Starter

Try this………

101 - 102 = 1

Make one move to create a true statement.

101 =102 - 1

101- 10² = 1

Numeracy across the curriculumProblem Solving and the approach to calculations

Objectives• To consider current images of mathematics and

mathematicians;• To explore numeracy V’s Maths;• To introduce activities to develop numerical literacy / oral

communication skills;• To improve interpretation and presentation of graphs, charts

and diagrams;• To improve reasoning and problem solving;• To explore possible areas for inter-departmental cooperation

in this type of activity (consistency).

Why do we need to raise standards in numeracy?KS2 SAT MATHS Current Year 7

2 15

3A

423B

3C

4A

764B

4C

5A

405B

5C

N 7

Grand Total 180

8% of the children are

below L3

32% are below a level

3 or below

74% below a level 4a or below

L4+ 64%

L5 22%

Is numeracy a problem?

Views of mathematicsMathematics is …• an important subject• nothing to do with real life• a boys’ subject• something you can either do or you can’t• about learning rules• about right and wrong answers

I'm sorry to say that the subject I most

disliked was mathematics. I have thought about it. I think the reason

was that mathematics leaves

no room for argument. If you made a mistake, that was all there

was to it.Malcom X

A good calculator does not need artificial aids. Lao Tze (604-531 B.C.) Tao Te Ching

I remember once going to see him when he was lying ill at Putney. I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. "No," he replied, "it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.“

Hardy, Godfrey H. (1877-1947) Ramanujan, London: Cambridge University Press, 1940.

I am ill at these numbers. William Shakespeare, (1564-1616) Hamlet.

I can’t do maths!!!!!!!!

"It is difficult to understand why so many people must struggle with concepts that are actually simpler than most of the ideas they deal with

every day. It is far easier to calculate a percentage than it is to drive a car." (Dewdney 1993, p. 1)

To many people, the words "math" and "simple" do not belong in the same sentence. Math has such an aura of difficulty around it that even people who are quite competent in other areas of life are not ashamed to admit they can't "do" math. Innumeracy is more socially acceptable and

tolerated than illiteracy (Dewdney 1993; Withnall 1995).

Influencing Attitudes• Poor learning experiences and fear of getting the ‘wrong’ answer

contribute to the negative impression many adults have of mathematics. Problems can be created if these views are passed on to pupils by staff or parents.

• Some teachers may put pupils under pressure in their lessons to perform mathematical routines that are insufficiently developed or are unfamiliar, this can reinforce negative feelings which pupils may already have.

• Some teachers may avoid the mathematical elements of their subject, thereby losing opportunities to demonstrate the necessity of mathematics.

Maths V’s Numeracy –What is numeracy?

“…an ‘at-homeness’ with numbers and an ability to cope with the mathematical demands of everyday life… An ability to have some appreciation and understanding of information which is presented in mathematical terms, for instance, graphs, charts or tables or by reference to percentage increase or decrease.”

(Cockcroft Report, 1982)

“Numeracy is a proficiency which involves confidence and competence with numbers and measures. It requires an understanding of the number system, a repertoire of computational skills and an inclination and ability to solve number problems in a variety of contexts. Numeracy also demands practical understanding of the ways in which information is gathered by counting and measuring, and is presented in graphs, diagrams, charts and tables”

(National Framework for teaching Mathematics, 1999)

Task 1 - Which of these are maths tasks and which are numeracy activities?

• Reading graphs• Planning a journey• Calculating area of pond liner required• Working out the length of a diagonal line using

Pythagoras• Drawing a pie chart• Converting metres to centimetres.• Mixing paint

Numeracy is a fundamental life skill.

Being numerate involves developing a confidence and competence in using number that allows individuals to solve problems, interpret and analyse information, make informed decisions, function responsibly in everyday life and contribute effectively to society. It gives increased opportunities within the world of work and sets down foundations which can be built upon through life-long learning.

Whilst numeracy is a subset of mathematics, it is also a core skill which permeates all areas of learning, allowing pupils the opportunity to access the wider curriculum.

It is therefore important that all teachers look for opportunities to develop and reinforce numeracy skills within their own teaching activities and through inter-disciplinary projects and studies.

Numeracy – Mathematical literacyNUMERACY IS NOT JUST ABOUT NUMBERS. Numeracy is a socially based activity that requires the ability to integrate math and communication skills (Withnall 1995).

It is intricately linked to language: words are the tools for translating numerical code and giving it meaning. Words can have everyday meanings as well as math meanings: for example, "and" is a conjunction, but in math it can also mean "plus."

Some words are math specific: numerator, multiplicand, divisor. Interpretation of these words can cause confusion for people with low literacy levels.

Why is maths talk so important?

In studying mathematics students are expected to:• discuss• explain• describe • argue a particular point of view (for

example, justifying a strategy for solving a problem).

Why do it?

Maths is about problem solvingProblem solving requires thinking skills

Thinking skills require academic language

The iceberg model

• Cognitive and academic language

• Basic interpersonal communicative skills

1. Look at these pairs of words. How do you recognise if these words are being used mathematically?

1. Look at these pairs of words. How do you recognise if these words are being used mathematically?

Task 2 – Mathematical literacy1. Add four more pairs of words with dual meanings.

2. Are there any words that have three or more meanings – mathematical or other (for example, “square” as in number, in shape or as units of area)?

3. Put three of these pairs in a context – a sentence or question to show usage.

4. How can you make the meanings more explicit?

Mathematical V’s every day

How many words can you think of?

How can you help?

• Use concrete reference in your room• Use Numeracy / literacy mats• Encourage discussion

Model the language - What am i?

•A hexagonal prism which is about 15 cm long and ½ cm wide. It usually has a cone at the end.

•A ring drawn in the air about 15cm diameter, now cut away a quarter of it. Attached to the ends of

the remaining part of the ring are 2 cylinders about 1cm deep with a diameter of 5cm.

Numeracy in Ofsted inspectionsWhat are they looking for?

• whether there is clear understanding and consistent practice among staff in the development of pupils’ mental skills, written methods of calculation and use of calculators;

• if pupils can identify and use an efficient strategy for the calculations they need to do;

• if pupils cope well with the mathematical demands made in different subjects, or are held back through lack of mathematical knowledge or poor basic skills in numeracy;

• how well numeracy and, where appropriate, other mathematical skills are taught, developed or practised in other subjects

Activity – Mental and oral work

• Everyone reads scales in everyday life – thermometers, tape measures or speedometers for example.

• Yet this is an area of mathematics which pupils often find difficult to transfer to other subjects.

Reading scales

© Crown copyright 2001

Scales

0 10

3

© Crown copyright 2001

Scales

0 20

6

© Crown copyright 2001

Scales

2 7

3.5

Which numbers are you happy with? (Work these out!)

147 + 149

224 ÷ 4

79 + 52

162 – 28

87 6

= 296

= 56

= 131

= 134

= 522

Calculating

Mental methods

Mental + thinking tools + jottings

Written methods 

Calculators

StrategiesNumber Facts:Doubles and HalvesNumber BondsTimes tables facts

Number Techniques:DecompositionMultiply and divide by 10, 100, 1000 etc.Change the orderEquivalencesNearest 10 and adjust

Calculate the answers in your heads. Then think about

the methods you used.

42 + 35 45 + 46

6 + 78 37 + 199

And subtraction…..?

67 – 32 54 – 28

60 – 19 2005 – 1996

Demonstration 1032 – 786 using an empty number line, for example:

So 1032 – 786 = 14 + 200 + 32 = 246. This method is very flexible –different pupils might choose different sized ‘steps’ to suit their thinking – but widely applicable.

46

56

50 656=50+6

Partitioning

50 – 30 = 20 Starting with what child can do mentally 8 – 2 = 6 Start by dealing with the tens 20 + 6 =26 Child can use known subtraction facts

58 - 32 152 - 41 50 + 8 100 + 50 + 2- 30 + 2 - 40 + 120 + 6 = 26 100 + 10 + 1 = 111

Decomposition of 58 - 32

This stage introduces: Expanded layout based on partitioning 1)Lining up vertically 2) Specific position of operation symbol 3)Lines to delineate answer

This stage introduces: Expanded layout based on partitioning 1)Lining up vertically 2) Specific position of operation symbol 3)Lines to delineate answer

How are children expected to multiply and divide now?

GraphsBar Chart to show representation of non-numerical data

0

1

2

3

4

5

6

7

8

9

10

walk train car bus other

Mode of Transport

Nu

mb

er o

f p

up

ils

0123456789

0

Fre

qu

ency

Height (cm)

"Bar Chart" to show representation of continuous data

Why is it incorrect?

0123456789

10

walk train car bus other

Nu

mb

er

of

pu

pils

Mode of Transport

Incorrect Use of Line Graph

Axis

eg

0 10 20 30 40 50 60 NOT

0 1 2 3 4 5 x

© Crown copyright 2001

Washing Up

Give a plausible explanation for the shape of this graph.

Real-Life

Gra

phs

Common difficulties in Handling Data

• Graphs and charts are incorrectly drawn or labelledFor example, the bars in a bar chart representing the votes cast for candidates in a school election are joined together or are of different widths

• Graphs and charts are read incorrectly or interpreted inappropriatelyFor example, the vertical scale marked in thousands on a population graph is misread: 350 000 is read as 350

• Mean, median and mode are confused or used inappropriatelyFor example, the mean is used when referring to the average monthly rainfall in India

• Data are represented by inappropriate graphs or chartsFor example, a pie chart is used to represent the distances of the different planets from the Sun

Common difficulties in Handling Data

• Activities are aimless or contexts inappropriateFor example, vast quantities of data are collected without any consideration of the purpose of the enquiry

• Undue time is spent on mechanical skills and there is insufficient emphasis on interpreting data and making inferencesFor example, pupils are taught to draw pie charts or calculate a mean without understanding of when it is appropriate to use these or how to interpret them

Common difficulties in Handling Data

The numeracy outcomes are organised around the following themes.

• Estimation and rounding • Number and number processes • Fractions, decimal fractions and percentages • Money • Time • Measurement • Information handling

All teachers should integrate outcomes from these different themes, enabling pupils to make connections in their learning through taking part in meaningful experiences within relevant contexts.

Links to other subjects:History and GeographyCollect dataDisplay of dataInterpretation of dataLine of best fitRates (Per hundred, thousand)ScaleGrid referencesArea/distanceApplication of the 4 operations

TechnologyLength, Area, VolumeMass/weightCollect, display and interpret data%, decimals and fractionsCostingsApplication of the operationsRatio and proportion

Science%, decimals, fractionsMass/weightHandling DataManipulate formulaeSpeed/distance/timeStandard form, large and small

numbersMeasures, Area, volumeApplication of the 4 operationsSquare and square rootsProportion and RatioLine of best fit

IT/Business Studies

Use of spreadsheetsFormulaeUse of moneyProfit and loss, break even%, decimals and fractionsData collection sheets /

questionnairesDisplay and interpretation of dataApplication of the 4 operations

Modern foreign languages and technologies (home economics): Planning and making a French meal – quantities of ingredients, measurement, using scales.

Numeracy outcome: I can use my knowledge of the sizes of familiar objects or places to assist me when making an estimate of measure. 

RE: Presentation of data relating to ethical issues.

Numeracy outcome: Having discussed, .  can interpret and draw conclusions from the information displayed, recognising that the presentation may be misleading. 

Numeracy outcome: I can work collaboratively, making appropriate use of technology to source information presented in a range of ways, interpret what it conveys and discuss whether I believe the information to be robust, vague or misleading. 

PSE: Population statistics, casualties in battles and wars

Numeracy draft outcome: I can solve problems by 

carrying out calculations with a wide range of fractions, decimal fractions and percentages, using my answers to make comparisons and inform choices for real life situations. 

Enterprise courses: Numeracy draft outcome: 

I can budget effectively, making use of technology and other methods, to manage money and plan for future expenses. 

What you can do?

‘All teachers have responsibility for promoting the development of numeracy. With an increased emphasis upon numeracy for all young people, teachers will need to plan to revisit and consolidate numeracy skills throughout schooling.’

- Building the Curriculum 1

Task

• Create a learning mat for your subject area.

1. Look through the numeracy policy and make yourself aware of the various numeracy strategies available for you to use in the classroom.

2. Ensure that you use the correct terminology in your class room.

3. Display the various different types of graphs and use the numeracy mats to help your students in lessons.

4. Encourage your form to become actively involved in the puzzle for the day competition, perhaps enter as a class.

Conclusion• Oral and mental mathematics includes much more

than rapid recall of number facts and mental tests

• There is a clear progression in calculation skills from mental skills through jottings to written methods and the use of calculators.

• Pupils should be encouraged to approach a calculation by first asking themselves what is the most appropriate method: mental, written or using a calculator.

STEM

• Are you making the pupils aware of stem careers linked to your subject area?

• STEM is a big area of focus in the UK currently – what do you do to promote STEM? What does the school do?

• What skills are required for STEM?