Mental Calculation Policy 2014

Transcription

1 Mental Calculation Policy 2014 RECEPTION Children count reliably with numbers from one to 20 and place them in order. Children can say which number is one more or one less than a given number up to 20 Finds the total number of items in two groups by counting all of them Using quantities and objects, they add and subtract two single- digit numbers and count on or back to find the answer. all addition and subtraction facts for numbers to 10. ( the story of each number) They use practical resources to solve multiplication and division problems. e.g. how many wheels on 3 cars? If there are 3 dogs in each house and 4 houses, how many dogs are there? e.g. share these 6 sweets between 3 people. They find halves of objects and shapes in practical situations: ie. Cut this banana into half Begin to count up and back to 50.

2 YEAR 1 Count up and back to and across 100, or from any given number Doubles and halves of all numbers to 10. halves of all Given a number, identify one more and one less numbers to 10. Number pairs with a total of 10 Odd and even numbers to 100 e.g. 3+7, or what to add to a single-digit number to make 10, e.g. 3+ = 10 e.g. ½ of 10 = 5 Number pairs with a total of 20 e.g. 14+6, or what to add to a number to make 20 e.g. 20 = 15+ The story of all numbers to 10. (know addition and subtraction facts for each number) e.g 7: 3+4, 5+2, 6+1, 7+0, 7-6 =, 7-5 = Add any single-digit number to or from a multiple of 10, e.g Addition doubles for all numbers to at least 10 e.g. 8+8 Skills (with jottings ) Add and subtract a pair of numbers less than 20 e.g , 18-3 Add or subtract a single digit number to a multiple of 10 e.g.10+7, , 10-3 = 60-3 = Add near doubles e.g. 5+6 Use patterns of similar calculations e.g. (10-0, 10-1, 10-2) Count on and back to zero in ones. Count up to and beyond 100 e.g. Practice counting from any number 45,46,47,48 or 87, 86, 85, 84 Count on and back in twos, fives and tens. Use practical resources to help visualise (socks, gloves, etc ) Recorder numbers when adding e.g. putting the largest number first Count on or back in ones, twos and tens Partition small numbers e.g. 8+3 = = e.g. 7+8 = Bridge through 10 and later 20 when adding a single digit number Add 9 to a single digit number by adding 10 and subtracting Use patterns of last digits, e.g. 0 and 5 when counting in fives

3 YEAR 2 Addition and subtraction facts for all numbers up to at least 10, e.g. 3+4, 8-5 The story of all numbers to 20 All pairs of multiples of 10 with totals up to 100, e.g , or 60 + = 100 What must be added to any two-digit number to make the next multiple of 10, e.g = 60 Addition doubles for all numbers to 20, e.g and multiple of 10 to 50, e.g Doubles of all numbers to 20 e.g. double 13, and corresponding halves e.g Doubles of multiples of 10 to 50 e.g. double 40, and corresponding halves Multiplication facts for the 2,3,5 and 10 timestables, and corresponding division facts e.g. 7x10, Odd and even numbers to 100 To be able to count in halves. e.g. ½, 1, 1½, 2, 2½,3 Skills ( with jottings ) Add or subtract a pair of single-digit numbers, including crossing 10, e.g. 5+8, 12-7 Add or subtract any single-digit number to or from a multiple of 10, e.g , 80 7 Add or subtract a single-digit number to or from a two-digit number, including crossing the tens boundary, e.g , 57 3, then , 52 7 Add or subtract a multiple of 10 to or from any two-digit number, e.g , Add or subtract 2 two digit numbers Add or subtract 3 one digit numbers Add 9, 19, 29,.or 11, 21, 31 (by adding multiples of 10 and adjusting) Add near doubles, e.g , Partition numbers in different ways e.g. 23 = , 23 = Double any multiple of 5 up to 50, e.g. double 35 Halve any multiple of 10 up to 100, e.g. halve 90 Find half of even numbers to 40 Find the total number of objects when they are organised into groups of 2, 3, 5, or 10 Reorder numbers when adding Partition: bridge through 10 and multiples of 10 when adding and subtracting Partition and combine multiples of ten and ones Use knowledge of pairs making 10 Partition: Count on in tens and ones to find total Partition: Count on or back in tens and ones to find the difference Partition: add tens and ones recombine Partition: subtract tens and then ones. E.g. subtract 27 by subtracting 20 then subtracting 7 Partition: add a multiple of 10 and adjust by 1 Partition: double and tens and ones separately, then recombine Use knowledge that halving is the inverse of doubling and that doubling is equivalent to multiplying by two Use knowledge of multiplication facts from the 2, 3, 5 and 10 times-tables, e.g. recognise that there are 15 objects altogether because there are three groups of five To multiply and divide by 10 by shifting the digits to the left for multiplication and right for division e.g. 23 x 10 = 230, = 4

4 YEAR 3 Count in multiples of 2, 3, 4, 5, 8, 10, 50 and 100 from 0 Be able to give ½, ⅓, ¼, ⅕ of a multiplication and division facts for the 2, 3, 4, 5, 8 number with no and 10 times table more than 3 digits e.g. ⅕ of 25 = 5 Continue to revisit addition and subtraction facts for all numbers to 20 Give 10 or 100 more or less than a given number e.g. 10 more than 345 is 355, 100 less than 145 is 45 quickly all number pairs that total 100 (multiples of 5 and multiples of 10) Round to the nearest 10 or 100 Add and subtract a 3 digit number and units Add and subtract a 3 digit number and tens Add and subtract a 3 digit number and hundreds Doubles and halves of all whole numbers to at least 20 e.g. double 15 = 30, half of 5 is 2.5 Accurately add and subtract numbers mentally including: a 3 digit number and ones e.g ; A three digit number and tens e.g ; A three digit number and hundreds e.g Add and subtract a near multiple of 10 by adding or subtracting 10, 20, 30 and adjusting all pairs of numbers that make 100. e.g , Find the difference between 3 digit numbers Add and subtract amounts of money and give change Find 8 times table by doubling the 4 times table Doubles and halves of multiples of 50 to 500 e.g. double 150, half of 200 Count up and back in 1/10ths Count on and back in hundreds, tens and ones Subtract by counting up from the smaller number to the larger number Partition: add hundreds, tens and units separately and then recombine Partition: add or subtract a multiple of 10 and then adjust, e.g = , = Use knowledge of place value and related calculations, e.g. work out = 290 using = 29 Partition: count on or back in minutes and hours, bridging through 60 (analogue and digital times) Partition numbers in different ways e.g. 146 = , 146 = Understand multiplication as: grouping Understand multiplication as : scaling e.g. A piece of ribbon is 4cm long. How long would a piece be that is 10 x longer. To multiply by 10, 100 or 1000 by shifting the digits to the left for multiplication and right for division and zero is used as a place holder Partition: when doubling and halving, double or halve the hundreds, tens and units separately, then recombine

5 YEAR 4 Multiplication and division facts for tables up to 12 x 12 Pairs of fractions that total 1 Sums and differences of pairs of multiples of 10, 100, 1000 Addition doubles of numbers e.g , and the corresponding halves Add and subtract a near multiple of 10 by adding or subtracting 10, 20, 30 and adjusting Find differences between two numbers by counting on To be able to round to the nearest 10, 100, 1000 To add and subtract multiples of 1, 10, 100, 1000 e.g = 1267, = 7816 quickly all number pairs that total 1000 e.g , Accurately add and subtract numbers mentally including two 3 digit numbers e.g , Partition into tens and units, adding the tens first e.g = ( ) + ( ) + (7 + 3) Recognise and use the factor pairs for known multiplication facts up to 144 e.g. the factor pairs of 12 are: 1 & 12, 2 & 6, 3 & 4 Double and halves of all numbers to 100 e.g. double 55 is 110, half of 71 is 35.5 Find quarters of numbers by halving a half e.g. ¼ of 120 = (120 2) 2 Multiply two digits by one digit by partitioning and adding totals together e.g. 24 x 8 = (20 x 4) + (4 x 8) Find the effect of dividing 1 or 2 digit numbers by 10 and 100, Identifying values of digits as ones, tenths and hundreds Be able to give ½, ⅓, ¼, ⅕ of number with no more than four digits e.g. ⅕ of 250 = 50 Add and subtract fractions with the same denominator Count on and back in hundreds, tens, ones and tenths Partition : add hundreds, tens or ones separately, and then recombine Subtract by counting up from the smaller number to the larger number Add or subtract a multiple of 10 or 100 and adjust Mentally perform multiplication and division calculations quickly and accurately, including multiplying by 0 and dividing by 1 Multiply by 20 by multiplying by 10 and then doubling the answer Partition: double or halve the tens and ones separately, then recombine Recognise and use factor pairs and commutativity in mental calculations

6 YEAR 5 Identify all multiples and factors including finding all factor pairs of a number & common factors of two numbers Add and subtract mentally with increasingly large numbers, e.g. 12,462 2,300 = 10,162 Find the difference by counting up through the next multiple of 10, 100 or 1000 e.g. the difference between 8006 and 2993 Doubles and halves of decimals e.g. half of 5.6, double 3.4 What must be added to any 4 digit number to make the next multiple of 1000 e.g = 5000 What must be added to a decimal with units and tenths to make the next whole number e.g = 8 Partition into thousands, hundreds, tens and units, adding the most significant digits first e.g = ( ) + ( ) + ( ) + ( ) Sums and differences of decimals e.g , Know and use the vocabulary of prime numbers, prime factors and composite (non-prime) numbers e.g. establish where a number up to 100 is prime and recall prime numbers up to 19 Multiply and divide numbers mentally drawing upon known facts Multiply and divide whole numbers and those involving decimals by 10, 100 and 1000 Doubles and halves of all numbers to 1000 Recognise and use square numbers and cube numbers, & the notation for squared² and cubed ³ Convert larger to smaller units of measurement using decimals to one place, e.g. change 2.6kg to 2600g, 3.5cm, 1.2m to 120cm Add or subtract any pairs of decimal fractions each with units and tenths, e.g , To be able to give a fraction of a number e.g. ⅟10 of 67 is 6.7 Use knowledge of place value and related calculations, e.g using Multiply by near multiples of 10 e.g. 29 x 6 = ( 30 x 6) 6 Partition: count on or back in minutes and hours, bridging through 60 (analogue and digital times) Multiply by 25 or 50 e.g. 48 x 25, 32 x 50 using equivalent calculations e.g. 48 x 100 4, 32 x 100 2

7 YEAR 6 Identify common factors, and common multiples Multiply and divide decimals by 10, Multiply by 25 by multiplying by 100 and dividing by 4 100, 1000 and 10,000 Add and subtract numbers mentally with increasingly large numbers e.g. 12, = 10,162 Find the difference by counting up through the next multiple of 10, 100, 10,000 e.g. the difference between 8006 and 2993 To be able to round decimal fractions to the nearest hundredth and thousandth eg rounded to the nearest hundredth is Accurately multiply and divide numbers mentally drawing upon known facts e.g 52 7 = 7 remainder 3 ( 7 x 7 = ) Multiply by near multiples of 10 e.g. 29 x 6 = (30 x 6) 6 Doubles and halves of all numbers to 10,000 Add near doubles of decimals Add or subtract a decimal with units and tenths,that is nearly a whole number. Partition into millions, hundreds of thousands, tens of thousands, thousands, hundreds, tens and units, adding the most significant digits first e.g = ( ) + ( ) Explore numbers, establish whether a number up to 1000 is prime and recall the prime numbers up to 19 Recognise and use square numbers and square roots and the notation or square² and square root Use knowledge of place value and related calculations e.g , , can be worked out using the related calculation Partition: add or subtract a whole number and adjust, e.g = , = Recognise how to scale up or down using multiplication Multiply and divide decimals by 10, 100, 1000 and 10,000 e.g. know that its digits move one, two, three or four places to the left or right relative to the decimal point and zero is used as a place holder