Broadwater Down Primary School Calculations Policy

Transcription

1 Broadwater Down Primary School Calculations Policy Division Reception Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Mental calculations Working at a practical level to gain experience of sharing and to become familiar with appropriate language. Can you share the 6 apples between 2 children? doubles of all numbers to 10 and corresponding halves. Practical work involving sharing into and sharing by. multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers Derive and use halves of two digit numbers to 50. Understand division as sharing and grouping. Know that division calculations can have a remainder. multiplication and division facts for the 3, 4 and 8 multiplication tables. Derive and use doubles of all numbers to 100 and the corresponding halves. Write and calculate mathematical statements for division using the multiplication tables that they know, including for two-digit numbers times one-digit numbers, using mental methods. Understand division is the inverse of multiplication. Recall multiplication and division facts for multiplication tables up to Use partitioning to double or halve numbers, including decimals to one decimal place. Use place value, known and derived facts to multiply and divide mentally, including: dividing by 1. Continue to recall multiplication and division facts for multiplication tables up to Use partitioning to double or halve numbers, including decimals to two decimal places. Divide numbers mentally drawing upon known facts. Divide whole numbers and those involving decimals by 10, 100 and Continue to recall multiplication and division facts for multiplication tables up to Use partitioning to double or halve any number. Perform mental calculations, including with mixed operations and large numbers. Associate a fraction with division and calculate decimal fraction equivalents (e.g ) for a simple fraction (e.g. 3/8). Divide by 0.1 and Understand how multiplication and division can be shown using an array. Understand division as sharing and grouping.

2 Written methods Can you share the 12 bananas between 3 children? Calculate mathematical statements for division within the multiplication tables and write them using the, division ( ) and equals (=) signs. Repeated subtraction using a number line to support the subtraction of each number. Write and calculate mathematical statements for division using the multiplication tables that they know, including for two-digit numbers by a one-digit numbers, using mental and progressing to formal written methods. Divide numbers up to three digits by a onedigit number progressing to formal written layout. Divide numbers up to 4 digits by a one-digit number using the formal written method of short division and interpret remainders appropriately for the context. Continue to divide numbers up to 4-digits by a two-digit whole number using the formal written method of short division. Divide numbers up to 4 digits by a two-digit whole number using chunking if needed. Informal recording, e.g. Children also learn how to use grouping to find the answers to division questions. There are 3 groups of 3 in How many 4s in 12? 12 4 = is the same as how many groups of 4 are there in 12? 12 jumps of 4 with 2 left over, 50 4 = 12 r 2 Chunking Moving to: a) How many 4s in 5? 1 remainder 1 b) Carry the remainder in front of the next digit, then how many 4s in 18? 4 remainder 2 c) Carry the remainder in front of the next digit, then how many 4s in 24? 6 d) How many 4s in 584? Find out How many 36s are in 972? by subtracting chunks of 36, until zero is reached (or until there is a remainder). Teach pupils to write a useful list first at the side that will help them decide what chunks to use, e.g. Useful list: 1x = 36 10x = x = 3600

3 Moving on to the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context. e.g. To calculate 748 divided by 51, First, set the sum out as shown: We work out 74 divided by 51, and write the answer (1) above the = 51, so we write this underneath 74. Subtract 51 from 74 to get the remainder (23). We now bring down the next digit (8) and write it on the end of the 23. We now work out 238 divided by 51, and write the answer (4) above the 8. You use

4 estimation skills here: 51 is roughly 50 and 4 50 = 200. You can work out 51 4 = 204 separately. We write 204 underneath the 238 and subtract to find the remainder. There are no more digits to bring down, so we have our answer: Use written division methods in cases where the answer has up to two decimal places.

5 Multiplication Reception Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Mental calculations Working at a practical level to gain experience of doubling and become familiar with appropriate language. How many eyes does one person have? How many pairs of eyes can you see? Lining up in 2s Finding a partner in P.E. Count forwards and backwards in multiples of twos, fives and tens. doubles of all numbers to 10 and corresponding halves. Use the vocabulary associated with multiplication. Introduce odd and even numbers. Practical work involving lots of. Practical work to show link between 2 lots of 4 and 4 lots of 2. Count in steps of 2, 3, and 5 from 0, and in tens from any number, forward or backward. multiplication facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers. Calculate mathematical statements for multiplication. Understand multiplication as repeated addition. Count from 0 in multiples of 4, 8, 50 and 100. multiplication facts for the 3, 4 and 8 multiplication tables. Derive and use doubles of all numbers to 100. Derive and use doubles of all multiples of 50 to 500. Write and calculate mathematical statements for multiplication using the multiplication tables that they know, including for two-digit numbers times onedigit numbers, using mental and progressing to formal written methods. Understand how multiplication can be shown using an array. Count in multiples of 6, 7, 9, 25 and Recall multiplication facts for multiplication tables up to Use partitioning to double numbers, including decimals to one decimal place. Use place value, known and derived facts to multiply mentally, including: multiplying by 0 and 1 and multiplying together three numbers. Recognise and use factor pairs and commutativity in mental calculations. Count forwards or backwards in steps of powers of 10 for any given number up to Continue to recall multiplication facts for multiplication tables up to Use partitioning to double numbers, including decimals to two decimal places. Multiply numbers mentally drawing upon known facts. Multiply whole numbers and those involving decimals by 10, 100 and Count forwards or backwards in steps of powers of 10 for any given number up to Continue to recall multiplication facts for multiplication tables up to Use partitioning to double any number. Perform mental calculations, including with mixed operations and large numbers. Multiply and divide 0.1 and 0.01.

6 Written Calculations Calculate mathematical statements for multiplication within the multiplication tables and write them using the multiplication ( ) and equals (=) signs. Children will begin repeated addition on a given number line and move on to using a blank number line. 3x5 = Children may use arrays as visual prompts. Write and calculate mathematical statements for multiplication using the multiplication tables that they know, including for two-digit numbers times onedigit numbers, using mental and progressing to formal written methods. 13 x 7 = 10 x 7 = 3 x 7 = On a number line 38 x 7 = Multiply two-digit (and three-digit numbers) by a one-digit number or two-digit number using the grid method, extend to bigger numbers. Introduction of vertical format linked to grid method. 38 x (30 x 7) 56 (8 x 7) 266 Multiply numbers up to 4 digits by a one- or two-digit numbers using a formal written method, including long multiplication for two-digit numbers is approximately = Moving to, Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication. e.g. To calculate : First, multiply by 7 (units): 158 x Then add a zero on the right-hand side of the next row. This is because we want to multiply by 60 (6 tens), which is the same as multiplying by 10 and by 6. Now multiply by 6: 158 x Now add your two rows together, and write your answer.

7 158 x So the answer is

8 Addition Reception Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Mental calculations Practical activities and discussions. Finding one more than a number from 1 to 10. Using vocabulary associated with addition. Questions should be real life and related to children s experiences. How many bears are there altogether? (adult asks orally) I have 4 bears and I add 2 more bears. How many do I have now? Represent and use number bonds and related within 20. Add and subtract one-digit and two-digit numbers to 20, including zero. Use knowledge that addition can be done in any order to do mental calculations more efficiently. to 20 fluently, and derive and use related facts up to 100. Add and subtract numbers using concrete objects, pictorial representations, and mentally, including: a two-digit number and ones a two-digit number and tens two two-digit numbers adding three one-digit numbers Use partitioning to reflect mental methods. for 100. Add and subtract numbers mentally, including: a three-digit number and ones a three-digit number and tens a three-digit number and hundreds for 100. Derive and use for 1 and 10 (with decimal numbers to one place). for multiples of 100 totalling Add and subtract numbers mentally combinations of one, two and three digit numbers and decimals to one decimal place numbers. for 1 and 10 (with decimal numbers to one place). Derive and use for 1 and 10 (with decimal numbers to two places). for 1 and 10 (with decimal numbers to two places). Perform mental calculations, including with mixed operations and large numbers and decimals. Use their knowledge of the order of operations to carry out calculations involving the four operations.

9 Written calculations Read, write and interpret mathematical statements involving addition (+) and equals (=) signs. Use a number track to count on for addition, counting on from the largest number: = 9 Put your finger on number five. Count on (count forwards) four. Then progress to a marked number line: = 12 Use a given number line to make jottings. Draw a number line to make informal jottings. Blank number lines, bridging through = = 84 or: Partitioning = = = = 135 Using informal pencil and paper methods (jottings) and introducing vertical addition. Adding TU and TU moving into HTU using jottings (most significant digit first) = = Add numbers with up to 4 digits using a vertical format, least significant digit first, extended to bigger number. Leading on to, children using the compact layout, involving carrying Add numbers with decimals to one decimal places using the formal written methods of columnar addition where appropriate. Add whole numbers with more than 4 digits, including using formal written methods (columnar addition) Add numbers with two decimal places using the formal written methods of columnar addition where appropriate. Add whole numbers and decimals using formal written methods

10 Subtraction Reception Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Mental calculations Practical activities and discussions. Finding one less than a number from 1 to 10. Using vocabulary associated with subtraction. Questions should be real life and related to children s experiences. Begin to relate subtraction to taking away. There are 5 starfish on a rock, the tide comes in and washes 2 away. How many are left? Represent and use number bonds and related subtraction facts within 20. Add and subtract one-digit and twodigit numbers to 20, including zero. to 20 fluently, and derive and use related facts up to 100. Add and subtract numbers using concrete objects, pictorial representations, and mentally, including: a two-digit number and ones a two-digit number and tens two two-digit numbers adding three one-digit numbers Use partitioning to reflect mental methods. for 100. Add and subtract numbers mentally, including: a three-digit number and ones a three-digit number and tens a three-digit number and hundreds for 100. Derive and use for 1 and 10 (with decimal numbers to one place). for multiples of 100 totalling Add and subtract numbers mentally combinations of one, two and three digit numbers and decimals to one decimal place numbers. for 1 and 10 (with decimal numbers to one place). Derive and use for 1 and 10 (with decimal numbers to two places). for 1 and 10 (with decimal numbers to two places). Perform mental calculations, including with mixed operations and large numbers and decimals. Use their knowledge of the order of operations to carry out calculations involving the four operations. Written calculations

11 Read, write and interpret mathematical statements involving subtraction (-) and equals (=) signs. Use a given number line to make jottings. Draw a number line to make informal jottings. Use a number line to count on and back for subtraction. Growing awareness of whether counting on or back is the most efficient method = = 15 5 = = 8 or with larger numbers, = = = 48 Awareness of whether counting on or back is the most efficient method. Use a number line to record complementary addition = = 47 or Partitioned numbers are then written under one another: Example: (Use of manipulatives to move on) Use vertical subtraction in expanded form. Expanded subtraction without crossing 10/100 s boundaries. Expanded subtraction crossing boundaries. Move towards contracted subtraction using decomposition. Example: =225 In this example 503 has to be partitioned into in order to carry out the subtraction calculation. This leads into the formal written method (there is potential for error in this example): Subtract whole numbers with more than 4 digits, including using formal written methods (columnar subtraction). Subtract numbers with two decimal places using the formal written methods of columnar subtraction where appropriate. Subtract whole numbers and decimals using formal written methods. Our aim is that by the end of Y6 children use mental methods (with jottings) when appropriate, but for calculations that they cannot do in their heads, they use an efficient formal written method accurately and with confidence There are no tens in the first number (503) so we have to exchange a hundred for 10 tens before we can exchange a ten for ten ones/units.