Mathematics standards file

Transcription

1 1 of 28 The National Strategies Primary Lydia Year 1 Secure level 1 Mathematics standards file About Lydia Lydia was born in April Lydia speaks English and Spanish at home. She attended the school s nursery class before moving into the Reception class. Lydia had in-school support during Year 1 to develop her reading, writing and phonological awareness. She also worked for a short period each day with a teacher assistant to support her development in number. Lydia is now a six-year-old. This standards file represents Lydia s attainment in the summer term of Year 1. Lydia s attainment across mathematics Subject level Ma1 Ma2 Ma3 Ma4 Secure level 1 High level 1 Secure level 1 Low level 1 Low level 2

2 2 of 28 The National Strategies Primary Ma1 Using and applying mathematics Coins that total 10p Uses coins to engage with the investigation. Recognises the value of 1p, 2p and 5p coins. Taps each coin an appropriate number of times as she counts on in ones to find the total. Finds several of the possible ways to make 10 pence. Has some collections that contain the same coins. Discuss further the collections that contain the same coins. Establish what is different about the collections, i.e. the coins are in a different order. Establish what is the same about the collections, i.e. same coins. Use counting on as a strategy to add objects and coin values, e.g. when finding the value of a 5p coin and five 1p coins, count on from five. Count in twos and fives. Sorting shapes

3 3 of 28 The National Strategies Primary Engages in practical classroom activity. Chooses her own criteria for sorting shapes: roll, stand. Refers to the sorted shapes to talk about what she has done. Reasons about the shapes in the intersection: they can roll and they can stand. Think of different criteria for sorting the same shapes.

4 4 of 28 The National Strategies Primary True or false addition and subtraction sentences Records addition and subtraction sentences spoken by the teacher. Uses symbols, +, and =. Understands addition as finding the total of two sets of objects. Understands subtraction as take away. Represents the calculations using cubes to check if true or false. Records cubes and her methods, e.g. crossing out cubes that are taken away. Correctly identifies true and false sentences. Shape patterns Recognises pattern repeats in sequences of shapes. Reasons about which shapes come next. Responds to questions about how she knows what comes next. Design own patterns for others to continue and check if they are correct. Measuring

5 5 of 28 The National Strategies Primary Suggests various non-standard units and measure stick for measuring. Chooses to use a ruler and centimetres. Measures to the nearest whole centimetre. Reasons that the item with the biggest number is longest. Identifies pen from her list as the longest but corrects herself. Correctly identifies the shortest item. Measure a range of lengths that cannot be compared directly and for a purpose, e.g. measure the width of a doorway to find if a table could be carried through it. Measure longer lengths using metres. Develop the vocabulary of comparison in the context of measuring activities.

6 6 of 28 The National Strategies Primary What the teacher knows about Lydia s attainment in Ma1, Using and applying mathematics Lydia uses a range of mathematics as an integral part of classroom activity. She is supported by her teacher s explanations of activities, by demonstrations using practical material, pictures and diagrams, and by group discussion. With this initial support, Lydia sustains her engagement with various mathematical activities. These include sorting shapes, copying and continuing repeating patterns of shapes, totalling collections of 1p, 2p and 5p coins, halving shapes and even numbers up to 10 and comparing lengths either directly or by measuring them with a ruler. Lydia is beginning to select the apparatus she needs such as cubes to support her calculation and a centimetre ruler to measure lengths. Lydia represents her work with objects and pictures. She is beginning to represent addition and subtraction calculations using the symbols +, and =. She manipulates diagrams presented on the interactive whiteboard, for example when she demonstrates finding half of a number by dragging images into two equal groups. She refers to the objects, pictures, diagrams and number sentences when she talks about what she has done. Lydia uses everyday and mathematical vocabulary. In talking about numbers of objects she uses more and most. Lydia uses shape names such as circle, triangle, square and rectangle. When comparing lengths she talks about longest and shortest and is beginning to use longer and shorter. When working with sequences of shapes, Lydia recognises the pattern of shapes that is repeated and talks about what comes next. She chooses her own criteria, such as stand and roll to sort 3-D shapes. Lydia uses overlapping rings to create a Venn diagram and reasons about how to place shapes that meet both criteria. She places those shapes into the intersection of the two sets. Lydia is beginning to reason about lengths measured in centimetres. She explains that the item in her list with the biggest number is longest.

7 7 of 28 The National Strategies Primary Summarising Lydia s attainment in Ma1, Using and applying mathematics In her recent development Lydia is beginning to meet some assessment criteria for level 2, in Communicating assessment focus, for example. Her teacher notes that Lydia uses knowledge, skills and understanding from across the mathematics curriculum: numbers and calculation, 2-D and 3-D shapes, position and movement, measuring lengths and handling data. Reading the complete level descriptions for levels 1 and 2 of Ma1, her teacher decides that Lydia s attainment in Using and applying mathematics is best described as level 1. Lydia meets all assessment criteria for level 1 and demonstrates her attainment consistently and in a range of contexts. She is also beginning to meet some criteria for level 2. Her teachers refines her judgement and records Lydia s attainment in Ma1, using and applying mathematics as high level 1. To progress into level 2, Lydia needs to develop her problem solving to make her own suggestions about how to get started, in the context of supportive group discussion. She needs to develop her reasoning, especially her reasoning about patterns in numbers.

8 8 of 28 The National Strategies Primary Ma2 Number Missing numbers Completes sequences that increase in steps of 1, filling in missing numbers. Reads and writes numbers to 20. Transposes digits for some teens numbers. Does not yet recognise missing numbers in decreasing sequence 15,, 12,, 9. Count backwards from 10 to 1, then 20 to 1. As others count backwards and stop, say what the next number should be. Work with sequences that increase and decrease in steps of 1 and 2. Halving shapes Cuts out circles and rectangles and folds them in half. Talks about folding into two and folding in half. Clarify that when a shape is folded into two equal pieces, each piece is called one half of the shape. Create a puzzle showing the half and the whole of several shapes for others to match.

9 9 of 28 The National Strategies Primary Halving numbers of objects Moves eight counters into two sets of four. Initially describes half of eight as four and four. Then responds correctly to What is one half of eight?. Uses fingers or cubes to check as she halves other even numbers up to 10 accurately. Knows even numbers of objects can be halved.

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11 11 of 28 The National Strategies Primary True or false Records addition and subtraction sentences spoken by the teacher. Uses symbols, +, and =. Understands addition as finding the total of two sets of objects. Understands subtraction as take away. Represents the calculations using cubes to check if true or false. Records cubes and her methods, e.g. crossing out cubes that are taken away. Correctly identifies true and false sentences. Calculation targets Finds doubles for numbers up to 5 and is beginning to know these facts. Finds half of even numbers to 10 sometimes using doubles facts. Knows addition and subtraction facts for numbers to 5 and some addition facts to 10. Consolidate addition and subtraction facts for numbers up to 5 and extend to number pairs that total 10.

12 12 of 28 The National Strategies Primary Coins that total 10p Uses coins to engage with the investigation. Recognises the value of 1p, 2p and 5p coins. Taps each coin an appropriate number of times as she counts on in ones to find the total. Finds several of possible ways to make 10 pence. Has some collections that contain the same coins. Discuss further the collections that contain the same coins. Establish what is different about the collections, i.e. the coins are in a different order and what is the same about the collections, i.e. same coins. Use counting on as a strategy to add objects and coin values. For example, when finding the value of a 5p coin and five 1p coins, count on from five. Count in twos and fives.

13 13 of 28 The National Strategies Primary Shopping problems In the starting activity of the lesson, solves problems spoken by the teacher. Records fruit shapes with price for each. Represents cost of 2 apples at 5p as an addition, using symbols + and =. Uses repeated addition to calculate cost of 4 bananas at 3p each. Represents problem of finding change as subtraction, using and =. Solve a range of word problems that involve pence, pounds or measures. Continue role-play in the class shop. Show-me board Copyright Compass. Used with kind permission.

14 14 of 28 The National Strategies Primary What the teacher knows about Lydia s attainment in Ma2, Number Lydia counts aloud to twenty and beyond and reads these numbers, on a ruler, for example. She counts sets of objects accurately, saying one number name for each item. Lydia writes these numbers although she sometimes transposes digits in the teens numbers. Lydia recognises which numbers are missing in sequences up to 20 that increase in steps of one. Although she counts up to 10 and back to 1, Lydia does not yet find missing numbers in sequences that decrease in steps of one. Lydia folds shapes into two equal pieces and recognises that each piece is half of the whole shape. She partitions small numbers of objects to find half of the number, checking for the same number on either side of her line. She explains why objects partitioned into sets of 4 and 6 do not show half of ten and adjusts the groups to show 5 and 5. Using her fingers and putting up the same number of fingers on each hand, Lydia demonstrates doubles of numbers to 5. She knows 2, 4, 6, 8 and 10 as even numbers. Asked what half means, Lydia explains, It means even numbers can half, that is even numbers can be halved. Asked for half of four, Lydia initially holds up four fingers on each hand. Prompted by the teacher s question, Is that half of four? she corrects herself. She goes on to demonstrate with her fingers that half of four is two. Lydia understands addition as finding the total of two or more sets. She understands subtraction as taking a number of objects away and finding how many remain. Lydia adds and subtracts numbers of objects to 10. To add, she puts out cubes to represent the numbers and then counts in ones from the first cube. She does not yet count on from the first number. To subtract she puts out cubes to represent the start number, takes away the appropriate number of cubes and then counts those that remain. Lydia uses fingers to work out pairs of numbers that add to 10, such as and or doubles of numbers up to 5. Lydia solves problems that involve money, where the unit is pence or pounds. She uses addition to represent finding the total cost of several items. She uses subtraction to represent finding change. Lydia knows the values of 1p, 2p, 5p and 10p coins. Making sets of 1p, 2p and 5p coins with a total of ten pence, Lydia counts in ones, tapping each coin an appropriate number of times. Lydia uses objects and pictures to represent numbers and calculations. She is also beginning to use the symbols +, and = to represent addition and subtraction as take away.

15 15 of 28 The National Strategies Primary Summarising Lydia s attainment in Ma2, Number Lydia meets most of the level 1 criteria across the assessment focuses for Ma2 to an extent. In the assessment focus Fractions, Lydia s understanding of halving is a recent development and Lydia has not yet used this mathematics in contexts such as filling containers so that they are half-full or reviewing her estimate of the width of the classroom when she measures to about half way across. She sometimes confuses halving with doubling when halving numbers of objects. In the assessment focus mental methods, Lydia knows that five and five make ten, but does not consistently demonstrate knowledge of any other addition facts. Reading the complete level descriptions for levels 1 and 2 confirms the teacher s first impression that Lydia s attainment is best described as level 1. Knowing that Lydia has yet to meet some level 1 assessment criteria fully and consistently in a range of contexts, her teacher refines her judgement to describe Lydia s attainment as secure level 1. To make further progress within level 1 and into level 2, Lydia should develop some strategies for counting larger numbers of objects such as grouping and counting them in twos, fives or tens. Grouping in tens and ones should also help Lydia begin to develop some understanding of place value and to avoid transposing digits when recording teens numbers. Lydia needs to consolidate her understanding of halving. She should develop strategies for addition such as counting on from the first or largest number and begin to remember addition facts such as pairs of numbers that add to ten.

16 16 of 28 The National Strategies Primary Ma3 Shape, space and measures 2-D shapes Picks up 2-D shapes and talks about them. Running her finger along one of the longer sides of a rectangle, explains, those are the lengths. Responding to the teacher s How many sides does it have?, Lydia then refers to sides and corners. Knows name of rectangle, circle, square, triangle. Describes sides as straight, curly, round. Explain what is the same about the rectangle and square and what is different. Identify rectangle, square, triangle and circle when these shapes are the faces of 3-D shapes. Work with a wider range of shapes, e.g. different types of triangle, pentagon and hexagon. 3-D shapes Knows name of pyramid, cube, cone, cuboid. Recognises 2-D shapes when they are faces of a 3-D shape: triangle on a pyramid; circles on a cylinder. Refers to the base of the pyramid and cone as the prism. Notices the cube looks like a dice. Talks about shapes that roll and/or stand.

17 17 of 28 The National Strategies Primary Refine her language for 3-D shapes, e.g. edges, faces, corners, to clarify her thinking about their features and properties. Count edges, vertices and faces attending to the appropriate feature consistently.

18 18 of 28 The National Strategies Primary Put into place Follows instructions to draw items in various positions in relation to a house. Responds correctly to positional language such as next to, beside, above, below, on top of, between, behind. Create own design with a limited number of shapes and give instructions to a partner to make the same design. Check own instructions by comparing own design with partner s version. Moves The Infant Video Toolkit 2Simple Software Used with kind permission. In a computer program, has a target destination and instructs a car to move to it. Uses symbols for forward and back with a number to move the car distances along streets. Uses symbols to turn the car right and left. Moves the car to the destination. Move the car to other destinations. Move the car to destinations in as few moves as possible. Challenge a partner to move the car along a chosen route. Begin to build up one complete set of instructions to take the car from a start position to its destination.

19 19 of 28 The National Strategies Primary The Infant Video Toolkit 2Simple Software Used with kind permission.

20 20 of 28 The National Strategies Primary Measuring Suggests various non-standard units and measure stick for measuring. Chooses to use a ruler and centimetres. Measures to the nearest whole centimetre. Reasons that the item with the biggest number is longest. Identifies pen from her list as the longest but corrects herself. Correctly identifies the shortest item. Measure a range of lengths that cannot be compared directly and for a purpose, e.g. measure the width of a doorway to find if a table could be carried through it. Measure longer lengths using metres. Develop the vocabulary of comparison in the context of measuring activities.

21 21 of 28 The National Strategies Primary Measuring Begins to balance parcels to find which parcel each of three story characters should carry: the heaviest for Dad, the next for Biff and the lightest for Kipper. Uses the balance to identify the heaviest and lightest when comparing two parcels. Balance objects against a number of uniform non-standard or standard units and use the results to put more than two objects into order. Consider again how the balance can be used to order three objects. Begin to refine comparative language to talk about the heavier/lighter and heaviest/lightest appropriately.

22 22 of 28 The National Strategies Primary What the teacher knows about Lydia s attainment in Ma3, Shape, space and measures Lydia talks about 2-D shapes referring to the number of sides and corners. She describes sides using her everyday language, straight, curly or round. Lydia names rectangles, squares, triangles and circles. Lydia also names 3-D shapes, for example cube, cuboid, pyramid and cone. As she talks about 3-D shapes, Lydia uses sides when talking about faces, vertices and edges. For example, she handles a cube and talks about it having twelve corners and twelve sides, possibly when thinking about the number of edges. She touches the vertices and edges of a cuboid and comments that it has eight sides and eight corners. Lydia also talks about a sphere having one side. When describing a pyramid and then a cone, Lydia uses the term prism for the base. Lydia responds to positional language such as above, below, between, next to and behind, when finding items in the classroom or following instructions for drawing different objects into a picture. In PE she responds to directional language such as forwards, backwards, left and right. Lydia makes whole turns and is beginning to demonstrate a half-turn. Although she does not yet give instructions using positional language, she uses symbols in a computer program to move a car around streets onscreen, entering one instruction at a time. She uses and with a number for forward and backward movements of different lengths and or which turn the car through a right angle to the left or right. Lydia measures lengths by direct comparison. When she talks about the comparison she tends to use longest or biggest to describe the longer of two items. Lydia uses a ruler to measure the length of various objects to the nearest centimetre. She lists objects and lengths. When asked which item is longest, she identifies it by looking for the largest number. Lydia uses a balance and knows which of two objects is heaviest or lightest. She does not yet understand how to use the balance to put three objects into order. Comparing two containers by filling one with water and pouring the contents into the other, Lydia finds which of them holds more.

23 23 of 28 The National Strategies Primary Summarising Lydia s attainment in Ma3, Shape, space and measures Lydia meets the criterion for level 1 in the assessment focus Properties of shape. She is also meets the criterion for Properties of position and movement since she responds to positional language even though she does not yet use it to give instructions. In measures, Lydia is beginning to order a number of objects using direct comparison of their lengths. She compares two objects and knows which weighs more or holds more. Lydia is not yet familiar with units such as the metre or litre to begin to recognise objects that are about the same length as, longer than, hold the same as, hold more than, etc. She does not yet meet the criterion related to time and ordering events. Reading the complete level descriptions for levels 1 and 2 and looking back at the Foundation Stage Profile (FSP) assessment scale for shape, space and measures, her teacher confirms that level 1 is a best fit for Lydia s attainment in Ma3. Considering how much of the level Lydia demonstrates, her teacher recognises that Lydia has a significant amount to learn and refines the judgement to low level 1 for Ma3. To make further progress within level 1, Lydia needs to develop vocabulary for the features of 3- D shapes. She should begin to use directional language to describe or explain movements. She should measure and order objects in a range of contexts including time: things that can be done in a very short amount of time and those that take longer; and the order of familiar events in the day.

24 24 of 28 The National Strategies Primary Ma4 Handling data Pets Uses a given table to record types of pet and names of children choosing each pet as their favourite. Responds to questions about the most popular and least popular pet. Use a tally to collect similar information. Pose questions about the data for her partner to answer. Sorting in science In a science lesson, chooses own criteria for sorting musical instruments. Sorts according to whether instruments need shaking or tapping. Uses a Venn diagram and explains why instruments belong where she has placed them. Consider whether some instruments might produce sound when shaken and when tapped and how they might be placed on the diagram. Sort instruments using other criteria.

25 25 of 28 The National Strategies Primary Shape data. RM Start Graph RM Education plc Sorts and counts 3-D shapes in the class collection. Uses ICT to design her own symbols to represent each type of shape. Uses ICT to produce a diagram with one symbol representing one shape. Responds to, Which shape do we have most of? and Which shape has the smallest number?. Record a key for symbols in her diagram. Create a pictogram that uses one symbol consistently throughout.

26 26 of 28 The National Strategies Primary What the teacher knows about Lydia s attainment in Ma4, Handling data Lydia sorts shapes and other objects using two criteria and Venn diagrams. She is beginning to overlap the set rings to create a region for objects that meet both criteria. Lydia measures the length of objects and records her results in a list. She also asks other children for information, such as their favourite type of pet, and records their names in a given table. Lydia organises information, for example she arranges 3-D shapes by type and counts how many of each shape there are, representing her results with a computer-generated diagram. Lydia also uses block graphs to represent information. In her graphs and diagrams, one block or symbol represents one object. Lydia refers to her Venn diagrams to talk about objects and their attributes. She explains the attributes of objects in the intersection. For example, sorting 3-D shapes using roll and stand she explains that the cone and cylinder in the intersection roll and stand. Lydia interprets the lists she makes. Interpreting her list of measurements, for example, she refers to the number of centimetres and talks about the longest object having the biggest number. Lydia interprets the block graphs and diagrams she creates. She counts blocks or symbols and is beginning to refer to the scale to read numbers represented in each column. Lydia talks about the most popular items and responds to questions about the least popular.

27 27 of 28 The National Strategies Primary Summarising Lydia s attainment in Ma4, Handling data Lydia meets assessment criteria for Ma4 at level 1 and towards the end of a recent unit of work she demonstrates most of the criteria for level 2. Reading the complete level descriptions for levels 1 and 2, her teacher decides that Lydia s attainment in Ma4 is best described as level 2. Since much of the progress is recent and Lydia has not yet demonstrated the attainment fully and consistently or in a range of contexts, her teacher refines the judgement to low level 2. To become more secure in level 2, Lydia should begin to make decisions about how to collect and record data. For example, with her group she might discuss the questions they will ask or categories they will use and how to draw a table to record the data. She should begin to use tallies to record information such as children s preferences more efficiently. She should draw block graphs to represent data in a range of situations and consider how to number the vertical axis to show clearly the number of blocks in a column. She should learn that a pictogram has a single symbol that can represent more than one object or occurrence.

28 28 of 28 The National Strategies Primary Acknowledgements Show-me board Copyright Compass. Used with kind permission. RM Start Graph RM Education plc. The Infant Video Toolkit 2Simple Software Used with kind permission. RM Start Graph RM Education plc