e.g. 4 pencils and a rubber cost 42p. If the rubber costs 10p what is the cost of one pencil? How much change would you get from a pound if you bought 6 pencils? + Addition + Year R Methods to be used by core of class Year 1 Methods to be used by core of Year 2 Methods to be used by core of Use pictures, tens frames, and other concrete resources to add two numbers together as a group or in a bar . See addition appendix 1- combining two parts to make a whole:part-whole model. As year R plus: Teach all the number bonds up to and including 10 and the related ‘Fact Family’ for each fact. Use concrete objects to combine groups to add and solve missing number problems. 3+__= 10 Show this using the part/whole model. Understand value – can partition numbers and recombine numbers Usually start with the biggest number (if counting on) 12 + 5 = 17 at the larger number on the number line and count on in ones or in one jump to find the answer. See addition appendix 1- combining two parts to make a whole: model. Appendix 2 starting at the bigger number and counting on. As year 1 plus: Addition can be done in any order (commutative) 34 + 56 or 56 + 34 Understand place value – can partition numbers & recombine Numbers 37= 30 + 7 30+7 = 37 Use partitioning to add numbers, first with concrete apparatus, then as a possible mental method. Have a of mental methods for calculating first with numbers to 20, then with numbers to 100 e.g. breaking numbers apart to use them flexibly, this may be with a bridging strategy (e.g. 7+5 could be thought of as 7+3+2 or 5+5+2), a compensating strategy (e.g. 7+9 could be thought of as 7+10 then -1) or by using a near double (e.g. 7+8 =14+1). Learn to add three numbers 4 + 7 + 6= 17 Put 4 and 6 together to make 10. Add on 7. Use number bonds e.g. 4+6=10 to work out 40+60=100 See addition appendix 2 starting at the bigger number and countingon. Appendix 3 regrouping to make 10. Appendix 4 adding three single Digits + = 47 25 60 12 then exchange to make 72
Multiplication Year 4 Year 5 Year 6 Expected Expected Expected recall multiplication and division facts for multiplication tables up to 12 × 12 use value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together 3 numbers recognise and use factor pairs and commutativity in mental calculations Use partitioning to double or halve any number, including decimals to one decimal place multiply and three-digit numbers by a one digit number using formal written layout Use estimation and inverse to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy. solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by 1 digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects identify multiples and factors, including finding all factor pairs of a number, and common factors of 2 numbers know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers establish whether a number up to 100 is prime and recall prime numbers up to 19 Use partitioning to double or halve any number, including decimals to two decimal places. Multiply and divide numbers mentally drawing upon known facts. multiply numbers up to 4 digits by a one- or number using a formal written method, including long multiplication for two-digit numbers multiply and divide numbers and those involving decimals by 10, 100 and 1,000 recognise and use square numbers and cube numbers, and the notation for squared (²) and cubed (³) solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes multiply multi-digit numbers up to 4 digits by a two digit whole number using the formal written method of long multiplication identify common factors, common multiples and prime numbers perform mental calculations, including with mixed operations and large numbers use their knowledge of the order of operations to carry out calculations involving the 4 operations problems involving addition, subtraction, multiplication and division use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy 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 multiply numbers with up to two decimal places by whole numbers problems which require answers to be rounded to specified degrees of accuracy