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The National Strategies | Primary | Primary Framework for literacy and mathematics Mathematics training standards file – David

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Mathematics training standards file – David Assessing pupils’ progress Standards file without AT and overall assessment summaries and no assessment guidelines to support inschool/external training standardisation activity.



Ma1 Using and applying mathematics

Bipods and Tripods

Teacher’s notes

• finds a starting point, tries a few ideas to help understand the problem, then identifies key facts and operations to be used

• approximates, then uses knowledge of tables to work out the number of legs on groups of Bipods and Tripods

• finds a solution with only one tripod then selfcorrects his work to find one solution which satisfies the given criteria

• explains his thinking orally and records it clearly.

Next steps

• develop a more systematic approach and organised way of recording

• compare his solution with others in the class to find other possibilities.



What the teacher knows about David’s attainment in Ma1

When solving problems, David suggests ways to get started, choosing appropriate equipment to help him, for example coins or a 100square. He independently carries out a simple investigation, sometimes using a systematic approach: for example, given a problem with a short list of clues, he follows them through, making sure each one is fulfilled. When faced with a more complicated problem he needs encouragement to continue, to read back and to check. He uses trial and improvement to find a solution that satisfies a set of two or three criteria.

David can discuss and explain his work, drawing on his mathematical knowledge and using appropriate language such as multiply, double, halve, triple. In his written work he records his thinking, often in an organised way. He can describe the methods and strategies he has used, for example: ‘I just used my times and divide to work out the answers. I know my three times table and my two times table facts.’



Ma2 Number

Number sequences

Teacher’s notes

• counts forward and backwards in small steps to find missing numbers in sequences

• uses jottings to support counting on or back in larger steps

• recognises negative numbers, counting backwards in ones, from 2 to –2.

Next steps

• find the rule for the sequence, for example ‘adding three each time’, then calculate with fewer jottings.



Inverse operations

Teacher’s notes

• finds the missing numbers in twodigit addition sentences

• when modelled, shows the related subtraction sentence, ordering the numbers correctly

• independently applies knowledge to final subtraction calculation.



Fraction dominoes



Teacher’s notes

• recognises halves and quarters of given shapes, including those divided into more than four squares

• independently matches a fraction to a diagram, in a game of dominoes

• creates his own domino fraction game, using 1/2, 1/4, 3/4 and 2/5.

Next steps

• recognise 3/4 represented in different ways, for example when a rectangle is showing 6/8.


David can count sets of objects reliably and is beginning to understand the place value of each digit in a threedigit number. He can recognise and continue number sequences which increase in steps of equal size, forwards and backwards, for example 12, 18, 24, 30, 36. He recognises odd and even numbers, and multiples of 2, 5 and 10. He can multiply twodigit whole numbers by 10 and single digits by 100. David represents multiplication as an array of dots and understands it as repeated addition.

He understands simple fractions such as 1/2, 1/4, 1/3, and can find those fractions of shapes. When a shape is divided into small squares or rectangles, he is able to find half and a quarter; however, he is unable to find 3/4 of a shape that is split up into 8 or 12 parts. David can solve simple problems involving fractions; he can find small unitary fractions of whole numbers, using diagrams or apparatus to help him, for example 1/3 of 9 = 3, 1/5 of 10 = 2.

He understands that subtraction is the inverse of addition and sometimes uses this knowledge to check his work. Mentally, he can double and halve twodigit numbers, knowing that halving is the inverse of doubling. He also demonstrates knowledge of inverse in multiplication and division, for example 3 × 7 = 21 so 21 ÷ 7 = 3.

Using mental recall of addition and subtraction facts to 10, he adds and subtracts twodigit numbers, for example 89 + 11 or 35 + 65.

He uses knowledge of place value when adding and subtracting multiples of 10: for example, he uses 5 – 3 to work out 50 – 30. David knows multiplication facts for the ×2 and ×10 tables and can find the related division facts with support. He multiplies by 3, 4 and 5, but does not yet have a quick recall of these tables facts.

He solves problems involving money and measures, using a number line and/or jottings to support his thinking. He can highlight the key words in a problem and uses this knowledge to select the appropriate operation. His preferred method for solving multiplication problems is repeated addition. He is beginning to solve division problems with support.

David consistently uses informal jottings such as a number line, where he jumps in large steps using multiples of 10 as ‘stepping stones’. He divides small numbers by sharing, using apparatus or marks on a page, and is beginning to divide twodigit numbers by 2, mentally. His written method for addition and subtraction of twodigit numbers involves partitioning the tens and units.



Ma3 Shape, space and measures

Right angles



Teacher’s notes

• recognises and finds right angles in regular and irregular shapes

• identifies right angles when bounded by vertical or horizontal lines.

Next steps

• recognise right angles in other orientations, for example at the ‘top’ of a triangle

• identify angles that are bigger or smaller than a right angle.

Carroll diagram

Teacher’s notes

• sorts 2D and 3D shapes using two given criteria: ‘has triangles’/‘has no triangles’ and ‘2 D shapes’/‘3D shapes’

• names and explains the properties of the shapes in each section

• understands each section of a Carroll diagram.

Next steps

• identify own criteria to sort shapes.



Balancing weights

Teacher’s notes

• uses standard units to weigh objects using balancing scales and weights (1 kg, 100 g and 10 g)

• records in kilograms and grams

• records results in a table.

Next steps

• begin to use decimal notation for weight, for example 1.150 kg

• use and read dial scales to weigh

• use standard units in a wider range of contexts, such as capacity.


David knows the names and properties of common 2D and 3D shapes, for example that a cuboid has six faces that can be squares and rectangles, a pentagon has five sides, a square has four right angles. He talks about and sorts shapes, using two criteria, independently, using



appropriate language such as corners, faces, symmetry, edges. He finds lines of symmetry in a square through folding.

David reflects simple patterns and shapes in a vertical mirror line and recognises shapes when rotated. In physical education., he makes full turns, half turns and quarter turns, clockwise and anticlockwise.

He recognises scales going up in tens, fives and ones, and labels missing numbers on scales. He measures to the nearest 1/2 cm using a ruler and can record the measurements using decimal notation, for example 7.5 cm. He tells the time using both analogue and digital clocks, and can calculate time durations within the hour, such as 15 minutes after 3:30 pm, or involving whole hours, such as three hours later. David is beginning to understand the relationship between centimetres and metres, that is 1 m = 100 cm so 2.5 m = 250 cm.



Ma4 Handling data

Tally chart and bar graph



Teacher’s notes

• records votes, using tally marks, and totals them to create a frequency table

• independently constructs bar chart where one unit on the vertical axis represents one child

• answers questions such as ‘How many pets altogether?’, ‘How many more dogs than snakes?’

Next steps

• label and title graph

• construct bar charts where the vertical axis goes up in twos

• use the mathematical convention of leaving a space between bars that represent discrete data.


David sorts shapes and numbers using a Carroll diagram. He collects information and records it, putting it into a list, given a table or a computer database. He creates block graphs and pictograms where one symbol represents one unit. He makes appropriate choices for collecting data, such as tally charts, but needs support to decide the best way to present the information, for example using a pictogram or a bar chart.

He answers questions about the data such as ‘How many more…?’ David extracts and interprets information from a range of bar charts. He reads scales labelled in twos, fives and tens and is beginning to read in between labelled divisions, for example between 10 and 12. He interprets pictograms where the symbol represents 2 or 10, including halfsymbols, but is not yet able to construct them independently.

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