# Assessing pupils’ progress in mathematics at Key Stage 3

## Assessment summary

Pupil M's attainment is best described as high level 3. His performance is between secure and high in all attainment targets.

**Using the Standards Files**

- The current Standards Files are based on work planned and assessed in relation to the 1999 National Curriculum programme of study. A new set of Standards Files based on the 2008 National Curriculum are currently in production, but the current set will provide useful guidance on making APP assessments against national standards in the transition period as the new programmes of study are introduced.
- The commentaries in the Standards Files are provided for guidance and reference, and are much more extensive than any teacher would be expected to make when carrying out APP assessments. It is also important to remember that APP encourages and enables a broader overview of current learning, and that there is no need to collect special portfolios of pupils’ work. Evidence from pupils’ written and oral work, backed up by brief teacher's notes where necessary, is all that is required.
- The evidence base presented in each Standards File is necessarily partial, as it would of course be impractical to reproduce all of each pupil's work. Examples of each pupil's work have been selected to provide evidence to support judgements against APP criteria. This evidence should be considered in conjunction with the teacher's notes, which will provide a broader context and further justification for the assessments that are made.

## Assessment focus-1

Numbers and the number systemContextHomework: To underpin the development of mental calculation skills and checking strategies, pupils used a number line to help them round to the nearest 10.

## Assessment focus-2

Calculating; Using and applying mathematicsContextClasswork: Investigating totals and differences with money. Pupils chose collections of coins and answered four questions about each collection.

## Assessment focus-3

CalculatingContextClasswork: In a lesson on division pupils derived division facts from known multiplication facts and then completed examples of division.

## What the teacher knows about Pupil M's attainment in number and algebra

Pupil M understands place value in numbers with up to five digits. He multiplies whole numbers by 10 and 100. He also divides by 10 or 100 where the answer is a whole number. Pupil M uses a number line as a model of the number system. He understands negative numbers in the context of counting backwards past zero on a number line and for recording temperatures below freezing. He understands decimals in the context of money and orders amounts involving pounds and pence and just pence expressed as pounds (e.g. £0.10).

## Summarising Pupil M's attainment in number and algebra

Pupil M's attainment in number and algebra is best described as high in level 3. To consolidate level 3 and move into level 4 he should consolidate his knowledge of multiplication facts and begin to develop the concepts of multiple and factor. This will help him to recognise a wider range of number patterns and broaden his mental calculation strategies. He needs to develop understanding of decimals and extend his use of decimals with one and two decimal places in contexts other than money, such as measures.

## Assessment focus-4

Shape, space and measuresContextClasswork: In a unit on 2-D shapes, pupils described quadrilaterals for a partner to name. Pupils recorded descriptions and their responses.

## Assessment focus-5

Shape, space and measuresContextHomework: In a unit on transformations, pupils reflected a design of shaded squares in a mirror line.

## What the teacher knows about Pupil M's attainment in shape, space and measures

Pupil M classifies 3-D and 2-D shapes using a range of mathematical properties. He uses numbers of sides, equal angles, equal sides and right angles to sort 2-D shapes. He uses numbers and shapes of faces and numbers of edges and vertices to sort 3-D shapes. He names 3-D shapes such as a cube, cuboid, pyramid, and prism. Pupil M recognises right angles and acute, obtuse and reflex angles in shapes. He names most quadrilaterals and recognises right-angled and equilateral triangles.

## Summarising Pupil M's attainment in shape, space and measures

Pupil M's attainment in shape, space and measures is best described as high level 3. To consolidate level 3 he needs to develop understanding of reflective symmetry. He also needs to begin to plot the reflection of each vertex of a shape using its distance from the mirror line. To make progress into level 4, Pupil M needs to recognise and use parallel lines in 2-D shapes. He needs to consolidate his understanding of area as a measure of surface and perimeter as a measure of length and to use the terms consistently.

## Assessment focus-6

Handling dataContextClasswork: In a unit on probability, each pupil was given a statement on A4 card. They sorted themselves into a line to represent the order of probability of the statements. Pupils then worked in pairs placing a selection of the statements using a probability scale from ‘impossible’ to ‘certain’ with ‘even chance’ as the mid-point.

## Assessment focus-7

Handling dataContextClasswork: In a unit on statistics, groups of pupils collected data on the types of cars in a car park. They used ICT to display information in a pictogram.

## What the teacher knows about Pupil M's attainment in handling data

Pupil M decides what data to collect to answer a question such as ‘What types of car are there in the school car park?’ In group discussion he refines the question by identifying categories for the data collection. Discussing the car park survey, for example, Pupil M decided the most common types of car would be saloon, hatchback, sports and 4x4. He decided to use ‘other’ to capture information about cars that did not fit his categories.

## Summarising Pupil M's attainment in handling data

Pupil M's attainment in handling data is best described as high level 3. To progress into level 4 he needs to begin to work with larger sets of data and to group data where appropriate. He needs to use the mode and range to describe sets of data and begin to compare sets of data. He should begin to construct and interpret simple line graphs.

## What the teacher knows about Pupil M's attainment in using and applying mathematics

Pupil M selects the mathematics to use in a range of classroom activities. In group discussion he clarifies a problem or investigation and this helps him to make decisions about the approach to use. For example, he discussed the types of cars that might be found in the car park and this helped him to design and use his data collection sheet. He chooses the equipment to use, for example, a ruler marked in millimetres to draw lines accurately or a calculator to calculate with larger numbers or to add a long list of numbers.

## Summarising Pupil M's attainment in using and applying mathematics

Pupil M's attainment in using and applying mathematics is best described as secure level 3. To consolidate this and make further progress into level 4, Pupil M needs to develop his checking procedures. He should check his answers to calculations as he works and check that results make sense in the context of the problem. He needs to solve a wider range of problems that relate to mathematical and practical contexts. He needs to be more systematic in his recording by putting results into order, for example, so that he can spot patterns more readily and check results.