Progression document curriculum mapMaths

IntentMaths is a journey and long-term goal, achieved through exploration, clarification, practice and application over time. At each stage of learning, children should be able to demonstrate a deep, conceptual understanding of the topic and be able to build on this over time.There are 3 levels of learning:

Shallow learning: surface, temporary, often lost  Deep learning: it sticks, can be recalled and used Deepest learning: can be transferred and applied in different contexts

The deep and deepest levels are what we are aiming for by teaching maths using the Mastery approach.ImplementationMultiple representations for all!Concrete, pictorial, abstractObjects, pictures, words, numbers and symbols are everywhere. The mastery approach incorporates all of these to help children explore and demonstrate mathematical ideas, enrich their learning experience and deepen understanding. Together, these elements help cement knowledge so pupils truly understand what they’ve learnt.All pupils, when introduced to a key new concept, should have the opportunity to build competency in this topic by taking this approach. Pupils are encouraged to physically represent mathematical concepts. Objects and pictures are used to demonstrate and visualise abstract ideas, alongside numbers and symbols.Concrete – children have the opportunity to use concrete objects and manipulatives to help them understand and explain what they are doing.Pictorial – children then build on this concrete approach by using pictorial representations, which can then be used to reason and solve problems.

Abstract – With the foundations firmly laid, children can move to an abstract approach using numbers and key concepts with confidence.Impact· Quick recall of facts and procedures· The flexibility and fluidity to move between different contexts and representations of  mathematics.· The ability to recognise relationships and make connections in mathematicsA mathematical concept or skill has been mastered when a child can show it in multiple ways, using the mathematical language to explain their ideas, and can independently apply the concept to new problems in unfamiliar situations.

EYFSDevelopment matters- Numbers MPS expectations MPS expectations continued

30-50 months•Uses some number names and number languagespontaneously.•Uses some number names accurately in play.•Recites numbers in order to 10.•Knows that numbers identify how many objects are in a set.•Beginning to represent numbers using fingers, marks on paper or pictures.•Sometimes matches numeral and quantity correctly.•Shows curiosity about numbers by offering comments or asking questions.•Compares two groups of objects, saying when they have the same number.•Shows an interest in number problems.•Separates a group of three or four objects in different ways, beginning to recognise that the total is still the same.•Shows an interest in numerals in the environment.•Shows an interest in

NCETM materials:Part–whole: identifying smaller numbers within a number (conceptual subitising – seeing groups and combining to a total)Children need opportunities to see small numbers within a larger collection. ‘Number talks’ allow children to discuss what they see. For instance, with giant ladybirds: ‘There are 5 spots altogether. I can see 4 and 1, I can see 3 and 2, and I can see 1 and 1 and 1 and 1 and 1.’ Encourage exploration of all the ways that ‘five’ can be and look. Inverse operationsChildren need opportunities to partition a number ofthings into two groups, and to recognise that those groups can be recombined to make the same total. Encourage children to say the whole number that the ‘parts’ make altogether.A number can be partitioned into different pairs of numbers Children need opportunities to explore a range of ways topartition a whole number. The emphasis here is onidentifying the pairs of numbers that make

When comparing capacities directly, children can pour from one container to another to find which holds more, or find one that is the same. However, children may conclude that if one container overflows that must mean ‘bigger’. Ensure that children have opportunities to see a jug of coloured water poured into a range of containershapes. Ask: ‘What do you think will happen if we pour this tall thin jugful into this short fat dish?’Comparing weight can be tricky to conceptualise. One way is to identify that greater mass is shown by a greater downward pull. Ask children to hold a carrier bag; encourage them to notice it feels as though their hand is being pulled down when something heavy is put in it. Place a carrier bag in each hand and identify which one is heavier, by discussing which arm feels more pulled down.Show this using a simple spring balance or a boxattached to elastic bands; identify that the elastic is being• encouraging children to compare different attributes in everyday situations: ‘I wonder who has the longest snake?’ ‘I wonder whose pot will hold the most

representing numbers.•Realises not only objects, but anything can be counted, including steps, claps or jumps.

40- 60 months•Recognise some numerals of personal significance.•Recognises numerals 1 to 5.•Counts up to three or four objects by saying one number name for each item.•Counts actions or objects which cannot be moved.•Counts objects to 10, and beginning to count beyond 10.•Counts out up to six objects from a larger group.•Selects the correct numeral to represent 1 to 5, then 1 to 10 objects.•Counts an irregular arrangement of up to ten objects.•Estimates how many objects they can see and checks by counting them.•Uses the language of ‘more’ and ‘fewer’ to compare two sets of objects.•Finds the total number of items in two groups by counting all of them.•Says the number that is one more than a given number.•Finds one more or one less from a group of up to five objects, then ten objects.

a total.Children can do this in two ways – physically separating agroup, or constructing a group from two kinds of things.A number can be partitioned into more than two numbersChildren need opportunities to explore the different ways that numbers can be partitioned, i.e. into more than two groups. Situations to promote this include increasing the number of pots to put a given amount into, e.g. planting ten seeds into three or more pots.Number bonds: knowing which pairs make a given numberChildren need opportunities to say how many are hidden in a known number of things. For example: ‘Five toys go into a tent, then two come out. How many are left in the tent?’ The child should respond that there are still three toys in the tent.More than / less thanChildren need progressive experiences where they can compare collections and begin to talk about which group has more things. Initially, the groups need to be very obviously different, with one group having a widely different number of things. Collections should also offer challenges, such as including more small things and fewer large things, to draw attention to the numerosity of the comparison, i.e. the number of things, not the size of them.Identifying groups with the same number of thingsChildren need the opportunity to see that

water?’ ‘I wonder which ball is the heaviest?’• cutting a piece of ribbon as long as a child’s arm and encouraging them to find things in the environment that are longer, shorter or the same length• focusing on asking for specific things according to their attributes. For example: 'Please can you pass me a ... that is ... than this one?'• when comparing directly, finding the odd one out, by providing a varied range of container shapes allcontaining the same amount of liquid except for one.'Which one do you think is the odd one out? Why? How will we check? Were we right?'• posing see-saw problems, relating to weight: ‘What can we do to make this side of the see-saw go down?’• using a simple spring balance to compare the weight of cargo for a toy boat• setting up a ‘balancing station’ with interesting things to weigh and to balance, indoors and outdoors• comparing different parcels, ensuring some of thesmaller parcels are heavy, and some of the largerparcels are light.Showing awareness of comparison in estimating and predictingAfter children have had lots of practical experiences of comparing attributes, they can begin to estimate and to predict. For instance, they can start to consider which

• In practical activities and discussion, beginning to use the vocabulary involved in adding and subtracting.•Records, using marks that they can interpret and explain.•Begins to identify own mathematical problems based on own interests and fascinations.

Early Learning GoalChildren count reliably with numbers from one to 20, place them in order and say which number is one more or one less than a given number. Using quantities and objects, they add and subtract two single-digit numbers and count on or back to find the answer. They solve problems, including doubling, halving and sharing.

Development matters- Shape, space and measure

30-50 months•Shows an interest in shape and space by playing with shapesor making arrangements with objects.•Shows awareness of similarities of shapes in the environment.•Uses positional language.•Shows interest in shape by sustained construction activity orby talking about shapes or

groups could consist of equal numbers of things. Children can check that groups are equal, by matching objects on a one-to-one basis.Comparing numbers and reasoningChildren need opportunities to apply their understanding by comparing actual numbers and explaining which is more. For example, a child is shown two boxes and told one has 5 sweets in and the other has 3 sweets in. Which box would they pick to keep and why? Look for the reasoning in the response they give, i.e. ‘I would pick the 5 box because 5 is more than 3 and I want more.’ Ifshown two numerals, children can say which is larger by counting or matching one-to-one. Children can compare numbers that are far apart, near toand next to each other. For example, 8 is a lot bigger than 2 but 3 is only a little bit bigger than 2.Knowing the ‘one more than/one less than’ relationship between counting numbersChildren need opportunities to see and begin togeneralise the ‘one more than/one less than’ relationship between sequential numbers. They can apply this understanding by recognising when the quantity does not match the number, i.e. if a pack is labelled as 5 but contains only 4, the children can identify that this is not right.Support children in recognising that if they add one, they will get the next number, or

container would be best to store a specific item in: 'Which box should Teddy have?', 'What will fit in here?'Comparing indirectlyChildren can then move onto using one thing to compare with two others, if, for example, asked to put things in order of height, weight or capacity. This may involve using a ‘go between’, for instance pouring a jugful of water into two bottles to see which holds more. Problems may be posed such as: ‘I would like to move this table outside – do you think it will fit through the door?’Continuing an AB patternChildren need the opportunity to see a pattern, to talk about what they can see, and to continue a pattern. At first, they will do this one item at a time, e.g. red cube, blue cube, red cube…verbalising the pattern helps. Children may then be asked to say what they would add next to continue it. Copying an AB patternCopying a pattern can be difficult for children if they have to keep comparing item by item. AB patterns are easiest – when presented to children, these should contain several repeats, to ensure that the pattern unit is evident. Discuss the nature of the pattern: how has the pattern been made? Patterns can have a range of features such as varying objects, size or orientation.Make their own AB patternAs children progress from continuing to copying patterns, they can be challenged

arrangements.•Shows interest in shapes in the environment.•Uses shapes appropriately for tasks.•Beginning to talk about the shapes of everyday objects,e.g. ‘round’ and ‘tall’.

40-60+ months•Beginning to use mathematical names for ‘solid’ 3D shapesand ‘flat’ 2D shapes, and mathematical terms to describeshapes.•Selects a particular named shape.•Can describe their relative position such as ‘behind’ or‘next to’.•Orders two or three items by length or height.•Orders two items by weight or capacity.•Uses familiar objects and common shapes to create andrecreate patterns and build models.•Uses everyday language related to time.•Beginning to use everyday language related to money.•Orders and sequences familiar events.•Measures short periods of time in simple ways.

if one is taken away, they will have the previous number. For example: ‘There are 4 frogs on the log, 1 frog jumps off. How many will be left? How do you know?’Counting: saying number words in sequenceChildren need to know number names, initially to five, then ten, and extending to larger numbers, including crossing boundaries 19/20 and 29/30.Counting back is a useful skill, but young children will find this harder because of the demand it places on the working memory.Counting: tagging each object with one number wordChildren need lots of opportunities to count things inirregular arrangements. For example, how many play people are in the sandpit? How many cars have we got in the garage? These opportunities can also include counting things that cannot be seen, touched or moved.Counting: knowing the last number counted gives the total so farChildren need the opportunity to count out or ‘give’ a number of things from a larger group, not just to count the number that are there. This is to support them in focusing on the ‘stopping number’ which gives the cardinal value.Subitising: recognising small quantities without needing to count them allSubitising is recognising how many things are in a group without having to count them one by one. Children need

to change the sample pattern or to create their own. A range of objects can be provided for children to decide what the features of the pattern are going to be. Children may find it easier to make a pattern with the same colours as the original but with different objects. For example, copying a red–blue cube pattern with red and blue dinosaurs is easier than with yellow andgreen cubes. Patterns can involve different aspects and modes such as sounds, words or actions: some children will need suggestions, while others will think of their own. As children construct the patterns, ensure they have opportunities to:• repeat the unit at least three times (big bear,small bear; big bear, small bear; big bear, smallbear). This is to ensure the child can sustain thepattern• make a specified pattern, e.g. ‘Can you do agreen, yellow pattern?’ This is to ensure the childcan apply their pattern understanding• choose their own rule, e.g. ‘I am going to make abig, small pattern.’ This is to ensure the child canidentify pattern features/rules/criteria• choose their own actions or sounds, e.g. clap,stamp… This is to help children generalise the

Early Learning GoalChildren use everyday language to talk about size,weight, capacity, position, distance, time and money tocompare quantities and objects and to solve problems.They recognise, create and describe patterns. Theyexplore characteristics of everyday objects and shapesand use mathematical language to describe them.

opportunities to see regular arrangements of small quantities, e.g. a dice face, structured manipulatives, etc., and be encouraged to say the quantity represented. Children also need opportunities to recognise small amounts (up to five) when they are not in the ‘regular’arrangement, e.g. small handfuls of objects.Numeral meaningsChildren need to have the opportunity to match a number symbol with a number of things. Look for opportunities to have a range of number symbols available, e.g. wooden numerals, calculators, handwritten (include differentexamples of a number).Conservation: knowing that the number does not change if things are rearranged (as long as none have been added or taken away)Children need the opportunity to recognise amounts that have been rearranged and to generalise that, if nothing has been added or taken away, then the amount is the same.Developing spatial awareness: experiencing different viewpointsChildren need opportunities to move both themselves and objects around, so they see things from differentperspectives. This will support them in visualising how things will appear when turned around and imagining how things might fit together. They need to make constructions, patterns and pictures,

idea of pattern. Spotting an error in an AB patternWhen working with AB patterns, children also need the opportunities to spot and correct errors. It is easiest to spot an extra item, then a missing item, then items swapped around. When presented with an AB pattern, children can be encouraged to describe it to make sure it is right. Then, to detect an error, they can track the pattern from the start. To begin with, children may know there is something wrong, but might not be able to say what the error is. They then might take several attempts to correct it, before being able to repair the error in one move.Identifying the unit of repeatThe key aspect of understanding patterns is identifying the smallest part of the pattern, or the ‘unit of repeat’ You can draw children’s attention to this when building patterns by picking up a unit at a time, e.g. a blue block and a red block together, and describing this as a ‘redblue pattern’, rather than a red, blue, red, blue, red, blue pattern. Children can also be asked to show the pattern unit which repeats, e.g. show two blocks, a red and a blueContinuing an ABC patternOnce children are secure with alternating patterns, they can tackle more complex pattern structures:ABC has more items in the unit of repeat, but alldifferent, e.g. red, blue, yellow; red, blue, yellow…

and select shapes which will fit when rotated or flipped in insert boards, shape sorters and jigsaws. These experiences will support them in noticing the results of rotating and reflecting images, and in visualising these.Developing spatial vocabularyChildren need opportunities to be exposed to and to use the language of position and direction:position: ‘in’, ‘on’, ‘under’ direction: ‘up’, ‘down’, ‘across’. Children also need opportunities to use terms which are relative to the viewpoint:‘in front of’, ‘behind’, ‘forwards’, ‘backwards’ (‘left’ and ‘right’ to be used later on as ideas develop).Create as many opportunities as possible to explore this language, taking advantage of play in the outdoors to explore sequences of body movements (following obstacle courses, directing a friend, etc.).Shape awareness: developing shape awareness through constructionThrough play – particularly in construction – children have lots of opportunities to explore shapes, the attributes of particular shapes, and to select shapes to fulfil a particular need. Support this exploration by discussing items built by children in terms of how towers are built and why certain shapes are chosen to make a tower, and the space that has been created within an enclosure. Ask:'How did you make that tower?', 'Why were those blocks good ones to use?'

ABB is more challenging because they have twoitems within the same unit of repeat, e.g. red, blue,blue; red, blue, blue… ABBC is more complex because it is longer, with three items, but also includes items which are the same, e.g. red, blue, blue, yellow; red, blue, blue, yellow… AABB may be simpler as there are just two items, both repeated, e.g. red, red, blue, blue; red, red, blue, blue…Children who have only experienced alternating ABC patterns may state that patterns such as ABBC are not patterns, as you cannot have two of the same colour next to each other. This highlights that children need lots of experience of a range of pattern types, so early misconceptions do not form about what makes a pattern. When working on continuing these patterns, children should be encouraged to focus on the unit of repeat, e.g. ‘I see you are making a red, blue, green pattern’. Ensure that children repeat the pattern at least three times andare encouraged to describe and say how they wouldcontinue.Make their own ABB, ABBC patternsAs with the first stages of making an AB pattern, the same range of experiences needs to be provided when the unit of repeat extends. A range of objects can be provided for children to decide what the features of the pattern are going to be. Patterns may include varied items and

Representing spatial relationshipsSmall world play and model building provide lots ofopportunities for children to describe things being ‘in front of’, ‘behind’, ‘on top of’ etc., and to consider objects from different perspectives. Drawing representations of these relationships is a further challenge. These drawings may include a simple representation of a three-dimensional object from a different viewpoint. For example, 'can you draw your construction from above, looking down on it?'Identifying similarities between shapesChildren need opportunities to construct and create things that represent objects in their environment. As they do this, they should notice shape properties of the object that they want to represent; encourage them to think about the appropriateness of the shapes they choose. Examples of this may include representing a ball as a circle, building a train from wooden rectangular blocks, or using a curved block for the elephant’s trunk.Showing awareness of properties of shapeAt this stage, children show increasing intentionality in their selection of shapes, for example using cylinders to represent wheels because they can roll. Draw children’s attention to specific properties by using specific language in everyday situations, while children may use informal language. Properties may include:• curvedness

modes, such as sounds and actions. Ensure that children have opportunities to:• repeat the unit at least three times (big bear,small bear, medium bear; big bear, small bear,medium bear; big bear, small bear, mediumbear). This is to ensure the pattern can besustained over a longer duration• make a specified pattern, e.g. ‘Can you do agreen, yellow, blue pattern?’ This is to ensure thechild can apply their pattern understanding• choose their own rule, e.g. ‘I am going to make abig, small, small pattern.’ This is to ensure thechild can identify pattern features/rules/criteria• choose their own actions or sounds, e.g. clap,stamp, twirl… This is to support children ingeneralising pattern structures.Spotting an error in an ABB patternWhen working with ABB patterns, children also need the opportunities to spot and correct errors. It is easiest to spot an extra item, then a missing item, then items swapped around. When presented with an ABB pattern, children can be encouraged to describe it to make sure it is right. Then, to detect an error, they can track the pattern from the start. To begin with, children may know there is something wrong, but might not be able to say what the error is. They

• numbers of sides and corners (2D) or edges,faces and vertices (3D)• equal sides• parallel sides• angle size, including right angles• 2D shapes as faces of 3D shapes.In play, children show that they are utilising thisknowledge by gathering specific items that are needed for their construction, e.g. making a bed for a teddy and gathering blocks of equal length to make the rectangle; taking time with constructing corners so the shapes fit together to make a right angle. Describing properties of shapeAs children construct, and appear to be utilising, theproperties of shapes, informally ask them about theirconstructions and representations. Children may usecomparisons such as ‘ball-shaped’ or ‘house-shaped’, or start to discriminate between shapes, e.g. a ‘fat’ triangle and a ‘pointy’ triangle, using informal language. With shapes such as triangles and rectangles, ensure that children are used to seeing a range of examples, and the same shape in different orientations, as well as different sizes, colours and materials.Developing an awareness of relationships between shapesAs children become more confident with specific shapes, encourage them to spot

then might take several attempts to correct it, before being able to repair the error in one move.Generalising structures to another context or modeAs children gain experience of symbolising patterns, they develop their experience of pattern structure. As they identify the unit of repeat and express it, they will be able to use this knowledge to create a pattern in a different medium, which follows the same structure. For example, a child might be working with a pattern like this:

You may ask them to describe the pattern, what comes next, what the rule is for their pattern, etc. If a child can do this confidently, they could be asked to recreate the samepattern rule with different objects. ‘Can you use the nature basket to create a pattern with the same rule?’The child would need to recognise they need threedifferent items, one of which is duplicated. They may say they will use a twig instead of the circle, a leaf instead of the square, a conker instead of the triangle, and create this instead:

shapes within shapes. You might talk about small triangles making a bigger triangle or identifying 2D faces of 3D shapes. Pattern blocks are a useful resource, since children can point out the shapes they have used tomake their whole pattern: Also encourage children to predict what will happen when paper is cut or folded, or shapes are combined. Ask: 'What shapes will we see?', 'What will happen if we fold the square• choosing 2D shapes to construct a 3D model, e.g.using triangles and rectangles to make a tent• making decorations by folding and cutting• making 3D shapes using interlocking shapesRecognising attributesIn this first stage, children are able to recognise thespecific attributes of (for example) length – that a stick is long; adults are tall. Their initial recognition may be a descriptor and over-applied (all straight things are long, and if it is not straight it cannot be long; all adults are tall). Children may use gestures or words to start to compare amounts of continuous quantities (length, capacity, weight), pointing to items that are big, tall, full or heavy. Children learn this vocabulary from the adults around them. Adults can seek opportunities to extend and refine conversations about things that are long, tall, high, heavy, full, etc. rather than just ‘big’. At this point children may not be using comparative language such as, 'You

Making a pattern which repeats around a circleAs children become more experienced with the structures of patterns, they can investigate whether patterns can continue indefinitely in a circle. Linking elephants, camels or making a necklace can provoke discussion about this. You then might lead discussions about whether the pattern works and how you can tell. If it doesn't work, can children explain why, and correct it so it does? Circles allow children to adjust the circle size, so they can add or take out

items.

Making a pattern around a border with a fixed number of spacesThis is where the children explore creating a patternaround a given space. In these sorts of activities, children have the additional

are taller than me.'

Comparing amounts of continuous quantitiesChildren can find something that is longer/shorter orheavier/lighter than a given reference item. They willutilise strategies such as direct comparison, e.g. placing objects side by side to determine which is longer. Children compare sizes, lengths, weights and capacities verbally and begin to use more specific terms, such as ‘taller than’, ‘heavier than’, ‘lighter than’, and ‘holds more than’, as well as more general comparative phrases, such as ‘not enough’, ‘too much’, and ‘a lot more’. When comparing lengths directly, children need to ensure that they align the starting points, and compare like-forlike, e.g. straightening skipping ropes before comparinglengths.

challenge of recognising if their pattern can ‘work’ – fit into the given space. It is useful to include indoor and outdoor spaces, e.g. creating an outdoor reading area and defining it with a border of carpet tiles. Children can create a pattern on the carpet tiles with cubes to see if their pattern works, e.g. one coloured cube per tile.Pattern-spotting around usAs children become pattern experts, look for opportunities to spot and study patterns in the environment. These patterns could be in construction, fabric, wrapping paper, wallpaper, etc. Look for opportunities to identify the unit of repeat and explain how it repeats. Consider other patterns, such as growing patterns, extending a cross shape, or spotting ‘staircase’ patterns of numbers going up in ones or twos. Children may make and spot spatial patterns, for example reflecting shapes or reversing an image. Stories and rhymes present a good opportunity to explore a growing pattern, e.g. ‘There was an Old Lady who Swallowed a Fly’, or ‘A Squash and a Squeeze’. Explore representing these diagrammatically – to see a staircase pattern, for example.

Year 1National Curriculum Objectives PIXL PLC key skills (Milestones) MPS expectations

Number – number and place value Pupils should be taught to: count to and across 100, forwards

and backwards, beginning with 0 or 1, or from any given number

count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens

given a number, identify one more and one less

identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least

read and write numbers from 1 to 20 in numerals and words.

Number and Place valuea. Can read numbers to 10 and extend to 20 in numeralsb. Can count accurately objects up to 20c. Can count independently numbers up to 20 forwards and backwardsd. Can count out a given number of objects up to 10 from a larger groupe. Can say 1 more than a number up to 10 and extend to 20f. Can say 1 less than a number up to 10 and extend to 20g. Can say 1 more than a number up to 100h. Can say 1 less than a number up to 100i. Can represent a number up to 10

To use manipulatives to support learning eg. Numicon, Base 10To use age appropriate sentence stems to develop oracy…BAD verbs: All should be used throughout mathematics teaching

NCETM materials:Spot the mistake:5,6,8,9What is wrong with this sequence of numbers?True or False?I start at 2 and count in twos. I will say 9What comes next?10+1 = 1111+1= 12

using practical equipment such as multi link cubesj. Can identify and represent a number using practical objects and pictorial representations including a number linek. Can solve simple problems involving place value

12+1 = 13Do, then explainLook at the objects. (in a collection). Are there more of one type than another? How can you find out?

Number – addition and subtractionPupils should be taught to: read, write and interpret

mathematical statements involving addition (+), subtraction

(–) and equals (=) signs represent and use number bonds and

related subtraction facts within 20 add and subtract one-digit and two-

digit numbers to 20, including zero solve one-step problems that involve

addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = – 9.

Number - addition, subtraction (mental and written)a. Can use number bonds to 10 and all the numbers in between e.g. 5 + 2 = 7b. Can use subtraction facts to 10 and all the numbers in between e.g. 4 - 3 = 1 c. Can use addition number bonds within 20d. Can use subtraction facts within 20e. Can read and understand mathematical statements that include +, - and = signsf. Can add two one-digit numbers using concrete objects or pictorial representationsg. Can subtract two one-digit numbers using concrete objects or pictorial representations e.g. 7 - 3 = 4h. Can add a two-digit number and a one-digit number within 20i. Can subtract a one-digit number from a two-digit numbers using concrete objects or pictorial representations e.g. 13 - 6 = 7j. Can solve simple problems involving addition using concrete objectsk. Can solve simple problems involving subtraction using concrete objects

NCETM materials:Continue the pattern10 + 8 = 1811 + 7 = 18Can you make up a similar pattern for the number 17?How would this pattern look if it included subtraction?Missing numbers9 + = 1010 - = 9What number goes in the missing box?Working backwardsThrough practical games on number tracks and lines ask questions such as “where have you landed?” and “what numbers would you need to throw to land on other given numbers?”What do you notice?11 – 1 = 1011 – 10 = 1Can you make up some other number sentences like this involving 3 different numbers?Fact familiesWhich four number sentences link these numbers? 12, 15, 3What else do you know?If you know this:

12 – 9 = 3what other facts do you know?Missing symbolsWrite the missing symbols ( + - =) in these number sentences:Convince meIn my head I have two odd numbers with a difference of 2. What could they be?Making an estimatePick (from a selection of number sentences) the ones where the answer is 8 or 9.Is it true that?Is it true that 3+4 = 4 + 3?

Number – multiplication and divisionPupils should be taught to: 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.

Number - multiplication and division (mental and written)a. Can double numbers up to 10 using practical objects and extend to 20b. Can halve numbers up to 10 using practical objects and extend to 20c. Can count in 2s to find out how many dots/cubes etc there are in an array or patternd. Can count in 10s to find out how many dots/cubes etc there are in an array or patterne. Can count in 5s to find out how many dots/cubes etc there are in an array or patternf. Can solve simple problems involving doubling and halving/sharing using concrete objects

NCETM materials:Making linksIf one teddy has two apples, how many apples will three teddies have?Here are 10 lego people If 2 people fit into the train carriage, how many carriages do we need?PracticalIf we put two pencils in each pencil pot how many pencils will we need?Spot the mistakeUse a puppet to count but make some deliberate mistakes.e.g. 2 4 5 610 9 8 6See if the pupils can spot the deliberate mistake and correct the puppet

Number – fractionsPupils should be taught to: recognise, find and name a half as

Number - fractions (including decimals and percentages)a. Can understand that two halves make

NCETM materials:What do you notice?

one of two equal parts of an object, shape or quantity

recognise, find and name a quarter as one of four equal parts of an object, shape or quantity.

one whole in a practical contextb. Can find 1/2 of a shape, object or group of objects in a practical contextc. Can find 1/2 of a quantityd. Can understand that 1/4 represents one of four equal parts of a wholee. Can find 1/4 of a shape or objectf. Can find 1/4 of a quantity

Choose a number of counters. Place them onto 2 plates so that there is the same number on each half. When can you do this and when can’t you?What do you notice?True or false?Sharing 8 apples between 4 children means each child has 1 apple.

MeasurementPupils should be taught to: compare, describe and solve

practical problems for: lengths and heights [for example, long/short, longer/shorter, tall/short,double/half] mass/weight [for example,

heavy/light, heavier than, lighter than]

capacity and volume [for example, full/empty, more than, less than, half, half full, quarter]

time [for example, quicker, slower, earlier, later]

measure and begin to record the following:

lengths and heights mass/weight capacity and volume time (hours, minutes, seconds) recognise and know the value of

different denominations of coins and notes

sequence events in chronological order using language [for example, before and after, next, first, today,

Measuresa. Can use the language related to length and height such as long, short, longer, shorter, tall, short, double, halveb. Can use the language related to mass and weight such as heavy, light, heavier than, lighter thanc. Can use the language related to capacity and volume e.g. Full, empty, more than, less than, half, half full, quarterd. Can use the language related to time such as quicker, slower, earlier, latere. Can solve simple problems involving comparing measures in a practical contextf. Can measure and begin to record length and height using non standard units and extend to standard unitsg. Can measure and begin to record mass and weight using non standard units and extend to standard unitsh. Can measure and begin to record capacity and volume using non standard units and extend to standard unitsi. Can recognise the value of different coins and notes

NCETM materials:Top tipsHow do you know that this (object) is heavier / longer / taller than this one?Explain how you know.Explain thinkingAsk pupils to reason and make statements about to the order of daily routines in school e.g. daily timetablee.g. we go to PE after we go to lunch. Is this true or false?What do we do before break time? etc.Application(Can be practical)Which two pieces of string are the same length as this book?PossibilitiesElla has two silver coins.How much money might she have?

yesterday, tomorrow, morning, afternoon and evening]

recognise and use language relating to dates, including days of the week, weeks, months and years

tell the time to the hour and half past the hour and draw the hands on a clock face to show these times.

j. Can tell the time on an analogue clock using o' clock and half past

Geometry – properties of shapesPupils should be taught to: recognise and name common 2-D

and 3-D shapes, including: 2-D shapes [for example, rectangles (including squares), circles and triangles]3-D shapes [for example, cuboids (including cubes), pyramids and spheres].

Geometry - properties of shapea. Can recognise and name 2D shapes such as squares, rectangles, circles and trianglesb. Can recognise and name 3D shapes such as cuboids, cubes and spheres

NCETM materials:What’s the same, what’s different?Find a rectangle and a triangle in this set of shapes. Tell me one thing that’s the same about them. Tell me one thing that is different about them.True or false?All 2-D shapes have at least 4 sidesOther possibilitiesCan you find shapes that can go with the set with this label?“Have straight sides”

Geometry – position and directionPupils should be taught to: describe position, direction and

movement, including whole, half, quarter and three quarter turns.

Geometry - position and directiona. Can describe position, direction and movement, including whole, half, quarter and three-quarter turns

NCETM materials:Working backwardsThe shape below was turned three quarter of a full turn and ended up looking like this.

What did it look like when it started? (practical)

Year 2National Curriculum Objectives PIXL PLC key skills (Milestones) MPS expectationsNumber – number and place valuePupils should be taught to: count in steps of 2, 3, and 5 from 0,

and in tens from any number, forward and backward

recognise the place value of each digit in a two-digit number (tens, ones)

identify, represent and estimate numbers using different representations, including the number line

compare and order numbers from 0 up to 100; use <, > and = signs

read and write numbers to at least 100 in numerals and in words

use place value and number facts to solve problems.

Number and place valuea. Can understand the value of 1s and 10s in any two - digit numberb. Can say 1 more and 1 less than a number up to 100c. Can partition one-digit numbers e.g. 7 = 4 + 3 or 5 + 2 or 6 + 1d. Can partition two-digit numbers in different combinations of 10s and 1s e.g. 43 = 40 + 3 or 30 + 13 or 20 + 23 or 10 + 33e. Can identify and represent two-digit numbers using different representations such as number lines or base ten apparatus etc.f. Can estimate where a two-digit number would be placed on a 0 - 100 number line where tens divisions are markedg. Can read and write numbers to at least 100 in numerals including using 0 as a place holder e.g. 109h. Can order more than two numbers using a blank number linei. Can solve problems using place value

To use manipulatives to support learning eg. Numicon, Base 10To use age appropriate sentence stems to develop oracy…BAD verbs: All should be used throughout mathematics teaching

NCETM materials:Spot the mistake:45,40,35,25What is wrong with this sequence of numbers?True or False?I start at 3 and count in threes. I will say 13?What comes next?41+5=4646+5=5151+5=56Do, then explain37 13 73 33 3If you wrote these numbers in order starting with the smallest, which number would be third?Explain how you ordered the numbers.

and number facts Do, then explain Show the value of the digit 2 in these numbers?32 27 92Explain how you know.Make up an exampleCreate numbers where the units digit is one less than the tens digit. What is the largest/smallest number?

Number – addition and subtraction Pupils should be taught to: 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

recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100

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 show that addition of two numbers

can be done in any order (commutative) and subtraction of one number from another cannot

recognise and use the inverse relationship between addition and

Number - addition, subtraction (mental and written)a. Can recall addition facts to 10 and 20 and all the numbers in between fluently e.g. 15 + 2 = 17b. Can recall subtraction facts to 10 and 20 and all the numbers in between fluently e.g. 14 - 3 = 11 c. Can use addition number bonds to 10 and 20 to derive related facts to 100 using multiples of 10 e.g. 70 + 30 = 100d. Can use subtraction facts to 10 and 20 to derive related facts to 100 using multiples of 10 e.g. 100 - 30 = 70e. Can add a two-digit number and 1s using concrete objects or pictorial representationsf. Can subtract a two-digit number and 1s using concrete objects or pictorial representationsg. Can add a two-digit number and 10s using concrete objects or pictorial representationsh. Can subtract a two-digit number and 10s using concrete objects or pictorial representationsi. Can add 2 two-digit numbers using concrete objects or pictorial

NCETM materials:Continue the pattern90 = 100 – 1080 = 100 – 20Can you make up a similar pattern starting with the numbers 74, 26 and 100?Missing numbers91 + = 100100 - = 89What number goes in the missing box?True or false? Are these number sentences true or false?73 + 40 = 11398 – 18 = 7046 + 77 = 12392 – 67 = 35Give your reasons.Hard and easy questionsWhich questions are easy / hard?23 + 10 =93 + 10 =54 + 9 =54 + 1 =Explain why you think the hard questions are hard?If you know this:

subtraction and use this to check calculations and solve missing number problems.

representationsj. Can subtract 2 two-digit numbers using concrete objects or pictorial representations where no regrouping is required e.g. 74 - 32k. Can subtract 2 two-digit numbers using concrete objects or pictorial representations where regrouping is required e.g. 63 - 36 = l. Can solve problems involving addition using concrete objects and pictorial representations involving numbers, quantities and measuresm. Can solve problems involving subtraction using concrete objects and pictorial representations involving numbers, quantities and measures

87 = 100 – 13what other facts do you know?Convince meWhat digits could go in the boxes?7 - 2 = 46Try to find all of the possible answers.How do you know you have got them all?Always, sometimes, neverIs it always, sometimes or never true that if you add three numbers less than 10 the answer will be an odd number

Number – multiplication and division Pupils should be taught to: recall and use multiplication and

division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers

calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs

show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot

solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication

Number - multiplication and division (mental and written)a. Can use the x, ÷ and = signs to write mathematical statementsb. Can recall and use multiplication facts for the 2 times tablec. Can recall and use division facts for the 2 times tabled. Can recall and use multiplication facts for the 5 times tablee. Can recall and use division facts for the 5 times tablef. Can recall and use multiplication facts for the 10 times tableg. Can recall and use division facts for the 10 times tableh. Can recognise and explain odd & even numbers within the context of the patterns in the 2, 5 and 10 multiplication tables

NCETM materials:Missing numbers10 = 5 x What number could be written in the box?Making linksI have 30p in my pocket in 5p coins. How many coins do I have?Making linksWrite the multiplication number sentences to describe this arrayX X XX X XWhat do you notice?Write the division sentences.Prove ItWhich four number sentences link these numbers? 3, 5, 15?True or false?

and division facts, including problems in contexts.

i. Can calculate mathematical statements for multiplication using the 2, 5 and 10 times tablesj. Can calculate mathematical statements for division using the 2, 5 and 10 times tablesk. Can solve problems involving multiplication using concrete objects or pictorial representations l. Can solve problems involving division using concrete objects and pictorial representations

When you count up in tens starting at 5 there will always be 5 units.Use the inverseUse the inverse to check if the following calculations are correct:12 ÷ 3 = 43 x 5 = 14

Number – fractionsPupils should be taught to: recognise, find, name and write

fractions 1/3, ¼, 2/4 and ¾ of a length, shape, set of objects or quantity

write simple fractions for example, ½ of 6 = 3 and recognise the equivalence of 2/4 and ½

Number - fractions (including decimals and percentages)a. Can understand that the bottom number (denominator) denotes the number of equal parts the whole is divided intob. Can understand that the top number in a fraction (numerator) denotes the number of equal parts representedc. Can understand 1/2 represents one of two equal parts of a wholed. Can find 1/2 of a shape or set of objectse. Can understand that 1/4 represents one of four equal parts of a wholef. Can find 1/4 of a shape or set of objectsg. Can understand 1/3 represents one of three equal parts of one wholeh. Can find 1/3 of a shape and set of objectsi. Can understand 2/4 represents two of four equal parts of a wholej. Can find 2/4 of a shape or set of objects

NCETM materials:Spot the mistake7, 7 ½ , 8, 9, 108 ½, 8, 7, 6 ½, … and correct itWhat comes next?5 ½, 6 ½ , 7 ½ , …., ….9 ½, 9, 8 ½, ……, …..What do you notice?¼ of 4 = 1¼ of 8 = 2¼ of 12 = 3Continue the patternWhat do you notice?True or false?Half of 20cm = 5cm¾ of 12cm = 9cmOdd one out. Which is the odd one out in this trio:½ 2/4 ¼ Why?What do you notice?Find ½ of 8.Find 2/4 of 8

k. Can recognise the equivalence between 2/4 and 1/2l. Can understand that 3/4 represents three of four equal parts of a wholem. Can find 3/4 of a shape or set of objectsn. Can write a fraction represented in a shape or set of objects (1/2, 1/3, 1/4, 2/4, 3/4)o. Can solve and write simple fractions such as 1/2 of 6 = 3

What do you notice?OrderingPut these fractions in the correct order, starting with the smallest.½ ¼ 1/3

MeasurementPupils should be taught to: 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

compare and order lengths, mass, volume/capacity and record the results using >, < and =

recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value

find different combinations of coins that equal the same amounts of money

solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change

compare and sequence intervals of time

tell and write the time to five

Measuresa. Can choose and use appropriate standard units to measure length and height (m/cm using rulers, metre sticks, tape measure etc.)b. Can choose and use appropriate standard units to measure mass (kg/g using scales, balance scales etc.)c. Can choose and use appropriate standard units to measure temperature (°C using thermometers.)d. Can choose and use appropriate standard units to measure capacity (l/ml using different measuring vessels.)e. Can compare and order two or more different measurements (length, mass, temperature or capacity/volume)f. Can use the symbol p for pence and £ for pounds when combining amounts to make a particular value e.g. 20p + 5p = 25p, £2 + £1 = £3g. Can solve simple problems in a practical context involving addition of money of the same unith. Can solve simple problems in a practical context involving subtraction

NCETM materials:UndoingThe film finishes two hours after it starts. It finishes at 4.30. What time did it start?Draw the clock at the start and the finish of the film.Explain thinkingThe time is 3:15pm.Kate says that in two hours she will be at her football game which starts at 4:15. Is Kate right? Explain why.PossibilitiesHow many different ways can you make 63p using only 20p, 10p and 1p coins?

minutes, including quarter past/to the hour and draw the hands on a clock face to show these times

know the number of minutes in an hour and the number of hours in a day.

of money of the same unit, including giving change including giving changei. Can tell the time on an analogue clock using o' clock, half past, quarter to and quarter pastj. Can tell the time on an analogue clock to five minutes

Geometry – properties of shapesPupils should be taught to: identify and describe the properties

of 2-D shapes, including the number of sides and line symmetry in a vertical line

identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces

identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]

compare and sort common 2-D and 3-D shapes and everyday objects.

Geometry - properties of shapea. Can identify and describe 2D shapes using knowledge of properties including number of sides (including in different orientations)b. Can identify a line of symmetry in 2D shapes c. Can identify and describe 3D shapes using knowledge of properties including number of faces, edges and verticesd. Can compare and sort 2D & 3D shapes including everyday objects using knowledge of properties

NCETM materials:VisualisingIn your head picture a rectangle that is twice as long as it is wide.What could its measurements be?Always, sometimes, neverIs it always, sometimes or nerver true that when you fold a square in half you get a rectangle.Other possibilitiesCan you find shapes that can go with the set with this label?

“Have straight sides and all sides are the same length”

Geometry – position and directionPupils should be taught to: order and arrange combinations of

mathematical objects in patterns and sequences

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 anticlockwise).

Geometry - position and directiona. Can describe position, direction and movement in terms of right angles for quarter, half and three-quarter turns (clockwise and anti-clockwise)

NCETM materials:Working backwardsIf I face forwards and turn three quarter turns clockwise then a quarter turn anti-clockwise describe my finishing position.What comes next?

Explain why

StatisticsPupils should be taught to:

Statisticsa. Can interpret pictograms where one

NCETM materials:True or false? (Looking at a simple

interpret and construct simple pictograms, tally charts, block diagrams and simple tables

ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity

ask and answer questions about totalling and comparing categorical data.

symbol represents one or more than one (1s, 2s, 5s, 10s)b. Can interpret a block diagram where the scale goes up in ones, fives or tensc. Can interpret tally charts d. Can interpret tablese. Can solve one step problems such as adding amounts e.g what is the total sum of money collected across a week?f. Can answer questions about totalling data e.g. How many people were asked altogether?g. Can answer questions about comparing data e.g. How many more people liked ...than ...?

pictogram) “More people travel to work in a car than on a bicycle”.Is this true or false?Convince me.Make up your own ‘true/false’ statement about the pictogramWhat’s the same, what’s different? Pupils identify similarities and differences between different representations and explain them to each other.Create a questions Pupils ask (and answer) questions about different statistical representations using key vocabulary relevant to the objectives.

Year 3National Curriculum Objectives PIXL PLC key skills (Milestones) MPS expectationsNumber – number and place valuePupils should be taught to: count from 0 in multiples of 4, 8, 50

and 100; find 10 or 100 more or less than a given number

recognise the place value of each digit in a three-digit number (hundreds, tens, ones)

compare and order numbers up to 1000

identify, represent and estimate

Number and place valuea. Can read and write numbers to at least 100 and extend to 1000 in numerals and wordsb. Can find 10 more or 10 less than a given number up to 100 and extend to 1000c. Can find 100 more or 100 less than a given number up to 1000d. Can understand the place value of each digit in a two-digit and three-digit

To use manipulatives to support learning eg. Numicon, Base 10To use age appropriate sentence stems to develop oracy…BAD verbs: All should be used throughout mathematics teaching

NCETM materials: Spot the mistake:50,100,115,200What is wrong with this sequence of

numbers using different representations

read and write numbers up to 1000 in numerals and in words

solve number problems and practical problems involving these ideas.

numbere. Can represent two-digit and three-digit numbers using different representations including the number line, base 10 apparatus etc f. Can compare and order numbers up to 100 and extend to 1000 sometimes using the <, > and = signs correctlyg. Can solve problems using place value and number facts

numbers?True or False?38 is a multiple of 8?What comes next?936-10= 926926 -10 = 916916- 10= 906Do, then explain835 535 538 388 508If you wrote these numbers in order starting with the smallest, which number would be third?Explain how you ordered the numbers.Do, then explainShow the3 value of the digit 3 in these numbers?341 503 937Explain how you know.Make up an example Create numbers where the digit sum is three. Eg 120, 300, 210What is the largest/smallest number?

Number – addition and subtractionPupils should be taught to: 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 with up to

three digits, using formal written methods of columnar addition and subtraction

estimate the answer to a calculation and use inverse operations to check answers

solve problems, including missing

Number - addition, subtraction (mental and written)a. Can fluently recall all addition and subtraction facts within 20b. Can add three single digit numbers mentallyc. Can add a two-digit and extend to three-digit number and ones mentallyd. Can add a two digit and extend to three-digit number and tens mentallye. Can subtract three single digit numbers mentallyf. Can subtract a two digit and extend to three-digit number and ones mentallyg. Can subtract a two digit and extend

NCETM materials:True or false? Are these number sentences true or false?597 + 7 = 614804 – 70 = 744768 + 140 = 908Give your reasons.Hard and easy questionsWhich questions are easy / hard?323 + 10 =393 + 10 =454 - 100 =954 - 120 =Explain why you think the hard

number problems, using number facts, place value, and more complex addition and subtraction.

to three-digit number and tens mentallyh. Can add two-digit and extend to three-digit numbers using the expanded column method (not bridging ten)i. Can add two-digit and extend to three-digit numbers using the expanded column method (bridging ten)j. Can subtract two-digit numbers using the expanded column method (not bridging ten)k. Can subtract two-digit numbers using the expanded column method (bridging ten)l. Can use knowledge of inverse operations to check answers to addition and subtraction calculations.m. Can solve problems including missing number problems involving additionn. Can solve problems including missing number problems involving subtraction

questions are hard?Convince me + +

The total is 201Each missing digit is either a 9 or a 1. Write in the missing digits.Is there only one way of doing this or lots of ways?Making an estimateWhich of these number sentences have the answer that is between 50 and 60174 - 119 333 – 276932 - 871Always, sometimes, neverIs it always, sometimes or never true that if you subtract a multiple of 10 from any number the units digit of that number stays the same.Is it always, sometimes or never true that when you add two numbers together you will get an even number

Number – multiplication and divisionPupils should be taught to: recall and use multiplication and

division facts for the 3, 4 and 8 multiplication tables

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

Number - multiplication and division (mental and written)a. Can recall and use multiplication and division facts for the 2, 5 and 10 times tablesb. Can recall and use multiplication and division facts for the 3 times tablec. Can write mathematical statements for known multiplication and division facts using x, ÷ and =d. Can multiply two-digit by one-digit numbers using informal methods such as arrays, base 10 apparatus etc

NCETM materials:Missing numbers24 = xWhich pairs of numbers could be written in the boxes?Making links Cards come in packs of 4. How many packs do I need to buy to get 32 cards?Making links4 × 6 = 24True or false?All the numbers in the two times table

methods 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.

e. Can multiply two digit by one digit numbers using partitioning and known facts (e.g. 24 x 3 = 3 x 4 = 12 and 3 x 20 = 60. 60 + 12 = 72)f. Can divide two-digit by one-digit numbers using informal methods such as known facts, arrays and number lines (repeated subtraction)g. Can solve missing number problems involving multiplication and divisionh. Can solve problems involving multiplication and division

are even.There are no numbers in the three times table that are also in the two times table.Use the inverse Use the inverse to check if the following calculations are correct23 x 4 = 82117 ÷ 9 = 14

Number – fractionsPupils should be taught to: count up and down in tenths;

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 write fractions of a discrete set of objects: unit fractions and nonunit fractions with small denominators

recognise and use fractions as numbers: unit fractions and non-unit fractions with small denominators

recognise and show, using diagrams, equivalent fractions with small denominators

add and subtract fractions with the same denominator within one whole [for example, 5/7 + 1/7 = 6/7 ]

compare and order unit fractions, and fractions with the same denominators

solve problems that involve all of the above.

Number - fractions (including decimals and percentages)a. Can understand the relationship between fractions, division and multiplication factsb. Can understand that the denominator denotes the number of equal parts the whole is divided intoc. Can understand that the numerator denotes the number of equal parts representedd. Can place 1/4, 1/2, 3/4 1 1/4, 1 1/2, 1 3/4 etc on a number linee. Can find 1/2, 1/4 or 3/4 of a shape or set of objectsf. Can place 1/3, 1 1/3, 1 2/3 , 2, 21/3 etc on a number lineg. Can understand 1/3 represents one of three equal parts of one wholeh. Can find 1/3 of a shape and set of objectsi. Can recognise that tenths arise from dividing an object into ten equal partsj. Can find one tenth of a shape or set of objects by dividing by 10

NCETM materials:Spot the mistakesix tenths, seven tenths, eight tenths, nine tenths, eleven tenths … and correct it.What comes next?6/10, 7/10, 8/10, ….., ….12/10, 11/10, ….., ….., …..What about 1/10 of 20? Use this to work out 2/10 of 20, etc.True or false?2/10 of 20cm = 2cm4/10 of 40cm = 4cm3/5 of 20cm = 12cmGive an example of a fraction that is less than a half. Now another example that no one else will think of.Explain how you know the fraction is less than a half. (draw an image)Ben put these fractions in order starting with the smallest. Are they in the correct order?One fifth, one seventh, one sixth

k. Can recognise and show using diagrams, counters or paper folding equivalent fractions with small denominators e.g 1/3 and 2/6l. Can solve problems involving fractions

Odd one out.Which is the odd one out in each of these trios½ 3/6 5/83/9 2/6 4/9Why?What do you notice?1/10 + 9/10 = 12/10 + 8/10 = 13/10 + 7/10 = 1Continue the patternCan you make up a similar pattern for eighths?The answer is 5/10, what is the question? (involving fractions / operations)

MeasurementPupils should be taught to: measure, compare, add and subtract:

lengths (m/cm/mm); mass (kg/g); volume/capacity (l/ml)

measure the perimeter of simple 2-D shapes

add and subtract amounts of money to give change, using both £ and p in practical contexts

tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks

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

Measuresa. Can understand the relationship between mm, cm, m and g, kg and ml, l.b. Can compare and order lengths using mm, cm and mc. Can measure lengths using appropriate measuring equipment and record using the correct unitd. Can compare and order mass using g and kge. Can measure mass using appropriate measuring equipment and record using the correct unitf. Can compare and order capacity using ml and lg. Can measure capacities using appropriate measuring equipment and record using the correct unith. Can calculate the value of the increment on a simple scale given some information e.g 0 to 100 in four

NCETM materials:Top TipsPut these measurements in order starting with the largest.Half a litreQuarter of a litre300 mlExplain your thinkingWrite more statements (You may choose to consider this practically)If there are 630ml of water in a jug. How much water do you need to add to end up with a litre of water?What if there was 450 ml to start with?Make up some more questions like thisTesting conditionsA square has sides of a whole number of centimetres.Which of the following measurements

know the number of seconds in a minute and the number of days in each month, year and leap year

compare durations of events [for example to calculate the time taken by particular events or tasks].

increments equals 25i. Can add amounts of money within £1 and extend beyond £1j. Can subtract an amount of money within £1 and extend to beyond £1k. Can combine amounts and calculate changel. Can tell the time to the nearest minutem. Can tell the time on a 24 hour digital clockn. Can calculate how long an event takes given the start and finish time e.g bus journeyo. Can calculate start/finish time given start/finish time e.g time a film finishes given start time

could represent its perimeter?8cm 18cm 24cm 25cmWorking backwardsTom’s bus journeytakes half an hour. He arrives at his destination at 9:25. At what time did his bus leave?9:05 8:55 8:45

Geometry – properties of shapesPupils should be taught to: draw 2-D shapes and make 3-D

shapes using modelling materials; recognise 3-D

shapes in different orientations and describe them

recognise angles as a property of shape or a description of a turn

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 horizontal and vertical lines and pairs of perpendicular and parallel lines.

Geometry - properties of shapea. Can recognise and describe the properties of 2D and 3D shapes using appropriate vocabulary (including in different orientations)b. Can compare and sort 2D and 3D shapes according to their geometric propertiesc. Can identify horizontal lines of symmetry in 2D shapesd. Can identify right anglese. Can identify whether angles are greater or less than a right anglef. Can recognise angles as a property of a shape e.g right angles in a squareg. Can solve problems and reason about shape

NCETM materials:Convince meWhich capital letters have perpendicular and / or parallel lines?Convince me.Always, sometimes, neverIs it always, sometimes or never that all sides of a hexagon are the same length.Other possibilitiesCan you find shapes that can go with the set with this label?“Have straight sides that are different lengths.”VisualisingI am thinking of a 3-dimensional shape which has faces that are triangles and squares. What could my shape be?

StatisticsPupils should be taught to:

Statisticsa. Can interpret pictograms where one

NCETM materials:True or false? (Looking at a bar chart)

interpret and present data using bar charts, pictograms and tables

solve one-step and two-step questions [for example, ‘How many more?’ and ‘How many fewer?’] using information presented in scaled bar charts and pictograms and tables.

symbol represents more than oneb. Can interpret bar charts where the scale goes up in twos or fives or tensc. Can understand how to present data in a simple pictogram, bar chart or table in an appropriate contextd. Can respond to questions such as 'How many more?' and 'How many fewer?'e. Can solve one step problems such as adding amounts e.g what is the total sum of money collected across a week?f. Can solve two step problems e.g how much more do the class need to collect to reach their total?

“Twice as many people like strawberry than lime”.Is this true or false?Convince me.Make up your own ‘true/false’ statement about the bar chart.What’s the same, what’s different?Pupils identify similarities and differences between different representations and explain them to each otherCreate a questions Pupils ask (and answer) questions about different statistical representations using key vocabulary relevant to the objectives.(see above)

Year 4National Curriculum Objectives PIXL PLC key skills (Milestones) MPS expectationsNumber – number and place value Number and place value To use manipulatives to support

Pupils should be taught to count in multiples of 6, 7, 9, 25 and

1000 find 1000 more or less than a given

number count backwards through zero to

include negative numbers recognise the place value of each

digit in a four-digit number (thousands, hundreds, tens, and ones)

order and compare numbers beyond 1000

identify, represent and estimate numbers using different representations

round any number to the nearest 10, 100 or 1000

solve number and practical problems that involve all of the above and with increasingly large positive numbers

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.

a. Can find 1000 more or 1000 less than a given number b. Can count backwards through zero in steps that are familiar from the previous year e.g.1, 2, 5, 10, 3c. Can understand the place value of each digit in a three-digit and four-digit numberd. Can compare and order numbers beyond 1000 e. Can represent numbers up to and beyond 1000 using different representations, including measuring equipmentf. Can round any number to the nearest 10, 100 or 1000, using the context of measuresg. Can solve problems using place value and number facts

learning eg. Numicon, Base 10To use age appropriate sentence stems to develop oracy…BAD verbs: All should be used throughout mathematics teaching

NCETM materials:Spot the mistake:950, 975,1000,1250What is wrong with this sequence of numbers?True or False?324 is a multiple of 9?Do, then explain5035 5053 5350 5530 5503If you wrote these numbers in order starting with the largest, which number would be third?Explain how you ordered the numbers.Make up an example Create four digit numbers where the digit sum is four and the tens digit is one. Eg 1210, 2110, 3010What is the largest/smallest number?Possible answersA number rounded to the nearest ten is 540. What is the smallest possible number it could be?What do you notice?Round 296 to the nearest 10. Round it to the nearest 100. What do you notice? Can you suggest other numbers like this?

Number – addition and subtractionPupils should be taught to: add and subtract numbers with up to

4 digits using the formal written

Number - addition, subtraction (mental and written)a. Can add two digit and extend to three digit numbers using the formal column

NCETM materials:True or false? Are these number sentences true or

methods of columnar addition and subtraction where appropriate

estimate and use inverse operations to check answers to a calculation

solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

method b. Can subtract two digit and extend to three-digit numbers using the formal column methodc. Can choose whether to add or subtract mentally or using a formal methodd. Can use knowledge of inverse operations to check answers to addition and subtraction calculations.e. Can solve two-step problems involving addition and subtraction, deciding which operation to use

false?6.7 + 0.4 = 6.118.1 – 0.9 = 7.2Give your reasons.Hard and easy questionsWhich questions are easy / hard?13323 - 70 =12893 + 300 =19354 - 500 =19954 + 100 =Explain why you think the hard questions are hard?Always, sometimes, neverIs it always sometimes or never true that the difference between two odd numbers is odd.

Number – multiplication and divisionPupils should be taught to: recall multiplication and division

facts for multiplication tables up to 12 × 12

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

recognise and use factor pairs and commutativity in mental calculations

multiply two-digit and three-digit numbers by a one-digit number using formal written layout

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

Number - multiplication and division (mental and written)a. Can recall and use multiplication and division facts for the 3, 4 & 8 times tablesb. Can recall and use multiplication and division facts for all the times table (learning 6, 12, 9, 11 and 7)c. Can multiply and divide mentally using derived facts such as 600 ÷ 3 = 200 because 2 x 3 = 6 or the associative law (2 x 6 x 5 = 10 x 6 = 60)d. Can multiply two digit and three digit by one digit numbers using short multiplicatione. Can divide two-digit by one-digit numbers using informal methods such as known facts, arrays and number lines (repeated subtraction)f. Can begin to divide three digit by one digit numbers with exact answers using short division

NCETM materials:Missing numbers72 = x Which pairs of numbers could be written in the boxes?Making links Eggs are bought in boxes of 12. I need 140 eggs; how many boxes will I need to buy?Use a fact63 ÷ 9 = 7Use this fact to work out126 ÷ 9 =252 ÷ 7 =Making linksHow can you use factor pairs to solve this calculation?13 x 12(13 x 3 x 4, 13 x 3 x 2 x 2, 13 x 2 x 6)Prove ItWhat goes in the missing box?6 x 4 = 512

such as n objects are connected to m objects.

g. Can solve problems involving multiplication and division

Number – fractions (including decimals)Pupils should be taught to: recognise and show, using diagrams,

families of common equivalent fractions

count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.

solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a wholenumber

add and subtract fractions with the same denominator

recognise and write decimal equivalents of any number of tenths or hundredths

recognise and write decimal equivalents to ¼, ½, ¾

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

round decimals with one decimal place to the nearest whole number

compare numbers with the same number of decimal places up to two decimal places

solve simple measure and money

Number - fractions (including decimals and percentages)a. Can order fractions, numbers and measures on a number line and recognise simple equivalenceb. Can show equivalent fractions using diagrams such as a fraction wall or a grid of squaresc. Can count in hundredthsd. Can place common fractions on a number line e.g. 1/4s, 1/2s, 1/3s,1/10s, 1/5se. Can find increasingly harder fractions of a set of objects e.g. 1/3, 1/6, 1/8 and non-unit fractions where the answer is a whole numberf. Can add fractions with the same denonimatorg. Can subtract fractions with the same denominatorh. Can recognise and write the decimal equivalent of any number of tenths or hundredthsi. Can recognise and write the decimal equivalent to 1/4, 1/2 and 3/4, showing it on a number linej. Can find the effect of dividing one and two digit numbers by 10 and 100, giving the answer in ones, tenths and hundredthsk. Can round numbers with one decimal place to the nearest whole number, using a number linel. Can compare numbers with the same number of decimal places, up to two

NCETM materials:Spot the mistakesixty tenths, seventy tenths, eighty tenths, ninety tenths, twenty tenths … and correct it.What comes next?83/100, 82/100, 81/100, ….., ….., …..31/100, 41/100, 51/100, ….., …..,What do you notice?1/10 of 100 = 101/100 of 100 = 12/10 of 100 = 202/100 of 100 = 2How can you use this to work out 6/10 of 200?6/100 of 200?Give an example of a fraction that is more than a half but less than a whole. Now another example that no one else will think of.Explain how you know the fraction is more than a half but less than a whole. (draw an image)Do, then explainCircle each decimal which when rounded to the nearest whole number is 5. 5.3 5.7 5.2 5.8Explain your reasoning Top tipsExplain how to round numbers to one decimal place?Odd one out. Which is the odd one out in each of

problems involving fractions and decimals to two decimal places.

decimal placesm. Can solve simple money/fraction problems up to two decimal places

these trio s¾ 9/12 4/69/12 10/15 2/3Why?What do you notice?Find 4/6 of 24Find 2/3 of 24What do you notice?Can you write any other similar statements?

MeasurementPupils should be taught to: Convert between different units of

measure [for example, kilometre to metre; hour to minute]

measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres

find the area of rectilinear shapes by counting squares

estimate, compare and calculate different measures, including money in pounds and pence

read, write and convert time between analogue and digital 12- and 24-hour clocks

solve problems involving converting from hours to minutes; minutes to seconds; years to months; weeks to days.

Measuresa. Can convert between metric units of lengthb. Can convert between metric units of massc. Can convert between metric units of capacityd. Can convert between units of timee. Can read, write and convert between analogue and digital 12 and 24 hour clocks f. Can estimate lengthg. Can estimate massh. Can estimate capacityi. Can measure and calculate the perimeter of rectangular shapes, including squaresj. Can find the area by counting squaresk. Can solve problems comparing and converting different units of measure, including money and time

NCETM materials:Top TipsPut these amounts in order starting with the largest.Half of three litresQuarter of two litres300 mlExplain your thinkingPosition the symbolsPlace the correct symbols between the measurements > or <£23.61 2326p 2623pExplain your thinkingTesting conditionsIf the width of a rectangle is 3 metres less than the length and the perimeter is between 20 and 30 metres, what could the dimensions of the rectangle lobe? Convince me.

Geometry – properties of shapesPupils should be taught to: compare and classify geometric

shapes, including quadrilaterals and triangles, based on their properties and sizes

Geometry - properties of shapea.Can compare and classify geometric shapes, including quadrilaterals and triangles based on their properties and sizes b.Can identify regular or irregular

NCETM materials:VisualisingImagine a square cut along the diagonal to make two triangles. Describe the triangles.Join the triangles on different sides to

identify acute and obtuse angles and compare and order angles up to two right angles by size

identify lines of symmetry in 2-D shapes presented in different orientations

complete a simple symmetric figure with respect to a specific line of symmetry.

polygonsc. Can identify acute and obtuse angles d. Can compare and order angles up to two right angles by sizee. Can identify lines of symmetry in 2D shapes presented in different orientationsf. Can complete a simple shape or diagram with respect to a specific line of symmetryg. Can solve problems involving shape

make new shapes. Describe them. (you could sketch them)Are any of the shapes symmetrical? Convince me.Always, sometimes, neverIs it always, sometimes or never true that the two diagonals of a rectangle meet at right angles.Other possibilitiesCan you show or draw a polygon that fits both of these criteria? What do you look for?”Has exactly two equal sides.””Has exactly two parallel sides.”

Geometry – position and directionPupils should be taught to: describe positions on a 2-D grid as

coordinates in the first quadrant describe movements between

positions as translations of a given unit to the left/right and up/down

plot specified points and draw sides to complete a given polygon.

Geometry - position and directiona. Can describe positions on a 2D grid as coordinates in the first quadrantb. Can describe movements between positions as translations of a given unit to the left/right and up/downc. Can plot specified points and draw sides to complete a given polygon

NCETM materials:Working backwardsHere are the co-ordinates of corners of a rectangle which has width of 5.(7, 3) and (27, 3)What are the other two co-ordinates?

StatisticsPupils should be taught to: interpret and present discrete and

continuous data using appropriate graphical methods, including bar charts and time graphs.

solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.

Statisticsa. Can present discrete and continuous data using appropriate graphical methods including bar charts and time graphsb. Can interpret discrete and continuous data using appropriate graphical methods including bar charts and time graphsc. Can solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphsd. Can solve problems involving

NCETM materials:True or false? (Looking at a graph showing how the class sunflower is growing over time) “Our sunflower grew the fastest in July”.Is this true or false?Convince me.Make up your own ‘true/false’ statement about the graph.What’s the same, what’s different?Pupils identify similarities and differences between different representations and explain them to each other

statistics

Year 5

National Curriculum Objectives PIXL PLC key skills (Milestones) MPS expectationsNumber – number and place valuePupils should be taught to: read, write, order and compare

numbers to at least 1 000 000 and determine the value of each digit

count forwards or backwards in steps of powers of 10 for any given number up to 1 000 000

interpret negative numbers in context, count forwards and backwards with positive and negative whole numbers, including through zero

round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 and 100 000

solve number problems and practical problems that involve all of the above

read Roman numerals to 1000 (M) and recognise years written in Roman numerals.

Can understand the place value of each digit in numbers up to 1 000 000a. Can read and write numbers up to 1 000 000 b. Can order and compare numbers up to 1 000 000c. Can understand the place value of each digit in numbers up to 1 000 000d. Can interpret negative numbers in context, such as temperaturee. Can round any number up to 1 000 000 to the nearest 10, 100, 1000, 10 000 or 100 000f. Can solve problems using place value and number facts

To use manipulatives to support learning eg. Numicon, Base 10To use age appropriate sentence stems to develop oracy…BAD verbs: All should be used throughout mathematics teaching

NCETM materials:Spot the mistake:177000,187000,197000,217000What is wrong with this sequence of numbers?True or False?When I count in 10’s I will say the number 10100?What comes next?646000-10000= 636000636000 –10000 = 626000626000- 10000 = 616000Do, then explain747014 774014 747017 774077 744444If you wrote these numbers in order starting with the smallest, which number would be third?Explain how you ordered the numbers.Do, then explainShow the value of the digit 5 in these numbers?350114 567432 985376 Explain how you know.Make up an example Give further examplesCreate six digit numbers where the digit sum is five and the thousands digit is two.

Eg 3002000 2102000What is the largest/smallest number?Possible answersA number rounded to the nearest thousand is 76000 What is the largest possible number it could be?What do you notice?Round 343997 to the nearest 1000. Round it to the nearest 10000. What do you notice? Can you suggest other numbers like this?

Number – addition and subtractionPupils should be taught to: add and subtract whole numbers

with more than 4 digits, including using formal written methods (columnar addition and subtraction)

add and subtract numbers mentally with increasingly large numbers

use rounding to check answers to calculations and determine, in the context of a problem, levels of accuracy

solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why.

Number - addition, subtraction (mental and written)a. Can add three digit and extend to four-digit numbers using the formal column method b. Can subtract three digit and extend to four-digit numbers using the formal column methodc. Can add and subtract increasingly large numbers mentally e.g. 12 462 - 2300 = 10 162d. Can use rounding to check answers to addition and subtraction calculations.e. Can solve mulit-problems involving addition and subtraction, deciding which operation and which method to use

NCETM materials:True or false? Are these number sentences true or false?6.17 + 0.4 = 6.578.12 – 0.9 = 8.3Give your reasons.Hard and easy questionsWhich questions are easy / hard?213323 - 70 =512893 + 300 =819354 - 500 =319954 + 100 =

Explain why you think the hard questions are hard?Convince me + 1475 = 6 24What numbers go in the boxes?What different answers are there?

Number – multiplication and divisionPupils should be taught to: identify multiples and factors,

including finding all factor pairs of a

Number - multiplication and division (mental and written)a. Can recall and use multiplication and division facts for all the times tablesb. Can multiply and divide mentally

NCETM materials:Missing numbers6 x 0.9 = x 0.036 x 0.04 = 0.008 x

number, and common factors of two numbers

know and use the vocabulary of prime numbers, prime factors and composite (nonprime) numbers

establish whether a number up to 100 is prime and recall prime numbers up to 19

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

multiply and divide numbers mentally drawing upon known facts

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

multiply and divide whole numbers and those involving decimals by 10, 100 and 1000

recognise and use square numbers and cube numbers, and the notation for squared and cubed

solve problems involving multiplication and division including using their knowledge of factors and multiples, squares and cubes

solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign

solve problems involving multiplication and division, including scaling by simple fractions and

using known factsc. Can multiply and divide whole numbers and decimals by 10, 100 and 1000d. Can multiply up to four-digit numbers by one-digit numbers using short multiplicatione. Can multiply up to four-digit numbers by two-digit numbers using long multiplicationf. Can divide up to four-digit numbers by one-digit using short divisiong. Can interpret remainders in context as fractions, decimals or by roundingh. Can identify multiples and factorsi. Can establish whether a number up to 100 is prime j. Can recall prime numbers up to 19k. Can recognise and use square numbers and cube numbersl. Can solve problems using multiples, factors, square numbers and cube numbersm. Can solve problems using simple scaling such as kilometres to metresn. Can solve problems using a mixture of all four operations, including missing number problems

Which numbers could be written in the boxes?Making links Apples weigh about 170 g each. How many apples would you expect to get in a 2 kg bag?Use a fact3 x 75 = 225Use this fact to work out450 ÷ 6 =225 ÷ 0.6 =To multiply by 25 you multiply by 100 and then divide by 4. Use this strategy to solve48 x 25 78 x 254.6 x 25Making links7 x 8 = 56How can you use this fact to solve these calculations?0.7 x 0.8 = 5.6 ÷ 8 =Always, sometimes, never?Is it always, sometimes or never true that multiplying a number always makes it bigger Is it always, sometimes or never true that prime numbers are odd.Is it always, sometimes or never true that when you multiply a whole number by 9, the sum of its digits is also a multiple of 9 Is it always, sometimes or never true that a square number has an even number of factors.

problems involving simple rates.Number – fractions (including decimals and percentages)Pupils should be taught to: compare and order fractions whose

denominators are all multiples of the same number

identify, name and write equivalent fractions of a given fraction, represented visually, including tenths and hundredths

recognise mixed numbers and improper fractions and convert from one form to the other and write mathematical statements > 1 as a mixed number [for example, 2/5 + 4/5 = 6/5 = 1 1/5 ]

add and subtract fractions with the same denominator and denominators that are multiples of the same number

multiply proper fractions and mixed numbers by whole numbers, supported by materials and diagrams

read and write decimal numbers as fractions [for example, 0.71 = 71/100 ]

recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents

round decimals with two decimal places to the nearest whole number and to one decimal place

read, write, order and compare numbers with up to three decimal places

solve problems involving number up

Number - fractions (including decimals and percentages)a. Can compare and order fractions whose denominators are multiples of the same number b. Can identify, name and write equivalent fractions of a given fraction, represented visuallyc. Can recognise mixed numbers and improper fractionsd. Can convert from mixed numbers to improper fractions and from improper fractions to mixed numberse. Can add fractions with the same denonimator and denominators that are multiples of the same numberf. Can subtract fractions with the same denonimator and denominators that are multiples of the same numberg. Can multiply proper fractions and mixed numbers by whole numbers using diagrams, bar models and/or fraction piecesh. Can read and write decimal numbers as fractions e.g. 0.71 = 71/100i. Can recognise and use hundredthsj. Can round decimals with 2 decimal places to the nearest whole number and to one decimal placek. Can read, write,order and compare numbers with up to three decimal placesl. Can solve problems involving numbers up to three decimal placesm. Can recognise the % symbol and understand that it relates to the number

NCETM materials:Spot the mistake0.088, 0.089, 1.0What comes next?1.173, 1.183, 1.193True or false? 0.1 of a kilometre is 1m.0.2 of 2 kilometres is 2m.0.3 of 3 Kilometres is 3m0.25 of 3m is 500cm.2/5 of £2 is 20pDo, then explainCircle each decimal which when rounded to one decimal place is 6.2. 6.32 6.23 6.27 6.17Explain your reasoning Top tipsExplain how to round decimal numbers to one decimal place?Odd one out. Which is the odd one out in each of these collections of 4 fractions6/10 3/5 18/20 9/1530/100 3/10 6/20 3/9Why?What do you notice?Find 30/100 of 200Find 3/10 of 200OrderingPut these numbers in the correct order, starting with the largest.7/10, 0.73, 7/100, 0.073 71%Explain your reasoning.What do you notice?¾ and ¼ = 4/4 = 1

to three decimal places 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 solve problems which require

knowing percentage and decimal equivalents of ½, ¼, 1/5, 2/5, 4/5 and those fractions with a denominator of a multiple of 10 or 25.

of parts per hundredn. Can write percentages as fractions with denominator 100 as part of a decimalo. Can understand that percentages, decimals and fractions are different ways of expressing proportionp. Can solve problems which require knowing percentage, decimal and fraction equivalence for 1/2, 1/4, fifths and multiples of 10 or 25

4/4 and ¼ = 5/4 = 1 ¼5/4 and ¼ = 6/4 = 1 ½ Continue the pattern up to the total of 2.Can you make up a similar pattern for subtraction?The answer is 1 2/5 , what is the question?

MeasurementPupils should be taught to: convert between different units of

metric measure (for example, kilometre and metre; centimetre and metre; centimetre and millimetre; gram and kilogram; litre and

millilitre) understand and use approximate

equivalences between metric units and common imperial units such as inches, pounds and pints

measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres

calculate and compare the area of rectangles (including squares), and including using standard units, square centimetres (cm2) and square metres (m2) and estimate

the area of irregular shapes estimate volume [for example, using

1 cm3 blocks to build cuboids (including cubes)] and capacity [for example, using water]solve problems

Measuresa. Can convert between different units of metric measures, using place valueb. Can understand and use equivalence between metric and imperial units of measure, such as inches, pounds and pintsc. Can measure and calculate the perimeter of composite rectilinear shapes, including squaresd. Can measure and calculate the area of a rectangle, including a squaree. Can estimate the area of an irregular shapef. Can estimate volumeg. Can estimate capacityh. Can solve problems involving converting units of timei. Can use all four operations to solve problems involving measure

NCETM materials:Top TipsPut these amounts in order starting with the largest.130000cm2 1.2 m213 m2Explain your thinkingUndoingA school play ends at 6.45pm. The play lasted 2 hours and 35 minutes. What time did it start?Other possibilities(links with geometry, shape and space)A cuboid is made up of 36 smaller cubes.If the cuboid has the length of two of its sides the same what could the dimensions be?Convince meWrite more statementsMr Smith needs to fill buckets of water. A large bucket holds 6 litres and a small bucket holds 4 litres.

involving converting between units of time

use all four operations to solve problems involving measure [for example, length,mass, volume, money] using decimal notation, including scaling.

If a jug holds 250 ml and a bottle holds 500 ml suggest some ways of using the jug and bottle to fill the buckets.

Geometry – properties of shapesPupils should be taught to: identify 3-D shapes, including cubes

and other cuboids, from 2-D representations

know angles are measured in degrees: estimate and compare acute, obtuse and reflex angles

draw given angles, and measure them in degrees (o)

identify: *angles at a point and one whole turn (total 360o)

*angles at a point on a straight line and ½ a turn (total 180o) *other multiples of 90o use the properties of rectangles to

deduce related facts and find missing lengths and angles

distinguish between regular and irregular polygons based on reasoning about equal sides and angles.

Geometry - properties of shapea. Can identify 3D shapes from 2D representationsb. Can estimate and compare acute, obtuse and reflex anglesc. Can draw anglesd. Can identify angles at a point and one whole turn (360˚)e. Can identify angles at a point on a straight line and 1/2 a turn (180˚)f. Can use properties of rectangles, including diagonals, to deduce related facts and find missing lengths and anglesg. Can distinguish between regular and irregular polygons based on reasoning round equal sies and anglesh. Can solve problems involving angles

NCETM materials:Convince meWhat is the angle between the hands of a clock at four o clock? At what other times is the angle between the hands the same?Convince meAlways, sometimes, neverIs it always, sometimes or never true that the number of lines of reflective symmetry in a regular polygon is equal to the number of its sides n.Other possibilitiesA rectangular field has a perimeter between 14 and 20 metres . What could its dimensions be?What’s the same, what’s different? What is the same and what is different about the net of a cube and the net of a cuboid?

Geometry – position and directionPupils should be taught to: 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.

Geometry - position and directiona. Can identify and represent the position of a shape following reflection, in lines parallel to the axesb. Can identify and represent the position of a shape following translationc. Can solve problems involving position

NCETM materials:Working backwardsA square is translated 3 squares down and one square to the right.Three of the coordinates of the translated square are:(3, 6) (8, 11) (8, 6)

of shapes What are the co-ordinates of the original square?

StatisticsPupils should be taught to: solve comparison, sum and

difference problems using information presented in a line graph

complete, read and interpret information in tables, including timetables

Statisticsa. Can solve comparison, sum and difference problems using information presented in a line graphb. Can complete, read and interpret information in tables, including timetables

True or false? (Looking at a train time table) “If I want to get to Exeter by 4 o’clock this afternoon, I will need to get to Taunton station before midday”.Is this true or false?Convince me.Make up your own ‘true/false’ statement about a journey using the timetable.What’s the same, what’s different? Pupils identify similarities and differences between different representations and explain them to each other

Year 6National Curriculum Objectives PIXL PLC key skills (Milestones) MPS expectationsNumber – number and place valuePupils should be taught to: read, write, order and compare

numbers up to 10 000 000 and determine the value of each digit

round any whole number to a required degree of accuracy

use negative numbers in context, and calculate intervals across zero

solve number and practical problems that involve all of the above.

Number and place valuea. Can read, write and order whole numbers up to 10 000 000b. Can read, write and order numbers up to 3 decimal placesc. Can round any whole number to the nearest 10, 100, 1000 etc d. Can round decimals to the nearest whole number and to one or two decimal placese. Can use place value to multiply whole numbers by 10, 100 or 1000f. Can use place value to multiply decimal numbers by 10, 100 or 1000g. Can use place value to divide whole numbers by 10, 100 or 1000h. Can use place value to divide decimal numbers by 10, 100 or 1000i. Can use negative numbers in context and calculate intervals across zero

To use manipulatives to support learning eg. Numicon, Base 10To use age appropriate sentence stems to develop oracy…BAD verbs: All should be used throughout mathematics teaching

NCETM materials:Spot the mistake:-80,-40,10,50What is wrong with this sequence of numbers?True or False?When I count backwards in 50s from 10 I will say -200Do, then explainShow the value of the digit 6 in these numbers?6787555 95467754 Explain how you know.

Make up an example Create seven digit numbers where the digit sum is six and the tens of thousands digit is two. Eg 4020000 What is the largest/smallest number?Possible answersTwo numbers each with two decimal places round to 23.1 to one decimal place. The total of the numbers is 46.2. What could the numbers be?

Number – addition, subtraction, multiplication and divisionPupils should be taught to: multiply multi-digit numbers up to 4

digits by a two-digit whole number using the formal written method of long multiplication

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 number using the formal written method of short division where appropriate, interpreting remainders according to the context

perform mental calculations, including with mixed operations and large numbers

identify common factors, common multiples and prime numbers

use their knowledge of the order of operations to carry out calculations involving the four operations

Number - addition, subtraction (mental and written)a. Can use mental methods of computation for additionb. Can use mental methods of computation for subtractionc. Can use efficient written methods of addition including column additiond. Can use efficient written methods of subtraction including column subtractione. Can add decimal numbers up to 3 dp (including money)f. Can subtract decimal numbers up to 3 dp (including money)Number - multiplication and division (mental and written)a. Can recall multiplication facts up to 12x12 and quickly derive corresponding division factsb. Can use tables and place value calculations with multiples of 10c. Can use mental methods of computation for multiplicationd. Can use mental methods of computation for divisione. Can use efficient written methods of

NCETM materials:True or false? Are these number sentences true or false?6.32 + = 8Give your reasons.Hard and easy questionsWhich questions are easy / hard?213323 - 70 =512893 + 37 =8193.54 - 5.9 =Explain why you think the hard questions are hard?Missing symbolsWrite the missing signs( + - x ÷) in this number sentence:What else do you know?If you know this:86.7 + 13.3 = 100what other facts do you know?Convince meThree four digit numbers total 12435. What could they be?Making an estimateCircle the number that is the best estimate to

solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why

solve problems involving addition, subtraction, multiplication and division

use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

multiplication including short and long multiplicationf. Can use efficient written methods of division including short and long divisiong. Can multiply a simple decimal by a single digith. Can identify multiples and common multiplesi. Can identify factors and common factorsj. Can recognise and describe square numbersk. Can recognise and identify prime numbers

Number - Solving numerical problemsa. Can solve problems choosing an appropriate mental or written strategy (all four operations)b. Can solve two-step problems choosing appropriate operations (all four operations)c. Can interpret calculator display within context (all four operations)d. Can use inverse operations to find missing numbers, including decimalse. Can 'undo' a two-step problemf. Can understand 'balancing' including the meaning of the 'equal' signg. Can understand the use of brackets and the order of operations

932.6 - 931.051.3 1.5 1.7 1.9Always, sometimes, neverIs it always, sometimes or never true that the sum of two consecutive triangular numbers is a square numberUse a fact12 x 1.1 = 13.2Use this fact to work out15.4 ÷ 1.1 =27.5 ÷ 1.1 =Making links0.7 x 8 = 5.6How can you use this fact to solve these calculations?0.7 x 0.08 = 0.56 ÷ 8 =Can you find?Can you find the smallest number that can be added to or subtracted from 87.6 to make it exactly divisible by 8/7/18?Always, sometimes, never?Is it always, sometimes or never true that dividing a whole number by a half makes the answer twice as big.Is it always, sometimes or never true that when you square an even number, the result is divisible by 4Is it always, sometimes or never true that multiples of 7 are 1 more or 1 less than prime numbers.

Number – fractions (including decimals and percentages)Pupils should be taught to: use common factors to simplify

fractions; use common multiples to

Number - fractions (including decimals and percentages)a. Can identify, name and write equivalent fractions of a given fraction represented visually

NCETM materials:What do you notice?One thousandth of my money is 31p. How much do I have?

express fractions in the same denomination

compare and order fractions, including fractions > 1

add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions

multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, ¼ x ½ = 1/8]

divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6]

associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 3/8 ]

identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places

multiply one-digit numbers with up to two decimal places by whole numbers

use written division methods in cases where the answer has up to two decimal places

solve problems which require answers to be rounded to specified degrees of accuracy

recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.

b. Can use common factors to simplify fractionsc. Can compare and order fractionsd. Can add and subtract fractionse. Can multiply fractions by whole numbersf. Can multiply pairs of fractions, writing the answer in its simplest formg. Can divide fractions by whole numbersh. Can convert mixed numbers to improper fractionsi. Can convert improper fractions to mixed numbersj. Can read and write decimal numbers as fractionsk. Can recognise approximate proportions of a whole number using percentagesl. Can recognise simple equivalence between fractions, decimals and percentages

True or false?25% of 23km is longer than 0.2 of 20km.Convince me.True or false?In all of the numbers below, the digit 6 is worth more than 6 hundredths.3.6 3.063 3.006 6.23 7.761 3.076Is this true or false?Change some numbers so that it is true.What needs tobe adde3d to 6.543 to give 7?What needs to be added to 3.582 to give 5?Circle the two decimals which are closest in value to each other. 0.9 0.09 0.99 0.1 0.01OrderingWhich is larger, 1/3 or 2/5? Explain how you know.Put the following amounts in order, starting with the largest.23%, 5/8, 3/5, 0.8Another and anotherWrite down 2 fractions with a total of 3 4/5.… and another, … and another, …

Ratio and proportionPupils should be taught to: solve problems involving the relative

sizes of two quantities where missing values can be found by using integer multiplication and division facts

solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison

solve problems involving similar shapes where the scale factor is known or can be found

solve problems involving unequal sharing and grouping using knowledge of fractions and multiples.

Ratio and Proportiona. Can understand, use and apply simple ratio to a real problemb. Can use and apply scale in real contextsc. Can understand and use the concept of proportion

NCETM materials:What else do you know?In a flower bed a gardener plants 3 red bulbs for every 4 white bulbs. How many red and white bulbs might he plant?If she has 100 white bulbs, how many red bulbs does she need to buy?If she has 75 red bulbs, how many white bulbs does she need to buy?If she wants to plant 140 bulbs altogether, how many of each colour should she buy?Do, then explainPurple paint is made from read and blue paint in the ratio of 3:5.To make 40 litres of purple paint how much would I need of each colour? Explain your thinking.

AlgebraPupils should be taught to: use simple formulae generate and describe linear number

sequences express missing number problems

algebraically find pairs of numbers that satisfy an

equation with two unknowns enumerate possibilities of

combinations of two variables.

Algebraa. Can understand simple expressions using words and symbolsb. Can use symbols to represent an unknown number or a variablec. Can use simple formulaed. Can generate and describe linear number sequences

NCETM materials:Connected Calculationsp and q each stand for whole numbers.p + q = 1000 and p is 150 greater than q.Work out the values of p and q.UndoingThe perimeter of a rectangular garden is between 40 and 50 metres. What could the dimensions of the garden be?

MeasurementPupils should be taught to: solve problems involving the

calculation and conversion of units of measure, using decimal notation up to three decimal places where

Measurementa. Can interpret, with appropriate accuracy, numbers on scales and a range of measuring instrumentsb. Can measure and calculate the perimeter of compound shapes

NCETM materials:Write more statementsChen, Megan and Sam have parcels. Megan’s parcel weighs 1.2kg and Chen’s parcel is 1500g and Sam’s parcel

appropriate 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

convert between miles and kilometres

recognise that shapes with the same areas can have different perimeters and vice versa

recognise when it is possible to use formulae for area and volume of shapes

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 [for example, mm3 and km3].

c. Can find the area of rectanglesd. Can find the area of parallelograms and trianglese. Can understand and use volume of cubes and cuboidsf. Can convert between units of metric measureg. Can understand and use the approximate equivalences between metric units and common imperial unitsh. Can solve problems involving conversion between units of time

is half the weight of Megan’s parcel. Write down some other statements about the parcels. How much heavier is Megan’s parcel than Chen’s parcel?UndoingA film lasting 200 minutes finished at 17:45. At what time did it start?Other possibilities(links with geometry, shape and space)A cuboid has a volume between 200 and 250 cm cubed.Each edge is at least 4cm long. List four possibilities for the dimensions of the cuboid..

Geometry – properties of shapesPupils should be taught to: draw 2-D shapes using given

dimensions and angles recognise, describe and build simple

3-D shapes, including making nets compare and classify geometric

shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons

illustrate and name parts of circles, including radius, diameter and

Geometry - properties of shapea. Can name 2D and 3D shapes and describe their propertiesb. Can compare and classify shapes according to their propertiesc. Draw given angles and measure them in degreesd. Can recognise nets of familiar 3D shapese. Can find missing angles in any triangles and quadrilateralsf. Can recognise angles where they meet at a point or on a straight line

NCETM materials:What’s the same, what’s different? What is the same and what is different about the nets of a triangular prism and a square based pyramid?VisualisingJess has 24 cubes which she builds to make a cuboid. Write the dimensions of cuboids that she could make.List all the possibilities.Other possibilitiesIf one angle of an isosceles triangle is 36 degrees.

circumference and know that the diameter is twice the radius

recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.

g. Can recognise angles which are vertically opposite and find missing anglesh. Can identify and name the parts of a circle and know that the diameter is twice the radius

What could the triangle look like – draw it.Are there other possibilities .Draw a net for a cuboid that has a volume of 24 cm3.

Geometry – position and directionPupils should be taught to: describe positions on the full

coordinate grid (all four quadrants) draw and translate simple shapes on

the coordinate plane, and reflect them in the axes.

Geometry - position and directiona. Can reflect simple shapes in a mirror line including the axesb. Can draw and translate simple shapes including on the coordinate planec. Can use and interpret coordinates in all 4 quadrants

NCETM materials:Working backwardsTwo triangles have the following co-ordinates:Triangle A: (3, 5) (7, 5) (4, 7)Triangle B:(3, 1) (7, 1) (4, 3)Describe the translation of triangle A to B and then from B to A.

StatisticsPupils should be taught to: interpret and construct pie charts

and line graphs and use these to solve problems

calculate and interpret the mean as an average

Statisticsa. Can read and interpret timetables and calendarsb. Can construct and interpret line graphsc. Can construct and interpret pie chartsd. Can calculate and interpret the mean of a data set

NCETM materials:Create questions Make up a set of five numbers with a mean of 2.7Missing information The mean score in six test papers in a spelling test of 20 questions is 15.Five of the scores were 13 12 17 18 16 What was the missing score?

Problem Solvinga. Can break down one and two-step problems involving whole numbers and decimals and all four operationsb. Can solve a puzzle or problem by selecting the appropriate mathematical information, calculations, methods or toolsd. Can consider alternative methods for solving a problem and the appropriateness or efficiency of each method

Communicatinga. Can present information and results in a clear and organised wayb. Can choose appropriate images or symbols to represent a problem

Reasoninga. Can check and interpret solutions within the context of a problemb. Can check the reasonableness of results with reference to the context or size of numbersc. Can identify and explore patterns, properties and relationships and propose a general statement involving numbers or shapes