# Assessing pupils’ progress in mathematics at Key Stage 3

## Assessment summary

Pupil C's attainment in each attainment target and in mathematics overall is best described as secure level 5.

**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

Calculating Context Homework: At the beginning of a unit on calculating and solving numerical problems, pupils solved a series of problems involving the four operations. They interpreted their answers in the context of the question.

## Assessment focus-2

Numbers and the number system; Calculating Context Classwork: A mental mathematics lesson starter comparing fractions, decimals and percentages. Pupils had to fill in the gaps (the circled numbers were given by the teacher).

## Assessment focus-3

Algebra Context Group work: During a unit on using algebra to express rules, groups of pupils sorted cards into sets of three. They substituted dice scores for d to check their results. They entered the calculations into a scientific calculator (algebraic logic) as a double check. Pupil C explained the results from her group to the rest of the class.

## Assessment focus-4

Algebra Context Classwork: Towards the end of a unit on using algebra to express rules, pupils manipulated algebraic expressions, including the use of a single pair of brackets.

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

Pupil C uses the order of operations in arithmetic. She has a good understanding of operations and relationships between them. She knows, for example, that addition and multiplication are commutative and that multiplication is distributive over addition and subtraction, and uses her own language to describe this. She has developed successful techniques for written calculations involving the four operations.

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

Pupil C's attainment in number and algebra is judged to be secure in level 5. To demonstrate evidence of working at high level 5 she needs to further develop methods for working with fractions and percentages. She needs to solve problems that involve ratio and direct proportion. Pupil C needs to develop her use of algebra so that she can express the rule for the nth term of a sequence.

## Assessment focus-5

Shape, space and measures Context Classwork: During a unit on calculating the area and perimeter of shapes, pupils solved problems involving compound shapes and mixed units of length.

## Assessment focus-6

Shape, space and measures Context Homework: In a unit of work on transformations, pupils reflected and translated shapes in all four quadrants.

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

Pupil C uses a range of properties of 2-D and 3-D shapes, recognising, for example, that the opposite faces of a cube are parallel and adjacent faces are perpendicular. Given a 2-D shape she finds all lines of reflective symmetry and identifies rotational symmetry. She reasons about shapes to solve a problem such as drawing a shape that has exactly two lines of symmetry. Pupil C solves problems involving angles at a point, at a point on a straight line and in a triangle. For example, she calculates the angle between intersecting diagonals of a regular octagon.

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

Pupil C's attainment in shape, space and measures is judged to be secure in level 5. To make further progress in this level she needs to develop her reasoning about shapes, positions and movements. She needs to construct a range of 3-D shapes to improve her reasoning about how a given net is related to the shape it will create. She needs to solve a range of problems such as drawing a quadrilateral that has exactly two lines of symmetry or two different isosceles triangles that both have a 30° angle.

## Assessment focus-7

Handling data Context Classwork: In a unit on statistics and probability, pupils estimated probabilities and experimented to test their estimates. Working in pairs, one pupil hid a coin in one hand while the other guessed which hand held the coin. Pupils estimated the number of times they expected to guess correctly if the experiment was repeated 20 times. They then carried out the experiment.

## Assessment focus-8

Handling data Context Homework: In a unit on statistics and probability, pupils expressed probabilities as fractions and recorded them on a 0 to 1 scale. Amongst other examples, they considered cards with the letters for HORSE and REINDEER, and in each of these cases the probability of drawing particular cards at random.

## Assessment focus-9

Handling data Context Classwork: In a unit on statistics, pupils used a spreadsheet that contained data on smoking habits in Wales and Scotland. They were shown how to construct pie charts. They then created their own pie charts, using the ICT, and compared data for the two countries.

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

Given a set of data, such as information about smoking habits in Scotland and Wales, Pupil C processes and represents the data, interprets the graphs and charts that she creates and comments on what they show. She poses questions and represents the data in different ways to find answers. She groups discrete data and represents it using a bar graph. She understands that pie charts show the proportion of the sample in each category and that when comparing two pie charts, the sample size may be relevant. She is beginning to recognise when data is represented in a misleading way.

## Summarising Pupil C's attainment in handling data

Pupil C's attainment in handling data is judged to be secure in level 5. To make further progress she needs to ask her own questions and plan how to collect the data needed to answer them. She needs to work with continuous data such as the heights of pupils in different year groups in the school.

## Assessment focus-10

Using and applying mathematics Context Classwork: In a unit on number sequences and patterns, pupils investigated the number of ‘tiles’ needed to border a rectangle that is one unit wide. Linking cubes were available for pupils to create the sequence of rectangles practically.

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

Given a starting point, such as finding the number of blue border tiles for a row of white tiles, Pupil C works methodically. In this example she increased the length of the row by one white tile at a time. When she investigated amounts that could be paid using no more than 10 coins, she worked from paying with one coin, two coins, etc. As she constructed a sequence of squares, using one diagonal of each square as an edge of the next, she was methodical in choosing which diagonal to use each time so that the design spiralled clockwise.

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

In using and applying mathematics Pupil C's attainment is judged to be secure at level 5. Her reasoning is a strong aspect of her performance. To make further progress in level 5 she needs to use her reasoning and experience of a range of problems to develop strategies for engaging with more complex problems. She needs to have problems and investigations introduced in a way that provides scope for her to make decisions about the approach to take. She needs to explain and justify the decisions she makes and the conclusions she draws.