maths app annotated_-_copy

Assessing pupils’ Assessing pupils’ progress in Mathematicsprogress in Mathematics

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KEYKEY

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All text in black is quoted from the Big Sheets. The entire text of the Mathematics Assessment Criteria appear in this

PowerPoint.

KEYKEY

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All Teacher’s notes in white are taken from the guidance on the DCSF website for primary and secondary school’s.

The links (in blue as below) are to the web-pages or documents from which each example is taken, which go into

more detail.

(Please note that some slides are used twice if they apply to two Assessment Focuses)

Primary Maths APP guidanceSecondary Maths APP guidance

http://nationalstrategies.standards.dcsf.gov.uk/search/secondary/results/nav%3A46145

THERE ARE TWO MAJOR THERE ARE TWO MAJOR AREAS OF ASSESSMENT AREAS OF ASSESSMENT

IN APP MATHS:IN APP MATHS:

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1) Using and applying mathematics, shape, space and measure and handling data

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2) Number and algebra

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LET’S BREAK THEM DOWN

A LITTLE

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NO, NO, NOT LIKE THATNOT LIKE THAT

Assessing pupils’ progress in Mathematics - Assessing pupils’ progress in Mathematics -

Using and applying Using and applying mathematics, shape, space and mathematics, shape, space and

measure and handling datameasure and handling data

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Using and applying Using and applying mathematicsmathematics

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Using and applying mathematicsUsing and applying mathematics

LEVEL 2LEVEL 2

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Teacher's notes

Identifies what she has to do.

Models the problem with paper circles and counters.

Starts by placing three counters on each paper circle.

Moves one counter at a time and checks results.

Writes numbers in the given diagram to record her arrangement of counters.

Finds arrangements where lines total 8 but forgets there must be a different number on each plate.

Places a different number on each plate and creates lines that add to 9.

APP mathematics standards file: Hannah (Year 2 secure level 2

Using and applying mathematics: LEVEL 2Using and applying mathematics: LEVEL 2

http://nationalstrategies.standards.dcsf.gov.uk/node/152736?uc=force_uj


LEVEL 3LEVEL 3

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Teacher's notes

understands the criteria: quilts have six squares and at least one square of each of three available patterns

decides to use a trial approach

identifies lines of symmetry

within the time limit, compares diagrams with others in the group to draw her own conclusion

in discussion with the teacher, convinces herself that it is not possible to make a quilt with two lines of symmetry

explains the problem to others.

APP mathematics standards file: Saleema (Year 4, secure level 3)




LEVEL 4LEVEL 4

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Teacher's notes

recognises the least recognises the least number that can be number that can be made is 2 and the made is 2 and the greatest is 18greatest is 18

works systematically works systematically to list all possible to list all possible addition pairs for addition pairs for each totaleach total

describes patterns in describes patterns in the columns of the columns of numbers she has numbers she has recordedrecorded

APP in mathematics at Key Stage 3: Standards file – Pupil B p.6


http://nationalstrategies.standards.dcsf.gov.uk/node/150774


LEVEL 5LEVEL 5

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Teacher's notes

works methodically, works methodically, drawing and labelling drawing and labelling rectangles of increasing rectangles of increasing lengthlength

presents her work in a presents her work in a clear and organised wayclear and organised way

identifies a pattern in identifies a pattern in results and expresses a results and expresses a generalisation using generalisation using function machinesfunction machines

predicts the number of predicts the number of border tiles needed for border tiles needed for much longer rectanglesmuch longer rectangles

poses her own questions poses her own questions to extend the work and to extend the work and investigates borders for investigates borders for rectangles that are 2 rectangles that are 2 units wide, then 3 units units wide, then 3 units widewide

APP in mathematics at Key Stage 3: Standards file – Pupil C p.18




LEVEL 6LEVEL 6

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Teacher's notes

uses trial and improvement to create parallelograms with the same base and area• uses trial and improvement to create parallelograms with the same base and area• looks for relationships between the parallelograms and the rectangle other than base and looks for relationships between the parallelograms and the rectangle other than base and

area area concludes that they all have the same (perpendicular) height even though the sloping concludes that they all have the same (perpendicular) height even though the sloping

sides are different lengthssides are different lengths asserts a formula is possible ‘but you must use height because the sloping side changes asserts a formula is possible ‘but you must use height because the sloping side changes

so you can’t use it’so you can’t use it’ gives the formula as gives the formula as A = b × hA = b × h

APP in mathematics at Key Stage 3: Standards file – Pupil R p.12




LEVEL 7LEVEL 7

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Teacher's notes

Selects appropriate Selects appropriate methods and methods and communicates communicates clearlyclearly

Solves multi-step Solves multi-step problems requiring problems requiring Pythagoras’ theoremPythagoras’ theorem

Calculates Calculates accurately using accurately using mental and mental and calculator methods calculator methods

APP in mathematics at Key Stage 3: Standards file – Pupil V p.11




LEVEL 8LEVEL 8

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Teacher's notes

sketches graphs to sketches graphs to represent height of water represent height of water against volume of water in against volume of water in the container (denoted by the container (denoted by time as it was assumed time as it was assumed that the volume was that the volume was increasing at a constant increasing at a constant rate)rate)

justifies shape of the graphjustifies shape of the graph

uses mathematical uses mathematical

language to discuss resultslanguage to discuss results

APP in mathematics at Key Stage 3: Standards file – Pupil N p.10



Shape, space and Shape, space and measuremeasure

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Shape, space and measure Shape, space and measure

LEVEL 2LEVEL 2

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Teacher's notes

Initially sorts 2-D shapes by colour only.

When asked to sort in a different way, classifies them by number of sides and colour.

When asked to sort in yet another way, classifies them by number of corners and colour.

Goes on to make labels such as 'red and has 3 sides' for each discrete set.

APP mathematics standards file: Hannah (Year 2 secure level 2)

Shape, space and measure: LEVEL 2Shape, space and measure: LEVEL 2



LEVEL 3LEVEL 3

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Teacher's notes

sorts 2–D shapes according to properties: quadrilateral/not quadrilateral and regular/not regular

knows that in a regular shape the sides are the same length and angles are equal

uses the number of sides and other properties to name 2–D shapes.





LEVEL 4LEVEL 4

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Teacher's notes

creates squares in creates squares in different orientations on different orientations on gridsgrids

uses coordinates in the uses coordinates in the

first quadrantfirst quadrant

finds families of squares, finds families of squares, for example, those with a for example, those with a vertex at (0, 0)vertex at (0, 0)

searches for pattern in the searches for pattern in the coordinates of vertices in coordinates of vertices in a row of overlapping, a row of overlapping, congruent squarescongruent squares

identifies a pattern in the identifies a pattern in the coordinates of one of the coordinates of one of the pairs of opposite vertices pairs of opposite vertices





LEVEL 5LEVEL 5

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Teacher's notes

interprets the diagrams interprets the diagrams and calculates edge and calculates edge lengths that are not lengths that are not givengiven

converts metres to converts metres to centimetres and centimetres and centimetres to centimetres to millimetres, even though millimetres, even though units are mixed in the units are mixed in the labels for each diagramlabels for each diagram

calculates mentally the calculates mentally the areas of rectangles and areas of rectangles and adds or subtracts areas adds or subtracts areas appropriatelyappropriately

in self-evaluation, in self-evaluation, reminds herself that ‘All reminds herself that ‘All units must be the same’units must be the same’





LEVEL 6LEVEL 6

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Teacher's notes

uses trial and improvement to create parallelograms with the same base and area• uses trial and improvement to create parallelograms with the same base and area• looks for relationships between the parallelograms and the rectangle other than base and looks for relationships between the parallelograms and the rectangle other than base and

area area concludes that they all have the same (perpendicular) height even though the sloping concludes that they all have the same (perpendicular) height even though the sloping

sides are different lengthssides are different lengths asserts a formula is possible ‘but you must use height because the sloping side changes asserts a formula is possible ‘but you must use height because the sloping side changes

so you can’t use it’so you can’t use it’ gives the formula as gives the formula as A = b × hA = b × h





LEVEL 7LEVEL 7

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Teacher's notes

Uses 2-D Uses 2-D representations of 3-D representations of 3-D shapesshapes

Uses the formula for Uses the formula for circumference and circumference and area of a circlearea of a circle

Calculates surface Calculates surface areas of compound areas of compound





LEVEL 8LEVEL 8

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Teacher's notes

uses standard formulae uses standard formulae for mensurationfor mensuration

calculates volumes and calculates volumes and

surface areas of surface areas of cylinders and right cylinders and right prismsprisms



Handling dataHandling data

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Handling data Handling data

LEVEL 2LEVEL 2

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Teacher's notes

After teacher introduction, sorts given numbers using criterion odd/not odd.

Organises work by crossing out each number as it is entered on to sorting diagrams.

Goes on to choose and enter additional numbers.

Reasons that 'not odd' numbers are 'even' and are the ‘answers’ when she recalls multiplication facts for 2.

APP mathematics standards file: Hannah (Year 2 secure level 2)

Handling data: LEVEL 2Handling data: LEVEL 2


LEVEL 3LEVEL 3

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Teacher's notes

uses tallies to record data in a given table

uses some conventions for a bar chart, such as bars of equal width and spaces between bars representing discrete data

responds to questions such as 'How many…?', 'How many more…?', 'Which is the most common…?'




LEVEL 4LEVEL 4

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Teacher's notes

decides on the choice decides on the choice of colours to offer in her of colours to offer in her surveysurvey

designs a table to designs a table to record other pupils’ record other pupils’ choices of favourite choices of favourite colourcolour

keeps a tally of choiceskeeps a tally of choices

describes the most describes the most common and least common and least common choicescommon choices

identifies the mode of identifies the mode of the set of datathe set of data




LEVEL 5LEVEL 5

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Teacher's notes

decides both outcomes, right hand and left hand, are equally likely and decides both outcomes, right hand and left hand, are equally likely and the probability of a correct guess is one halfthe probability of a correct guess is one half

records the results of experiments clearlyrecords the results of experiments clearly

explains ‘you can’t expect to get exactly ten out of 20 each time’ and ‘if explains ‘you can’t expect to get exactly ten out of 20 each time’ and ‘if you did a 100 you should get about 50’you did a 100 you should get about 50’




LEVEL 6LEVEL 6

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Teacher's notes

identifies the mode and calculates the mean of sets of dataidentifies the mode and calculates the mean of sets of data explains and justifies choice of average in discussionexplains and justifies choice of average in discussion




LEVEL 7LEVEL 7

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Teacher's notes Generates data using ICTGenerates data using ICT Processes the data to calculate relative frequencies of the Processes the data to calculate relative frequencies of the

outcome ‘six’outcome ‘six’ Uses relative frequency to compare outcomesUses relative frequency to compare outcomes Comments on results and relates them to the original problem Comments on results and relates them to the original problem




LEVEL 8LEVEL 8

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Teacher's notes

constructs cumulative frequency curvesconstructs cumulative frequency curves

constructs box plots from cumulative frequency curves constructs box plots from cumulative frequency curves



Assessing pupils’ progress in Mathematics - Assessing pupils’ progress in Mathematics -

Number and algebraNumber and algebra

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AlgebraAlgebra

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AlgebraAlgebra

LEVEL 2LEVEL 2

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AlgebraAlgebra

LEVEL 3LEVEL 3

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AlgebraAlgebra

LEVEL 4LEVEL 4

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AlgebraAlgebra

LEVEL 5LEVEL 5

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Teacher's notes

understands understands multiplication is multiplication is distributive over distributive over addition and addition and subtractionsubtraction

multiplies by multiplies by fractions and fractions and decimals such as decimals such as 3/4 and 0.63/4 and 0.6

substitutes values substitutes values to check her result to check her result has the same value has the same value as the original as the original expression expression


Algebra: LEVEL 5Algebra: LEVEL 5

AlgebraAlgebra

LEVEL 6LEVEL 6

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Teacher's notes

solves linear solves linear equations with the equations with the unknown on one unknown on one side onlyside only

generally generally transforms both transforms both sides in the same sides in the same wayway

also uses two-step also uses two-step inverse operationsinverse operations

calculates with calculates with decimals mentallydecimals mentally



AlgebraAlgebra

LEVEL 7LEVEL 7

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Teacher's notes

finds the product of two linear expressionsfinds the product of two linear expressions simplifies the resulting quadratic expressions simplifies the resulting quadratic expressions identifies the difference of two squares as a special identifies the difference of two squares as a special

case case



AlgebraAlgebra

LEVEL 8LEVEL 8

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Teacher's notes

factorises quadratic expressions with a positive factorises quadratic expressions with a positive coefficient of coefficient of x-squaredx-squared

partitions the partitions the x-term to obtain common factorsx-term to obtain common factors uses a grid method to find factorsuses a grid method to find factors



Numbers Numbers and the number systemand the number system

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Numbers and the number system Numbers and the number system

LEVEL 2LEVEL 2

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Teacher's notes

Shown shapes made with linking cubes, understands how the shapes in the sequence 'grow'. Shown shapes made with linking cubes, understands how the shapes in the sequence 'grow'.

Asked to find the number of cubes in the tenth shape, chooses to record on a whiteboard. Asked to find the number of cubes in the tenth shape, chooses to record on a whiteboard. Writes numbers 1 to 10 and above them records the number of cubes in the first shape, second shape, third… etc. Writes numbers 1 to 10 and above them records the number of cubes in the first shape, second shape, third… etc. Grows the shape and records the number of cubes. Grows the shape and records the number of cubes. Explains his record, 'I had to find the tenth so I wrote one, two, three, four, five, six, seven, eight, nine, ten. I had Explains his record, 'I had to find the tenth so I wrote one, two, three, four, five, six, seven, eight, nine, ten. I had

three shapes to start with so I wrote one, three, five. I know there are two jumps between so I added on two to each three shapes to start with so I wrote one, three, five. I know there are two jumps between so I added on two to each number.'. number.'.

Demonstrates he has recorded the correct number of cubes for the tenth shape by counting the cubes in his model. Demonstrates he has recorded the correct number of cubes for the tenth shape by counting the cubes in his model. Knows the number of cubes is always odd. Knows the number of cubes is always odd. Predicts the number of cubes in shapes up to the twentieth. Predicts the number of cubes in shapes up to the twentieth.

APP mathematics standards file: Bradley (Year 1 secure level 2)

Numbers and the number system: LEVEL 2Numbers and the number system: LEVEL 2


LEVEL 3LEVEL 3

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Teacher's notes

recognises the rule in sequences that go up in steps of a recognises the rule in sequences that go up in steps of a regular size, including those that begin with negative regular size, including those that begin with negative numbersnumbers

relates these sequences to recent work on temperaturerelates these sequences to recent work on temperature finds missing numbers and continues the sequence.finds missing numbers and continues the sequence.




LEVEL 4LEVEL 4

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Teacher's notes

recognises the least recognises the least number that can be number that can be made is 2 and the made is 2 and the greatest is 18greatest is 18

works systematically works systematically to list all possible to list all possible addition pairs for addition pairs for each totaleach total

describes patterns in describes patterns in the columns of the columns of numbers she has numbers she has recordedrecorded




LEVEL 5LEVEL 5

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Teacher's notes

uses equivalence between fractions, decimals and uses equivalence between fractions, decimals and percentagespercentages

expresses an improper fraction as a mixed numberexpresses an improper fraction as a mixed number reduces some of the fractions to their simplest formreduces some of the fractions to their simplest form understands place value in decimals as well as whole understands place value in decimals as well as whole

numbersnumbersAPP in mathematics at Key Stage 3: Standards file – Pupil C p.7



LEVEL 6LEVEL 6

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Teacher's notes

knows and uses procedures for the knows and uses procedures for the conversion of fractions, decimals and conversion of fractions, decimals and percentagespercentages

expresses decimals with two or three expresses decimals with two or three decimal places as fractions with a decimal places as fractions with a denominator of 100 or 1000 denominator of 100 or 1000 appropriately appropriately

reduces fractions to their simplest form reduces fractions to their simplest form by cancelling common factorsby cancelling common factors

expresses 3.335 as a mixed number and expresses 3.335 as a mixed number and 2 5/6 as a percentage greater than 1002 5/6 as a percentage greater than 100

divides the numerator by the divides the numerator by the denominator to convert a fraction to a denominator to convert a fraction to a decimal, using a written method of decimal, using a written method of division, and then multiplies by 100 to division, and then multiplies by 100 to convert the decimal to a percentageconvert the decimal to a percentage




LEVEL 7LEVEL 7

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Teacher's notes

converts between mixed numbers and converts between mixed numbers and improper fractionsimproper fractions

finds common denominatorsfinds common denominators adds, subtracts, multiplies and divides adds, subtracts, multiplies and divides

fractionsfractions




LEVEL 8LEVEL 8

81

Teacher's notes

uses an algebraic method to convert uses an algebraic method to convert a recurring decimal to a fractiona recurring decimal to a fraction

Next stepsNext steps

explore patterns arising from explore patterns arising from converting rational numbers to converting rational numbers to decimal form, for example, by decimal form, for example, by division division

reason about the resultsreason about the results

demonstrate and justify a non-demonstrate and justify a non-calculator method for converting a calculator method for converting a recurring decimal to a fractionrecurring decimal to a fraction



CalculatingCalculating

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LEVEL 2LEVEL 2

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LEVEL 3LEVEL 3

85


LEVEL 4LEVEL 4

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LEVEL 5LEVEL 5

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Teacher's notes

solves a word problem without a calculator identifies the appropriate operation to use uses a non-calculator method to divide a three-digit by a two-digit number rounds up after the division explains why rounding up is appropriate


Calculating: LEVEL 5Calculating: LEVEL 5


LEVEL 6LEVEL 6

89

Teacher's notes

adds and subtracts mixed numbers by expressing the fractional parts with a common denominator

solves subtraction problems that involve breaking down a unit, e.g. 3 1/9 – 5/7

uses addition and subtraction as inverse operations to find missing values

usually reduces fractions to their simplest form




LEVEL 7LEVEL 7

91

Teacher's notes

converts between mixed numbers and converts between mixed numbers and improper fractionsimproper fractions

finds common denominatorsfinds common denominators adds, subtracts, multiplies and divides adds, subtracts, multiplies and divides

fractionsfractions




LEVEL 8LEVEL 8

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Teacher’s notesTeacher’s notes

identifies square numbers and factor pairs identifies square numbers and factor pairs manipulates surds competently and simplifies sums and productsmanipulates surds competently and simplifies sums and products uses accurate notationuses accurate notation



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