long term plan core subjects- maths

Long Term Plan Core subjects- Maths

Autumn 1 Autumn 2 Spring 1 Spring 2 Summer 1 Summer 2

Fluency count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number. Use the language of: equal to, more than, less than (fewer), most, least Given a number identify one more and one less. Tell the time to the hour and half past the hour and draw the hands on a clock face to show these times.

count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number. Represent and use number bonds and related subtraction facts within 20. Compare, describe and solve practical problems for: Lengths, heights, mass/weight, capacity and volume.

count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens. read and write numbers from 1 to 20 in numerals and words. Recognise, find and name a half as one of two equal parts of an object shape or quantity. Recognise and name common 2D and 3D shapes.

count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens. Represent and use number bonds and related subtraction facts within 20. Compare, describe and solve practical problems for: Lengths, heights, mass/weight, capacity and volume.

count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens Use the language of: equal to, more than, less than (fewer), most, least Tell the time to the hour and half past the hour and draw the hands on a clock face to show these times.

count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens read and write numbers from 1 to 20 in numerals and words. Recognise, find and name a half as one of two equal parts of an object shape or quantity. Recognise and name common 2D and 3D shapes.

Reasoning Odd one out Convince me True or false?

Odd one out Convince me True or false?





Problem solving solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 = - 9

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-place value Count and order numbers to 100.

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

use place value and number facts to solve problems

Addition & subtraction

Understanding symbols = + - Finding 1 more/less to 100. Number bonds to 10 /20.

Adding and subtracting money. Counting on and back to add and take away single digits.

Adding and subtracting 10 more/less to 100+.

Adding and subtracting double digits and crossing 10s.

Use addition and subtraction strategies to find missing numbers.

Using numberlines to add and take away.

Multiplication & division

Counting in 2s, 5s and 10s. Solve practical problems using groups of 2s, 5s 10s.

Understanding symbols x and %. Use symbols correctly when recording sums.

Understanding arrays and grouping. Drawing own arrays to record work.

Fractions (decimals & percentages)

Doubles and halves – shapes.

Doubles and halves – numbers.

Quarters – numbers and shapes.

Measurement

Weight and length. Non standard and standard units.

Time. Reading and writing o’clock and half past times. Money. Recognising coin values and finding totals.

Weight and length. Non standard and standard units.

Time. Reading and writing o’clock and half past times. Money. Finding change.

Weight, Length and Capacity. Using standard and non-standard units to solve problems.

Solving problems involving money and time.

Properties of shape 2D Properties – space shape pictures. 3D – building rockets.

Identifying 2D and 3D shapes in toys.

2D and 3D shapes in Castles. (Klee – Art)

Use and identify properties of 2 and 3D shapes.

Solve problems involving 2 and 3 D shapes.

Direction & movement

Position of aliens and planets.

Programme Beebots to follow direction.

Use Minecraft to build castles.

Plot and map dinosaur island. Find co-ordinates on treasure island.

Give Peter Rabbit instructions to escape Mr MacGregor.

Make whole, half and quarter turns when looking for big game.

Data Handling.

Tallys of aliens/stars. Venn diagrams – science.

Reading and creating bar charts of dinosaurs.

Venn diagrams – favourite vegetables.

Solving problems and answering questions from data about animals.



Fluency NC

Whole numbers, counting and place value Read and spell mathematical vocabulary

Place value and number bonds Read and spell mathematical vocabulary

Place value, number bonds and related facts. Read and spell mathematical vocabulary

Recognise, describe and make comparisons. Read and spell mathematical vocabulary

Recognise, describe and make comparisons. Read and spell mathematical vocabulary

Reasoning Taken from progression maps on NCTEM

True/False Continue the pattern Missing numbers What comes next?

Autumn 1 and… What is the same/different? What else do you know?

Previous terms and…. Fact familities Spot the mistake Make up an example

Previous terms and… Always, sometimes, never Hard and easy questions Working backwards

Previous terms and… Do, then explain… Convince me

All reasoning tasks taught over year.

Problem solving Taken from maths problem solving and picture maths

‘Colourful Caterpillars’ (finding all possibilities) ‘Butterflies’ (place value)

‘Grow fast’ (length) ‘Playing ball’ (addition and subtraction)

‘Stuck on a roof’ (finding rules and describing patterns) ‘Mrs Muddle’ (diagram problems and visual puzzles)

‘Money Box Safe’ (multiplication and division) ‘Chocolate pieces’ (fractions)

‘Money bags’ (logic problems) ‘Help me!’ (Diagram problems and visual puzzles)

‘Holiday time’ (time) ‘Summer Holiday’ (finding all the possibilities)

Number-place value NC

Count in steps of 2, 5 and 10 from any number. Recognise value of each digit in a two digit number. Compare and order numbers. Read and write numbers to 100 in numerals.

Recognise value of each digit in a two digit number. Count in steps of 2, 5 and 10 from any number forward and backward. Read and write numbers to 100 in words and numerals.

Compare and order numbers using <> Explore ways of partitioning numbers. Estimate numbers.

Count in steps of 2,3,5 and 10. Use place value and number facts to solve problems.

Use place value and number facts to solve problems.

Addition & subtraction NC

Using concrete objects and pictorial representations for solving calculations with numbers. Recall and use addition facts for 20.

Using concrete objects and pictorial representations for solving calculations with numbers, quantities and measures. Recall and use addition facts for 20 and related facts for up to 100. Begin to explore written methods.

Develop use of number line for addition and subtraction. Explore inverse operations. To explore related facts.

Develop written and mental methods for adding: two digit and ones, two digit and tens, two two digits, adding three one digits. To know that addition is commutative and subtraction is not. To know the terms sum and difference.

To use mental, practical and written methods for solving problems involving addition and subtraction. To solve missing number problems.

Multiplication & division NC

To recognise odd and even numbers. To know what multiplication is. To use arrays and repeated addition for multiplication. To recall multiplication facts for 2,5 and 10.

To explore methods for division including sharing and grouping using practical equipment.

To explore how a number line can be used for multiplication and division. Revise methods for multiplication and division. Begin to make links between the two.

To know that multiplication can be done in any order and division cannot. Continue developing methods. Begin to solve problems involving multiplication and division.

Fractions (decimals & percentages) NC

To explore half of discreet and continuous quantities.

Recognise, find and name fractions of lengths and shapes (thirds and quarters)

To count in fractions Find fractions of a number

Equivalence

Measurement NC

Length (measuring, comparing, ordering) Recognising value of coins, comparing and ordering totals. Recap days/months and intervals of time inc oclock and half past.

Mass (measuring, comparing, ordering) Finding totals of money.

Temperature (measuring, comparing and ordering) Quarter past/to on the clock.

Capacity (comparing, ordering and measuring) Tell and write the time to five minutes. Record pounds and pence accurately.

Choosing units of measure, accurately reading scales. Solving problems with money including giving change.

Properties of shape NC

2D shape 3D shape Compare and sort common 2d and 3d shapes.

Direction & movement NC

Exploring patterns – ordering and arranging using mathematical equipment.

Positional language Rotation

Statistics NC

Pictograms (interpreting)

Tallies (data collection) Tables/bar charts (presenting data)

Asking and answering questions about data.


Autumn 1 School is Back!

Autumn 2 Beyond the Wild Wood

Spring 1 Romans: Heroes or Villains

Spring 2 The Land of Giants

Summer 1 Eco-Warriors

Summer 2 Curses and Crypts

Fluency (KPIs)

Number & place value

Addition and Subtraction

Multiplication and Division

Shape Fractions Measurement

Reasoning Show me… Which is the odd one out? Visualising

Convince me … What is the same? What is different?

Prove it… Inverse operations Recall number facts to justify answers.

What do you notice? Look for patterns. Missing number sentences

Make links Test statements Spot the mistake Equivalent calculations

Visualising Always, Sometimes, Never What comes next?

Problem solving ‘How would we count?’ Using counting NRICH

Using measures Using fractions, equivalent fractions

Using perimeter of shape

Using money Using calculations

Number-place value Recognise the place value of each digit in a three digit number (hundreds, tens, ones) Compare and order numbers to 1000. Read and write numbers to at least 1000 in numerals and in words.

Count from 0 in multiples of 4, 8, 50 and 100; find 10 or 100 more or less than a given number. Identify, represent and estimate numbers using different representations.

Solve number problems and practical problems involving these ideas.

Addition & Add and subtract Estimate the answer to a Solve problems

subtraction

numbers mentally. Add and subtract numbers with up to three digits, using formal written methods of columnar addition and subtraction.

calculation and use inverse operations to check answers.

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


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 more formal written methods.

Solve problems, including missing number, involving multiplication and division, including positive integer scaling problems and correspondence problems in which n objects are connected to m objects.


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

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

Recognise and show, using diagrams, equivalent fractions with small denominators. Add and subtract fractions with the same denominator within one whole. Compare and order unit fractions, and fractions with the same denominators.

denominators. Measurement

Measure, compare, add and subtract lengths (m/cm/mm);mass (kg/g); volume/capacity l/ml) Know the number of seconds in a minute and the number of days in each month, year and leap year. Compare durations of events.

Tell and write the time for 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.

Properties of shape Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations; and describe them with increasing accuracy.

Measure the perimeter of simple 2D shapes.

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


Recognise angles as a property of a 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.

Statistics

Interpret and present data using bar charts, pictograms and tables.

Solve one- step and two-step questions using information presented in scaled bar charts and pictograms and tables.

Autumn 1

Autumn 2

Spring 1

Spring 2

Summer 1

Summer 2

Fluency Using NRICH

‘Pairs of Numbers’

‘Strike it Out’ ‘Totality’ ‘Shape times Shape’ ‘Mystery Matrix’ ‘Four Go’

Reasoning 2D Shapes

Times Tables Number Fractions ( decimals and %)

Times Tables Measures

Problem solving 1 step word problems + and - Using the inverse to check calculations

1 step word problems * and / Using the inverse to check calculations

2 step word problems + and – • Solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why.

Fractions • Solve 2 step * and \ number and practical problems with increasingly large positive numbers. • Solve simple measure and money problems involving fractions and decimals to two decimal places.

Measures

Number-place value • recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones) • find 1000 more or less than a given number • order and compare numbers beyond 1000 • identify, represent and estimate numbers using different representations

Th H T U • count backwards through zero to include negative numbers

• Count in multiples of 6, 7, 9, 25 and 100. • Count backwards through zero to include negative numbers • Round any number to the nearest 10, 100 or 1000 • Compare numbers with the same number of decimal places up to two decimal points.

Th H T U and decimals • Find 1000 more or less than a given number • Rounding numbers to the nearest 10, 100 or 1000 • Read Roman numerals to 100 and understand how the numeral system changed to include the concept of zero and place value. • Round decimals with one decimal place to

Revision

the nearest whole number


Th H T U + Th H T U • add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate

Using the inverse

Th H T U . 1/10

• Estimate and use inverse operations to check answers to a calculation.


• recall multiplication and division facts for multiplication tables up to 12×12 Times Tables

Mental and written multiplication

• 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. • Multiply two-digit and three-digit numbers by a one-digit number using formal written layout.

• Recognise and use factor pairs and commutativity in mental calculations. • Solve problems involving multiplying and adding, including using the distributive law and harder multiplication problems, such as which n objects are connected to m objects.


• recognise and write decimal equivalents to ½ ¼ 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

• Count up and down in hundredths; recognise that hundredths arise when dividing an object by a hundred and dividing tenths by ten. • Identify, name and write equivalent fractions of a given fraction, including

• Solve problems involving increasing harder fractions to calculate quantities, • Recognise and write decimal equivalents to ½, ¼ and ¾ and fractions to divide quantities, including non-unit fractions where the answer is a

tenths and hundredths. • Recognise ad write decimal equivalents of any number of tenths or hundredths.

whole number. • Add and subtract fractions with the same denominator.

Measurement

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

Length and Perimeter • convert between different units of measure [for example, kilometre to metre; hour to minute]

• Convert between different units of measure [for example, kilometre to metre; hour to minute] • Measure and calculate the perimeter of a rectilinear figure (including square) in cm and m. • Estimate, compare and calculate different measures, including money in pounds and pence.

Area, decimals, volume, capacity and mass • Measure and calculate the area of a rectilinear figure

Properties of shape • compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes

• Identify acute and obtuse angles and compare and order angles up to two-right angles by size.

Tesselation 2D


Co-ordinates • Describe positions on a 2D grid as co-ordinates in the first quadrant.

Changing Position

Position and area

Statistics

• Interpret and present discrete data

using bar charts and continuous data using line



Fluency (KPIs)

Number & place value Addition & subtraction Multiplication & division

Fractions Measurement Geometry and statistics

Reasoning (Taken from NCETM progression grids)

Spot the mistake True/false What comes next? Do, then explain

True/ false Hard and easy questions Convince me Making an estimate

Missing numbers Making links Use a fact Prove it Always, sometimes, never Use the inverse Size of an answer

Spot the mistake What comes next? What do you notice? Complete the pattern Odd one out Ordering Continue the pattern

Top tips Undoing Other possibilities Write more statements Testing conditions Working backwards

What’s the same/different? Visualising Convince me Always, sometimes, never True/false Create a question

Problem solving (Big maths investigations)

Using negative numbers

Using perimeter and length.

Using squares and cubes

Using addition and subtraction Converting time units.

Using factors and multiples

Using 3 decimal places.

Number-place value Values up to 1000000 Count forwards & backwards up to 100000 Negative and positive

Rounding up to 1000000 Roman numerals-recognising years and up to 1000.

Negative and positive Rounding


With more than 4 digits using column method Mental methods

Mental methods Recap column method Use rounding to check calculations

Mental methods Mental methods


Dividing 4 digits by 1 digit using short division Short and long multiplication Identifying factors

Mental methods Multiply and divide whole numbers and those involving decimals by 10,100 and 1000. Recognising square

Mental methods Recap short and long division Prime factors and prime numbers vocabulary.

Mental methods Prime numbers to 100 and recalling to 19.

and cube numbers


Recognise and use thousandths. Read, write and order numbers up to 3 decimal places.

Comparing and ordering Equivalent Add and subtract fractions Write decimals as fractions

Recognise mixed numbers and improper fractions Multiply proper fractions and mixed numbers by whole numbers. Round decimals with 2 places to the nearest whole

Recognise percentage relates to parts of 100. Writing percentages as fractions and decimals. Solve problems which require percentage and decimal equivalents.

Measurement

Converting between units of measure Equivalence between imperial and metric Perimeter Length

Time Area and volume Money

Mass

Properties of shape Nets and 3D solids Irregular and regular Recognising angles

Drawing angles Use properties of rectangles to deduce related facts and missing angles


Reflection and translation

Statistics

Solve comparison, sum and difference problems using line graphs Timetables

Ratio & proportion (years 5 & 6)

Scaling by simple fractions and problems involving simple rates

Algebra (years 5 & 6)

Distributive law

Long Term Plan Maths


Fluency Four operations Rapid recall of times tables up to 12 x 12

practise calculations with simple fractions and decimal fraction equivalents to aid fluency,

Reasoning solve number and practical problems that involve all of the below

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

following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language

Problem solving Using negative numbers

identify common factors, common multiples and prime numbers

Using squares and cubes

Using addition and subtraction Converting time units.

Number-place value read, write, order and compare numbers up to 10 000 000 and determine the value of each digit

Rounding up to 1000000 Roman numerals-recognising years and up to 1000.

Negative and positive Rounding


With more than 4 digits using column method Mental methods

solve problems involving addition, subtraction, multiplication and division

Mental methods Recap column method Use rounding to check calculations

interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context

Mental methods Mental methods


divide numbers up to 4 digits by a two-digit whole number using the formal written

Mental methods Multiply and divide whole numbers and those involving decimals by 10,100

Mental methods Recap short and long division Prime factors and prime numbers

Mental methods Prime numbers to 100 and recalling to 19.

method of long division Identifying factors

and 1000. Recognising square and cube numbers

vocabulary.


Recognise and use thousandths. Read, write and order numbers up to 3 decimal places.

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

compare and order fractions, including fractions > 1

Recognise mixed numbers and improper fractions Multiply proper fractions and mixed numbers by whole numbers. Round decimals with 2 places to the nearest whole

associate a fraction with division and calculate decimal fraction equivalents

Recognise percentage relates to parts of 100. Writing percentages as fractions and decimals. Solve problems which require percentage and decimal equivalents.

Measurement

Converting between units of measure Equivalence between imperial and metric Perimeter Length

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

Time Area and volume Money

Mass

Properties of shape draw 2-D shapes using given dimensions and angles

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 3dp

Nets and 3D solids Irregular and regular Recognising angles HA- calculate the area of parallelograms and triangles

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

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

Use properties of rectangles to deduce related facts and missing angles


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.

Statistics

Solve comparison, sum and difference problems using line graphs Timetables

calculate and interpret the mean as an average.

interpret and construct pie charts and line graphs and use these to solve problems

Ratio & proportion (years 5 & 6)

Scaling by simple fractions and problems involving simple rates

Word problems involving ratio

Algebra (years 5 & 6)

express missing number problems algebraically

use simple formulae

long term plan core subjects- maths

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