Mathematics standards file Greg secure level 3 Ma1 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 hunt 1 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. What the teacher knows about Greg s attainment in Ma2 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. Summarising Greg s attainment in Ma2 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. What the teacher knows about Greg s attainment in Ma3 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. Summarising Greg s attainment in Ma3 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. What the teacher knows about Greg s attainment in Ma4 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. Summarising Greg s attainment in Ma4 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