MULTIPLICATION CALCULATION GUIDANCE. Year 1
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- Belinda Johns
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1 MULTIPLICATION CALCULATION GUIDANCE Year 1 solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher. Year 2 recall and use multiplication facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers calculate mathematical statements for multiplication within the multiplication tables and write them using the multiplication ( ), and equals (=) signs show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot solve problems involving multiplication using materials, arrays, repeated addition, mental methods, and multiplication including problems in contexts. Year 3 recall and use multiplication facts for the 3, 4 and 8 multiplication tables write and calculate mathematical statements for multiplication using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental and progressing to formal written method solve problems, including missing number problems, involving multiplication including integer scaling problems and correspondence problems in which n objects are connected to m objects. Year 4 recall multiplication facts for multiplication tables up to use place value, known and derived facts to multiply mentally, including: multiplying by 0 and 1; multiplying together three numbers recognise and use factor pairs and commutativity in mental calculations multiply two-digit and three-digit numbers by a one-digit number using formal written layout solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects.
2 Year 5 solve problems involving multiplication and division where larger numbers are used by decomposing them into their factors multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers multiply numbers mentally drawing upon known facts multiply whole numbers and those involving decimals by 10, 100 and 1000 solve problems involving addition, subtraction, multiplication and division and a combination of these, including understanding the meaning of the equals sign solve problems involving multiplication and division, including scaling by simple fractions and problems involving simple rates. Year 6 multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication perform mental calculations, including with mixed operations and large numbers. use their knowledge of the order of operations to carry out calculations involving the four operations solve problems involving addition, subtraction, multiplication and division use estimation to check answers to calculations and determine, in the context of a problem, levels of accuracy. STAGE 1 Develop multiplication as repeated grouping (repeated addition of sets of the same size) using practical apparatus and diagrams.
3 STAGE 2 Develop an understanding of multiplication using arrays and number lines showing repeated groups. Use number lines to show repeated grouping (repeated addition of sets of the same size). STAGE 3 Develop the use of x and = symbols to record calculations horizontally. Use arrays and other practical apparatus to illustrate commutativity (that multiplication calculations can be carried out in any order) e.g. 2 x 5 arrives at the same product as 5 x 2. Begin to derive new facts from known facts e.g. 3 x 2 = 6 (known fact) 30 x 2 = x 2 = 600 etc.
4 40 20 STAGE 4 Begin to use understanding of place value and partitioning to carry out multiplication of two- digit by one -digit numbers 15 x x 4 = 40 5 x 4 = = 60 Use grid approaches to illustrate as appropriate using practical apparatus to support Develop expanded recording in columns and then move to formal written method, using practical apparatus to support as required. T U T U x 4 x (5 x 4) (10 x 4) 2 6 0
5 STAGE 5 Extend written approaches to HTU x U, then to ThHTU x U Illustrate using partitioning approaches as required 215 x x 4 = x 4 = 40 5 x 4 = = 860 Illustrate using grid approaches as required Develop expanded recording in columns and then move to formal written method, using practical apparatus to support as required. H T U H T U x 4 x ( 5 x 4) ( 10 x 4) ( 200 x 4) 8 6
6 STAGE 6 Extend written approaches to HTU x TU and ThHTU x TU Illustrate using grid approaches as required 26 x = 338 Develop expanded recording in columns and then move to formal written method of long multiplication, using practical apparatus to support as required. H T U H T U x 1 3 x ( 6 x 3) ( 20 x 3) ( 6 x 10) ( 10 x 20) x = 2938
7 Develop expanded recording in columns and then move to formal method of long multiplication, using practical apparatus to support as required. H T U H T U x 1 3 x ( 6 x 3) ( 20 x 3) ( 200 x 3) ( 6 x 10) ( 20 x 10) ( 200 x 10) In addition to these stages, staff should also refer to the Big Maths scheme when planning their lessons. Children should be encouraged to follow the FAB (mental maths) progression, which is a key feature of the Big Maths scheme. Below are the Progress Drives related to Subtraction, which teachers should address when planning Maths. Fact Families I know the fact families for 1d+1d (L2) 3+4=7, 4+3=7, 7-3=4, 7-4=3 I can turn 1d+1d facts into multiples of 10 (L2) 30+40=70, 40+30=70, 70-30=40, 70-40=30 When given a single fact, I know the fact family (L3) 23+41=64, 41+23=64, 64-23=41, 64-41=23 I know the fact families for 1dx1d facts (L4) 2x9=18, 9x2=18, 18 2=9, 18 9=2 I know smile multiplication fact families (L4) 20x90=1800, 90x20=1800, =90, =20 Multiply by 10,100,1000 I can multiply whole numbers by 10 (L1) I can multiply whole numbers by 100 (L2) I can multiply decimals by 10 (L3) I can multiply decimals by 100 (L4) I can multiply whole numbers and decimals by 1000 (L5)
8 Smile Multiplication I can multiply multiples of 10 (L3) I can write smile multiplication times tables I can write smile multiplication fact families (L4) I can do smile multiplication for tenths (L4) I can do smile multiplication for hundredths (L5) Coin Multiplication I can complete a 1,10, card I can complete a 1,2,5,10 card I can complete a full coin card I know when to add 2 multiples together I know when to add 3 multiples together Multiple Factor, Square,Prime I know what a multiple is (L4) I know what a factor is (L4) I understand square numbers (L4) I understand prime numbers (L5) Doubling the Big Maths way / \ / \ \ / \ / 428
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