Maths at Leighton Primary School

Transcription

1 Maths at Leighton Primary School

2 Maths at Leighton Primary School Mathematics provides pupils with a set of tools that allow children to understand the world by making connections. These tools include logical reasoning, problem solving skills and the ability to think in abstract ways. Mathematics is important in everyday life and it is important for us that children develop a positive and enthusiastic attitude towards mathematics that will stay with them throughout their lives. We are dedicated to making sure that all pupils master the key concepts of mathematics, appropriate for their level of ability, in order that they make progress and avoid gaps in their understanding which could become barriers to learning as they move through education. We aim to provide the pupils with a mathematics curriculum and high quality teaching to produce individuals who are numerate, independent, inquisitive, and enquiring. We aim to equip them with the skills to talk confidently about mathematics by convincing themselves or others that a conjecture is true. We follow the Concrete- Pictorial- Abstract approach to teaching mathematical concepts. When introducing a new concept to children, we help give the maths meaning by first modelling it using practical resources e.g. hundreds, tens and units blocks, counters, Numicon etc. Children are encouraged to work through problems using these resources to help them understand the maths they are doing. When they have a good understanding, they will use pictures instead to represent the maths they are learning before moving on to the abstract stage which is just numbers. Some children move quickly through these stages whereas others will need to spend longer at each stage to really embed the learning.

3 In Reception, children count and order numbers to 20. They learn mathematical vocabulary that lets them compare numbers, shapes and measures. They begin to add and subtract two single digit numbers using practical resources. The children learn to solve problems including doubling, halving and sharing. They are encouraged to see patterns, describing them and also creating their own. At Key Stage 1, our focus is to give children a confidence and fluency with whole numbers, counting and place value. Children mentally calculate addition, subtraction, multiplication and division questions and use informal methods to record their answers. Through the use of practical resources, they solve problems, explain their reasoning and explore patterns and relationships between numbers. At Key Stage 2, children continue to become fluent with the 4 operations and place value. The mental and written calculations they perform are with increasingly large whole numbers. The children develop their addition, subtraction, multiplication and division skills by applying them to fractions and decimals. Practical resources and pictorial representations continue to be used to embed these more difficult mathematical concepts. We have a dedicated and skilled Numbers Counts teacher, Mrs Reynolds, who teaches a targeted Year 3 maths group during maths lessons and who also provides additional maths intervention for children in Years 3 and 4 who have fallen behind in maths. She works very closely with the children in the intervention groups 3-4 times a week for a whole term to unpick the mathematical misconceptions these pupils have made, reteach the learning and help them catch up to their peers. The progression grids below, show how the different mathematical skills progress from Reception to Year 6.

4 Reception months Number Shape, Space and Measure Recognise some numerals of personal significance. Recognises numerals 1 to 5. Counts up to three or four objects by saying one number name for each item. Counts actions or objects which cannot be moved. Counts objects to 10, and beginning to count beyond 10. Counts out up to six objects from a larger group. Selects the correct numeral to represent 1 to 5, then 1 to 10 objects. Counts an irregular arrangement of up to ten objects. Estimates how many objects they can see and checks by counting them. Uses the language of more and fewer to compare two sets of objects. Finds the total number of items in two groups by counting all of them. Says the number that is one more than a given number. Finds one more or one less from a group of up to five objects, then ten objects. In practical activities and discussion, beginning to use the vocabulary involved in adding and subtracting. Records, using marks that they can interpret & explain. Begins to identify own mathematical problems based on own interests and fascinations. Beginning to use mathematical names for solid 3D shapes and flat 2D shapes, and mathematical terms to describe shapes. Selects a particular named shape. Can describe their relative position such as behind or next to. Orders two or three items by length or height. Orders two items by weight or capacity. Uses familiar objects & common shapes to create & recreate patterns & build models. Uses everyday language related to time. Beginning to use everyday language related to money. Orders and sequences familiar events. Measures short periods of time in simple ways.

5 Reception- Early Learning Goals Number Shape, Space and Measure Count reliably with numbers from 1 to 20. Place numbers 1 to 20 in order. Say which number is one more or one less than a given number. Using quantities and objects, add two single-digit numbers and count on to find the answer. Using quantities and objects, subtract two single-digit numbers and back to find the answer. Solve problems, including doubling, halving and sharing. Use everyday language to talk about size, weight, capacity, position, distance, time, money, to compare quantities and objects and to solve problems. Recognise, create and describe patterns. Explore characteristics of everyday objects & shapes & use mathematical language to describe them.

6 Year 1 Maths Key Objectives 1 Count to and across 100 from any number 2 Count, read and write numbers to 100 in numerals 3 Read and write mathematical symbols: +, - and = 4 Identify "one more" and "one less" 5 Use number bonds and subtraction facts within 20 Add and subtract 1-digit and 2-digit numbers to 20, 6 including zero 7 Recognise, find and name a half 8 Recognise, find and name a quarter 9 Measure and begin to record length, mass, volume and time 10 Recognise and know the value of all coins and notes 11 Use language to sequence events in chronological order 12 Recognise and use language relating to dates 13 Tell the time to the half-hour, including drawing clocks 14 Recognise and name common 2-D shapes 15 Recognise and name common 3-D shapes

7 Year 2 Maths Key Objectives 1 Count in steps of 2s, 3s and 5s, and steps of 10 2 Recognise place value in two-digit numbers 3 Compare and order numbers up to 100 using <, > and = Recall and use number addition/subtraction facts to 20, and 4 derive related facts Add and subtract mentally and with objects one- and two-digit 5 numbers Understand and use the inverse relationship between addition and 6 subtraction Know 2, 5 and 10 tables, including recognising odd & even 7 numbers 8 Calculate mathematical statements using x and symbols Recognise, find, name and write 1/3, 1/4, 1/2 and 3/4 of size, 9 shape or quantity 10 Write simple fraction facts, e.g. 1/2 of 6 = 3 Combine amounts of money to make a value, including using 11 and p symbols 12 Tell the time to the nearest 5 minutes, including drawing clocks Describe properties of 2-D shapes, including number of sides and 13 symmetry Describe properties of 3-D shapes, including number of edges, 14 vertices and faces 15 Interpret and construct simple tables, tally charts and pictograms

8 Year 3 Maths Key Objectives 1 Count in multiples of 4, 8, 50 and Compare and order numbers up to Add and subtract numbers mentally, including round numbers to HTU 4 Add and subtract using standard column method 5 Estimate answers to calculations and use the inverse to check answers 6 Know 3, 4 and 8 tables 7 Count up and down in tenths Understand that tenths are objectives or quantities divided into ten 8 equal parts 9 Compare and order simple fractions 10 Recognise and show equivalent fractions 11 Find and write fractions of a set of objects Add and subtract fractions with common denominators (less than 12 one) 13 Measure, compare and calculate measures using standard units 14 Measure the perimeter of simple 2-D shapes 15 Add and subtract money, including giving change Tell and write the time from an analogue clock, including using 16 Roman numerals 17 Estimate and read time to the nearest minute 18 Identify horizontal, vertical, parallel and perpendicular lines 19 Identify whether angles are greater or less than a right angle 20 Interpret and present data using bar charts, pictograms and tables

9 Year 4 Maths Key Objectives 1 Count backwards through zero, including negative numbers 2 Recognise place value in four-digit numbers 3 Round any number to the nearest 10, 100 or Know tables up to Use place value and number facts to carry out mental calculations 6 Use factor pairs and commutativity in mental calculations 7 Use short multiplication method 8 Recognise and use hundredths 9 Recognise and write decimal equivalents to ¼, ½ and ¾ Divide one- or two-digit numbers by 10 and 100, using tenths and 10 hundredths 11 Round decimals with one decimal place to the nearest whole number 12 Compare numbers up to two decimal places Convert between different units of metric measurement, including 13 money 14 Find the area of rectilinear shapes by counting squares 15 Solve problems converting units of time 16 Compare and classify shapes, including quadrilaterals and triangles Complete a simple symmetric figure with respect to a specific line of 17 symmetry. 18 Describe positions on a 2-D grid using co-ordinates 19 Describe translations using a given unit to the left/right and up/down 20 Interpret and present discrete and continuous data on appropriate graphs

10 Year 5 Maths Key Objectives 1 Interpret negative numbers in context 2 Read Roman numerals to 1000, including years 3 Recognise and use square and cube numbers, and know the notation 4 Use rounding to check answers and determine accuracy 5 Identify multiples and factors, including finding factor pairs and common factors 6 Use vocabulary: prime numbers, prime factors and composite numbers 7 Know prime numbers up to 19 8 Multiply and divide numbers by 10, 100 or 1000, including decimals 9 Use long multiplication for multiplying numbers of up to 4 digits by one or two digits 10 Divide numbers using standard written short division 11 Convert between mixed numbers and improper fractions 12 Compare and order fractions whose denominators are multiples of the same number 13 Identify, name and write equivalent fractions including tenths and hundredths 14 Add and subtract fractions with denominators that are multiples of the same number 15 Multiply proper fractions and mixed numbers by whole numbers with support 16 Read and write decimal numbers as fractions 17 Round decimals with 2 decimals places to whole number or to one decimal place 18 Read, write, order and compare numbers with up to 3 decimal places 19 Recognise % symbol and explain as a fraction with denominator 100 (parts out of 100) 20 Understand and use common approximate conversions between metric and imperial 21 Measure and calculate the perimeter of composite rectilinear shapes

11 22 Calculate the area of rectangles, and estimate the area of irregular shapes 23 Use the properties of rectangles to find missing lengths and angles 24 Distinguish between regular and irregular polygons 25 Identify 3-d shapes from 2-d representations 26 Know angles are measured in degrees and compare acute, obtuse and reflex angles 27 Draw and measure angles to the nearest degree 28 Identify angles at a point, in a turn and on a straight line 29 Describe and represent the result of a reflection or translation 30 Complete, read and interpret information in tables, including timetables Year 6 Maths Key Objectives 1 Use negative numbers to calculate intervals across zero 2 Divide numbers using long division, interpreting the remainders as appropriate 3 Use order of operations to carry out calculations 4 Use common factors to simplify fractions 5 Compare and order fractions of any size 6 Add and subtract fractions with different denominators and mixed numbers 7 Multiply simple pairs of proper fractions 8 Divide proper fractions by whole numbers 9 Calculate decimal fraction equivalents for simple fractions 10 Multiply a number with up to two decimal places by whole numbers 11 Use written division with answers of up to two decimal places 12 Solve problems involving the calculation of percentages 13 Recall and use equivalences between fractions, decimals and percentages 14 Solve problems using ratio using multiplication and division facts 15 Solve problems involving similar shapes where the scale factor is

12 known 16 Solve problems involving proportion, using knowledge of fractions and multiples 17 Use simple formulae 18 Generate and describe linear number sequences 19 Express missing number problems algebraically 20 Convert units of measure between smaller and larger units 21 Convert between miles and kilometres 22 Calculate the area of parallelograms and triangles 23 Calculate and compare volume of cubes and cuboids 24 Illustrate and name parts of a circle 25 Finding missing angles in triangles, quadrilaterals and regular polygons 26 Recognise vertically opposite angles and find missing angles 27 Describe positions on the full co-ordinate grid 28 Translate shapes on a co-ordinate grid and reflect in the axes 29 Construct and interpret pie charts

13 Math Predictions This table shows the percentage of children in a year group who should achieve the expected level of a child their age by July Year group % of children who should achieve ageexpected outcomes Year 1 71% Year 2 63% Year 3 63% Year 4 62% Year 5 63% Year 6 68%

14 Elements of Good Practice in the Teaching of Maths Monitoring Process Maths books to what extent are objectives evident? Teachers should ensure that the content of the lesson is pitched correctly. Most children will be working on objectives from their year group, with a minority working on below age-related expectations. Books will show maths learning going through the journey from simple fluency tasks to deeper thinking tasks. How are we collecting information to enable the monitoring process? Reading records and journals, guided reading (teacher) records, pupil reading workbooks, discussions with pupils about their reading interests, challenges, how often they read with an adult, breakdown strategies, discussions with teachers and support staff, phase leader reading questionnaire How are we monitoring the quality of class teaching? Head Teacher and Teaching and Learning Lead observe class maths lessons and discuss with pupils. Afterwards, valuable discussion with teacher(s) outlines strengths, next steps and ideas for improving practice. How are we monitoring the quality of teaching and learning for intervention groups and its impact? Phase leaders and class teachers carefully select pupils who are at risk of not achieving their end of year target in maths. Appropriate intervention is put in place such as: Number Sense: calculations, Number Sense: mental fluency, First Number 1 and 2. In addition, we have a dedicated Numbers Count teacher who works with specific year groups and who provides additional maths support for children 3 4 times a week.

15 Elements of Good Practice in the Teaching of Maths at Leighton Maths lessons show that teachers are thinking carefully about how to introduce new mathematical concepts by demonstrating with pictures and practical resources. This gives meaning to the maths they are learning. Teachers are also encouraging children to use these resources to support their own learning. Evidence in lessons and books of the high expectations teachers have of their pupils. Objectives are appropriate for their year group or the needs of the pupils and are in line with the new curriculum. Teachers and support staff provide high quality feedback in the form of small group discussion and written comments in marking. Evidence in books of a mixture of activities used to teach a particular concept. Often teachers will start with fluency tasks that test the recall of key facts and include missing number questions, matching activities, making comparisons. Then moving on to reasoning activities where pupils need to either agree or disagree with a statement giving a clear explanation and proving it using maths. There are then problem solving activities that further deepen learning. Evidence pupils are becoming more familiar with the practical resources in classrooms and teachers are becoming better at prompting children to use them. Resources are available to children: either on desks or in a designated area. Maths displays in classrooms clearly indicate the unit of work children are working on and provides visual models for pupils to refer to. Intervention groups have been put in place to target certain pupils vulnerable of reaching their end of year target. Progress of these carefully selected pupils are monitored regularly by class teacher and phase leader. Half termly summative assessments are given to pupils to inform teacher planning and pupil progress.

16 Supporting Learning at Home Be positive when talking about maths. Not everyone has positive memories about their maths learning at school but try not to share these with your child or they may start thinking like that themselves. Point out maths in everyday life. When shopping, cooking, travelling, try to include your child in activities involving numbers and measuring. Praise your child for their effort and show them that by working hard they can improve. Maths is not just about getting the answers right and being the quickest to finish: it is about the process and the thinking behind the problem. Encourage them to learn their times tables up to 12 x 12. Having a good knowledge of times tables is key to successfully working with fractions, decimals, percentages, division and ratio etc. These web links lead to a variety of websites that will support and extend the learning that takes place in school. - A variety of math games as well as games for literacy and science - Games to develop a strength with times tables - More games to develop a strength with times tables - Even more games to develop a strength with times tables - A place to find English, maths and science games for children in EYFS, Year 1 and Year 2

17 - A place to find English, maths and science games for children in Year 3 to Year 6 We also have a calculation and a fraction/decimal/percentages policy that show you how we teach these concepts. On the policies, there are examples that detail the way to work out the 4 operations and fractions.