Mathematics standards file Daniel low level 3 Ma1 Using and applying mathematics Ma2 Number Ma3 Shape, space and measures Ma4 Handling data
Ma1 Using and applying mathematics Bean bag shot problem finds the lowest and highest total lists total from scoring 2 three times as the middle score
works systematically: all scores the same and then two scores the same continues to find 9 of 10 possible scores omits the total from scoring 1 + 2 + 5 from one of each score. Next steps find out which numbers between the lowest and highest totals cannot be made with scores from three bean bags. Daniel s own bean bags problem
sets a new problem to challenge a friend chooses larger scores finds 9 of 10 possible total scores with support of probing questions, finds tenth possibility, one bean bag in each bucket to give 4 + 8 + 9 = 21. Numbers on a line draws an empty 0 100 number line and positions 25, 50 and 75 with reasonable accuracy places markers appropriately for his secret numbers, 33, 47 and 61 decides his friend s estimates of 49 and 65 are reasonable explains that the estimate of 45 for his 33 marker is not good because 45 would be closer to 50 not 25 and 33 is about halfway between. What the teacher knows about Daniel s attainment in Ma1 When breaking into a problem, Daniel suggests ways to get going. He becomes very focused when he pursues a line of enquiry and is keen to work through to draw conclusions. He can sustain his interest over a number of days. When solving problems like the bean bag problem, Daniel works systematically to find possible scores. He records clearly and in an organised way. He perseveres to find as many scores as possible. He checks and explains how he knows there cannot be other scores. He appreciates the nature of problems he is given and sets challenging examples for his friends to solve. He solves problems in a range of contexts, most successfully when working with numbers, money and measures. For example, he measures heights accurately to find
out which children in the class could go on a ride at the theme park, where there is a minimum height requirement of 1 m 45 cm. To solve the problem, he explains, We don t need to know how tall each person is. We just need to measure whether they are as tall as the 1 m 45 cm mark and put them on the list: Can go on the ride/can t go on the ride. Daniel thinks about others solutions and comments on whether they are appropriate or feasible. Summarising Daniel s attainment in Ma1 In class discussion, Daniel suggests ways to approach problems. He works mentally as he solves problems but records clearly and is beginning to appreciate different purposes for recording, for example to remember what he has done so far, to check his work and to share and compare solutions. He is beginning to work systematically and this is reflected in the way he organises his recording. He uses and interprets a range of diagrams and mathematical symbols such as +,,, and =. In discussion he demonstrates his reasoning, for example by finding an example to match a general statement given by the teacher. His performance in this AT is best described as working securely in level 3. To make further progress within level 3, Daniel needs to experience a range of problems involving shape, position and movement as well as number problems and investigations.
Ma2 Number Adding three-digit numbers understands 789 as 700 + 80 + 9 uses partitioning to add three-digit numbers.
Fractions of a number in oral work considers unit fractions relates fractions to sharing (division) understands that of a number is less than of that number. Coins problem represents seven 5p coins how much is that? as a multiplication
understands multiplication as repeated addition represents the addition as jumps of a regular size on a number line. Arrays selects an appropriate array to represent a multiplication writes own multiplication story in real-life context to match a given array. Ways to add 9 in oral work, suggests different methods to add 9 uses +10 and then 1 to add 9
draws a number line on his mini-whiteboard to demonstrate suggests 53 + 7 + 2 as an alternative method using 60 as a landmark on the number line. Sharing with your friends uses doubling with halving as the inverse in discussion with the teacher, responds to a suggested real-life context for the calculation.
Apples problem derives multiplication facts from knowledge of 2 table and doubling interprets the problem as How many fours make 34? and records 8 and a half through discussion, concludes that Mrs Bond needs to buy 9 packs of four apples. What the teacher knows about Daniel s attainment in Ma2 Daniel understands place value in three-digit numbers and is beginning to work with four digits. He rounds numbers to the nearest 10 and knows that 349 is closer to 300 than 400. He places two-digit numbers reasonably accurately on a number line he has drawn, initially showing 0, 50 and 100 as landmarks. He has experienced negative numbers, minus 1, minus 2, etc., in the context of temperatures that are below zero. Daniel finds one-half and one-quarter of a number of objects. He is beginning to relate fractions to division. He calculates one-third of numbers such as 12 as well as finding other unit fractions of larger numbers practically, by partitioning sets of cubes into an appropriate number of groups. He is beginning to understand the relative size of different unit fractions. For example, he understands that of a set of sweets is more than of the set. Daniel understands subtraction as the inverse of addition. He uses this to complete calculations with missing numbers or, for example, to generate the related subtraction sentences, given an addition. He understands multiplication as repeated addition and represents examples as jumps of a constant size on a number line. He knows how an array of counters can be used to represent a multiplication. He uses his knowledge of
doubles facts to halve numbers. When solving division problems he interprets the remainder, sometimes with the support of probing questions, to decide whether to round up or down. He uses an empty number line to support mental addition of two two-digit numbers. He uses addition facts to 10 and the strategy of jumping to the next multiple of 10 on the number line when he adds or finds a difference. He also uses this knowledge when subtracting to check the accuracy of his answer. Daniel knows multiplication facts for 2, 5 and 10. He uses the addition and multiplication facts that he knows to derive others. For example, he uses 6 + 4 = 10 to derive 60 + 40 = 100. He uses partitioning to add three-digit numbers and number line methods to add and subtract. When multiplying and dividing he is beginning to use known multiplication facts for 2, 5 and 10 to multiply larger numbers. Daniel solves word problems where he needs to add and subtract money and measures, including those that involve bridging tens. He writes time problems for others to solve with solutions, for example The film starts at quarter to 9 and ends two and a half hours later. What time does it end? Quarter past 11. Summarising Daniel s attainment in Ma2 Daniel s attainment in Ma2 is best described as working at the lower end of level 3. He shows understanding of place value when he partitions a three-digit number into its hundreds, tens and units parts. Given a two-digit or three-digit number he can round to the nearest ten or say which hundred is nearest. He uses decimal notation for p including recording the total of two 1 and five 1p coins as 2.05 and knows that negative numbers are used in temperature. Daniel recalls addition facts to 10 and 20. He adds two two-digit numbers mentally and uses mental and number line methods to subtract. He is beginning to use a written method of partitioning and recombining to add three-digit numbers. Daniel uses his knowledge of the 2, 5 and 10 tables to derive other multiplication and division facts. He solves problems involving multiplication and division and is beginning to interpret remainders. He uses unit fractions and is beginning to use fractions that are several parts of the whole, for example in the context of time. To make further progress within Ma2 level 3, Daniel needs to work with negative numbers in contexts such as counting backwards past 0 or using a calculator to explore whether order matters in subtraction. He also needs to develop his understanding of fractions that are several parts of a whole and simple equivalent fractions. He needs to develop his written methods for adding three-digit numbers and to extend his knowledge of times tables to support division and his multiplication of larger numbers.
Ma3 Shape, space and measures Reading scales reads scales on a variety of measuring instruments works out values between labelled divisions. What the teacher knows about Daniel s attainment in Ma3 Daniel knows the mathematical names for shapes such as square, rectangle, circle, triangle, pentagon, hexagon and octagon. He uses folded paper to check whether angles are right angles. He sorts shapes by the number of sides and properties such as all edges the same length or has a right angle. Using ICT, Daniel gives instructions for forward movements and quarter turns to draw rectangles and other irregular shapes. He also uses these instructions to move the cursor into a target area of the screen. Daniel knows that sand, for example, can be weighed in grams and kilograms, and water can be measured in litres and millilitres. He knows length can be measured in millimetres, centimetres, metres and kilometres. He finds out how much sand will balance with different given weights: 10 g, 20 g, 50 g, 100 g and 500 g. He knows from practical experience of weighing that a small bag of crisps is more likely to weigh 50 g than 500 g. From an interactive teaching program, he reads scales to the nearest labelled division and makes sensible estimates of values between divisions: for example, he reads 67 g on a scale marked in ones and fives and labelled every 10 g. He knows all of the fraction times, that is quarter past, half past and quarter to. He is beginning to read times past the hour in five-minute intervals, such as 20 minutes past one, 35 minutes past
Summarising Daniel s attainment in Ma3 Daniel s profile across the AFs for Ma3 is uneven. He is weaker in properties of shape, position and movement and stronger in measures. His performance across Ma3 is best described as working at the top of level 2. Daniel uses mathematical names for common 2-D and 3-D shapes and describes properties such as numbers of sides. He distinguishes between straight and turning movements when he instructs a programmable toy. He understands angle as a measure of turn and recognises quarter turns as right angles. He uses standard metric units of length, capacity and mass and standard units of time when modelled in interactive teaching programs and in practical activity.
Ma4 Handling data Venn diagram handles data in the context of a science topic sorts foods using the criteria Good for teeth and Bad for teeth puts foods with some ingredients that are good for teeth and other ingredients that are bad in the intersection checks that other children in the group sort foods correctly helps create a group record independently decides to label the intersection Not sure.
Colours
takes red, blue, yellow or green cubes from a bag records the colours taken accurately as tallies and completes the frequency table creates a block graph of the data using given axes, with a vertical scale labelled in ones independently labels axes and gives graph a title explains which colour was drawn most often and how many counters were drawn altogether answers questions such as How many more green cubes than yellow cubes did you get? Next steps draw own axes when creating a block graph work with larger numbers and/or a grid size that requires the use of scale, for example using one block to represent 2 or 5. What the teacher knows about Daniel s attainment in Ma4 Daniel keeps an accurate tally and uses his knowledge of counting in fives to read a tally chart where larger numbers are represented. He uses Venn and Carroll diagrams to sort items using two criteria such as even and in 5 table or has 4 sides and has a right angle. Daniel records results in a block graph where one block represents one item or event. When colouring blocks to create bars or columns, he is beginning to use the labelled axis and height of bars to read their value, rather than counting blocks. He is beginning to interpret graphs where one symbol represents two items or where the axis is labelled in twos. He answers questions that involve comparing two categories or the whole data set. From the class graph about shoe fastenings he answers questions such as How many more children wear laces than buckles? and How many children took part in the survey? He poses similar questions about his own graphs for other children to answer. Summarising Daniel s attainment in Ma4 Daniel s attainment in Ma4, Handling data, is best described as low level 3. He sorts items using more than one criterion. He interprets information in tables and block graphs. He constructs block graphs where the block represents one item, although he interprets graphs where the symbol represents more than one. To make further progress in Ma4 level 3, Daniel needs to learn to construct his own bar charts and pictograms with symbols that represent a group of units and to work more independently in deciding how to record the information he gathers.
Overall assessment summary for Daniel Daniel s teacher judges that his mathematics is low level 3. His strengths are in using and applying mathematics and his feel for number and measures. His performance is slightly lower in working with properties of shape, position and movement. Assessment guidelines