Helping Our Children To Achieve

Welcome Maths is FUN!

How Maths teaching has changed

- To give children the chance to explore ways of finding an answer, and being able to explain why it works

- To give them the key skills needed to solve real world problems and examples

- To provide opportunities to apply these skills in practical situations

Developing understandingPrompting thinking & questioningProviding opportunities to manipulate,

experience and see (use of resources)Develop thinking through investigationReasoning and making connectionsEngaging in talkEnabling learning through drawing attention to.Encouraging children to make links and

generalise

Changing attitudes towards Maths . . .

5 12 21

Which is the odd one out, and why?

Right then, time for a warm up!

No hands up! 1 min talk to a neighbour! Everyone has generalised!

FS and KS1 Mental ArithmeticThe emphasis in KS1 is on mental arithmetic BUT based on practical activities. Useful things to practise at home include:•Doubles and halves•Bonds of 10, 20 and 100•Adding 2 small numbers•Adding or subtracting•Using different vocabulary

KS2 Mental MathsH T U

Times tables and division facts

Number bonds up to 100

Doubling and Halving

Rounding and estimating

x 10, x 100 (DON’T ADD A 0!)

STRONG MENTAL CALCULATION STRATEGIESQuick recall of Number bonds to 20, 50 and 100.

Times tables knowledge 2x, 5x, 10x3x, 4x, 6x, 8x, 9x7x

When ready, the children will move on to more formal written methods. Moving to written procedures too fast can mean:

•Children add/subtract the digits in a column by rote, without understanding what their value is, or what a sensible answer is likely to be•Children who rely on written procedures can be more likely to look for a calculator when stuck, not a mental strategy•Children can hide their understanding of mathematical concepts behind having a good memory for procedure.

for larger numbers, or too many numbers to deal with mentally

Written Methods

When? Why?How? Where?

What?

We will attempt to touch on as many written methods as we can in the time we have. Please stay at the end and ask if you are unsure or have any further questions.

resources to support understanding

Addition• Counting on using objects• Counting on using number line /

tracks• Counting on using a hundred

square• Blank number line (bridging)• Partitioning• Column addition

Addition

48 + 35

Sum

Total Plus

All togetherMore than

ADDITION: Number tracks / ADDITION: Number tracks / lineslines

3 + 2 =

| | | | | | | | | | |

0 1 2 3 4 5 6 7 8 9 10

and 2 more

| | |

0 3 5

Addition : Number linesAddition : Number lines

38 +26 10 10 1 1 1 1 1 1

38 48 58 59 60 61 62 63 64

427 + 358 300 50 3 5

427 727 777 780 785

ADDITION : partitioning36 + 45 = 30 + 40 + 6

+ 5 = 70 + 11 = 81

or

36 + 45 = 36 + 40 + 5 = 76 + 5 = 81

Use of dienes blocks can support this.

Stage 2: Partitioning continued Partitioned numbers are then written under

one another. This mirrors the column method and also links mental methods.

 

ADDITION : Vertical : column addition

4776

110 13

123

Try these out on your table using the resources 2 more than 95 + 8 =Total of 25 and 4174 plus 27134 + 217 =

• Counting back using objects • Counting back using a number line• Counting back using a hundred square• Blank number line• Partitioning

Subtraction

SUBTRACTION: Number linesSUBTRACTION: Number lines

5 – 2 =

| | | | | | | | | | |

0 1 2 3 4 5 6 7 8 9 10

2 less

| | |

0 3 5

SUBTRACTION: 73 – 26 =

+4 +40 + 3

0 26 30 70 73

-4 -40 -3

0 26 30 70 73

SUBTRACTION COUNTING BACK85 - 37 =

- 7 -30 48 55 85

Or finding the difference

Counting on 354 – 188 =

354 – 188 = 12 154

188 200 354

End of year 4 This method would be supported with practical apparatus. Once confident this then leads to the column method. The amount of time spent teaching and practising the expanded method will depend on how secure the children are in their recall of number f acts and with partitioning. Example: 563 − 241 Expanded method leading to

500 60 3200 40 1300 20 2

563241322

Start by subtracting the ones, then the tens, then the hundreds. Ref er to subtracting the tens, f or example, by saying ‘sixty take away f orty’, not ‘six take away f our’.

Examples : try these!Find 2 less than 7What is 27 – 13?62 – 45 =Take away 19 from 9672 – 46What’s the difference between 87 and 105?

How would you tackle this number sentence? Can you explain your method?

Multiplication• Doubles – objects / beadstring • Counting in steps of 2,5,10• Counting objects• Pictures• Number lines• Times tables• Arrays• Grid method

Arrays and numberline Children represent by drawings, counters,

cubes and begin to link to number line as repeated

addition

8 x 23 = 8 x 10 + 8 x 10 + 8 x 3

= 80 + 80 + 24= 184This develops into the grid method.8 x 23 =

X 10 10 3  8 80 80 24 =1

84

leading to

X 20 3  8 160 24 =

184

Multiplication

Double 75 times 63 lots of 423 x 7=13 x 24=

Product

Multiply

Lots of

Times

ArrayRepeated Addition

Division• Halving• Sorting hoops and objects• Pictures• Related times tables facts

Division

‘84 sweets shared equally between 6 children’

How many 6’s go into 84? 84 divided by 6?

84 shared by 6?

There is no need to divide! Use

your tables knowledge!

Examples As with multiplication, division is recorded as arrays, number lines or number sentences. ******** 16 8 = 2 ******** 0 8 16 (I start at zero and count in 8s until I get to 16)

Remainders Number lines can also be used for more complex calculations, where the pupil is working with multiples of the divisor. 33 9 = 9x1=9 9x1=9 9x1=9 6 left (remainder) x x x x x x 0 9 18 27 33 so 33 9 = 3 r 6

196 7 = 7x10=70 7x10=70 7x8=56 0 70 140 196 so 196 7 =28 Place value understanding is needed to count on in multiples of the divisor.

Use of ‘I know’ boxes I know:10 x 7 = 70SO 20 X 7 = 140(I HAVE 56 LEFT) 8 LOTS OF 7=56 SO 196 7 = 28 ( AS I KNOW 28 X 7 = 196) 

Helping at homeSome Dos…

…And Some Don’ts!

• Play (maths) with your child• There are opportunities for

impromptu learning in games with real people that you can't get from a DS or Xbox

• Let your child win or be better than you

• Otherwise all they learn is that you are better at maths than them

• Recognise that there is more than one way of doing calculations

• You may have learned one method, but children are actively encouraged to seek out alternative methods in school and choose one which works for them, no matter how long winded

• Be an actor• Get excited about maths and your

child will get excited too

• Don't expect them to understand after you've explained it once

• It is normal for a child to 'get it' one day, and then in a different context not know how to find an answer

• Don't tell them you are hopeless at maths

• You may remember maths as being hard, but you were probably not hopeless, and even if you were, that implies to your child, “I was hopeless at maths, and I'm a successful adult, therefore maths is not important”

• Don't get into an argument over homework

• It will be something that your child has covered in class, and if they really can't do it without a lot of tears and frustration, leave it and LET US KNOW!

Ideas taken from Maths for Mums and Dads Eastaway, R. and Askew, M. (2010)

 

Helping at home KS1/ FS• Play board games • Cook – measuring and weighing• Look at numbers in the environment e.g.

telephone keys, number plates, door numbers, book pages, sleeps until Christmas!

• Money • Comparing heights• Birthdays, Months of the year, Days of

the week• Time

 

Props around the house KS2• A prominent clock- digital and analogue is even better. Place it somewhere where you can talk

about the time each day.• A traditional wall calendar-Calendars help with counting days, spotting number patterns and• Board games that involve dice or spinners-helps with counting and the idea of chance• A pack of playing cards- Card games can be adapted in many ways to learn about number

bonds, chance, adding and subtracting• A calculator- A basic calculator will help with maths homework when required, there are also

many calculator games you can play, too.• Measuring Jug-Your child will use them in school, but seeing them used in real life is invaluable.

Also useful for discussing converting from metric to imperial• Dried beans, Macaroni or Smarties- for counting and estimating• A tape measure and a ruler- Let your child help when measuring up for furniture, curtains etc• A large bar of chocolate (one divided into chunks)- a great motivator for fractions work• Fridge magnets with numbers on- can be used for a little practice of written methods• Indoor/outdoor Thermometer- especially useful in winter for teaching negative numbers when

the temperature drops below freezing• Unusual dice- not all dice have faces 1-6, hexagonal dice, coloured dice, dice from board games

all make talking about chance a little more interesting• A dartboard with velcro darts- Helps with doubling, trebling, adding and subtracting.

Ideas taken from Maths for Mums and Dads Eastaway, R. and Askew, M. (2010)

Homework!

• Related to classwork

• Use method shown in class

• Check with teacher if unsure!

• It’s the child’s responsibility to complete their homework!