Mathematics guidance: key stages 1 and 2 Non-statutory guidance for the national curriculum in England Year 6 June 2020 Summary This document is one chapter of the full publication Mathematics guidance: key stages 1 and 2 Non-statutory guidance for the national curriculum in England. An overview of the ready-to-progress criteria for all year groups is provided below, followed by the specific guidance for year 6. To find out more about how to use this document, please read the introductory chapter. 2 Ready-to-progress criteria: year 1 to year 6 The table below is a summary of the ready-to-progress criteria for all year groups. Strand Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 NPV 1NPV–1 Count within 3NPV–1 Know that 10 4NPV–1 Know that 10 5NPV–1 Know that 10 6NPV–1 Understand the 100, forwards and tens are equivalent to 1 hundreds are equivalent tenths are equivalent to relationship between backwards, starting with hundred, and that 100 is to 1 thousand, and that 1 one, and that 1 is 10 powers of 10 from any number. 10 times the size of 10; 1,000 is 10 times the size times the size of 0.1. 1 hundredth to 10 million, apply this to identify and of 100; apply this to Know that 100 and use this to make a work out how many 10s identify and work out how hundredths are equivalent given number 10, 100, there are in other three- many 100s there are in to 1 one, and that 1 is 100 1,000, 1 tenth, 1 digit multiples of 10. other four-digit multiples times the size of 0.01. hundredth or 1 of 100. Know that 10 hundredths thousandth times the size are equivalent to 1 tenth, (multiply and divide by 10, and that 0.1 is 10 times 100 and 1,000). the size of 0.01. 2NPV–1 Recognise the 3NPV–2 Recognise the 4NPV–2 Recognise the 5NPV–2 Recognise the 6NPV–2 Recognise the place value of each digit place value of each digit place value of each digit place value of each digit place value of each digit in two-digit numbers, and in three-digit numbers, in four-digit numbers, and in numbers with up to 2 in numbers up to 10 compose and decompose and compose and compose and decompose decimal places, and million, including decimal two-digit numbers using decompose three-digit four-digit numbers using compose and decompose fractions, and compose standard and non- numbers using standard standard and non- numbers with up to 2 and decompose numbers standard partitioning. and non-standard standard partitioning. decimal places using up to 10 million using partitioning. standard and non- standard and non- standard partitioning. standard partitioning. 1NPV–2 Reason about 2NPV–2 Reason about 3NPV–3 Reason about 4NPV–3 Reason about 5NPV–3 Reason about 6NPV–3 Reason about the location of numbers to the location of any two- the location of any three- the location of any four- the location of any the location of any 20 within the linear digit number in the linear digit number in the linear digit number in the linear number with up to 2 number up to 10 million, number system, including number system, including number system, including number system, including decimals places in the including decimal comparing using < > identifying the previous identifying the previous identifying the previous linear number system, fractions, in the linear and = and next multiple of 10. and next multiple of 100 and next multiple of 1,000 including identifying the number system, and and 10. and 100, and rounding to previous and next multiple round numbers, as the nearest of each. of 1 and 0.1 and rounding appropriate, including in to the nearest of each. contexts. 3 Strand Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 NPV 3NPV–4 Divide 100 into 4NPV–4 Divide 1,000 into 5NPV–4 Divide 1 into 2, 6NPV–4 Divide powers of 2, 4, 5 and 10 equal parts, 2, 4, 5 and 10 equal 4, 5 and 10 equal parts, 10, from 1 hundredth to and read scales/number parts, and read and read scales/number 10 million, into 2, 4, 5 and lines marked in multiples scales/number lines lines marked in units of 1 10 equal parts, and read of 100 with 2, 4, 5 and 10 marked in multiples of with 2, 4, 5 and 10 equal scales/number lines with equal parts. 1,000 with 2, 4, 5 and 10 parts. labelled intervals divided equal parts. into 2, 4, 5 and 10 equal parts. 5NPV–5 Convert between units of measure, including using common decimals and fractions. NF 1NF–1 Develop fluency in 2NF–1 Secure fluency in 3NF–1 Secure fluency in addition and subtraction addition and subtraction addition and subtraction facts within 10. facts within 10, through facts that bridge 10, continued practice. through continued practice. 1NF–2 Count forwards 3NF–2 Recall 4NF–1 Recall 5NF–1 Secure fluency in and backwards in multiplication facts, and multiplication and division multiplication table facts, multiples of 2, 5 and 10, corresponding division facts up to and corresponding up to 10 multiples, facts, in the 10, 5, 2, 4 , and recognise division facts, through beginning with any and 8 multiplication products in multiplication continued practice. multiple, and count tables, and recognise tables as multiples of the forwards and backwards products in these corresponding number. through the odd numbers. multiplication tables as multiples of the corresponding number. 4NF–2 Solve division problems, with two-digit dividends and one-digit divisors, that involve remainders, and interpret remainders appropriately according to the context. 3NF–3 Apply place-value 4NF–3 Apply place-value 5NF–2 Apply place-value knowledge to known knowledge to known knowledge to known additive and multiplicative additive and multiplicative additive and multiplicative number facts (scaling number facts (scaling number facts (scaling facts by 10). facts by 100) facts by 1 tenth or 1 hundredth). 4 Strand Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 AS 1AS–1 Compose 2AS–1 Add and subtract 3AS–1 Calculate 6AS/MD–1 Understand numbers to 10 from 2 across 10. complements to 100. that 2 numbers can be parts, and partition related additively or numbers to 10 into parts, multiplicatively, and including recognising odd quantify additive and and even numbers. multiplicative relationships (multiplicative relationships restricted to multiplication by a whole number). 1AS–2 Read, write and 2AS–2 Recognise the 3AS–2 Add and subtract 6AS/MD–2 Use a given interpret equations subtraction structure of up to three-digit numbers additive or multiplicative containing addition ( ), ‘difference’ and answer using columnar methods. calculation to derive or subtraction ( ) and questions of the form, complete a related equals ( ) symbols, and “How many more…?”. calculation, using relate additive arithmetic properties, expressions and inverse relationships, and equations to real-life place-value contexts. understanding. 2AS–3 Add and subtract 3AS–3 Manipulate the 6AS/MD–3 Solve within 100 by applying additive relationship: problems involving ratio related one-digit addition Understand the inverse relationships. and subtraction facts: add relationship between and subtract only ones or addition and subtraction, only tens to/from a two- and how both relate to the digit number. part–part–whole structure. Understand and use the commutative property of addition, and understand the related property for subtraction. 2AS–4 Add and subtract 6AS/MD–4 Solve within 100 by applying problems with 2 related one-digit addition unknowns. and subtraction facts: add and subtract any 2 two- digit numbers. 5 Strand Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 MD 2MD–1 Recognise 3MD–1 Apply known 4MD–1 Multiply and 5MD–1 Multiply and For year 6, MD ready-to- repeated addition multiplication and division divide whole numbers by divide numbers by 10 and progress criteria are contexts, representing facts to solve contextual 10 and 100 (keeping to 100; understand this as combined with AS ready- them with multiplication problems with different whole number quotients); equivalent to making a to-progress criteria equations and calculating structures, including understand this as number 10 or 100 times (please see above). the product, within the 2, quotitive and partitive equivalent to making a the size, or 1 tenth or 1 5 and 10 multiplication division. number 10 or 100 times hundredth times the size. tables. the size. 2MD–2 Relate grouping 4MD–2 Manipulate 5MD–2 Find factors and problems where the multiplication and division multiples of positive whole number of groups is equations, and numbers, including unknown to multiplication understand and apply the common factors and equations with a missing commutative property of common multiples, and factor, and to division multiplication. express a given number equations (quotitive as a product of 2 or 3 division). factors. 4MD–3 Understand and 5MD–3 Multiply any apply the distributive whole number with up to property of multiplication. 4 digits by any one-digit number using a formal written method. 5MD–4 Divide a number with up to 4 digits by a one-digit number using a formal written method, and interpret remainders appropriately for the context. 6 Strand Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 F 3F–1 Interpret and write 6F–1 Recognise when proper fractions to fractions can be represent 1 or several simplified, and use parts of a whole that is common factors to divided into equal parts.