Mathematics standards file Greg – secure level 3wsassets.s3.amazonaws.com/ws/nso/pdf/abacac01b079275bb960c7317e625...Mathematics standards file – Greg ... In Ma2 Greg is best described

The National Strategies | Primary | Primary Framework for literacy and mathematics

Mathematics standards file – Greg

QCA © Crown copyright 2008

Mathematics standards file Greg – secure level 3Ma1 Using and applying mathematics

Ma2 Number

Ma3 Shape, space and measures

Ma4 Handling data




Ma1 Using and applying mathematics

Rows of coins

Teacher’s notes

uses trial and improvement to look for different combinations that satisfy the first criterion

makes changes based on calculations made




chooses own method of recording

recognises halves and doubles.

Next steps

solve more complex problems with a greater number of criteria to be met

work systematically to find more than one possible solution.




Treasure hunt1

1 ‘Treasure hunt’ resource in Mathematical challenges for able pupils in Key Stages 1 and 2,

Primary National Strategy




Teacher’s notes

works systematically to find different combinations

checks each combination against the set criteria

explains method of working

chooses to record results in a table

reasons that he has found all possible combinations as both pirates must have at least one jewel, to make it fair!

What the teacher knows about Greg’s attainment in Ma1

Greg uses trial and improvement to solve problems and is beginning to work systematically. He listens to classroom discussions about how to solve a problem, and then selects his own method from those discussed. He chooses appropriate operations and makes use of suitable equipment, such as coins or different coloured cubes.

He organises his own work and draws tables to record results. He explains methods chosen to solve problems. He sometimes checks results against original criteria.

With encouragement Greg looks for patterns, but does not always find them. In a similar way, he may not find all possible combinations. When prompted, he is usually able to explain his reasoning. He poses problems for others to solve.

Summarising Greg’s attainment in Ma1

Greg is best described as at secure level 3 in Ma1. He tries different approaches to overcome difficulties. He records his results in an organised way and is beginning to explain his thinking. To improve, he needs to develop his knowledge of number patterns to help him make predictions.




Ma2 Number

Equivalent fractions

Teacher’s notes

identifies equivalent fractions using a fraction wall

explains his methods.

Next steps

find more than one equivalent fraction and look for patterns.




Fraction wholes

Teacher’s notes

uses diagrams initially, then works out the complements mentally

records clearly.




Problem solving: Two-step problems

Teacher’s notes

solves two-step number problems, explaining methods and recording clearly

uses partitioning to multiply a two-digit number by a single digit

works backwards to find a missing number.




Next steps

record steps in the order of the inverse operations, for example 15 3 = 5; 5 – 2 = 3.

Problem solving: Number stories

Teacher’s notes

makes up sensible number stories for given number sentences – rejects idea of 435 people on a bus as not credible and chooses a concert instead

recognises the importance of sharing equally for a division problem.




Next steps

make up number stories for two-step problems.

Multiplying by partitioning

Teacher’s notes

partitions amounts to be multiplied

multiplies single digits by multiples of 10 or 100

uses an efficient method to add products.




Next steps

use the grid method

begin to use short, efficient written method.


Greg can read, write and order numbers beyond 1000; he knows the place value of each digit including tenths. He can multiply and divide whole numbers by 10 and 100 and is able to divide by 10 where the answer is a decimal, for example 456 10. Greg rounds three-digit numbers to the nearest 10 or 100. He can continue number sequences that increase or decrease by the same small whole number each time, e.g. 56, 52, 48, __, __. He knows multiples of 2, 3, 4, 5 and 10.

He recognises and uses simple fractions that are several parts of a whole. Given a selection, he identifies those greater than . He colours fractions of a shape, for example , and finds or unit fractions of a set of objects or numbers, for example of 20, of 12. He orders decimals with one decimal place, and two decimal places in the context of money. He recognises the decimal equivalents of

, and .

Greg knows that subtraction is the inverse of addition. He derives associated division facts from known multiplication facts and understands that halving is a way of ‘undoing’ doubling.

He has a quick recall of number facts to 20 and uses this knowledge to add and subtract two-digit numbers mentally, for example 36 + 48 = __ or 84 – 29 = __. He recalls ×2, ×3, ×4, ×5 and ×10 tables and most associated division facts. He uses known facts and place value to calculate with bigger numbers, for example 40 3 or 160 + 30.

Greg chooses appropriate methods to solve problems, for example a mental method to calculate 58 + 19 and a written method to work out 256 + 467. When answering mixed word problems he can select which of the four operations is appropriate.

He uses efficient written methods of addition and subtraction using three-digit numbers, choosing decomposition when subtracting. In the context of money he is able to add and subtract decimals where bridging is required. He multiplies three-digit numbers by a single digit using partitioning. He is not yet confident to use a written method when dividing a two-digit number by a single digit, preferring pictorial processes. He is able to use a calculator to check his answers to addition, subtraction and multiplication problems.


In Ma2 Greg is best described as at secure level 3. In order to progress further, he needs to consolidate his knowledge of multiplication facts and apply his skills




consistently and independently across a broader range of problems, including those involving division with remainders.




Ma3 Shape, space and measures

Sorting 3-D shapes

Teacher’s notes

uses a Carroll diagram to sort 3-D shapes using own criteria

chooses own criterion ‘pyramid’, but needs support to think of ‘not a pyramid’

counts faces of a range of shapes and decides on criterion ‘more than seven faces’/‘less than seven faces’, not taking account of ‘exactly 7 faces’

sorts shapes accurately, explaining the properties of the shapes in each section of the Carroll diagram.




Reading scales

Teacher’s notes

interprets scale to work out value of each unlabelled division

marks 250 g on scale and uses this to find where 225 g should be

knows 1 kg is 1000 g and marks 750 g on dial.




Next steps

read scales over 1 kg

read and interpret different scales such as a scale going up in 50 g, 20 g or 25 g, labelled every 100 g.


Greg names regular and irregular shapes including quadrilaterals, pentagons, hexagons and octagons by counting sides and corners. He recognises reflection symmetry in some 2-D shapes, for example all the lines of symmetry of a square, rectangle and equilateral triangle. He draws 2-D shapes where some of the edges are horizontal or vertical, but is not yet confident to draw shapes in different orientations. He recognises some nets of 3-D shapes such as cube, cuboid, triangular prism.

He identifies right angles, but misses some when shapes are presented in different orientations. He finds angles greater and less than 90, but does not yet know the vocabulary acute and obtuse.

Greg completes symmetrical shapes where the line of symmetry is horizontal or vertical. He understands moving through quarter and half turns clockwise and anticlockwise, left and right.

He is beginning to understand coordinates, but often confuses the order of the numbers in the brackets. Using ICT, Greg creates and explains patterns according to a rule, such as ‘turn through 90’.

Greg knows 100 cm = 1 m and uses this to convert 3.5 m into 350 cm. He knows kg = 500 g and km = 500 m. He measures to the nearest unit, for example the length of the classroom is 9 m, and in design and technology he measures material to make a pencil case that holds pencils measuring 14.5 cm. He is beginning to measure in millimetres and tenths of a centimetre. He reads analogue time and digital time on a 12-hour clock to the nearest minute: for example, he draws the hands on an analogue clock to show 3:08. He calculates durations that cross the hour, for example from 6:30 pm to 7:15 pm. He works out areas of shapes by counting squares and half squares. In science, he is able to measure capacity to the nearest 100 ml, up to 1 litre.


Overall Greg's attainment is at secure level 3 in Ma3. He is able to classify 3-D and 2-D shapes, recognising and using mathematical properties. He uses standard metric units of length, capacity and mass in a range of contexts and across several areas of the curriculum. To progress further within the level, he needs to recognise shapes and angles in different orientations and develop his mathematical vocabulary to describe angles.




Ma4 Handling data

Gathering and representing data




Teacher’s notes

collects data and records it in a frequency table including tallies and totals

initially chooses a very small scale then self-corrects choosing two squares to represent one child

after discussion realises the bars to represent discrete data should not touch and constructs horizontal axis independently

labels axes and gives the graph a title

interprets his graph by writing and answering questions such as ‘What shoe size do most children take?’, ‘How many children were included in the survey?’, ‘How many children take between size 2 and size 4 shoes?’

Next steps

work with data where one square on the vertical axis represents 2, 5 or 10.


Greg poses questions and suggests what data to collect to answer them, such as ‘What is the most popular pet owned by children in the class?’ He collects data and decides how to record it, for instance using tally marks, frequency tables, lists.

Greg sorts data into Carroll and Venn diagrams, explaining what he is doing and why, for example in a Venn diagram when 12 is placed in the intersection of two circles representing multiples of 3 and of 4. He constructs bar charts and pictograms, but needs some support to decide which is the most appropriate method of recording. In pictograms, he uses one symbol to represent more than one unit, for example one picture to represent ten vouchers when showing how many each class has collected. He applies his knowledge of data handling in science lessons to create graphs.

He interprets graphs where the scale on the vertical axis goes up in labelled increments of 2, 5 and 10, reading accurately when the bar is on a labelled division and beginning to read between labels.


Greg is best described as working securely within level 3 in Ma4. To progress further he needs to become more independent in representing data and have greater experience of interpreting graphs with a variety of scales.




Overall assessment summary for Greg

Greg’s teacher judges his attainment across mathematics as working securely at level 3. Although Ma2 is more secure than the other ATs, he is best described as at secure level 3 in each.

Assessment guidelines













Documents

Mathematics standards file Greg – secure level 3wsassets.s3.amazonaws.com/ws/nso/pdf/abacac01b079275bb960c7317e625...Mathematics standards file – Greg ... In Ma2 Greg is best described