# Key Stage 2 Mathematics Programme of Study

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1 Deeloping numerical reasoning Identify processes and connections Represent and communicate Reiew transfer mathematical to a ariety of contexts and eeryday situations identify the appropriate steps and information needed to complete the task or reach a solution select appropriate mathematics and techniques to use select and use suitable instruments and units of measurement choose an appropriate mental or written strategy and know when it is appropriate to use a calculator estimate and isualise size when measuring and use the correct units explain results and procedures clearly using mathematical language refine informal methods of recording written calculations, moing to formal methods of calculation when deelopmentally ready use appropriate notation, symbols and units of measurement select and construct appropriate charts, diagrams and graphs with suitable scales recognise, and generalise in words, patterns that arise in numerical, spatial or practical situations isualise and describe shapes, moements and transformations select from an increasing range of checking strategies to decide if answers are reasonable interpret answers within the context of the problem and consider whether answers, including calculator, analogue and digital displays, are sensible draw conclusions from data and recognise that some conclusions may be misleading or uncertain Key Within the table, text taken from the LNF will appear as non-bold. Text that has been extended from the LNF or that is a specific Mathematics Programme of Study skill will appear as bold. These are further identified by the following icons. Extended skill p Programme of study skill When combined with the LNF statements, these form the Key Stage 2 Mathematics Programme of Study. N.B. In order to comply with accessibility and legibility, these tables hae been designed to be printed at their optimum size of A3. Page 1 of 10

2 number Use number facts and relationships read and write numbers to compare and estimate with numbers up to 100 explain the alue of a digit in numbers up to use mental strategies to recall number facts within 20 recall 2, 3, 4, 5 and 10 multiplication tables and use to sole multiplication and diision problems multiply numbers by 10 identify multiples of 2, 3, 4, 5 and 10; use the term multiple identify odd and een numbers up to read and write numbers to compare and estimate with numbers up to use mental strategies to recall multiplication tables for 2, 3, 4, 5, 6 and 10 and use to sole diision problems multiply and diide numbers by 10 and 100 identify multiples of 2, 3, 4, 5, 6 and 10; use the terms multiple and factor read and write numbers to compare numbers with 1 and 2 decimal places use mental strategies to recall multiplication tables for 2, 3, 4, 5, 6, 8 and 10 and use to sole diision problems multiply and diide numbers and decimals by 10 and 100 identify multiples of 2, 3, 4, 5, 6, 8 and 10; use the terms multiple and factor identify prime numbers as haing only two factors; recognise that 1 is not a prime number identify prime numbers below 10 read and write numbers to 1 million and numbers to 3 decimal places use mental strategies to recall multiplication tables up to 10 x 10 and use to sole diision problems multiply numbers and decimals by a multiple of 10, e.g. 15 x 30, 1.4cm x 20 identify multiples of numbers up to 10; use the terms multiple and factor identify common multiples of two numbers identify common factors of two numbers identify prime numbers know prime numbers below 20 Key: Normal text: LNF statement Extended skill p Programme of study skill Page 2 of 10

3 number Fractions, decimals, percentages and ratio use hales and quarters hale 2-digit numbers in the context of number, money and measures find fractional quantities linked to known multiplication facts, e.g. 1 3 of 18, 1 5 of 15 recognise a quarter as a half of a half hale 3-digit numbers in the context of number, money and measures find fractional quantities using known table facts, e.g. 1 6 of 30cm recognise fractions that are seeral parts of a whole, e.g. 2 3, 3 10 use understanding of simple fraction and decimal equialences when measuring and calculating, e.g. ½ = 0.5, 1 10 = 0.1 calculate fractional quantities, e.g. 1 8 of 24 = 3, so 5 8 of 24 = 15 use doubling and haling strategies when working with simple proportions share objects in a gien ratio, e.g. red blocks and blue blocks in a ratio of 1:2 recognise connections between fractions, e.g. one-tenth is half of one-fifth add and subtract fractions with the same denominator add fractions with the same denominator to make a whole use understanding of simple fraction, decimal and percentage equialences, e.g. find 25% of 60cm and know that this is equialent to ¼ of 60cm calculate percentage quantities based on 10%, e.g. 20%, 5%, 15% use simple ratio and proportion use ratio to express two or more quantities in words state the proportion of a whole that each share represents, e.g. recognise that in a ratio of 1:3, 1 part represents a quarter of the total find equialent fractions and use these to add and subtract fractions simplify fractions Key: Normal text: LNF statement Extended skill p Programme of study skill Page 3 of 10

5 measuring Length, weight/mass, capacity recognise that perimeter is the distance around a shape use standard units to estimate and measure: length: measure on a ruler to the nearest ½ cm weight/mass: use 5g, 10g and 100g weights capacity: use litres and half litres; measure to the nearest 100ml p choose between metric units to measure a length measure and calculate the perimeter of squares and rectangles select and use appropriate standard units to estimate and measure length, weight/mass and capacity measure on a ruler to the nearest mm and record using a mix of units, e.g. 1cm 3mm use weighing scales with diisions to weigh objects to the nearest 5g, 10g, 25g or 100g measure capacities to the nearest 50ml or 100ml conert metric units of length to smaller units, e.g. cm to mm, m to cm, km to m choose appropriate metric units to measure length, weight/mass and capacity measure and calculate perimeters make estimates of length, weight/mass and capacity based on knowledge of the size of real-life objects use measuring instruments with 10 equal diisions between each major unit, and record using decimal notation, e.g. 4.2cm, 1.3kg make use of conersions, e.g. ¼ of a km = 250m recognise the appropriateness of units in different contexts read and interpret scales or diisions on a range of measuring instruments make estimates of length, weight/mass and capacity based on knowledge of the size of real-life objects, recognising the appropriateness of units in different contexts record measurements in different ways, e.g. 1.3kg = 1kg 300g use the language of imperial units in daily use, e.g. miles, pints Key: Normal text: LNF statement Extended skill p Programme of study skill Page 5 of 10

6 measuring Time tell the time to the nearest 5 minutes on an analogue clock and calculate how long it is to the next hour read hours and minutes on a 12-hour digital clock using am/pm conentions calculate start times, finish times and durations using hours, 30-minute interals and 15-minute interals tell the time to the nearest minute on analogue clocks read hours and minutes on a 24-hour digital clock time and order eents in seconds use calendars to plan eents calculate start times, finish times and durations using 5-minute interals conert between 12- and 24-hour clock times estimate the number of minutes eeryday actiities take to complete read and use analogue and digital clocks time eents in minutes and seconds, and order the results calculate start times, finish times and durations using hours and minutes carry out practical actiities inoling timed eents and explain which unit of time is the most appropriate estimate the length of time eeryday actiities take to complete, extending to hours and quarters of hours use and interpret timetables and schedules to plan eents and actiities and make calculations as part of the planning process estimate how long a journey takes time eents in minutes and seconds to the nearest tenth of a second conert between standard units of time estimate the length of time eeryday actiities take to complete with increasing accuracy Temperature take temperature readings using thermometers and interpret readings aboe and below 0 C take temperature readings using thermometers and interpret readings aboe and below 0 C measure and record temperatures inoling positie and negatie readings calculate temperature differences, including those inoling temperature rise and fall across 0 C measure and record temperatures inoling positie and negatie readings calculate temperature differences, including those inoling temperature rise and fall across 0 C Key: Normal text: LNF statement Extended skill p Programme of study skill Page 6 of 10

7 measuring Area and olume Angle and position find areas by counting squares identify right angles recognise that two right angles make a half turn, and that four right angles make a full turn describe an angle as more or less than a right angle use the four compass points to describe directions recognise olume in practical contexts use a protractor to check if an angle is more or less than a right angle use eight compass points to describe direction calculate, estimate and compare the area of squares and rectangles using standard units find olumes by counting and other practical methods recognise acute and obtuse angles draw and measure acute angles in multiples of 10 degrees use coordinates to specify location calculate the area of squares and rectangles recognise reflex angles draw accurately and measure acute and obtuse angles in multiples of 5 degrees calculate a missing angle within a right angle, on a straight line or around a point use grid references to specify location geometry Shape recognise and classify triangles, squares, rectangles, pentagons and hexagons, including irregular cases identify congruent shapes recognise 3D shapes, including prisms recognise, classify and sketch polygons with up to eight sides, including irregular shapes recognise and classify 3D shapes, using their own criteria recognise and classify triangles, using their own criteria identify congruent shapes and justify whether two or more shapes are congruent recognise tetrahedra and square based pyramids recognise and sketch different types of quadrilaterals explore the tessellation of different shapes identify a net of a cube Key: Normal text: LNF statement Extended skill p Programme of study skill Page 7 of 10

8 geometry Construction draw lines to the nearest half centimetre draw lines to the nearest millimetre recognise and draw perpendicular and parallel lines draw and label lines accurately, e.g. AB draw squares, rectangles and right angled triangles accurately construct solids from gien nets draw cubes and cuboids on isometric paper draw nets of cubes on square paper Moement identify lines of symmetry in 2D shapes draw horizontal and ertical lines of symmetry draw lines of symmetry draw the reflection of a shape in a horizontal or ertical line draw the reflection of a shape in any line complete a partly drawn shape after rotation translate a shape on squared paper horizontally or ertically find all the lines of symmetry for a gien shape identify rotational symmetry of shapes identify symmetrical properties of regular polygons algebra Number sequences explore sequences of whole numbers inoling addition and subtraction, e.g. counting in 2s, 3s and 4s from different starting points write the next two (or more) terms in sequences that inole addition or subtraction explore sequences of positie whole numbers inoling addition and subtraction in 2s, 3s, 4s, 5s, 6s, 8s and 10s from different starting points write the next two (or more) terms in sequences that inole addition or subtraction recognise and state the difference in sequences that inole adding or subtracting write the next two (or more) terms in sequences show that a number is in the sequence and/or find the position number by continuing the sequence or otherwise find the term to term rule for ascending and descending sequences, e.g. 3, 7, 11, 15 add 4 generate a sequence gien the first term and the term to term rule consider spatial patterns, e.g. square numbers Key: Normal text: LNF statement Extended skill p Programme of study skill Page 8 of 10

9 algebra Expressions and formulae explore general statements through practical actiities, e.g. that a + a + a = 3a, 3 x a = 3a and a + a + a + b + b = 3a + 2b simplify expressions inoling the addition of one ariable, e.g. 5t + 3t = 8t Functions and graphs use one and two step function machines to generate input and output inoling addition and subtraction within 100; express, in words, the operations of function machines use one and two step function machines to generate input and output using all four operations; express, in words, the operations of function machines use multistep function machines to generate input and output using all four operations; express, in words, the operations of function machines read, plot and write coordinates in one quadrant, e.g. (2, 4) express output generated from one step function machines using algebra identify the coordinates of a missing point from a regular shape refer to the x axis and the y axis Equations and inequalities find an unknown in one step equations and use this to derie other facts, e.g = 100 therefore = list numbers that are greater than or less than another number read statements about numbers expressed using an inequality sign, e.g. 6 > 4 use < > to describe whether a number is less than or greater than another find an unknown in two step equations, e.g. 4 x + 1 = 25 sole one step equations using letters to present unknowns with integer solutions, e.g. 6 + a = 10 and b + b = 8 use < > to describe whether a number is less than or greater than another, working with different types of numbers construct and sole one step equations with whole number solutions list numbers between two points using the terminology less than or equal to and greater than or equal to Key: Normal text: LNF statement Extended skill p Programme of study skill Page 9 of 10

10 data Collect and record data Present and analyse data Interpret results represent data using: lists, tally charts, tables and diagrams bar charts and bar line graphs labelled in 2s, 5s and 10s pictograms where one symbol represents more than one unit using a key Venn and Carroll diagrams extract and interpret information from charts, timetables, diagrams and graphs. represent data using: lists, tally charts, tables and diagrams bar charts and bar line graphs labelled in 2s, 5s and 10s pictograms where one symbol represents more than one unit using a key Venn and Carroll diagrams extract and interpret information from charts, timetables, diagrams and graphs. represent data using: lists, tally charts, tables, diagrams and frequency tables bar charts, grouped data charts, line graphs and conersion graphs extract and interpret information from an increasing range of diagrams, timetables and graphs (including pie charts) use mean, median, mode and range to describe a data set represent data using: lists, tally charts, tables, diagrams and frequency tables bar charts, grouped data charts, line graphs and conersion graphs extract and interpret information from an increasing range of diagrams, timetables and graphs (including pie charts) use mean, median, mode and range to describe a data set Probability use the words certain and impossible to describe the likelihood of an eent occurring recognise that some eents are impossible and some eents are certain recognise that some eents are more likely than others use the words likely, unlikely and een chance. use numbers to describe the likelihood of an eent, e.g. a one-in-six chance recognise that some eents are equally likely identify the outcomes of simple eents, e.g. flipping a coin, rolling a dice. Key: Normal text: LNF statement Extended skill p Programme of study skill Page 10 of 10

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