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Transforming lives through learning Scottish Survey of Literacy & Numeracy Transforming lives through learning Support material for Measurement First Level - Area Produced by Education Scotland

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Scottish Survey of Literacy and Numeracy 2011 Performance in Measurement in P4 Based on the recent 2011 Survey of Literacy and Numeracy, evidence indicates that more than half of P4 pupils answered correctly, questions based on the measurement organiser. I can estimate how long or heavy an object is, or what amount it holds, using everyday things as a guide, then measure or weigh it using appropriate instruments and units.MNU 1-11 I can estimate the area of a shape by counting squares or other methods. MNU 1-11b

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Scottish Survey of Literacy and Numeracy 2011 Evidence from this survey suggests that pupils have difficulty with the following aspects of measurement at P4: Reading scales where the value of an intermediate graduation needs to be deduced Counting squares to measure area of irregular shapes involving whole and half square centimetres. Multi-step and word problems, particularly those without a diagrammatical representation Measuring lengths and weights involving every-day objects, particularly when involving halves or quarters.

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Evidence also suggests that learners are more successful with the following aspects of measurement at P4. Ordering objects in weight and length when they have a visual representation Finding the area of regular shapes which only involve whole square centimetres. Scottish Survey of Literacy and Numeracy 2011

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In the 2011 Scottish Survey of Literacy and Numeracy, in a question similar to this, most learners answered correctly. Question A box of apples is put on a scale What did the box of apples weigh?

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In the 2011 Scottish Survey of Literacy and Numeracy, in a question similar to this, around two fifths of learners answered correctly. Question How much do the apples weigh? A153 grams B150 grams D190 grams C180 grams

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In the 2011 Scottish Survey of Literacy and Numeracy, in a question similar to this, around a third of learners answered correctly. Question Angus is 1m 19 cm tall. Mark is 14 cm shorter than Angus. Sam is 10 cm taller than Mark. How tall is Sam?

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In the 2011 Scottish Survey of Literacy and Numeracy, in a question similar to this, about a third of learners answered correctly. Question Jill pours milk into a measuring jug. How much milk is in the jug? 3 litres 2 litres 1 litres

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In the 2011 Scottish Survey of Literacy and Numeracy, in a question similar to this, about a third of learners answered correctly. Question Camilla is growing cress seeds. She measures the height of the tallest seedling. Measure the height of the drawing of the cress seedling in millimetres. How often are learners given the opportunity to work with millimetres.

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Measurement at First level I can estimate how long or heavy an object is, or what amount it holds, using everyday things as a guide, then measure or weigh it using appropriate instruments and units. MNU 1-11a

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Scottish Survey of Literacy and Numeracy 2011 In the Scottish Survey of Literacy and Numeracy, in a question similar to this, almost a third of learners answered correctly. Question Which unit of length would you use to measure the distance between Edinburgh and Glasgow? Tick ( ) one box. Acentimetre Bmillimetre Ckilometre Dmetre

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Pupil responses A4% B8% C66% D21% 1% of pupils did not attempt this question.

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Scottish Survey of Literacy and Numeracy 2011 A question focusing on reading a scale to measure length: About half of pupils answered this question correctly. Question What is the length of this paper clip to the nearest centimetre?

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First Level - Experiences & Outcomes I can estimate the area of a shape by counting squares or other methods. MNU1-11b

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First Level - Area Recent surveys, including 2011 Scottish Survey of Literacy and Numeracy, show that children find it difficult to estimate the area of a shape. What strategies would be appropriate to develop this concept with learners?

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I am developing a sense of size and amount by observing, exploring, using and communicating with others about things in the world around me. MNU 0-01a I have experimented with everyday items as units of measure to investigate and compare sizes and amounts in my environment, sharing my findings with others. MNU 0-11 It is crucial that before children try to estimate the area of a shape, they first understand what the term area relates to. Children must understand that area is the amount of surface enclosed within the boundaries of a two-dimensional shape. First Level – Initial understanding Building on prior learning from early level Es and Os

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Before engaging in the measurement of shapes children should be encouraged to look at objects in their environment able to discuss surface coverage and size able to compare e.g. the floor surface of the gym hall, playgrounds or sports field, the top of the dining tables or classroom tables, or the surface of display boards….

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For example Based on evidence from this survey, almost half of pupils achieved the correct answer for this question. Question Each square has an area of 1 square centimetre. What is the area of the shaded shape (in square centimetres)? Scottish Survey of Literacy and Numeracy 2011 Exemplars

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By inspection, how do learners compare the amount of surface for different shapes? Can they always make this judgement through inspection? If inspection is not appropriate, what other methods could be used to compare the area of two different shapes? Reflective questions

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First Level – Introducing the concept of Area (direct and indirect comparisons) Using a variety of non standard units of measurement e.g. hands, bottle tops, counters etc, children should be given the opportunity to explore how to compare the area of 2 shapes or objects such as jotters/books/tables. Encourage children to discuss the problems associated with using such a variety of different measuring units.

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Using non standard units for estimating the area of regular shapes

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Estimating the area of irregular shapes Having developed the understanding of measuring area using squares: What learning activities will support estimating the area of irregular shaped objects? What part will rounding play in the process?

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Square Units Through discussion, children should understand the inconsistencies and gaps caused by using non-standard units of measurement (counters/hands etc) that area is always measured in square units. People often use square centimetres, square metres or square kilometres for measuring area.

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In the 2011 Scottish Survey of Literacy and Numeracy, in a question similar to this, almost a third of learners answered correctly. Question Donald draws a triangle on a grid. What is the area of the triangle? Each square = 1 square centimetre (cm 2 ).

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Reflective questions How can we ensure that children understand what a square centimetre or square metre looks like? Can they think of situations when a square metre would be a better unit of measurement than square centimetres?

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Square Unit of Measurement Allow children the opportunity to measure, draw or identify square units (cm or m) using rulers, measuring tapes, metre sticks or trundle wheels ensuring they understand that all sides must measure 1. Children should then explore laying squares over a surface to enable them to calculate the area through the counting of squares. For example, children can use square centimetre pieces of paper to calculate the area of their reading book. Do they think that using these square centimetres would be a suitable way of measuring a classrooms or playgrounds area? What could they use instead? (introduce square metres of paper) 1 1 1 1

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1 cm 2

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1 m 2

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1 km 2

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Progressing from estimating to calculating For regular shapes, the progression from estimating to calculating involves counting squares Can you support children to link their learning of repeated addition to multiplication using area? 3 3 3 3 3 + 3 + 3 + 3 + 3 is the same as…. 5 sets of 3 = 5 x 3 = 15 3

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By allowing children to use practical materials they can explore making the possible combinations of length and breadth e.g. laying out 24 building blocks or 24 paper squares in different ways. relating practical activities to costs of materials, carpets etc. using whole numbers. Practical exploration

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Some practical ideas for AREA – considering Bloom’s Taxonomy The following activities are ideas to promote HIGHER ORDER THINKING skills in children. ANALYSING – breaking information into parts to explore understanding and relationships (organising/comparing/deconstructing) Calculate the areas of these compound shapes in square centimetres (breaking into rectangles). Which has the greatest area? Creating Evaluating Analysing Applying Understanding Remembering

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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.

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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.

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www.educationscotland.gov.uk

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