Year 6 Autumn 1 Possible Success Criteria  identify the value of each digit in numbers given to three decimal places and multiply  Understand place value in numbers with up to three decimal places and divide numbers by 10, 100 and 1000 giving answers up to three decimal places  Multiply whole numbers by 10 (100, 1000)  read, write, order and compare numbers up to 10 000 000 and determine the value of  Divide whole numbers by 10 (100, 1000) when the answer is a whole number Place value each digit  Multiply (divide) numbers with up to three decimal places by 10 (100, 1000)  use negative numbers in context, and calculate intervals across zero  Understand (order, write, read) place value in numbers with up to eight digits  identify common factors, common multiples and prime numbers  Understand and use negative numbers when working with temperature  solve problems which require answers to be rounded to specified degrees of  Understand and use negative numbers when working in other contexts accuracy  Know the meaning of a common multiple (factor) of two numbers  round any whole number to a required degree of accuracy  Identify common multiples (factors) of two numbers  Know how to test if a number up to 120 is prime  Approximate any number by rounding to the nearest 1 000 000 Mathematical Language (Common) multiple (Common) factor  Approximate any number by rounding to a specified degree of accuracy; e.g. nearest 20, 50  Understand estimating as the process of finding a rough value of an answer or calculation Place value Divisible  Use estimation to predict the order of magnitude of the solution to a (decimal) calculation Digit Prime number, Composite number  Check the order of magnitude of the solution to a (decimal) calculation Negative number

 perform mental calculations, including with mixed operations and large numbers  Combine addition and subtraction when multiplying mentally  solve addition and subtraction multi-step problems in contexts, deciding  Multiply a two-digit number by a single-digit number mentally Calculation which operations and methods to use and why  Add a three-digit number to a two-digit number mentally (when bridging of hundreds is  multiply multi-digit numbers up to 4 digits by a two-digit whole number required) using the formal written method of long multiplication  Multiply a four-digit number by a two-digit number using long multiplication  solve problems involving addition, subtraction and multiplication  Estimate multiplication calculations that involve multiplying up to four-digit numbers by  use their knowledge of the order of operations to carry out calculations a two-digit number  use estimation to check answers to calculations and determine, in the  Estimate division calculations that involve dividing up to a four-digit number by a two- context of a problem, an appropriate degree of accuracy digit number  Estimate multiplication calculations that involve multiplying numbers with up to two decimal places by whole numbers Mathematical Language Multiply, Multiplication, Times,  Identify when addition, subtraction or multiplication is needed as part of solving multi- Product step problems Addition Commutative  Explain why addition or subtraction is needed at any point when solving multi-step Subtraction Factor problems Sum, Total Short multiplication  Solve multi-step problems involving addition, subtraction and/or multiplication Difference, Minus, Less Long multiplication  Know that addition and subtraction have equal priority Column addition Estimate  Know that multiplication and division have equal priority Column subtraction Notation  Know that multiplication and division take priority over addition and subtraction Operation The approximately equal symbol ()  divide numbers up to 4 digits by a two-digit whole number using the formal  Use short division to divide a four-digit number by a one-digit number written method of long division; interpret remainders as whole number  Use short division to divide a three- (or four-) digit number by a two-digit number remainders, fractions, or by rounding, as appropriate for the context  Understand the method of long division Division  divide numbers up to 4 digits by a two-digit number using the formal written  Use long division to find the remainder at each step of the division method of short division where appropriate, interpreting remainders according to  Know how to write, and use, the remainder at each step of the division the context  Use long division to divide a three- (or four-) digit number by a two-digit number  use written division methods in cases where the answer has up to two decimal  Write the remainder to a division problem as a remainder places  Write the remainder to a division problem as a fraction  solve problems involving division  Extend beyond the decimal point to write the remainder as a decimal  use their knowledge of the order of operations to carry out calculations involving the  Identify when division is needed to solve a problem four operations  Extract the correct information from a problem and set up a written division calculation Mathematical Language Notation  Interpret a remainder when carrying out division Commutative Remainders are often abbreviated to Divide, Division, Divisible ‘r’ or ‘rem’ Divisor, Dividend, Quotient, Remainder Factor Short division, Long division Remainder, Estimate

Year 6 Autumn 2 Possible Success Criteria  recognise that shapes with the same areas can have different perimeters and vice  Recognise that shapes with the same areas can have different perimeters and vice versa versa  calculate the area of parallelograms and triangles  Know that the area of a parallelogram is given by the formula area = base × height Calculating  calculate, estimate and compare volume of cubes and cuboids using standard units,  Know that the area of a triangle is given by the formula area = ½ × base × height = Space including cubic centimetres (cm³) and cubic metres (m³), and extending to other units base × height ÷ 2 = 푏ℎ [for example, mm³ and km³] 2  Know that the volume of a cuboid is given by the formula volume = length × width ×  recognise when it is possible to use formulae for area and volume of shape height  solve problems involving the calculation and conversion of units of measure, using  Calculate the area of a parallelogram (triangle) decimal notation up to three decimal places where appropriate  Recognise when it is possible to use a formula for the area of a shape Cubic centimetre, centimetre cube Mathematical Language  Estimate the volume of cubes and cuboids Perimeter, area, volume, capacity Formula, formulae Convert  Choose appropriate units of volume Square, rectangle, parallelogram, triangle  Calculate the volume of a cuboid Composite rectilinear Length, breadth, depth, height, width  Recognise when it is possible to use a formula for the volume of a shape Polygon  Convert between metric units of area in simple cases Cube, cuboid Notation Millimetre, Centimetre, Metre, Kilometre  Abbreviations of units in the metric  Convert between metric units of volume in simple cases 2 2 2 Square millimetre, square centimetre, system: km, m, cm, mm, mm , cm , m , 2 3 3 3 square metre, square kilometre km , mm , cm , km  use, read, write and convert between standard units, converting measurements  Convert between non-adjacent metric units; e.g. kilometres and centimetres of length, mass, volume and time from a smaller unit of measure to a larger  Use decimal notation up to three decimal places when converting metric units unit, and vice versa, using decimal notation to up to three decimal places  Convert between Imperial units; e.g. feet and inches, pounds and ounces, pints and Measuring gallons  Solve problems involving converting between measures Space  State conclusions using the correct notation and units Mathematical Language Hour, minute, second Length, distance Inch, foot, yard Mass, weight Pound, ounce Volume Pint, gallon Capacity Metre, centimetre, millimetre Notation Tonne, kilogram, gram, milligram Abbreviations of units in the metric system: Litre, millilitre m, cm, mm, kg, g, l, ml Abbreviations of units in the Imperial system: lb, oz  draw 2-D shapes using given dimensions and angles  Use a protractor to draw angles up to 180°  recognise, describe and build simple 3-D shapes, including making nets  Use a protractor to work out and construct reflex angles Shape and  compare and classify geometric shapes based on their properties and sizes  Use a ruler to draw lines to the nearest millimetre Angles and find unknown angles in any triangles, quadrilaterals, and regular polygons  Use squared paper to guide construction of 2D shapes  illustrate and name parts of circles, including radius, diameter and circumference and  Complete tessellations of given shapes know that the diameter is twice the radius  Know the names of common 3D shapes Mathematical Language Triangle, Scalene, Right-angled, Isosceles,  Use mathematical language to describe 3D shapes Equilateral  Construct 3D shapes from given nets Protractor Polygon, Regular, Irregular  Use ‘Polydron’ to construct nets for common 3D shapes Measure Pentagon, Hexagon, Octagon, Decagon,  Draw accurate nets for common 3D shapes Nearest Dodecagon  Find all the nets for a cube Construct Circle, Radius, Diameter, Circumference,  Use a net to visualise the edges (vertices) that will meet when folded Sketch Centre  Know the definitions of special triangles Parallel Cube, Cuboid, Cylinder, Pyramid, Prism  Know the definitions of special quadrilaterals Diagonal Net  Classify 2D shapes using given categories; e.g. number of sides, symmetry Edge, Face, Vertex (Vertices) Angle  Know the angle sum of a triangle Visualise  Know the angle sum of a quadrilateral Quadrilateral, Square, Rectangle, Notation  Know how to find the angle sum of a any polygon Parallelogram, (Isosceles) Trapezium, Dash notation to represent equal lengths  Use the angle sum of a triangle to find missing angles Kite, Rhombus, Delta, Arrowhead in shapes and geometric diagrams Right angle notation  Find the missing angle in an isosceles triangle when only one angle is known  Use the angle sum of a quadrilateral to find missing angles  Know how to find the size of one angle in any regular polygon

Reasoning opportunities and probing questions Suggested activities Possible misconceptions  Convince me that 109 is a prime number KM: Maths to Infinity: Directed numbers  Some pupils can confuse the language of large (and

 Jenny writes 2.54 × 10 = 25.4. Kenny writes 2.54 × 10 = 25.40. who do KM: Extend the idea of Eratosthenes' sieve to a 12 by 12 grid small) numbers since the prefix ‘milli- means ‘one

you agree with? Explain why. KM: Exploring primes activities: Artistic Eratosthenes sieve thousandth’ (meaning that there are 1000 millimetres in  Look at this number (24 054 028). Show me another number (with 4, 5, KM: Use Powers of ten to demonstrate connections. a metre for example) while one million is actually a 6, 7 digits) that includes a 5 with the same value. And another. And NRICH: Factor-multiple chains thousand thousand. NRICH: The Moons of Vuvv another …  Some pupils may not realise that degrees (°) and  Convince me that 67 rounds to 60 to the nearest 20 NRICH: Round and round the circle degrees Celsius (°C) are two different and distinct units  Convince me that 1 579 234 rounds to 2 million to the nearest million NRICH: Counting cogs of measurement KM: Maths to Infinity Rounding  Some pupils may think that 1 is a prime number

PLACEVALUE NCETM: Place Value Reasoning  Some pupils may truncate instead of round Learning review  Some pupils may round down at the half way point, www.diagnosticquestions.com rather than round up.

 Find missing digits in otherwise completed long multiplication KM: Long multiplication template  Some pupils may write statements such as 140 - 190 = calculations KM: Maximise, minimise. Adapt ideas to fit learning intentions. 50  Convince me that 2472 × 12 = 29664 KM: Maths to Infinity: Complements  When subtracting mentally some pupils may deal with  Why have you chosen to add (subtract, multiply)? KM: Maths to Infinity: Multiplying and dividing columns separately and not combine correctly; e.g. 180  Jenny writes 1359 ÷ 18  7.55. Comment on Jenny’s approximation. NRICH: Become Maths detectives – 24: 180 – 20 = 160. Taking away 4 will leave 6. So  Lenny writes 2.74 × 13  26. Do you agree with Lenny? Explain your NRICH: Exploring number patterns you make the answer is 166. answer. NRICH: Reach 100  When checking the order of magnitude of a division KM: Stick on the Maths CALC6: Checking results calculation some pupils may apply incorrect reasoning

NCETM: Addition and Subtraction Reasoning NRICH: Four Go about the effect of increasing the divisor by a factor of NCETM: Multiplication and Division Reasoning NCETM: Activity A(i) 10, thinking that it also makes the solution greater by a NCETM: Activity G factor of 10; e.g. 1400 ÷ 20: 1400 ÷ 2 = 700 so 1400 ÷

20 = 7000. CALCULATION Learning review  The use of BIDMAS (or BODMAS) can imply that www.diagnosticquestions.com division takes priority over multiplication, and that addition takes priority over subtraction. This can result in incorrect calculations.

MEASURING SPACE CALCULATING DIVISION SPACE NCETM:    NCETM:    NCETM:   

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 Show me an example of a net of a cube. And another. And another … KM: Visualising 3D shapes  Some pupils will read the wrong way round the scale on  What is wrong with this attempt at a net of a cuboid? How can it be KM: Tessellating Tess a typical semi-circular protractor, therefore using 180° - changed? KM: Fibonacci’s disappearing squares required angle KM: Unravelling dice  Some pupils may measure from the end of a ruler, NRICH: Making spirals rather than the start of the measuring scale NRICH: Cut nets  Some pupils may think that several repeats of a shape NRICH: Making cuboids in any pattern constitutes a tessellation  How many different ways are there to complete these nets? KM: Shape work: Many of the activities are suitable for this unit.  When given a net of a 3D shape some pupils may think  Convince me that a rhombus is a parallelogram KM: Dotty activities that the number of vertices of the 3D shape is found by  Jenny writes that ‘Diameter = 2 × Radius’. Kenny writes that ‘Radius = 2 KM: Investigating polygons. Tasks one and two. counting the number of ‘corners’ on the net × Diameter’. Who is correct? KM: Special polygons  Some pupils may think that a ‘regular’ polygon is a  What is the same and what is different: a square and a rectangle? NRICH: Where Are They? ‘normal’ polygon  NRICH: Round a Hexagon  Some pupils may think that all polygons have to be NRICH: Quadrilaterals regular SHAPE andANGLES NCETM: Geometry - Properties of Shapes Reasoning KM: 6 point circles, 8 point circles and 12 point circles can be  Some pupils may think that a square is only square if used to support and extend the above idea ‘horizontal’, and even that a ‘non-horizontal’ square is called a diamond Learning review  The equal angles of an isosceles triangle are not always www.diagnosticquestions.com the ‘base angles’ as some pupils may think

Mastery indicators Non Negotiables - Essential knowledge  Multiply and divide numbers with up to three decimal places by 10, 100, and 1000  Know percentage and decimal equivalents for fractions with a denominator of 2, 3, 4, 5, 8 and 10  Use long division to divide numbers up to four digits by a two-digit number  Know the rough equivalence between miles and kilometres  Use simple formulae expressed in words  Know that vertically opposite angles are equal  Generate and describe linear number sequences  Know that the area of a triangle = base × height ÷ 2  Use simple ratio to compare quantities  Know that the area of a parallelogram = base × height  Write a fraction in its lowest terms by cancelling common factors  Know that volume is measured in cubes  Add and subtract fractions and mixed numbers with different denominators  Know the names of parts of a circle  Multiply pairs of fractions in simple cases  Know that the diameter of a circle is twice the radius  Find percentages of quantities  Know the conventions for a 2D coordinate grid  Solve missing angle problems involving triangles, quadrilaterals, angles at a point and angles on a  Know that mean = sum of data ÷ number of pieces of data straight line  Calculate the volume of cubes and cuboids  Use coordinates in all four quadrants  Calculate and interpret the mean as an average of a set of discrete data