Mathematics standards file John high level 3 Ma1 Using and applying mathematics Ma2 Number Ma3 Shape, space and measures Ma4 Handling data
Ma1 Using and applying mathematics Generally odd and even
Teacher s notes understands general statements tries several examples and uses the results to complete a general statement has support with creating examples and completing the first general statement works independently with other statements. Next steps investigate situations from which he can formulate his own rule or general statement.
Wow fact-ors!
Teacher s notes works independently knows multiplication facts for 2, 4, 5 and 10 tables uses these facts to derive other multiplication and division facts factorises given numbers and counts the number of factors understands definitions based on the number of factors a number has uses definitions to identify which type of number he has factorised. What the teacher knows about John s attainment in Ma1 When working on problems that involve finding how many ways, John perseveres to find further solutions. In the Wow fact-ors! investigation, he perseveres to find all factor pairs for each of the numbers. He is beginning to check his work, for example by making sure that his solution to a problem makes sense in the context of the problem. John talks about his work using familiar mathematical vocabulary appropriately. He refers to his written work when providing explanations. John demonstrates his reasoning, for example by completing generalisations about adding and subtracting odd and even numbers. When given incomplete generalisations, John works through appropriate examples, draws conclusions from them and completes the generalisation. He also uses definitions of prime and square numbers based on their numbers of factors. By finding the number of factors for given numbers, John is able to identify those which are prime or square. Summarising John s attainment in Ma1 John understands a general statement and finds an example to match it, which is typical of performance at level 3. He needs more experience of a wider range of problems, with input on breaking into a problem and developing systematic approaches, to make further progress within level 3 and into level 4.
Ma2 Number Improper fractions and mixed numbers Teacher s notes interprets fractions diagrams recognises the unit, for example the circle that represents 1 records shaded areas as improper fractions and as mixed numbers. Next steps create own diagrams to illustrate improper fractions or mixed numbers use own diagrams to support converting improper fractions to mixed numbers and vice versa.
Chunking
Teacher s notes is secure with multiplication facts for 2, 4, 5 and 10 tables uses known multiplication facts to derive others uses a vertical method for addition and subtraction efficiently in guided work, uses chunking to divide a three-digit by a single-digit number checks by using multiplication as the inverse of division begins to relate chunking to short division does not yet use the chunking method of division independently or recall it when he has not practised it recently. Book shelf problem Teacher s notes solves a word problem involving addition and subtraction interprets information in a table adds two-digit numbers mentally subtracts using complementary addition
explains how he knows his answer is correct. Next steps solve problems using multiplication or division with addition or subtraction, including those that involve interpreting a remainder. What the teacher knows about John s attainment in Ma2 John recognises number patterns including larger multiples of 5 and 10 and square numbers up to 10 10. He uses his knowledge of multiplication facts to find factor pairs and to check whether a number is prime, as in Wow fact-ors!. John understands place value in two-digit and three-digit numbers and uses it to order numbers, to round to the nearest 10 or 100 and to multiply whole numbers by 10. John understands negative numbers in the context of temperature and counting backwards past 0. He calculates small changes in temperature across 0 Celsius. John understands unit fractions and those fractions that are several parts of a whole, such as, that he uses frequently. He knows the percentage equivalents of fractions such as,, and. He needs further work to understand equivalent fractions more fully and to order fractions, on a number line, for example. John uses diagrams to help him to convert mixed numbers to improper fractions and vice versa. John understands addition and subtraction as inverses, multiplication as repeated addition and division as the inverse of multiplication. He uses repeated addition to generate multiplication facts, for example when he multiplies 1.25 by 5 and records 1 1.25 = 1.25, 2 1.25 = 2.50 John uses a range of mental strategies to add whole numbers and decimals with one decimal place. He uses complementary addition when he subtracts mentally. He uses column methods to add and subtract two-digit and three-digit numbers, including examples that involve bridging or decomposition of either the tens or hundreds. He has good recall of multiplication facts for 2, 4, 5 and 10 tables and uses them to derive associated multiplication and division facts. He multiplies a two-digit or three-digit number by numbers up to 10 using a grid method. John knows about chunking as a method of dividing larger numbers, and about short division, but is not yet confident in dividing a three-digit number by a single-digit or two-digit number independently. John solves whole number problems that involve using one operation and those that involve both addition and subtraction. Summarising John s attainment in Ma2 In Ma2 John is best described as working at the top end of level 3, even though he shows some aspects of level 4. He needs to consolidate his understanding of place value in whole numbers to multiply by 100 as well as by 10. He also needs to develop his understanding of place value in decimals, to use decimal notation not just for
money but also for measures, and to add and subtract decimals with two places. John needs to develop his understanding of equivalent fractions, which will also help him to order fractions. As well as calculating with decimals, John needs to develop written methods for division of larger numbers.
Ma3 Shape, space and measures 3-D shape problem
Teacher s notes interprets an isometric drawing and uses linking cubes to build the 3-D shape represented relates the 3-D shape to a different type of diagram. Next steps build own 3-D shape and design a set of instructions for someone else to build the same shape without looking at it. Reflecting 2-D shapes
Teacher s notes reflects shapes on a square grid uses the (perpendicular) distance of vertices from the mirror to reflect accurately uses mirror lines that are presented vertically, horizontally or diagonally. What the teacher knows about John s attainment in Ma3 John sorts shapes using properties such as number of edges and corners or reflection symmetry in 2-D shapes. He reflects 2-D shapes on a square grid in a mirror that is presented vertically or horizontally although is less consistently accurate with a mirror line presented diagonally. He is beginning to use the perpendicular distance of a vertex from the mirror line to help him reflect shapes accurately when they are not parallel to the mirror line. John is less experienced and confident in translating shapes. He makes 3-D shapes, using linking cubes, from a 2-D diagram. He needs more experience of making nets of cuboids and triangular prisms, for example, to be able to solve problems such as matching solids to their nets or completing a net where part of it is given. John uses non-standard and standard metric units to measure length, capacity and mass. He measures to the nearest cm and records longer lengths using a mixture of metres and centimetres: 3 m 45 cm, for example. He knows about area as a measure of surface and perimeter as a linear measure but needs support to remember which term refers to which measurement. He finds areas by counting squares. John is not very accurate in using a protractor to measure angles. He uses standard units of time, reads the time from an analogue clock and calculates time durations that do not go over the hour. For example, John calculates how long an event lasts if it begins at quarter past two in the afternoon and ends at 2:55 pm. Summarising John s attainment in Ma3 In Ma3 John is a strong level 3. In working with shapes, he needs more experience of making 3-D models from nets to progress into level 4. In position and movement he needs to work more independently with reflecting shapes, recognising rotations and drawing 2-D shapes in different orientations on grids. In measures John needs to interpret numbers on a wider range of measuring instruments and scales, to learn to use a protractor to measure angles with reasonable accuracy, and to distinguish between perimeter and area independently.
Ma4 Handling data Dice investigation 1
Teacher s notes works independently to find the frequency of dice scores 1 to 6 constructs a table of results keeps an accurate tally and interprets it sketches a bar graph, labelling the vertical axis in ones predicts that 4 will be the most common score identifies scores 1 and 3 as the modes of his data does not yet understand the term frequency (that is, in this investigation, the frequency of particular scores on the dice). Next steps combine the results of the whole class discuss combined results, including the significance of the mode draw conclusions from the larger sample about the likelihood of each dice score use squared paper to draw graphs more accurately use scales where one interval represents 2 or 5 to record combined results.
Sorting numbers Teacher s notes works independently to sort numbers 1 to 50 using given criteria records all numbers below the diagram and begins by crossing off those he has sorted in discussion with the teacher concludes that there are no odd multiples of 6.
What the teacher knows about John s attainment in Ma4 John uses a Carroll diagram to sort shapes and numbers using two criteria. For shapes he uses criteria such as has a line of symmetry and has four sides. John uses a tally to record a count and interprets it accurately. He draws tables of results and interprets them. He uses information from a table to draw graphs, and numbers the vertical axis in ones. He is not yet consistent in labelling axes or recording any conclusions from the information he presents. He uses much of the handling data vocabulary that is appropriate for the year group but does not yet fully understand the terms frequency, mode and range. John has been introduced to mode but needs more experience to understand the types of situation in which knowing the mode of a set of data could be helpful. Summarising John s attainment in Ma4 In Ma4 John s performance is best described as at secure level 3. He constructs bar charts, and to consolidate his attainment within level 3 he needs to use a scale for the vertical axis where one division represents more than one item. He also needs experience of interpreting and creating pictograms.
Overall assessment summary for John John s teacher judges his attainment across mathematics as working at the top of level 3. His attainment in Ma2 and Ma3 is slightly higher than it is in Ma1 and Ma4. Assessment guidelines