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Maths

Maths Statement of Intent

 

The 2014 National Curriculum for Maths aims to ensure that all children:

 

  • Become fluent in the fundamentals of Mathematics
  • Are able to reason mathematically
  • Can solve problems by applying their Mathematics

 

At Radcliffe on Trent, these skills are embedded within Maths lessons and developed consistently over time. We believe that Maths is an important, creative discipline that helps us to understand and change the world. We want all pupils at Radcliffe on Trent to experience the beauty, power and enjoyment of Mathematics and develop a sense of curiosity about the subject alongside a clear understanding. Our curriculum aims to foster an enthusiasm for Maths: we want our children to have positive ‘can do’ attitudes and promote the fact that ‘We can all do Maths!’ We believe all children can achieve in mathematics, and teach for secure and deep understanding of mathematical concepts through manageable steps. We use mistakes and misconceptions as an essential part of learning and provide challenge through rich and sophisticated problems. Our underlying aim is to help children become confident in their conceptual understanding and use of maths so that they have the self-belief and determination to succeed when presented with a challenge. 

 

Implementation

What do we teach? What does this look like?

 

Our whole curriculum is shaped by our school vision which aims to enable all children to flourish to become the very best version of themselves they can possibly be. We teach the National Curriculum, supported by a clear skills and knowledge progression and draw from on wide range of resources, including White Rose and the NCETM. This ensures that skills and knowledge are built on year by year and sequenced appropriately to maximise learning for all children.

Our lesson planning is based on National Curriculum Statements and focuses on manageable, progressive steps to allow all children to engage in the learning. Our children are taught Mathematics for approximately 1 hour daily and support is determined during each lesson to ensure secure understanding based on the needs of the child. Challenge is visible throughout the whole session, where children are asked to reason and prove their understanding at a deeper secure level.

Within lessons:

  • The large majority of children progress through the curriculum content at the same pace.
  • Teachers reinforce an expectation that all children are capable of achieving high standards in Mathematics.
  • Re-caps on previous learning are included, using a ‘Last Week/Last Term’ or ‘Yesterday/Last Week’ approach, to embed areas of learning. Teachers aim to use ‘Mini Maths’ or ‘Guided Group’ sessions outside of the Maths hour, to tackle misconceptions and consolidate learning if not understood in the main teaching session.
  • Differentiation is achieved by emphasising deep knowledge and through individual support and intervention.
  • Teaching is underpinned by methodical curriculum design and supported by carefully crafted lessons and resources to foster deep conceptual and procedural knowledge.
  • Practice and consolidation play a central role. Carefully designed variation within this builds fluency and understanding of underlying mathematical concepts.
  • Teachers use precise, targeted questioning in class to test conceptual and procedural knowledge and assess children regularly to identify those requiring intervention, so that all children keep up.
  • Children are encouraged to explain their thinking to gain proficiency in articulating mathematical reasoning, using relevant mathematical vocabulary

 

Impact

What will this look like?

By the time our children leave school at the end of KS2 we aim for them to:

  • become fluent in the fundamentals of mathematics so that they develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately

 

  • be able to solve problems by applying their mathematics to a variety of problems with increasing sophistication, including in unfamiliar contexts and to model real-life scenarios

 

  • be able to reason mathematically by following a line of enquiry and develop and present a justification, argument or proof using mathematical language

 

  • have an appreciation of number and number operations, which enables mental calculations and written procedures to be performed efficiently, fluently and accurately to be successful in mathematics

 

ROTJS Maths Curriculum

 

Year 3

Year 4

Year 5

Year 6

Number and Place Value                         

Count from 0 in multiples of 2, 3, 4, 5, 8, 10, 50 and 100.

Count from 0 in multiples of 2, 3, 4, 5, 6, 7, 8, 9, 10, 25, 50, 100 and 1000.

Count forwards or backwards in steps of 1000, 10,000 and 100,000 from any given number to 1 million.

Find 10 and 100 more or less than a given number.

Find 10 and 100 and 1000 more or less than a given number.

Understand the place value of each digit in a 3-digit number using increasingly larger numbers.

Recognise the place value of each digit in a 4-digit number.

Identify the value of each digit in numbers given to three decimal places.  

Read, write, order and compare numbers to 3 decimal places.

Compare and order numbers up to 1000.

Order and compare numbers beyond 1000 to 10 000.

Read, write, order and compare whole numbers to at least 1,000,000 in figures and words, and know what each digit represents.

Read, write, order and compare numbers up to 10,000,000 and determine the value of each digit.

Identify, represent and estimate numbers to 1000 using different representations.

Identify, represent and estimate numbers beyond 1000 using different representations.

As year 4 to continue.

 

Round any whole number to the nearest 10, 100 or 1000 and link estimation and rounding numbers to the use of measuring instruments.

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

Round any whole number to a required degree of accuracy.

 

 

Round decimals with 1 decimal places to the nearest whole number.

Round decimals with 2 decimal places to the nearest whole number and to the nearest tenth.

Round decimals with 3 decimal places to a given degree of accuracy (tenths/hundredths or whole number)

Number and Place Value (continued)                        

 

Find the effect of multiplying and dividing a one- or two-digit number by 10 and 100. Identify the value of the digits as ones, tenths and hundredths.

Multiply and divide any positive number (including decimals to 2 places) up to 100, 000 by 10, 100 and 1, 000 and understand the effect.

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.

 

Use a variety of representations to count in ones, tens and hundreds.

Count backwards from a given number through zero.

Count forwards and backwards with positive and negative whole numbers through zero and interpret negative numbers in context

 Use negative numbers in context, and calculate intervals across zero.

 

Complete number sequences with missing numbers or continue sequences and describe the rule.

Recognise, describe and complete linear number sequences, including those involving fractions and decimals, and find the term-to-term rule.

Recognise, describe and complete and continue linear number sequences, including those involving fractions and decimals, and find the term-to-term rule.

Solve number problems and practical problems that involve the understanding of place value.

Solve number problems that involve the rounding of numbers and an understanding of place value.

Solve number problems that involve the rounding of numbers and understanding of place value.

Solve number and practical problems that involve all of the above, including contextual.

Solve problems that involve estimation.

Apply understanding of place value and rounding to solve problems that involve estimation, some contextual.

Solve number problems and practical problems that involve all of the above - these can contextual i.e. measures/time.

Solve problems which require answers to be rounded to specified degrees of accuracy and use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

ROTJS Maths Curriculum

 

Year 3

Year 4

Year 5

Year 6

Addition and Subtraction

Add and subtract 1, 2 and 3 digit numbers to a 3 digit number mentally.

Add and subtract number mentally with increasingly larger numbers (up to 4 digits) to improve fluency.

Add and subtract numbers mentally with increasingly large numbers e.g. 12,462 – 2,300 = 10,162

Perform mental calculations, including those with mixed operations and larger numbers, e.g. (154 x 3) + 18 or double 3,450 then divide by 10.

Add numbers with up to 3 digits, (this could include introducing some children to extended columnar addition).

Add numbers with up to 4 digits using an efficient method to improve fluency (mostly the formal columnar method for addition).

Continue to add and subtract whole numbers with more than 4 digits, including using efficient written methods.

NB: Most children should now be using columnar addition and subtraction.

Continue to add and subtract whole numbers with more than 4 digits, including using efficient written methods to improve fluency.

Subtract numbers with up to 3 digits, (this could include introducing some children to extended columnar subtraction).

Subtract numbers with up to 4 digits using an efficient method to improve fluency (mostly the formal columnar method for subtraction).

 

 

Add and subtract decimals, including a mix of whole numbers and decimals, and those with different numbers of decimal places and find complements of 1.

Add and subtract decimals with different numbers of decimal places using columnar addition and subtraction.

Estimate the answer to a calculation using rounding to 10/100 and use inverse operations to check answers.

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

Apply understanding of rounding to check for reasonability of answers to addition and subtraction calculations. e.g. 4,789 + 3,621 = 8,410: Check: 5,000 + 3,500 = 8,500

Use estimation, rounding and inverse operations to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.

Addition and Subtraction (continued)

Add and subtract in practical contexts. i.e. amounts of money, including mixed units, and give change using manageable amounts.

Add and subtract in practical contexts, with increasing complexity, i.e. amounts of money, including mixed units, and calculate change.

Add and subtract pairs of decimal fractions in the context of money and measures, using appropriate written methods, e.g. £12,408.67 + £9,639.84 or 193.87m – 109.89m.

 

 

 

Use knowledge of the order of operations to carry out calculations involving the four operations:

e.g. 3 + 6 x (5 + 4) ÷ 3 - 7 using the order of operations.

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

Solve addition and subtraction one and two-step problems deciding which operations and methods to use and why.

Solve increasingly complex addition and subtraction multi-step problems deciding which operations and methods to use and why.

Solve a range of increasingly complex multi-step problems involving addition, subtraction, multiplication and division, in contexts, deciding which operations and methods to use and why.

Solve problems relating to the addition and subtraction of numbers in the context of measures, including: money recording £ and p separately; length (m, cm, mm), mass (kg, g) and capacity (l/ml)

Solve addition and subtraction multi-step problems in contexts such as measures and money.

 

Solve addition and subtraction multi-step problems in contexts such as measures and money using decimal notation.

 

Solve problems involving addition, subtraction, multiplication and division of units of measure (e.g. length, mass, volume, money) using decimal notation

 

Solve missing numbers calculations.

Solve ‘find the missing number’ calculations using understanding of inverse operations.

Solve increasingly complex ‘find the missing number’ calculations using understanding of inverse operations.

Apply understanding of addition and subtraction to solve calculations with missing numbers, including columnar calculations.

ROTJS Maths Curriculum

 

Year 3

Year 4

Year 5

Year 6

Multiplication and Division

Recall and use x and ÷ facts for the 2, 3, 4, 5, 10 and 8 multiplication tables.

Recall/use known multiplication/division facts to aid fluency. Recall and use multiplication/division facts for up to 12 x 12.

Continue to recall and use multiplication and division facts for multiplication tables up to 12 x 12 to aid fluency.

 

 

 

 

Identify multiples and factors of a number with increasing fluency, including finding all factor pairs of a number, and common factors of two numbers

Identify multiples and factors of a number with increasing fluency (as year 5) and recognise the link with finding equivalent fractions.

 

 

Know and use the vocabulary of prime numbers, prime factors and composite (nonprime) numbers and establish whether a number up to 100 is prime using knowledge of multiplication facts and be able to recall prime numbers up to 19.

 

Find the effect of multiplying and dividing a one- or two-digit number by 10 and 100. Identify the value of the digits as ones, tenths and hundredths.

Multiply and divide any positive number (including decimals to 2 places) up to 100, 000 by 10, 100 and 1, 000 and understand the effect.

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

 

 

Use known multiplication and division facts to derive more complex related facts.

Extend mental calculation methods to three digit numbers to derive facts. Understand the impact of multiplying by 0 and 1 and dividing by 1.

Solve problems involving multiplication and division where larger numbers are used by decomposing them into their factors to create equivalent statements or by using an understanding of square and cubed numbers.

Perform mental calculations, including with mixed operations and large numbers e.g. (154 x 3) + 18 or double 3,450 then divide by 10.

 

 

 

Multiplication and Division (continued)

Use efficient mental methods, like commutativity and associativity to solve multiplication and division statements.

Use understanding of place value, efficient mental methods and  known and derived facts to multiply and divide mentally, including multiplying together three numbers.

Multiply and divide numbers mentally drawing upon known facts.

 

Use knowledge and understanding of the order of operations to carry out calculations involving all four rules of number.

 

Recognise and use factor pairs and commutativity in mental calculations.

Recognise and use square numbers and cube numbers and use the related notation and vocabulary

Identify common factors, common multiples and prime numbers

Write and calculate mathematical statements for multiplication using known multiplication tables, including for TO x O using mental methods and reliable written methods.

Multiply two-digit and three-digit numbers by a one-digit number using an efficient method written method (could include the formal columnar method for some children).

Continue to practise multiplying using the formal columnar method for short multiplication up to 4 digits by one digit.

 

Multiply 4-digit numbers by one digit   number using the formal columnar method for short multiplication to promote and maintain fluency.

 

 

Multiply 2 and 3 digit numbers by a 2-digit number using an appropriate method (this could include formal columnar method).

Multiply up to 4-digit numbers by a 2- digit number using the formal

columnar method for

long multiplication.

Write and calculate mathematical statements for division using known multiplication tables, including for TO ÷ O using reliable written methods.

Use understanding of place value, known and derived facts to divide 2-digit numbers by a one-digit number (to include remainders) using an efficient informal method e.g. grouping on a number line. Extend

(as appropriate) to 3 digit by one digit calculations continuing to use reliable written methods.

Continue to divide numbers up to 4-digits by a one-digit number using the efficient written method of short division. Begin to interpret non-integer answers to division in different ways according to the context e.g. write remainders as fractions or decimals or round remainders to the nearest integer.

Continue to practise short division of up to 4-digit numbers by a 1-digit number using the formal columnar method for short division to promote and maintain fluency.

Interpret remainders to division as whole numbers, fractions, decimals or by rounding as appropriate for the context.

Multiplication and Division (continued)

 

 

 

Divide numbers up to 4 digits by a 2-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

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

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

Solve missing number calculations, involving multiplication and division.

Solve missing number calculations, involving multiplication and division.

 

 

Understand the meaning of the equals sign by solving missing number calculations. Use and explain the equals sign to indicate equivalence, including in increasingly complex missing number problems.

As year 5 tackling increasingly more complex calculations.

 

 

Solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit.

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

Solve a range of multi-step problems, rounding answers to a specified degree of accuracy if required.

 

Solve multiplication and division word problems in contexts, including corresponding problems in which n objects relates to m objects.

Solve one and two step word problems in contexts, involving multiplication and division with increasingly large positive numbers, including corresponding problems in which n objects relates to m objects.

Solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the = sign in balancing calculations.

 

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

 

Solve multiplication and division positive integer scaling problems, including relating to measures.

Solve multiplication and division positive integer scaling problems, including relating to measures.

Solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates.

As year 5, plus solve problems which require exploring the order of operations using brackets.

ROTJS Maths Curriculum

 

Year 3

Year 4

Year 5

Year 6

Fractions

 

Count up and down in tenths and connect tenths to place value, decimal measures and to division of a quantity or one-digit number by 10.

Count up and down in hundredths and understand that hundredths arise when dividing an object by 100 and dividing tenths by 10.

Recognise and use thousandths and relate them to tenths, hundredths and decimal equivalents.

 

Count in simple fractions and decimals forwards and backwards.

Extend counting, using decimals and fractions including bridging zero.

 

Recognise and use unit fractions and non-unit fractions as numbers.  

Understand that decimals and fractions are different ways of expressing numbers and proportions.

Understand that percentages, decimals and fractions are different ways of expressing proportions.

Recognise, find and write unit fractions of a discrete set of objects. Find non-unit fractions with small denominators of a set of objects.

Find non-unit fractions of quantities, involving increasingly harder fractions.

 

Continue to develop understanding of fractions as numbers, measures and operators by finding fractions of numbers and quantities.

  Calculate fractions and percentages of numbers and quantities.

Understand the relation between unit fractions as operators (fractions of) and division by integers.

Understand the relation between non-unit fractions and multiplication/ division of quantities, with particular emphasis on tenths and hundredths.

Make connections between percentages, fractions and decimals.

 

Understand how division is used to calculate decimal fraction equivalents.

Compare and order fractions with the same denominator and common unit fractions.

Continue to compare and order fractions with the same denominator and common unit fractions.

Compare and order fractions whose denominators are all multiples of the same number.

 

Compare and order fractions, including fractions higher than one. Use common multiples to express fractions in the same denomination in order to compare size.

Fractions (continued)

Add and subtract fractions with the same denominator within one whole.

Add and subtract fractions beyond one whole and apply through a variety of problems.

 

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

 

Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions. Apply this understanding to solve complex problems.

 

 

Multiply proper fractions and mixed numbers by whole numbers using materials and diagrams to support.

Multiply simple pairs of proper fractions, simplifying the answer Use cancellation to simplify the fractions before multiplying.

 

 

 

Divide proper fractions by whole numbers.

Investigate finding fractions equivalent to 1/2, 1/4, 1/3 using unifix cubes or counters and drawn circles.

Use factors and multiples to recognise equivalent fractions and simplify where appropriate.

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

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

Recognise and show, using diagrams, equivalent fractions with small denominators.     

Recognise and show, using diagrams, families of common equivalent fractions.

Recognise mixed numbers and improper fractions, convert from one form to the other and write mathematical statements.

Use common factors to simplify fractions.

 

Make comparisons and order decimal amounts and quantities to the same number of decimal. places (to 2 places) representing numbers in several ways.

Read, write, order and compare decimal numbers with up to 3 decimal places of decimal places representing numbers in several ways.

Mentally add and subtract tenths and one digit whole numbers and tenths to include complements of 1

 

 

Fractions (continued)

 

Recognise and write decimal equivalents of any number of tenths or hundredths. Recognise and write decimal equivalents to 1/4, 1/2, 3/4.

Read and write decimal numbers as fractions.

 

Recall and use equivalences between simple fractions and decimals and including in different contexts.

 

 

Recognise the percent symbol (%) and understand that percent relates to ‘number of parts per 100’. Write percentages as a fraction with a denominator of 100 and as a decimal.

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

Solve problems involving finding fractions of quantity.

Solve problems involving increasingly harder fractions to calculate quantities.  Solve simple measure and money problems involving decimals to two decimal places.

Solve problems involving fractions with a denominator of a multiple of 10 or 25.

 

Use understanding of the relationship between unit fractions and division to work backwards by multiplying a quantity that represents a unit fraction to find the whole quantity.

Solve problems involving adding and subtracting of simple fractions to 1.

Solve problems involving using fractions to divide quantities, including non-unit fractions where the answer is a whole number.

Solve problems involving numbers up to 3 decimal place.

Solve problems which require knowing percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5 and 4/5

Solve problems which require answers to be rounded to specified degrees of accuracy.

ROTJS Maths Curriculum

 

Year 3

Year 4

Year 5

Year 6

Measurement

Confidently recognise the value of coins by adding and subtracting money, recording £ and p separately.  Give change, in both £ and p.

 

 

 

Measure and compare confidently in practical contexts, using correct tools and units. Use a wider range of measures including comparing and using mixed units.

Convert between different units of measure using an understanding of place value and decimal notation to record metrically, including money.

Convert between different units of metric measure, e.g. km/m; cm/m; cm/mm; g/kg; litre/mil.

Use, read, write and convert between standard units, converting measurements of length, mass, volume and time (smaller to larger unit, and vice versa) using decimal notation to three decimal places.

Understand how the comparison of measures involves simple scaling and how this relates to multiplication.

Use understanding of place value and decimal notation to record metric measures, including money. Use multiplication to convert from larger to smaller units.

Use knowledge of place value and multiplication and division to convert between standard units, e.g. approximate equivalences between metric units and common imperial units such as inches, pounds & pints.

Connect conversion, e.g. from kilometres to miles, to a graphical representation as preparation for understanding linear/proportional graphs.

 

Begin to understand the difference between volume and capacity.

Estimate volume, e.g. by using 1 cm3 blocks to build cuboids (including cubes) and estimate capacity, e.g. by using water.

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

Measure the perimeter of 2D shapes in cm and mm to find their perimeter.

Measure and calculate the perimeter of rectilinear figures in centimetres and metres. Express perimeter algebraically as 2 (a + b) in shapes where a & b are the two dimensions.

Calculate the perimeter of rectangles and related composite shapes, including using the relations of perimeter or area to find unknown lengths.

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

Measurement (continued)

 

 

Understand the term ‘area’ and how it differs from perimeter.

Calculate the area of shapes by counting squares and extend to include more complex shapes.

Compare the area of rectangles using standard units, square centimetres (cm2) and square metres (m2) and estimate the area of irregular shapes. Calculate the area from scale drawings using given measurements.

Relate the area of rectangles to parallelograms and triangles, for example, by dissection, and calculate their areas, understanding and using the formulae (in words or symbols) to do this.

Estimate and read time on analogue and digital 12-hour clocks to nearest minute using appropriate vocabulary.

Read write and convert time between analogue and digital 12-hour and 24-hour clocks.

Apply understanding of time through problems involving converting between units of time.

Continue to apply understanding of time through increasingly complex problems involving converting between units of time.

Record and compare time in seconds, minutes and hours using appropriate vocabulary.

Convert between different units of time, e.g. 1 hour = 60 minutes, 1 minute = 60 seconds, 365 days = 1 year.

Convert between different units of time, requiring multi-step conversions, e.g. seconds to days.

Use/read Roman numerals from I to XII, on 12-hour analogue clocks.

Read Roman numerals to 100. Understand that over time, the numeral system changed to include the concept of zero and place value.

Continue to reinforce through History contexts.

 

Solve problems involving telling and recording time and calculating time duration.

Solve problems involving reading, converting and calculating time, including converting from hours to minutes; minutes to seconds; years to months; weeks to days.

Solve problems involving converting between units of time

Continue to apply understanding of time through increasingly complex problems involving converting between units of time.

Solve problems relating to addition and subtraction of measures, incl. money.

Solve one- and two-step word problems, including those involving money, measures, area and perimeter.

Use all four operations to solve problems involving measure, e.g. length, mass, volume and  money using decimal notation, including scaling.

Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places.

Connect decimals and rounding to drawing and measuring straight lines in centimetres, in a variety of contexts.

Apply understanding of rounding and calculation strategies to: estimate, compare and calculate in different measures, including money in pounds and pence.

Apply understanding of rounding and calculation strategies to: estimate, compare and calculate in different measures, including money in pounds and pence.

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.

ROTJS Maths Curriculum

 

Year 3

Year 4

Year 5

Year 6

Geometry

Identify, describe, sort and classify 2D and 3D shapes. Record classifications on Venn and Carroll diagrams, incl. those involving more than one criterion.

Compare and classify geometric shapes, including quadrilaterals and triangles, based on properties and sizes.

Identify 3-D shapes, including cubes and other cuboids, from 2-D representations e.g. drawing shapes on isometric paper.

Compare and classify geometric shapes based on their properties.

Apply this understanding to make and draw geometric shapes based on their properties and sizes.

Describe the properties of 2D and 3D shape using vocabulary incl. horizontal and vertical lines,  lengths of lines and acute and obtuse for angles.

Classify shapes using geometrical properties, extending to classifying different triangles, e.g. isosceles, equilateral, scalene and quadrilaterals, e.g.  parallelogram, rhombus and trapezium.

Understand that angles are measured in degrees. Estimate and compare acute, obtuse and reflex angles.

Describe the properties of shapes and explain how unknown angles and lengths can be derived from known measurements.

Understand terms perpendicular parallel and identify pairs of perpendicular/parallel lines in shapes.

Compare and order angles in preparation for using a protractor and compare lengths and angles to decide if a polygon is regular or irregular.

Draw given angles, and measure them in degrees ° using a protractor accurately. Use conventional markings for parallel lines and right angles.

Draw shapes and nets accurately, using measuring tools and conventional markings and labels for lines and angles.

Understand rounding and decimal measures (mm) when measuring and drawing lines to create shapes.

Continue to develop understanding of rounding and decimal measures (mm) when measuring and drawing lines to create shapes.

Become accurate in drawing lines with a ruler to the nearest millimetre, and measuring with a protractor.

Draw 2-D shapes using given dimensions and angles, e.g. Construct a triangle from a given set of instructions.

 

Geometry (continued)

Recognise that 2 right angles = ½ turn, 3 = ¾ turn and 4 = full turn. Understand angle as a description of a turn and that a straight line is 2 right angles.

Estimate and reason about the size of angles based on their understanding of degrees in a ¼, ½, ¾ and full turn.

Identify that angles at a point and one whole turn total 360°, angles at a point on a straight line and in 1/2 a turn total 180° and other multiples of 90°.

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

Identify angles greater than  or less than a right angle; use terms acute and obtuse to describe them.

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

Use the properties of rectangles (including squares) to deduce related facts and find missing lengths and angles.

Find unknown angles in any triangles, quadrilaterals, and regular polygons.

 

Draw regular and irregular triangles, rectangles, squares, pentagons and hexagons. Measure their perimeters.

Compare lengths of sides and angles to decide whether polygons are regular or irregular.

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

Continue to reason about regular and irregular polygons based on showing an understanding of equal sides and angles.

 

 

Understand that in rectangles all angles are right angles and  diagonals bisect each other.

Understand that in rectangles all angles are right angles, diagonals are congruent and bisect each other, one diagonal separates the rectangle into two congruent triangles.

Illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius. These relationships might be expressed algebraically for example, d = 2 × r.

 

 

Complete a simple symmetric figure with respect to a specific line of symmetry, including where the line of symmetry does not dissect the original shape.

Use the term diagonal and make conjectures about the angles formed between sides, and between diagonals and parallel sides, and other properties of quadrilaterals.

Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them.

Draw symmetric patterns using a variety of media. Identify lines of symmetry in 2-D shapes presented in different orientations.

Recognise, describe and build simple 3-D shapes, including making nets.

 

Geometry Position and Direction

 

 

Describe positions on a 2-D grid as coordinates in the first quadrant, including on a partially labelled grid.

Describe positions on a 2-D grid as coordinates in the first and second quadrant, including on a partially labelled grid.

Describe positions on the full coordinate grid (all four quadrants), including on a partially labelled grid.

 

 

Draw a pair of axes in one quadrant, with equal scales and integer labels. Read, write and use pairs of coordinates, for example (2, 5), including using coordinate plotting ICT tools.

Draw and label a pair of axes in all four quadrants with equal scaling to knowledge of one quadrant to all four quadrants, including the use of negative numbers.

 

 

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

Recognise and use reflection and translation in a variety of diagrams, including continuing to use a 2-D grid and coordinates in the first quadrant. Reflection should be in lines that are parallel to the axes.

Recognise and use reflection and translation in a variety of diagrams, including continuing to use a 2-D grid and coordinates in all four quadrants.  Reflection should be in lines that are parallel to the axes.

 

 

Describe movements between positions as translations of a given unit to the left and right and up and down. Give the coordinates of its vertices in the new position.

Identify, describe and represent the position of a shape following a translation, using the appropriate language, and know that the shape has not changed.

Draw and label rectangles, squares, parallelograms and rhombuses, specified by coordinates in the 4four quadrants, predicting missing coordinates using the properties of shapes. Could be expressed algebraically, e.g. translating vertex (a, b) to (a – 2, b + 3); (a, b) and (a + d, b + d) being opposite vertices of a square of side d.

ROTJS Maths Curriculum

 

Year 3

Year 4

Year 5

Year 6

Statistics

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

Interpret discrete (certain values, i.e. numbers on a dice)  and continuous data (variable values, i.e. height) using appropriate graphical methods, including bar charts and time graphs.

Interpret discrete and continuous data. Connect work on coordinates and scales to their interpretation of time graphs.

Interpret and construct pie charts and line graphs and use these to solve problems.

 

Sort and classify objects, numbers or shapes with to two criteria, and display this work on Venn and Carroll diagrams.

Sort and classify objects, numbers or shapes with 2 or 3 criteria, and interpret Venn and Carroll diagrams to retrieve information.

Complete, read and interpret information in tables, including timetables.

Connect work on angles, fractions and percentages to the interpretation of pie charts.

 

Raise questions that might be investigated and collect data to answer it. Record the data onto a class tally chart. Test hypotheses.

Create a set of questions to be answered from presented data, in graphical or tabular form. Raise questions and hypotheses for investigation.

 

Encounter and draw graphs relating two variables, arising from their own enquiry and in other subjects.

Recognise that a tally involves grouping in fives and that this helps them to count the frequencies quickly and accurately.

 

Calculate and interpret the mean as an average.

Understand and use simple scales in pictograms and bar charts with increasing accuracy.

Understand and use a greater range of scales in graphical representations with increasing accuracy.

Know when it is appropriate to find the mean of a data set.

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

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

Solve comparison, sum and difference problems using information presented in a line graph.

Solve comparison, sum and difference problems using information presented in a full range of graphical representations.

 

Statistics (continued)

Collect and present data in a range of contexts.

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

Connect conversion from kilometres to miles in measurement to its graphical representation.

 

 

Begin to relate the graphical representation of data to recording change over time.

Begin to decide which representations of data are most appropriate and why.

ROTJS Maths Curriculum

 

General

These final two units are only introduced in year 6

 

Year 6

Algebra

Year 6

 

Ratio and Proportion

Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts.

Use simple formulae in mathematics and science; use symbols and letters to represent variables and unknowns in mathematical situations. Understand and use symbols to represent missing numbers, lengths, coordinates and angles.

 

Solve problems involving the calculation of percentages (for example, of measures, and such as 15% of 360) and the use of percentages for comparison.

Generate and describe linear number sequences. Make generalisations of number patterns.

 

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

Express missing number problems algebraically, e.g. equivalent expressions (for example, a + b = b + a)

 

Solve problems involving unequal sharing and grouping using knowledge of fractions and multiples, for example, ‘for every egg you need three spoonfuls of flour’.

Find pairs of numbers that satisfy an equation with two unknowns.

 

Consolidate understanding of ratio when comparing quantities, sizes and scale drawings by solving a variety of problems. E.g. use the notation a:b to record work.

Enumerate possibilities of combinations of two variables; number puzzles (for example, what two numbers can add up to).

 

Sticky Knowledge

The ‘Non-negotiables’ we expect all our children to be able to do by the end of each year

Year 3

Year 4

Year 5

Year 6

Know 2x, 5x and 10x tables securely.

 

Count backwards in ones from any given number.

 

Number bonds: Recall and use addition and subtraction facts to 20 fluently.

 

Halve and double numbers to 20.

 

Find 1/2 of a given number of objects by sharing.

 

Understand the place value of tens and ones.

 

Name common 2D shapes.

 

 

 

 

Know 2x, 3x, 4x, 5x and 10x tables securely.

 

Count on and back in ten’s and ones

 

Number bonds to 100: Recall and use addition and subtraction facts to 20 fluently.

 

Halving and doubling (including 30, 50, 100)

 

Understand that to find 1/2 needs ÷ by 2, 1/4 needs ÷ by 4, and 1/3 needs ÷ by 3.

 

Have an effective written method for addition and subtraction.

 

Name common 2D and 3D shapes.

 

Know odd and even numbers.

Securely know times tables to 12 x 12.

 

Be able to use the standard formal method for addition and subtraction.

 

Have an effective written method for

multiplication and division.

 

Know key measures conversions: centimetre to metre, millimetres to centimetres etc., in length, capacity and weight.

 

Recognise and generate equivalent fractions.

 

Draw an accurate line in millimetres with a ruler.

 

Identify common 2D and 3D shapes based on their properties.

 

Add and subtract any number

 

Recall times tables to 12 x 12 with fluency.

 

Have a secure understanding of PV to 1,000,000 and to 3 decimal places.

 

Be able to use the standard formal method for addition, subtraction, multiplication and division.

 

Be able to add, subtract and multiply fractions using an understanding of equivalence.

 

Have a secure recall of KS2 mathematical vocabulary.

 

Key Vocabulary

Year 3 and earlier

Number and place value

Operations

+ - x ÷

Measure

Geometry (position and direction)

Geometry (properties of shape)

Fractions

Data/statistics

Numbers to one hundred

Hundreds

Teens numbers

Hundred more/less

Ones, tens, hundreds

First, second, third…

Digits

Forwards

Backward

How many…?

Order

More, most, largest, greatest

Least, less, fewer,

Before, after, next, between, above, below

Odd, even

Sequence

Estimate

Predict

> greater than

< less than

Numeral

Zero

Compare

Double, half, halve, halfway

Subtract, take away

Difference

Multiplication

Multiply, times

Multiple of

Divide, division, share

Groups of

Array, row, column Exchange

Plus, minus

Sum, total, altogether

Equal to

Scale up

Partition

Recombine

 

 

Quarter past/to Approximately, Roughly

Kilometre, metre Centimetre, Millimetre

Length, height, Width, depth

Perimeter

Kilogram, gram

Litre, millilitre

Hours, minutes, seconds

Temperature, Degrees

Days of the week: Monday, Tuesday, etc.

Seasons: spring, summer, autumn, winter

Day, week, month, year, weekend

Leap year

Twelve-hour clock

Twenty-four hour clock

 

Rotation

Clockwise,

Anticlockwise

Straight line

Ninety degree turn, Right angle

North, south, east, west, N, S, E, W Horizontal, vertical, diagonal

Beside, next to, Opposite

Apart

Between, middle, Edge, centre

Left, right, up, down, Forwards, backward Sideways

Greater/less than ninety degrees

Orientation (same orientation, different orientation)

Symmetry Symmetrical,

Line of symmetry

Rectangle (including square), rectangular

Circle, circular

Triangle, triangular

Hexagon, hexagonal

Octagon, octagonal

Quadrilateral

Right-angled

Face, edge, vertex, vertices

Cube, cuboid

Pyramid

Pentagon, pentagonal

Sphere,

Cone

Cylinder

Mirror line, reflection

Shape

Flat, curved,

Straight, round Hollow, solid

Face, side, edge

Whole

Equal parts, four equal parts

One half, two halves

A quarter, two quarters, three quarters

One third,

A third

Equivalence Equivalent

Numerator, denominator

Unit fraction, non-unit fraction

Compare and order Tenths

Count, tally, sort

Vote

Graph

Block graph, Pictogram

Represent

Group, set

List, table

Label, title

Most popular, most common

Least popular, least common#

Chart, bar chart Frequency table, Carroll diagram

Venn diagram

Axis, axes

Diagram

 

 

 

 

 

 

 

 

 

 

Year 4: Additional vocabulary

Number and place value

Operations

+ - x ÷

Measure

Geometry (position and direction)

Geometry (properties of shape)

Fractions

Data/statistics

Tenths, hundredths Decimal (places) Round (to nearest) Thousand more/less than

Negative integers Count through zero Roman numerals (I to C)

 

Multiplication facts (up to 12x12)

Division facts

Inverse Derive

Convert

Coordinates Translation

Quadrant

x-axis, y-axis Perimeter and area

Parallel, perpendicular

Horizontal, vertical

Quadrilaterals Triangles

Right angle

acute and obtuse angles

Equivalent decimals and fractions

Continuous data

Line graph

Year 5: Additional vocabulary

Number and place value

Operations

+ - x ÷

Measure

Geometry (position and direction)

Geometry (properties of shape)

Fractions

Data/statistics

Powers of 10

 

Factor pairs Composite numbers

Prime number

Prime factors

Square number

Cubed number Formal written method

Efficient written method

Volume

Imperial units

Metric units

Coordinates Translation

Quadrant

x-axis, y-axis Perimeter and area

Reflex angle Dimensions

Regular and irregular Polygons

Proper fraction Improper fraction Mixed numbers Percentage

Half, quarter,

fifth, two fifths, four fifths

Ratio

Proportion

 

Year 6: Additional vocabulary

Number and place value

Operations

+ - x ÷

Geometry (position and direction)

Geometry (properties of shape)

Fractions

Data/statistics

Algebra

Numbers to ten million

Order of operations Common factors

Common multiples

Four quadrants (for coordinates)

Vertically opposite (angles) Circumference

Radius

Diameter

Degree of accuracy Simplify

Mean

Pie chart

Construct

Linear number Sequence

Substitute

Variables

Symbol

Known values

Questions we ask children and prompts we use in all year groups to stimulate reasoning and mathematical thinking:

 

 

  • Explain why ...
  • I wonder why ...
  • How do you know ...?
  • What will happen if ...?
  • How will you know ...?
  • How can we find out ...?
  • Is there another way ...?
  • What makes you think that ...?
  • What if…
  • Prove it!
  • What do you notice?
  • Tell me more
  • Can you give me another example? ... and another?
  • What’s the same? What’s different?
  • If I know this, what else do I know?
  • What do you already know? What do you need to find out?
  • Convince me ...
  • What might happen if I change …?
  • Can you describe…?
  • What could you try next?
  • How did you work it out?
 
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