Maths Workshop for Parents Handy hints on terminology and calculation methods

Intro Theory Methods for multiplication and division Place value multiplication and division Order of Operations Factors and Multiples Prime Factorisation

Do it your way! 25x19 5% of 86 248-99 103-98 ½ of 378 1+2+3+4+5+6+7+8+9+10+11= 25x10x2- 25 = 475 or 4x25 = 100 so 16x25 = 400 +3x25 10% is 8.6 5% is 4.3 Look for pairs that make 10 (4) = 40 + 10 = 50 + 11=61 + 5 = 66. More efficient – make 12s – 12x5 = 60 + 6 = 66

Mentally add and subtract any pair of 2-digit numbers For most children during the latter part of year 3 Children will be using a variety of mental methods by this time Teachers will use professional judgement – this is only describing how most children will develop. Now we’ll have a look at what we mean by mental methods DOES NOT MEAN NO WRITING DOWN. -Mental calc. goes on in all years – doesn’t stop and isn’t replaced by written methods – more about this later.

Mental first 56+ 29 or 56 +29 Children cease to “say” the numbers, seeing only digits in columns e.g. “6 add 9” instead of “56 add 29” Need to keep the focus on saying the numbers so they get a sense of the size of the answer and learn to estimate it e.g. 56 can be rounded to 60, 29 is nearly 30 so answer round about 90. Talk about common errors Do 56 add 30 = 86, then subtract 1 Now demonstrate partitioning and the likely mistakes with vertical. This understanding of the relative size of numbers and the likely size of an answer is crucial to efficient calculation. Demonstrate place value ITP using 13 and 31

This is most sensibly done by counting back, not by decomposition 2000 -102 This is most sensibly done by counting back, not by decomposition Take 100, 1900, then 2 1898. Now demo the decomposition. Show first 342 – 197, then this one

25x8 or 25 x 8 Children relying on written procedures forget how much they can do mentally. 25x8 is double 25x4 Talk about the differences between mental and written.

The calculating repertoire “Brain paper”: Mental recall of number facts Mental methods of calculation Real paper (and use of calculators) Jottings to record mental calculations Informal written methods Standard written methods A helpful analogy – when you run out of brain paper (i.e. when there are too many bits to keep in your head) you can use proper paper to help but you are still working things out in your head – just keeping track of the thinking. Informal written methods are based on the mental methods children are learning – an interim step between doing everything in your head to using a standard method for large numbers that you can’t handle mentally. They do not look like the traditional standard methods that you would have learned – reason why maths books look a bit different. Give a couple of number line examples e.g. 28+ 36 and 64-28

The calculating continuum Mental Recall Mental Calculations with jottings Informal Methods Expanded Written Methods Standard Written Methods Calculator

The calculating repertoire Children constantly move up and down the continuum Learning a new method of calculating does not mean other ways are no longer relevant Children should always be looking for calculations they can do wholly or partly mentally By the time chn get to the national tests in year 6 they need to have a repertoire of strategies, including written methods so they can look at a calculation and decide on the best way of doing it. Ask themselves – “Can I do any of this in my head? What do I need to jot down? What’s the best method for tackling this? E.g. remember 103-98 – small answer because numbers are close together – count on. 3003 – 2998 , same type of subtraction so do it same way. Demo the number line. But 3004 – 1847, could do mentally – demo. on number line, but could begin to be at the limit for some children of what they are comfortable with mentally so perhaps best with a more formal method. This is the point at which teachers use their professional judgements to move children on to more formal methods.

A structured approach to calculation An approach based on the skills of mental calculation: Remembering number facts Using known facts to derive new ones Familiarity with the number system and relationships between numbers Having a repertoire of mental calculation strategies Understanding of the four operations and how they are related Deriving e.g. 6+4=10 – demonstrate Seeing that 103-98 gives the same result as 3003-2998 and knowing the answer is small because the numbers are close together. Add/subtract, mult/div are opposites. Mult. Is a short cut way of doing repeated addition 4+4+4 is 4x3 and div. is repeated subtraction 12/4 can be found by taking groups of 4 away until you can’t do it any more. Having a repertoire doesn’t mean that they are taught to do the same thing in so many ways that they get totally confused. It means guiding their instinctive ways of doing something through talking about it, allowing time for them to see someone else’s way, discussing what might be the best way to do it. The National Curriculum, which must be followed by all schools, by law, only states the kind of calculations that children need to be taught at each level; it does not specify any method.

Addition and subtraction Partitioning is an important strategy children must learn A number line is a method of informal calculation that works for any size of number, for both operations. Knowing 33+ 25 = 58 leads to the following: 25+ 33 = 58, 58-33 = 25, 58-25 = 33 25+ ? = 58 ?+? = ?+? Demo the partitioning – incl knowing decimals e.g. 3.3 + 2.5 is 5 + 0.8- understanding of place value crucial to success in calculation. Then show how this links to using a number line

Multiplication and division Multiplication is repeated addition, division is repeated subtraction Doubling, halving, partitioning, and multiplying by 10, 100, 1000 are essential mental strategies 3x4=12 leads to 4x3, 12÷3, 12÷4, 6x4, etc, 30x4, 300x4, 120÷4 etc Children need to see facts as arrays Show 3x4, 4x3 and mult. div on number line Having gone through this show grid method and chunking

Moving from informal to formal methods At every stage, teachers first use examples that children can easily do mentally Children then see how the steps in a written procedure link to what they do in their heads They then move to using numbers that cannot easily be dealt with mentally, including money and decimal numbers Partitioning and place value are crucial concepts and estimation of size of answers is essential. Emphasise that the expanded methods can be used in SATs – NC only specifies what calculations chn need to do, not how they do them. All they need to be able to do is show each step in the calculation. Re-emphasise though that teachers are expected to move children to a compact standard method if appropriate since they are, in the end, the most efficient for complex large numbers.

Long multiplication Grid method Compact / formal / column method

Long division Chunking Bring down remainders (DMSBR)

Place value multiplication and division Move digits one column to the left to x10 Move digits one column to the right to ÷10 Essential skill Measure conversions Percentages

Order of operations (BIDMAS) 32 + 4 x (7 – 2) B = brackets I = indices D = division or M = multiplication A = addition or S = subtraction = 32 + 4 x 5 = 9 + 4 x 5 = 9 + 20 = 29

Factors and multiples You multiply two or more numbers together to find their product. The product of 2 and 7 is 14: 2 x 7 = 14 14 is a multiple of 2 and is also a multiple of 7 Any whole number can be written as the product of two factors.

Factors and multiples You can list all the factor pairs of a number or You can write the factors in a list If there are only two factors, the number is a prime number A square number has an odd number of factors

HCF and LCM Highest Common Factor Lowest Common Multiple

Prime Numbers and Prime Factorisation Important to learn divisibility rules Try to recognise primes up to 100

Open Forum Any specific queries? Future workshops?