solving
	Solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher Lots of Biscuits! Lots of Biscuits! Help share out the biscuits the children have made. Share Bears Share Bears Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over? Doubling Fives Doubling Fives This activity focuses on doubling multiples of five.	Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts Are You Well Balanced? Are you well Balanced? Can you work out how to make each side of this balance equally balanced? You can put more than one weight on a hook. Magic Plant Magic Plant On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday? The Amazing Splitting Plant The Amazing Splitting Plant Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks? Catrina's Cards Catrina's Cards How would you find out how many football cards Catrina has collected? The Tomato and the Bean The tomato and the bean At the beginning of May, Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height? Lots of Lollies Lots of Lollies 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? Growing Garlic Growing Garlic Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had? Our Numbers Our Numbers 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 Ip Dip "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 ...? Birthday Sharing Birthday Sharing It's Sahila's birthday and she is having a party. How could you answer these questions using a picture, with things, with numbers or symbols?	Solve problems, including missing number problems, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects Follow the Numbers Follow the numbers What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules. A Square of Numbers A Square of Numbers Can you put the numbers 1 to 8 into the circles so that the four calculations are correct? What's in the Box? What's in the Box? This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box? What Do You Need? 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? How Do You Do It? How do you do it? This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient. Journeys in Numberland Journeys in Numberland Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores. This Pied Piper of Hamelin 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!	Solve problems involving multiplying and adding, including using the distributive law to multiply two-digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects	Solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes Division Rules Division Rules This challenge encourages you to explore dividing a three-digit number by a single-digit number. Odd Squares Odd Squares Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this? Curious Number 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? Cubes Within Cubes Cubes within Cubes We start with one yellow cube and build around it to make a 3×3×3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?	Solve problems involving addition, subtraction, multiplication and division Statement Snap Statement Snap You'll need to know your number properties to win a game of Statement Snap... Always, Sometimes or Never? Number Always, sometimes or never? Number Are these statements always true, sometimes true or never true? 4 by 4 Mathdokus 4 by 4 Mathdokus Can you use the clues to complete these 4 by 4 Mathematical Sudokus?	Number Operations and Calculation Methods
					Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign Four Goodness' Sake Four goodness' sake Use 4 four times in a calculation. What answers can you get? Make 100 Make 100 Find at least one way to put in some operation signs to make these digits come to 100. Highest and Lowest Highest and Lowest Put operations signs between the numbers 3, 4, 5 and 6 to make the highest possible number and lowest possible number. Multiply Multiples 1 Multiply Multiples 1 Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it? Multiply Multiples 2 Multiply Multiples 2 Can you work out some different ways to balance this equation? Multiply Multiples 3 Multiply Multiples 3 Have a go at balancing this equation. Can you find different ways of doing it?
					Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates
Ratio and Proportion
						Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts Pumpkin Pie Problem Pumpkin Pie Problem Peter wanted to make two pies for a party. His mother had a recipe for him to use. However, she always made 80 pies at a time. Did Peter have enough ingredients to make two pumpkin pies? Orange Drink Orange Drink A 750 ml bottle of concentrated orange squash is enough to make fifteen 250 ml glasses of diluted orange drink. How much water is needed to make 10 litres of this drink? Rectangle Tangle Rectangle Tangle The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the shapes? Jumping Jumping After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?	Ratio, Proportion and Rates of Change
						Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples In the Money In the Money One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?	Ratio, Proportion and Rates of Change
Scaling
						Solve problems involving similar shapes where the scale factor is known or can be found	Angles, Polygons and Geometrical Proof

Number - Fractions, Decimals and Percentages

EYFS	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Post-Primary
Counting in Fractional Steps
			Count up and down in tenths	Count up and down in hundredths			Fractions, Decimals and Percentages
Recognising Fractions
	Recognise, find and name a half as one of two equal parts of an object, shape or quantity Fair Feast Fair Feast Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have? Happy Halving Happy Halving Can you split each of the shapes below in half so that the two parts are exactly the same? Halving Halving These pictures show squares split into halves. Can you find other ways? Two Halves Two Halves This task provides children with the opportunity to investigate halving different shapes and check that they have made two halves.	Recognise, find, name and write fractions $\frac{1}{3}$, $\frac{1}{4}$, $\frac{2}{4}$ and $\frac{3}{4}$ of a length, shape, set of objects or quantity	Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators Fraction Match Fraction Match A task which depends on members of the group noticing the needs of others and responding.	Recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten	Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents (appears also in Equivalence)		Fractions, Decimals and Percentages
			Recognise that tenths arise from dividing an object into 10 equal parts and in dividing one-digit numbers or quantities by 10
	Recognise, find and name a quarter as one of four equal parts of an object, shape or quantity		Recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators
Comparing Fractions
			Compare and order unit fractions, and fractions with the same denominators		Compare and order fractions whose denominators are all multiples of the same number	Compare and order fractions, including fractions >1 More Fraction Bars More Fraction Bars What fraction of the black bar are the other bars? Have a go at this challenging task! Extending Fraction Bars Extending Fraction Bars Can you compare these bars with each other and express their lengths as fractions of the black bar?	Fractions, Decimals and Percentages
Comparing Decimals
				Compare numbers with the same number of decimal places up to two decimal places	Read, write, order and compare numbers with up to three decimal places	Identify the value of each digit in numbers given to three decimal places	Fractions, Decimals and Percentages
Rounding Including Decimals
				Round decimals with one decimal place to the nearest whole number Round the Dice Decimals 1 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?	Round decimals with two decimal places to the nearest whole number and to one decimal place Round the Dice Decimals 2 Round the Dice Decimals 2 What happens when you round these numbers to the nearest whole number?	Solve problems which require answers to be rounded to specified degrees of accuracy	Fractions, Decimals and Percentages
Equivalence (including Fractions, Decimals and Percentages)
		Write simple fractions e.g. $\frac{1}{2}$ of 6 = 3 and recognise the equivalence of $\frac{2}{4}$ and $\frac{1}{2}$ (appears also in Multiplication and Division of Fractions)	Recognise and show, using diagrams, equivalent fractions with small denominators Matching Fractions Matching fractions Can you find different ways of showing the same fraction? Try this matching game and see.	Recognise and show, using diagrams, families of common equivalent fractions Fractional Triangles Fractional Triangles Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths. Fractional Wall Fractional Wall Using the picture of the fraction wall, can you find equivalent fractions?	Identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths Tumbling Down Tumbling Down Watch this animation. What do you see? Can you explain why this happens?	Use common factors to simplify fractions; use common multiples to express fractions in the same denomination	Fractions, Decimals and Percentages
				Recognise and write decimal equivalents of any number of tenths or hundredths	Read and write decimal numbers as fractions (e.g. 0.71 = $\frac{71}{100}$)	Associate a fraction with division and calculate decimal fraction equivalents (e.g. 0.375) for a simple fraction (e.g. $\frac{3}{8}$)
					Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents
				Recognise and write decimal equivalents to $\frac{1}{4}$; $\frac{1}{2}$; $\frac{3}{4}$	Recognise the per cent symbol (%) and understand that per cent relates to 'number of parts per hundred', and write percentages as a fraction with denominator 100, and as a decimal	Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts Doughnut Percents Doughnut percents Can you make doughnuts by matching these fractions, decimals and percentages?
Addition and Subtraction of Fractions
			Add and subtract fractions with the same denominator within one whole (e.g. $\frac{5}{7}$ + $\frac{1}{7}$ = $\frac{6}{7}$)	Add and subtract fractions with the same denominator	Add and subtract fractions with the same denominator and denominators that are multiples of the same number A4 Fraction Addition A4 Fraction Addition Try adding fractions using A4 paper. A4 Fraction Subtraction A4 Fraction Subtraction This task offers opportunities to subtract fractions using A4 paper. Fraction Fascination Fraction Fascination This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.	Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions Fraction Lengths Fraction Lengths Can you find combinations of strips of paper which equal the length of the black strip? If the length of the black is 1, how could you write the sum of the strips?	Number Operations and Calculation Methods
					Recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number (e.g. $\frac{2}{5}$ + $\frac{4}{5}$ = $\frac{6}{5}$ = $1 \frac{1}{5}$)		Number Operations and Calculation Methods
Multiplication and Division of Fractions
		Write simple fractions e.g. $\frac{1}{2}$ of 6 = 3 and recognise the equivalence of $\frac{2}{4}$ and $\frac{1}{2}$ (appears also in Equivalence)	Recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators		Multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams	Multiply simple pairs of proper fractions, writing the answer in its simplest form (e.g. $\frac{1}{4}$ × $\frac{1}{2}$ = $\frac{1}{8}$); multiply one-digit numbers with up to two decimal places by whole numbers	Number Operations and Calculation Methods
						Divide proper fractions by whole numbers (e.g. $\frac{1}{3}$ ÷ 2 = $\frac{1}{6}$)	Number Operations and Calculation Methods
Multiplication and Division of Decimals
						Multiply one-digit numbers with up to two decimal places by whole numbers	Number Operations and Calculation Methods
				Find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths		Identify the value of each digit to three decimal places and multiply and divide numbers by 10, 100 and 1000 where the answers are up to three decimal places
						Use written division methods in cases where the answer has up to two decimal places
Problem Solving
			Solve problems that involve all of the above	Solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number Chocolate Chocolate There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time? Fractions in a Box Fractions in a Box The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box. Andy's Marbles Andy's Marbles Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.	Solve problems involving numbers up to three decimal places Forgot the Numbers Forgot the Numbers On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they? Route Product Route Product Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?	Solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison Would You Rather? Would You Rather? Would you rather: Have 10% of £5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?	Fractions, Decimals and Percentages Number Operations and Calculation Methods
				Solve simple measure and money problems involving fractions and decimals to two decimal places	Solve problems which require knowing percentage and decimal equivalents of $\frac{1}{2}$, $\frac{1}{4}$, $\frac{1}{5}$, $\frac{2}{5}$, $\frac{4}{5}$ and those with a denominator of a multiple of 10 or 25 Matching Fractions, Decimals and Percentages Matching Fractions, Decimals and Percentages Can you match pairs of fractions, decimals and percentages, and beat your previous scores?

Algebra

EYFS	Year 2	Year 6	Post-Primary
Patterns
Talk about and identify the patterns around them Extend and create ABAB patterns - stick, leaf, stick, leaf Notice and correct an error in a repeating pattern Continue, copy and create repeating patterns Collecting Collecting In this task, children make a collection out of some items and then discuss what they notice about their collection, focusing on the shapes and patterns that they can make. Pattern Making Pattern Making In this activity, there are lots of different patterns for children to make, describe and extend. Developing Pattern Awareness with Young Children Developing Pattern Awareness with Young Children This article explores the importance of pattern awareness with young children. A	Order and arrange combinations of mathematical objects in patterns and sequences School Fair Necklaces School fair necklaces How many possible symmetrical necklaces can you find? How do you know you've found them all? Poly Plug Pattern Poly Plug Pattern Create a pattern on the small grid. How could you extend your pattern on the larger grid? Missing Middles Missing Middles Can you work out the domino pieces which would go in the middle in each case to complete the pattern of these eight sets of three dominoes? Break It Up! Break it up! 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? Hundred Square Hundred Square A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19? Three Ball Line Up Three Ball Line Up Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land. Caterpillars Caterpillars These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square? Cube Bricks and Daisy Chains Cube bricks and daisy chains Daisy and Akram have made some number patterns. Can you find out which pattern is longer? Domino Patterns Domino Patterns What patterns can you make with a set of dominoes? Circles, Circles Circles, Circles 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? Repeating Patterns Repeating Patterns Try continuing these patterns made from triangles. Can you create your own repeating pattern? A City of Towers A City of Towers In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses? Domino Sequences Domino Sequences Find the next two dominoes in these sequences. What's happening? What's happening? Shapes are added to other shapes. Can you see what is happening? What is the rule? Paper Patchwork 1 Paper Patchwork 1 Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown? Paper Patchwork 2 Paper Patchwork 2 Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?		Patterns and Sequences
Sequences
		Generate and describe linear number sequences Break It Up! Break it up! 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? Domino Sets Domino sets How do you know if your set of dominoes is complete?	Patterns and Sequences
Equations
		Express missing number problems algebraically Plenty of Pens Plenty of Pens Amy's mum gave 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? Different Deductions Different Deductions There are lots of different methods to find out what the shapes are worth - how many can you find?	Equations and Formulae
		Find pairs of numbers that satisfy number sentences involving two unknowns Price Match Price Match Can you find pairs of differently sized windows that cost the same?
		Enumerate all possibilities of combinations of two variables
Formulae
		Use simple formulae Doplication Doplication We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes? Diagonal Sums Diagonal Sums In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice? Finding 3D Stacks Finding 3D stacks Can you find a way of counting the spheres in these arrangements?	Equations and Formulae

Measurement

EYFS	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Post-Primary
Comparing and Estimating
Make comparisons between objects relating to size, length, weight and capacity Packing Packing This activity involves sorting toys into categories by using comparing and classifying skills. I Have a Box I Have a Box In this activity, having access to a mystery box will spark children's imagination and encourage them to describe what they notice about the box. Tubes and Tunnels Tubes and Tunnels When investigating these tubes, children will have the opportunity to practise using everyday language to talk about length, size and position. The Spring Scale The Spring Scale Using the spring scale in this activity provides an engaging context in which children can explore and discuss the weight of different objects. Presents Presents Comparing wrapped presents gives children the chance to explore and discuss weight, including the idea that large objects aren't necessarily the heaviest. Long Creatures Long Creatures In this task, making a variety of long creatures out of card will provide an opportunity for children to discuss and compare lengths. Water, Water ... Water, Water ... This task provides a real-life context for children to compare capacities in order to choose the biggest container for their lemonade. Balances Balances In this activity, children will use the language of weight when comparing objects on a balance scale. Mud Kitchen Mud Kitchen When playing in this mud kitchen, children will be using the language of size and capacity to choose utensils for different tasks. Making Caterpillars Making Caterpillars By making 'caterpillars', children have an opportunity to practise using language of length and width, and non-standard measures to compare lengths. Wrapping Parcels Wrapping Parcels In this activity, children have the opportunity to wrap some toys and to measure and discuss the size of the box or wrapping paper that they will need. Sock Washing Line Sock Washing Line In this task, children are encouraged to spot pairs of socks and to order the socks by size and length on the washing line. How Long Are You? How long are you? Children use everyday language to talk about size, to compare quantities and objects and to solve problems Cooking With Children Cooking with Children By following some simple recipes in this task, children can practise the skills of measuring and counting ingredients.	Compare, describe and solve practical problems for: lengths & heights [e.g. long/short, longer/shorter, tall/short, double/half] mass/weight [e.g. heavy/light, heavier than, lighter than] capacity & volume [e.g. full/empty, more than, less than, half, half full, quarter] time [e.g. quicker, slower, earlier, later] Wallpaper Wallpaper These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it? Sizing Them Up Sizing them Up Can you put these shapes in order of size? Start with the smallest. Different Sizes Different Sizes A simple visual exploration into halving and doubling. Bottles (1) Bottles (1) For this activity which explores capacity, you will need to collect some bottles and jars. Bottles (2) Bottles (2) In this activity focusing on capacity, you will need a collection of different jars and bottles. Seesaw Shenanigans Seesaw Shenanigans A group of animals has made a seesaw in the woods. How can you make the seesaw balance? Thirsty? Thirsty? Can you lay out the pictures of the drinks in the way described by the clue cards? The Animals' Sports Day The animals' sports day One day, five small animals in my garden had a sports day. Who do you think won each race?	Compare and order lengths, mass, volume/capacity and record the results using >, < and = Making Longer, Making Shorter Making Longer, Making Shorter Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod? Order, Order! Order, Order! Can you place these quantities in order from smallest to largest? Compare the Cups Compare the Cups You'll need a collection of cups for this activity.		Estimate, compare and calculate different measures, including money in pounds and pence (appears also in Measuring) Discuss and Choose Discuss and Choose This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.	Calculate and compare the area of squares and rectangles including using standard units, square centimetres (cm²) and square metres (m²) and estimate the area of irregular shapes (appears also in Measuring) Numerically Equal Numerically Equal Can you draw a square in which the perimeter is numerically equal to the area? Fitted Fitted Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle? Making Boxes Making Boxes Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume? Ribbon Squares Ribbon Squares What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether? Brush Loads Brush Loads How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.	Calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units such as mm³ and km³ Next Size Up Next size up The challenge for you is to make a string of six (or more!) graded cubes.	Perimeter, Area and Volume
					Estimate volume (e.g. using 1cm³ blocks to build cubes and cuboids) and capacity (e.g. using water) Pouring Problem Pouring Problem What do you think is going to happen in this video clip? Are you surprised?
	Sequence events in chronological order using language [e.g. before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening] Times of Day Times of Day These pictures show some different activities that you may get up to during a day. What order would you do them in?	Compare and sequence intervals of time	Compare durations of events, for example to calculate the time taken by particular events or tasks
			Estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes and hours; use vocabulary such as o'clock, a.m./p.m., morning, afternoon, noon and midnight (appears also in Telling the Time) Watch the Clock Watch the clock During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen? Wonky Watches Wonky Watches Mandeep's watch loses two minutes every hour. Adam's watch gains one minute every hour. Can you work out what time they arrived at the airport?
Measuring and Calculating
	Measure and begin to record the following: lengths and heights mass/weight capacity and volume time (hours, minutes, seconds) How Tall? How Tall? A group of children are discussing the height of a tall tree. How would you go about finding out its height? Can You Do It Too? Can you do it too? Try some throwing activities and see whether you can throw something as far as the Olympic hammer or discus throwers.	Choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels Little Man Little Man The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks? Car Journey Car Journey This practical activity involves measuring length/distance.	Measure, compare, add and subtract: lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml) Olympic Starters Olympic Starters Look at some of the results from the Olympic Games in the past. How do you compare if you try some similar activities? Oh! Harry! Oh! Harry! A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?	Estimate, compare and calculate different measures, including money in pounds and pence (appears also in Comparing) Discuss and Choose Discuss and Choose This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.	Use all four operations to solve problems involving measure (e.g. length, mass, volume, money) using decimal notation including scaling	Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate (appears also in Converting)	Perimeter, Area and Volume
			Measure the perimeter of simple 2D shapes	Measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres	Measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres Through the Window 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? Area and Perimeter Area and perimeter What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.	Recognise that shapes with the same areas can have different perimeters and vice versa
	Recognise and know the value of different denominations of coins and notes	Find different combinations of coins that equal the same amounts of money	Add and subtract amounts of money to give change, using both £ and p in practical contexts How Much Did It Cost? How Much Did it Cost? Use your logical thinking skills to deduce how much Dan's crisps and ice cream cost altogether.
		Recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value Five Coins Five Coins Ben has five coins in his pocket. How much money might he have?
		Solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change The Puzzling Sweet Shop The Puzzling Sweet Shop There were cola bottles for 2p, mini eggs for 3p, marshmallow twists for 5p and lollipops for 7p in the sweet shop. What could each of the children buy with their money? Fruity Pairs Fruity Pairs Which two items of fruit could Kate and Sam choose? Can you order the prices from lowest to highest?
				Find the area of rectilinear shapes by counting squares Torn Shapes Torn Shapes These rectangles have been torn. How many squares did each one have inside it before it was ripped? Twice as Big? Twice as Big? Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.	Calculate and compare the area of squares and rectangles including using standard units, square centimetres (cm²) and square metres (m²) and estimate the area of irregular shapes Numerically Equal Numerically Equal Can you draw a square in which the perimeter is numerically equal to the area? Fitted Fitted Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle? Making Boxes Making Boxes Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume? Ribbon Squares Ribbon Squares What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether? Brush Loads Brush Loads How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.	Calculate the area of parallelograms and triangles
						Calculate the area of parallelograms and triangles; calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units [e.g. mm³ and km³]. Next Size Up Next size up The challenge for you is to make a string of six (or more!) graded cubes.
						Recognise when it is possible to use formulae for area and volume of shapes
Telling the Time
Begin to describe a sequence of events, real or fictional, using words such as 'first', 'then…' Timing Timing In this task, children will practise using a variety of timers to work out how many items they can put into a jar before the time finishes. Calendar Muddle Calendar Muddle This activity encourages children to think about times of day and the order in which they do different activities throughout the day.	Tell the time to the hour and half past the hour and draw the hands on a clock face to show these times	Tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times What Is the Time? What is the time? Can you put these times on the clocks in order? You might like to arrange them in a circle. Stop the Clock Stop the Clock This is a game for two players. Can you find out how to be the first to get to 12 o'clock?	Tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks 5 on the Clock 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? How many Times? How many Times? 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.? The time is ... The time is ... Can you put these mixed-up times in order? You could arrange them in a circle. Clocks Clocks These clocks have been reflected in a mirror. What times do they say? Two Clocks Two Clocks These clocks have only one hand, but can you work out what time they are showing from the information? Approaching Midnight Approaching Midnight Here's a strategy game with lots to explore. Can you find out enough to guarantee a win, no matter what the settings?	Read, write and convert time between analogue and digital 12- and 24-hour clocks
	Recognise and use language relating to dates, including days of the week, weeks, months and years Snap Snap Try this version of Snap with a friend - do you know the order of the days of the week?	Know the number of minutes in an hour and the number of hours in a day Matching Time Matching Time Try this matching game which will help you recognise different ways of saying the same time interval.	Estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes and hours; use vocabulary such as o'clock, a.m./p.m., morning, afternoon, noon and midnight Watch the Clock Watch the clock During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen? Wonky Watches Wonky Watches Mandeep's watch loses two minutes every hour. Adam's watch gains one minute every hour. Can you work out what time they arrived at the airport?
				Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days	Solve problems involving converting between units of time
Converting
		Know the number of minutes in an hour and the number of hours in a day Matching Time Matching Time Try this matching game which will help you recognise different ways of saying the same time interval.	Know the number of seconds in a minute and the number of days in each month, year and leap year	Convert between different units of measure (e.g. kilometre to metre; hour to minute)	Convert between different units of metric measure (e.g. kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and millilitre)	Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places
				Read, write and convert time between analogue and digital 12- and 24-hour clocks	Solve problems involving converting between units of time	Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate
				Solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days	Understand and use approximate equivalences between metric units and common imperial units such as inches, pounds and pints	Convert between miles and kilometres

Geometry

EYFS	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Post-Primary
Identifying Shapes and Their Properties
Talk about and explore 2D and 3D shapes (for example, circles, rectangles, triangles and cuboids) using informal and mathematical language: 'sides', 'corners', 'straight', 'flat', 'round' Shapes in the Bag Shapes in the Bag In this task, children put their hands into a bag and describe what shape they think they can feel and why. Making Footprints Making Footprints In this activity, children will develop an awareness of the faces of 3D shapes by using them to make 'footprints' in soft dough. Exploring 2D Shapes Exploring 2D shapes In this task, children will make shapes out of loops of string and discuss what they notice about their shapes.	Recognise and name common 2D and 3D shapes, including: 2D shapes [e.g. rectangles (including squares), circles and triangles] 3D shapes [e.g. cuboids (including cubes), pyramids and spheres] Three Squares Three Squares What is the greatest number of squares you can make by overlapping three squares? Jig Shapes Jig Shapes Can you each work out what shape you have part of on your card? What will the rest of it look like? Always, Sometimes or Never? KS1 Always, sometimes or never? KS1 Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?	Identify and describe the properties of 2D shapes, including the number of sides and line symmetry in a vertical line Shapely Lines Shapely Lines This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way? Let's Investigate Triangles Let's Investigate Triangles Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make? Colouring Triangles Colouring Triangles Explore ways of colouring this set of triangles. Can you make symmetrical patterns? Chain of Changes Chain of Changes In this activity, shapes can be arranged by changing either the colour or the shape each time. Can you find a way to do it? Complete the Square Complete the Square Complete the squares - but be warned some are trickier than they look! Inside Triangles Inside Triangles How many different triangles can you draw which each have one dot in the middle? Exploded Squares Exploded Squares Can you create symmetrical designs by cutting a square into strips? Poly Plug Rectangles Poly Plug Rectangles 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? Triangle or No Triangle? Triangle or No Triangle? Here is a selection of different shapes. Can you work out which ones are triangles, and why?		Identify lines of symmetry in 2D shapes presented in different orientations Stringy Quads Stringy Quads This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help! Let Us Reflect Let Us Reflect Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?	Identify 3D shapes, including cubes and other cuboids, from 2D representations Guess What? Guess What? Can you find out which 3D shape your partner has chosen before they work out your shape? Shadow Play Shadow Play Here are shadows of some 3D shapes. What shapes could have made them?	Recognise, describe and build simple 3D shapes, including making nets Cut Nets Cut Nets Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together? Making Cuboids Making Cuboids Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make? Sponge Sections Sponge Sections You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.	Angles, Polygons and Geometrical Proof 3D Shapes
Combine shapes to make new ones - an arch, a bigger triangle, etc. Compose and decompose shapes so that children recognise a shape can have other shapes within it, just as numbers can Making a Picture Making a Picture This task provides an opportunity for children to work together to make a picture, discussing with each other which position they want to put each shape in.		Identify and describe the properties of 3D shapes, including the number of edges, vertices and faces Building with Solid Shapes Building with Solid Shapes We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them? Skeleton Shapes Skeleton Shapes How many balls of modelling clay and how many straws does it take to make these skeleton shapes?				Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius.
		Identify 2D shapes on the surface of 3D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]
Drawing and Constructing
Select shapes appropriately: flat surfaces for building, a triangular prism for a roof, etc. Building Towers Building Towers In this task, children will explore 3D shapes when selecting which shapes to use in their tower.			Draw 2D shapes and make 3D shapes using modelling materials; recognise 3D shapes in different orientations and describe them Overlaps Overlaps What does the overlap of these two shapes look like? Try picturing it in your head and then use some cut-out shapes to test your prediction. Overlapping Again Overlapping Again What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation. Board Block Challenge Board Block Challenge Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent? Building Blocks Building Blocks Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself? A Puzzling Cube A Puzzling Cube Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube? The Third Dimension The Third Dimension Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper? Inky Cube 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? Square Corners Square Corners What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?	Complete a simple symmetric figure with respect to a specific line of symmetry Symmetry Challenge Symmetry Challenge How many symmetric designs can you make on this grid? Can you find them all? ReflectoR ! RotcelfeR ReflectoR ! RotcelfeR Can you place the blocks so that you see the reflection in the picture?	Draw given angles, and measure them in degrees (°) How Safe Are You? How Safe Are You? How much do you have to turn these dials by in order to unlock the safes? Olympic Turns Olympic Turns This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles. Six Places to Visit Six Places to Visit Can you describe the journey to each of the six places on these maps? How would you turn at each junction?	Draw 2D shapes using given dimensions and angles Baravelle Baravelle What can you see? What do you notice? What questions can you ask? Shape Draw Shape Draw Use the information on these cards to draw the shape that is being described.	Construction
						Recognise, describe and build simple 3D shapes, including making nets (appears also in Identifying Shapes and Their Properties) Cut Nets Cut Nets Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together? Making Cuboids Making Cuboids Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make? Sponge Sections Sponge Sections You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.	Construction
Comparing and Classifying
		Compare and sort common 2D and 3D shapes and everyday objects Data Shapes Data shapes Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want? Cubes Cut Into Four Pieces Cubes Cut into Four Pieces Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set? Paper Partners Paper Partners Can you describe a piece of paper clearly enough for your partner to know which piece it is? Matching Triangles Matching Triangles Can you sort these triangles into three different families and explain how you did it?		Compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes Nine-Pin Triangles Nine-Pin Triangles How many different triangles can you make on a circular pegboard that has nine pegs? Seeing Rhombuses Seeing Rhombuses Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a rhombus. Quad Match Quad match A task which depends on members of the group noticing the needs of others and responding. Four Triangles Puzzle Four Triangles Puzzle Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together? Cut it Out Cut it Out Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into? Shapes on the Playground Shapes on the Playground Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues? What Shape? What shape? This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen. Seeing Parallelograms Seeing Parallelograms Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a parallelogram. Sorting Logic Blocks Sorting Logic Blocks This activity focuses on similarities and differences between shapes. Seeing Squares Seeing Squares Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.	Distinguish between regular and irregular polygons based on reasoning about equal sides and angles Egyptian Rope Egyptian Rope The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this? Bracelets Bracelets Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?	Compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons Where are they? Where are they? Use the isometric grid paper to find the different polygons. Name That Triangle! Name That Triangle! Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know? Quadrilaterals Quadrilaterals How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle? Triangles all Around Triangles all Around Can you find all the different triangles on these peg boards, and find their angles? Round a Hexagon Round a hexagon This problem shows that the external angles of an irregular hexagon add to a circle. Diagonally Square Diagonally Square Ayah conjectures that the diagonals of a square meet at right angles. Do you agree? How could you find out? Always, Sometimes or Never? Shape Always, sometimes or never? Shape Are these statements always true, sometimes true or never true?	Angles, Polygons and Geometrical Proof
Angles
			Recognise angles as a property of shape or a description of a turn		Know angles are measured in degrees; estimate and compare acute, obtuse and reflex angles Estimating Angles Estimating angles How good are you at estimating angles?		Angles, Polygons and Geometrical Proof
			Identify right angles, recognise that two right angles make a half-turn, three make three quarters of a turn and four a complete turn; identify whether angles are greater than or less than a right angle	Identify acute and obtuse angles and compare and order angles up to two right angles by size	Identify: angles at a point and one whole turn (total 360°) angles at a point on a straight line and $\frac{1}{2}$ a turn (total 180°) other multiples of 90°	Recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles
			Identify horizontal and vertical lines and pairs of perpendicular and parallel lines National Flags National Flags This problem explores the shapes and symmetries in some national flags.		Use the properties of rectangles to deduce related facts and find missing lengths and angles Making Rectangles Making Rectangles A task which depends on members of the group noticing the needs of others and responding.
Position, Direction and Movement
Understand position through words alone - for example, "The bag is under the table," - with no pointing Describe a familiar route Discuss routes and locations, using words like 'in front of' and 'behind' Obstacle Course Obstacle Course As children move around an obstacle course, adults can model positional language, encourage children to describe their own movement and create their own course. Small World Play Small World Play This activity provides an engaging context for children to consider the space they will allocate for some 'small world' toys. Scooters, Bikes and Trikes Scooters, Bikes and Trikes When waiting for a ride on outdoor toys, children can consider which route they might take around the outside area and how long they will spend on their toy. Position With Wellies Position with Wellies This task uses the familiar situation of a shelf of objects to encourage children to use positional language and follow directions to find their wellies. Paths Paths By making 'paths' out of different materials and discussing these, children will develop their shape and space language in this activity.	Describe position, direction and movement, including half, quarter and three-quarter turns Turning Turning Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described? Tangram Tangle Tangram Tangle If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make? Olympic Rings Olympic rings Can you design your own version of the Olympic rings, using interlocking squares instead of circles? 2 Rings 2 Rings The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?	Use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anti-clockwise) Walking Round a Triangle Walking round a triangle This ladybird is taking a walk round a triangle. Can you see how much she has turned when she gets back to where she started? Turning Man Turning Man Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures. Coloured Squares Coloured Squares Use the clues to colour each square. Triangle Animals Triangle Animals How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all? Cover the Camel Cover the Camel Can you cover the camel with these pieces?		Describe movements between positions as translations of a given unit to the left/right and up/down			Transformations Functions and graphs
Select, rotate and manipulate shapes to develop spatial reasoning skills Can You Build This? Can you build this? Children explore characteristics of shapes, using everyday and mathematical language to describe them, talk about positions, and solve problems. The Importance of Shape and Space in the Early Years The importance of shape and space in the early years In this article for EY practitioners, Dr Sue Gifford discusses children's early spatial thinking and how this predicts their mathematical understanding and achievement. A				Describe positions on a 2D grid as coordinates in the first quadrant Coordinate Challenge Coordinate Challenge Use the clues about the symmetrical properties of these letters to place them on the grid. Eight Hidden Squares Eight hidden squares On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?	Identify, describe and represent the position of a shape following a reflection or translation, using the appropriate language, and know that the shape has not changed Transformations on a Pegboard Transformations on a Pegboard How would you move the bands on the pegboard to alter these shapes? More Transformations on a Pegboard More Transformations on a Pegboard Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.	Describe positions on the full coordinate grid (all four quadrants) Ten Hidden Squares Ten Hidden Squares These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares? Treasure Hunt Treasure Hunt Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
				Plot specified points and draw sides to complete a given polygon A Cartesian Puzzle A Cartesian puzzle Find the missing coordinates which will form these eight quadrilaterals. These coordinates themselves will then form a shape with rotational and line symmetry.		Draw and translate simple shapes on the coordinate plane, and reflect them in the axes
Pattern
Talk about and identify the patterns around them Extend and create ABAB patterns - stick, leaf, stick, leaf Notice and correct an error in a repeating pattern Continue, copy and create repeating patterns Collecting Collecting In this task, children make a collection out of some items and then discuss what they notice about their collection, focusing on the shapes and patterns that they can make. Pattern Making Pattern Making In this activity, there are lots of different patterns for children to make, describe and extend. Developing Pattern Awareness With Young Children Developing Pattern Awareness with Young Children This article explores the importance of pattern awareness with young children. A		Order and arrange combinations of mathematical objects in patterns and sequences School Fair Necklaces School fair necklaces How many possible symmetrical necklaces can you find? How do you know you've found them all? Poly Plug Pattern Poly Plug Pattern Create a pattern on the small grid. How could you extend your pattern on the larger grid? Missing Middles Missing Middles Can you work out the domino pieces which would go in the middle in each case to complete the pattern of these eight sets of three dominoes? Break It Up! Break it up! 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? Hundred Square Hundred Square A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19? Three Ball Line Up Three Ball Line Up Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land. Caterpillars Caterpillars These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square? Cube Bricks and Daisy Chains Cube bricks and daisy chains Daisy and Akram have made some number patterns. Can you find out which pattern is longer? Domino Patterns Domino Patterns What patterns can you make with a set of dominoes? Circles, Circles Circles, Circles 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? Repeating Patterns Repeating Patterns Try continuing these patterns made from triangles. Can you create your own repeating pattern? A City of Towers A City of Towers In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses? Domino Sequences Domino Sequences Find the next two dominoes in these sequences. What's Happening? What's happening? Shapes are added to other shapes. Can you see what is happening? What is the rule? Paper Patchwork 1 Paper Patchwork 1 Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown? Paper Patchwork 2 Paper Patchwork 2 Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?					Patterns and Sequences

Statistics

EYFS	Year 2	Year 3	Year 4	Year 5	Year 6	Post-Primary
Interpreting, Constructing and Presenting Data
	Interpret and construct simple pictograms, tally charts, block diagrams and simple tables Ladybird Count Ladybird Count Some children were playing a game. Make a graph or picture to show how many ladybirds each child had. Sticky Data Sticky Data You'll need to work in a group on this problem. Use your sticky notes to show the answer to questions such as 'how many girls are there in your group?'. Carroll Diagrams Carroll Diagrams Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?	Interpret and present data using bar charts, pictograms and tables Going for Gold Going for Gold Looking at the Olympic Medal table, can you see how the data is organised? Could the results be presented differently to give another nation the top place? Real Statistics Real Statistics Have a look at this table of how children travel to school. How does it compare with children in your class? The Car That Passes The car that passes What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas? Class 5's Names Class 5's names Class 5 were looking at the first letter of each of their names. They created different charts to show this information. Can you work out which member of the class was away on that day? If the World Were a Village If the World Were a Village This activity is based on data in the book 'If the World Were a Village'. How will you represent your chosen data for maximum effect? Our Sports Our Sports This problem explores the range of events in a sports day and which ones are the most popular and attract the most entries. Now and Then Now and Then Have a look at the results for some events at past Olympic Games. Can you use these to predict the results at the next Olympics? The Domesday Project The Domesday Project Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?	Interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs Take Your Dog for a Walk Take your Dog for a Walk Use the interactivity to move Pat. Can you reproduce the graphs and tell their story? Venn Diagrams Venn diagrams How will you complete these interactive Venn diagrams?	Complete, read and interpret information in tables, including timetables	Interpret and construct pie charts and line graphs and use these to solve problems	Statistics
	Ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity Sort the Street Sort the Street Sort the houses in my street into different groups. Can you do it in any other ways?
	Ask and answer questions about totalling and comparing categorical data
Solving Problems
		Solve one-step and two-step questions [e.g. 'How many more?' and 'How many fewer?'] using information presented in scaled bar charts and pictograms and tables	Solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs How Big Are Classes 5, 6 and 7? How Big Are Classes 5, 6 and 7? Use the two sets of data to find out how many children there are in Classes 5, 6 and 7.	Solve comparison, sum and difference problems using information presented in a line graph	Calculate and interpret the mean as an average Birdwatch Birdwatch Have a look at this data from the RSPB 2011 Birdwatch. What can you say about the data?	Statistics

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Interpreting, Constructing and Presenting Data

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