Children’s ideas of mathematics

Maths can sometimes be challenging so can also make some people feel

uncomfortable!

We will be discussing what is needed for children to become

confident and competent mathematicians, who have a strongly developed ‘sense of

number’.

Using Loop Cards – working together & having fun

Awe and Wonder

National Numeracy Strategy 1999National Numeracy Strategy 1999“Raise achievement in mental calculation.”“Mental calculation requires efficient methods of working with numbers ‘in your head’ and NNS says that teaching written methods too early can prejudice children’s chances of this.” Emphasis on being ‘numerate’ – hence its name of ‘Numeracy Strategy’.

Mathematics Curriculum from Mathematics Curriculum from September 2014September 2014DFE:

“The majority of the new national curriculum will come into force from September 2014, so schools have a year to prepare to teach it. From September 2015, the new national curriculum for English, mathematicsmathematics and science will come into force for years 2 and 6”. “Teachers should develop pupils’ numeracy and mathematical reasoning in all subjects so that they understand and appreciate the importance of mathematics. Pupils should be taught to apply arithmetic fluently to problems.”

Primary Framework Mathematics 2006 Primary Framework Mathematics 2006 Introduced in 2006 and revised in 2011.‘A clearer structure for teaching mathematics has been provided by simplifying the structure of the objectives’. Debatable!

Each child’s entitlementBest chance when assessedSecondary schoolFurther education

Adults use maths in everyday life

For a chosen career

Practical approaches to develop understanding, confidence and

enjoyment.

Traditional methods to develop and consolidate knowledge and skills.

PoliciesSchemes of workPlanning for learningChildren’s work Practical resources

Mathematical language is crucial to children’s development of thinking.

Understanding spoken or written instructions‘draw a line between…’ find two different ways to…’

Being familiar with mathematical vocabulary e.g. ‘difference’ ‘subtract’, ‘divide’, ‘product’

Understanding confusing mathematical terms e.g. ‘odd’ ‘table’, ‘area’ – these have different everyday meaning in

English

From September 2014 the mathematics curriculum will be organised into …

Number, measures, geometry, statisticsIn addition Year 6 will be taught Ratio & Proportion and algebra

Fractions

Percentages

Temperatur

eTime

Money

2 & 3D shape

Angles Data Handling

Area

Perimeter Decimals

Understanding of NumberUnderstanding of NumberWhatever stage the children are at with their learning, and whatever method is being used, it must be underpinned by a secure and appropriate knowledge of

number facts, along with those mental skills that are needed to both carry out the process and judge it was successful.

Alphabet Land The new number names for 1,2,3,4 .. Are A,B,C,D …

You must NOT translate these number names into the banned names one, two, three …

Answer the following questions in order. You may use finger, objects or construct a number line (with the new number names) to help you.

How many fingers on your left hand?How many fingers do you have altogether?C + D = ?B + E = ?K – B = ?G + D = ?D x C = ?

What strategies are you using?

Practical – using fingers helps!Relationships between numbers and the strategies for addition,

subtraction, multiplication.

Answers to ‘Alphabet Land’

GE iG K L

Developing a sense of number

By the time children leave primary school they will have been taught mental, written (and calculator)

methods that they understand and can use correctly.

Children should be able to decided which method is the most appropriate

when faced with a calculation.

There are many ‘correct’ strategies but it is more effective for children to learn just a few and learn

them well. Refer to the school’s Calculation Policy.

Lewis Carroll: ‘Alice Through the Looking Glass’ talking with Humpty Dumpty

“How many days are there in a year?”“Three hundred and sixty-five,” said Alice.“And how many birthdays have you?”“One.”“And if you take one from three hundred and sixty-five, what remains?”“Three hundred and sixty-four of course!”Humpty Dumpty looked doubtful.“I’d rather see that done on paper,” he said.

4.5

27 old age pensioners want to go to see the lights in Blackpool in 6 taxis and want to share the taxis.

How many taxis will be needed?

You have 27p to spend and want to buy CHOCOLATE.The chocolate bars cost 6p How many chocolate bars can you buy?

What is 27 divided by 6? But what if the question is

…..

5

4

Problem Solving … Problem Solving … Put the numbers 1 to 4 in the circles so that the

difference between each pair of joined numbers is more than 1

(Year 1)

Put 15 buttons in three boxes so that each box has 3 more buttons

than the one before.

(Year 2)

Count all the rectangles in this diagram.

(Year 4)

X 4 9

8 18

3 12

35 14

2

Complete this multiplication

table

(Year 6)

Answers … Answers …

2 4 1 3

X 5 4 9 2

2 10 8 18 4

3 15 12 27 6

7 35 28 63 14

1 5 4 9 2

1 2 3

4 5 6

7 8 9

10

11

12

13

14

15

19 20 21

22 16 17 18

24

23

26

25

36 35

3429

30

31

2728

33

32

36

This section outlines the key concepts, facts and skills that form the development of children’s calculation strategies

Four Operations of Number

Ways of recording Children learn to use models and images – eg number lines to record or explain steps As mental methods become more refined so too are their informal written methodsThese methods become more efficient and succinct; leading to effective written methods

Carry out a standard written method of column addition

Partition and recombine

Using number lines

Carry out a standard written method of column subtraction

4

55

63

32 x 3 = 96 123 x 7 = 861 23 x 17 = 391

Up to 3 by 1-digit division …. with remainders …

but no ‘carrying’ within the problem

3 by 1-digit division …. with remainders and ‘carrying’ within

the problem

Division by repeated subtractionSharing

Know by heart all the facts for 2,3,4,5,6,7 and 10 x tables

ANDAND

Recognise and use multiplication as the inverse of division …….

7 x 6 = 42 42 ÷ 6 = 7

TalkPlaying games Consolidating learning … eg counting onPractical tasks… cooking, sewing, DIYConstruction toys TimeMoneyMeasures – estimatingReinforcement of number bonds, tables … learning by ‘heart’ Being positive

You have worked hard and completed activities …

•Enjoying mathematics •NOT been writing•NOT worked alone or in silence

Thank you for supporting our mathematics information evening!