Transforming lives through learning

Scottish Survey of Literacy & Numeracy

Transforming lives through learning

Support material for Measurement

Second Level - Area

Produced by Education Scotland

Scottish Survey of Literacy and Numeracy 2011Performance in Measurement at Second Level

Based on the recent SSLN 2011 survey, evidence indicates that over half of P7 pupils answered correctly, questions based on the measurement organiser.

I can use my knowledge of the sizes of familiar objects or places to assist me when making an estimate of measure. MNU 2-11a

I can use the common units of measure, convert between related units of the metric system and carry out calculations when solving problems MNU 2-11b

I can explain how different methods can be used to find the perimeter and area of a simple 2D shape or volume of a simple 3D object. MNU 2-11c

Evidence from this survey also suggests that pupils have difficulty with other aspects of measurement at P7:•Calculating volumes•Where fractions, decimal fractions and percentages was a secondary organiser•Area and perimeter•Conversion of units, especially those involving decimal fractions.

Scottish Survey of Literacy and Numeracy 2011

This presentation will:

•Explore aspects of measurement pupils find challenging•Consider why these aspects cause particular difficulties•Identify strategies to support learning with the aim of promoting deeper understanding

Second Level - Experiences & Outcomes

I can use the common units of measure, convert between related units of the metric system and carry out calculations when solving problems.

MNU2-11b

Common units of measure

• Length : mm, cm, m and km

• Area: mm2, cm2, m2 and km2

• Volume: mm3, cm3, m3 and km3

• Mass: mg, g, kg and tonne

2011 Scottish Survey of Literacy and Numeracy

Based on evidence from the survey, less than half of pupils gave the correct response to this question.

QuestionHow many grams are there in 4.75 kg?

“I can use the common units of measure, convert between related units of the metric system.” MNU 2-11b

Pupil responses include:• A 4750 g• B 475 g• C 4500 g• D 4075 g

Reflective questionHow would you plan learning and teaching to resolve the

‘common errors’?

Support for multiplication at Second Level can be found on the Education Scotland website.

UnitsWhy do learners find the conversion of units so challenging?

Is it the unit conversion or the inability to multiply and divide by 10, 100 and 1000 that causes difficulty?

Exploring the language of units could enhance learners’ understanding.

Through learners understanding the significance of the prefixes ‘centi-’, ‘milli-’ and ‘kilo-’ , converting between units becomes easier.

Language of MeasureBuilding on language from the Es and Os in First level

For example:I have discussed the important part that numbers play in the world and explored a variety of systems that have been used by civilisations throughout history to record numbers.

MTH 1-12a

Metric system ~ milli

• Latin for thousand ( mille)• Millennium• millipede• milliamp

Metric system ~ centi

• French for hundred• Century• Centurion• U.S. currency

Metric system ~ kilo

• Ancient Greek for thousand• kilograms• kilobytes• kilocalories• kilohertz

Based on evidence from the survey, less than half of pupils gave the correct response to this question.

QuestionWhich of the following is the most likely to be nearest to the weight of an average man?

Tick () one box.A 8.5 kgB 85 kgC 185 kgD 850 kgE 1850 kg

Scottish Survey of Literacy and Numeracy 2011

Reflective questionWhat real life contexts could you include, when planning learning and teaching, to enable pupils to select appropriate units for length, area and weight?

Pupil responses

Second Level - Experiences & Outcomes

I can explain how different methods can be used to find the perimeter and area of a simple 2D shape or volume of a simple 3D object.

MNU2-11c

Building on First Level areaThe following Es and Os contribute to progression in learning within MNU 2-11c

MNU 1-11a

MNU 1-11b

MNU 1-01a

MNU 1-02a

MNU 1-03a

MTH 1-16a

Units and AreaHere is an example of a question that has been shown to be problematic for learners.

Question: Find the area of the rectangle

50cm

0.25m

• Why does a question like this cause difficulty?• Does over reliance on using a formula reinforce the

difficulty?• How do we enable learners to interrogate a question to

extract the relevant information?

0.5 m0.5 m

0.25 m

50 cm

25 cm 0.25 m

1 m

1 m

25 cm

25 cm

25 cm

25 cm

50 cm 50 cm

100 cm = 1 m

Based on evidence from the survey, a quarter of pupils gave the correct response to this question.

Question:A 4 cm square is cut from a piece of card which is 8 cm by 6 cm.

What is the area of the card remaining after the square is cut?

Scottish Survey of Literacy and Numeracy 2011

8 cm

4 cm

6 cm

Pupil responsesReflective questionHow would you plan learning and teaching to improve the number of pupils, who can successfully answer this type of question?

Reflective questionsConsider the following questions:

How often do you: •Emphasise the part units play in area calculations?•Plan rich learning tasks which consolidate learning of area?•Consider other shapes where the product of length and breadth is not applicable?•Plan tasks which involve conversion of units?

Different methods to find the area of 2D shapes: Area of a triangle

It is important that learners consider the relationship between rectangles and triangles. They should be encouraged to investigate why the area of a triangle is half the area of the corresponding rectangle.

Through an investigative approach, learners should establish that the area of a triangle is one half that of the corresponding rectangle, a formula can then be discussed.

Consider this triangle . . .

12 cm

16 cm

12 cm

16 cm

Developing numeracy

Calculating the area of the type of triangle in the previous slide, discussion could support the development of incorporating a secondary organiser eg fraction or decimal fraction.

•Is the area ½ of 12 multiplied by 16?•Is the area ½ of 16 multiplied by 12?•Is the area 12 multiplied by 16 and then halved?•Do we need to half both?•What could determine which number we should half, to simplify the number calculation?

Key features to consider when planning CPD for learning and teaching

• There is a clear developmental sequence throughout the lesson , learners recognise links with earlier work, build on prior learning in numeracy and confidently use their knowledge within familiar and unfamiliar contexts.

• An appropriate balance between developing and synthesising/using key facts.

• Programmes of study and practitioners’ lesson plans make effective use of prior learning to build on learners’ numeracy knowledge and skills including second and third level interface.

• Learners confidently use mental strategies.

Key features to consider when planning CPD for learning and teaching

• Learners give explanations of their reasoning as well as their methods.

• Non-routine problems, open ended tasks and investigations are often used by learners to develop their problem solving skills to develop their problem solving skills including reasoning and generalising.

• Staff introduce new numeracy terms, vocabulary and symbols meaningfully and expect and encourage correct use.

The Numeracy Principles and Practice Paper is essential reading for everyone and can be used to prompt discussion amongst staff.

www.educationscotland.gov.uk