Programmes in Action

Discovery Bay International School

Mathematics Programmes in Action Mathematics Programmes in Action

Contents:

 The structure of a mathematics lesson

o The mental maths session

o The whole class teaching session

o The group and / or individual work session

o The Plenary

 Grouping across the year groups

 Weekly and unit planning

 Assessment

 Contribution of mathematics to teaching in other curriculum areas

 Monitoring and Review of mathematics

 Appendix Mathematics Programmes in Action

Mathematics is taught 5 times a week and each lesson is 45 – 60 minutes in duration.

The DBIS mathematics programme is structured around the renewed Primary National Numeracy Framework.

The Abacus and Abacus Evolve Scheme, Maths On Target, Level Up and Myimaths all support the NNS Framework and the learning and teaching of mathematics at DBIS (Please refer to section 3 and 4 of the Maths Education Plan also.)

The structure of a mathematics lesson

The mental maths session

 There should be a clear start and finish to this section.

 It should be 8 –12 minutes long.

 It should take place at the start of each maths lesson (5 days a week).

 The mental maths section should be thoroughly planned.

 There should be a variety of questioning. For example using a mixture of open and closed questions skilfully framed, adjusted and targeted to make sure that pupils of all abilities are involved – including SEN and ESL children.

 Teachers should allow children appropriate time to answer questions.

 There should be high expectations for all children.

 All children should have the opportunity to attempt answering all questions.

 All children should be seated so that they can clearly here and see the teacher.

 The teacher should identify misconceptions and if they can be quickly corrected do so. Otherwise move on and address them at a later date.  Children should be enthusiastic and willing to attempt all questions.

The whole class teaching session

 This section should come directly after the mental maths section and there should be a clear start and finish to it.

 Direct teaching to the whole class should be no less than 15 minutes and no longer than 30 minutes.

 The learning objectives should be shared with the children at the beginning of this section.

 The teacher should demonstrate a thorough understanding and knowledge of the mathematical content of the lesson.

 Work (including range of vocabulary) should be taken from the correct unit of the NNS for each particular age range. The only exceptions to this should be children with specific learning difficulties in mathematics or children who have gaps in their mathematical learning.

 Work should be thoroughly planned and the teacher should have clear objectives and actively extend the children’s mathematical knowledge and understanding and challenge their thinking by building upon skills already acquired.

 Wherever possible teachers should model ideas and link them to previous work and other areas of learning.

 Students should be given clear instructions about what is expected from them.

 The teacher should have high expectations for all children.

The group and / or individual work session

 Practical and or written work should be on the same theme for the whole class.

 Group work should be differentiated at no more than 3 levels of difficulty with focused teaching of one or two groups for part of the time.

 Whole class investigations should allow for differentiation through extension activities and additional support for those groups or individuals who require it. Please steer clear of differentiation by volume.

 All students should have easy access to and be taught how to use appropriate resources to aid their learning and to ensure that they are participating in the lesson.

 All students should be on task.  Classroom assistants should be used effectively to aid students’ mathematical learning.

 Teachers should make informal assessments throughout the lesson and then use this information in future planning.

 Teachers should identify misconceptions and correct them.

 There should be opportunities for teachers and students to demonstrate a variety of methods to one another and to explain their reasoning.

 Wherever possible, mathematics should be linked to other curriculum areas and real life.

 Throughout the lesson there should be positive feedback for individuals and groups.

 Students should be encouraged to have a go and to share ideas and equipment with their peers before approaching the teacher.

 Students should enjoy mathematics!

The Plenary

 This section will come at the end of the mathematics lesson.

 It will sum up and review the work covered during the maths lesson.

 Homework may be given at this time.

 Please refer to the PowerPoint presentation found on the share drive for further reference.  \\share\Curriculum\Maths\New Maths\Teaching a maths lesson.pps Mathematics Programmes in Action

Grouping across the year groups

Students from Year 3 to Year 6 are grouped by ability across the year group using the following methods and criteria;

 Teachers must consult with previous year groups to gain understanding of the new students at the beginning of the school year.

 The previous year’s maths assessments must be consulted before groupings are set

 Every effort must be made to ensure that students are placed in the right group from the start

 Teachers must seriously consider individual cases before moving students between groups. Moving to a higher ability group is fine but the consequences of a student moving to a lower group are more far reaching.

 New students to DBIS - All new students must be thoroughly assessed before being placed in a group. Please ensure that you read previous school’s reports for background information but final decisions are made after internal assessments.

(Please refer to section 4, Maths Groupings, of the Maths Education Plan) Mathematics Programmes in Action

Weekly and unit planning

Maths short term planning is based on the units of work from the renewed Primary National Numeracy Strategy (NNS)

Templates for the 2 or 3 week planning sheets are provided for all teachers

The Learning objectives are already inserted on the sheets as are the student’s learning outcomes

Teachers must fill in the remaining columns:  Mental warm up  Whole class introduction  Independent / Group Focus and Activities  Plenary / Key Questions  Vocabulary – that can be taken straight from the NNS units of work

The independent / group work must be related to the learning objectives

Term Overview

All year groups are provided with a term over indicating when units of work must be taught

(Please refer to section 5, Planning, of the maths Education Plan)

Reference;

All unit plans are on the share drive – in Year Group folders All weekly templates are also on the share drive All term overviews can be found on the share drive \\share\Curriculum\Maths\Teaching and Learning Maths\Planning\Year # Mathematics Programmes in Action

Assessment

The teaching and learning cycle

Teaching a unit of work will need careful initial and ongoing planning, informed by an assessment of children's learning. A cycle that supports this process in the Primary Framework for mathematics is set out below.

Assess – plan – teach – practise – apply – review

The cycle indicates the importance of undertaking some initial assessment at the start of the unit to monitor children's preparedness for the work. This initial assessment may indicate a need to revisit some earlier learning to refresh the knowledge, skills or understanding needed to ensure children cope with and make progress in the unit. Day-to-day assessment of children's achievements and progress over the unit will provide information about children's general attainment and progress and identify any children who might need additional support. Regular reviews provide opportunity to take stock of children's learning.

Reviews of learning are a key teaching and assessment tool. They can involve brief in- lesson pauses to determine whether children can recall some knowledge or a key idea, can share with one another the next steps in a calculation or can explain to their partner a strategy that demonstrates they are able to solve the problem. The reviews can be more substantial and take up a significant part of the lesson or form a plenary before some new learning is introduced. Such reviews are carefully planned with clear learning objectives in mind. The aim is to assess the depth of children's learning and use this information to plan the next steps. These reviews will involve probing questions, extended dialogue or a series of short activities that draw on past learning and incorporate use and application of the mathematics that has been taught.

Assessment for Learning (Ongoing, formative) Assessment for Learning is the process of seeking and interpreting evidence for use by learners and their teachers to decide where the learners are in their learning, where they need to go and how best to get there

Assessment of Learning (Snapshot, summative)

Assessment of learning is any assessment that summarises where learners are at a given point in time – it provides a snapshot of what has been learned (in terms of both attainment and achievement)

Five key factors that improve learning through assessment:

 Providing effective feedback to children  Actively involving children in their own learning  Adjusting teaching to take account of the results of assessment  Recognising the profound influence assessment has on the motivation and self- esteem of children, both of which are crucial to learning  Considering the need for children to be able to assess themselves and to understand how to improve.

Assessment of Learning timetable:

Term 1 – 2 assessments (mid term and end of term) Term 2 – 1 assessment (end of term) Term 3 – Year 1 – Final assessments Year 2 – QCA end of Key Stage 1 Mathematics test (SATs) Years 3-5 – QCA Optional mathematics tests Year 6 – QCA end of Key Stage 2 Mathematics test (SATs)

All of the above tests are taken in June

Students will also undertake an Incas assessment in term 3.

(Please refer to section 6, Assessment, of the Mathematics Education Plan) Mathematics Programmes in Action

Contribution of mathematics to teaching in other curriculum areas

English

Mathematics contributes significantly to the teaching of English in our school by actively promoting the skills of reading, writing, speaking and listening. For example, we encourage students to read and interpret problems in order to identify the mathematics involved. The students explain and present their work to others during plenary sessions. Younger students enjoy stories and rhyme that rely on counting and sequencing. Older students encounter mathematical vocabulary, graphs and charts when using non-fiction texts.

Information and communication technology (ICT)

Students use and apply mathematics in a variety of ways when solving problems using ICT. Younger students use ICT to communicate results with appropriate mathematical symbols. Older students use it to produce graphs and tables when explaining their results or when creating repeating patterns, such as tessellations. When working on control, students use standard and non-standard measures for distance and angle. They use simulations to identify patterns and relationships. (please refer to section 4, Mathematics and I.C.T, of the Maths Education Plan)

Personal, social and health education (PSHE) and citizenship

Mathematics contributes to the teaching of personal, social and health education, and citizenship. The work that students do outside their normal lessons encourages independent study and helps them to become increasingly responsible for their own learning. The planned activities that students do within the classroom encourage them to work together and respect each other’s views. We present older students with real-life situations in their work on the spending of money.

Spiritual, moral, social and cultural development

The teaching of mathematics supports the social development of our students through the way we expect them to work with each other in lessons. We group students so that they work together, and we give them the chance to discuss their ideas and results. The study of famous mathematicians around the world contributes to the cultural development of our students.

Teaching mathematics to students with special needs

We teach mathematics to all students, whatever their ability. It is part of the school curriculum policy to provide a broad and balanced education to all students. We provide learning opportunities that are matched to the needs of students with learning difficulties. Work in mathematics takes into account the targets set for individual students in their Individual Education Plans (IEPs). (Please refer to section 4, Targeted Support and Intervention, of the Maths Education Plan)

Mathematics Programmes in Action

Monitoring and Review of mathematics

Monitoring of the standards of student’s work and of the quality of teaching in mathematics is the responsibility of the Deputy Principals, Maths Curriculum Team Leader and the Maths Curriculum Team. Their work also involves supporting colleagues in the learning and teaching of mathematics, being informed about current developments in the subject, and providing strategic leadership and direction for the subject in the school. The Primary Principal gives the School Principal an annual summary in which he evaluates strengths and weaknesses in the subject and indicates areas for further improvement. Appendix

In this section you will find examples of:

 A planning sheet – an example of planning

 A maths overview for a term – an example

(please refer to section 3, Content, of the Maths Education Plan)

Reviewed and updated:

April 2013 – Daniel Philo. April 2014 – Daniel Philo. DBIS Short term Mathematics Plan Class: Y6 Week: Term 2, Weeks 4 and 5 Date: 27/1/14 – 24/2/14 (CNY) Maths Unit: 6C2 – 2 weeks

End of unit self-assessment Beginning: Developing: Mastering: Read scales that use integers with intervals of 5, Read scales that use integers with intervals of Read scales that use integers with intervals of any interval with 10 and 20 accurately. Pupils use standard units 100, 1000, ½ and 1/4. Pupils understand the integers and complex fractions and decimals. Pupils understand and to measure length, ‘weight’, capacity and time in relationship between metric units. They begin to use scale in the context of maps a range of contexts. They read times on the make sensible estimates using standard units in and drawings. They are familiar with the Imperial units still in analogue clock and the date from a calendar. relation to everyday situations. They understand common use. They convert one metric unit to another. They They choose and use a range of units and and use the twelve and twenty-four hour clocks. understand and use negative numbers in context. They use instruments, interpreting, with reasonable Pupils collect, group and order discrete data with timetables involving the twenty-four hour clock. accuracy, numbers on a range of measuring given class intervals. They represent and interpret Pupils design and use a data collection sheet and interpret the instruments. data using a range of graphs, tables and results. They calculate and use the mean and range of discrete Pupils extract and interpret information diagrams. They construct and interpret data. They construct and interpret simple line graphs. They presented in simple tables and lists. They collect, pictograms where the symbol may represent a interpret graphs and diagrams, including pie charts, and draw display and interpret data in pictograms and bar group of units. They interrogate a simple data conclusions. They insert and interrogate data in a computer charts in order to communicate information. base for one criterion. They understand and use database. They place events in order of ‘likelihood’ and use simple vocabulary associated with probability, appropriate words to identify chance, such as fifty-fifty and evens. such as certain, uncertain, impossible, likely, unlikely and fair.

Objectives over 2 Day Mental warm up Whole Class Introduction Independent / Group Focus & Plenary Key weeks Activities Key Vocabulary Children’s learning Questions outcomes • Solve problems Mon WALT: Activity: WALT and Activity: LA/MA – MyMaths website, Shape, When would measure, by collecting, WILF: Converting units, Metric you need to measureme Conversion and Converting know such nt selecting, Develop the Use the S.O.D.A Convert between Discuss Measures. methods in size processing, ability to apply activity of the day standard metric conversion rates presenting and real life? compare the knowledge to reinforce quick units of e.g. 100cm = 1m interpreting data, HA – Level Up 4-6, page 136, When have unit, and mental recall, measurements And perform using ICT where question 4 on to page 137. the standard understanding calculation and with decimal examples of appropriate; students unit that has problem solving values. converting from draw conclusions Extension group – Level Up 5-7, used them? metric unit, accumulated skills. one to another; and identify page 214. imperial unit thus far to 1.45m = further questions measuring mental problem 2.87kg = to ask scale, contexts. I can use data to division solve problems Tues WALT: Activity: WALT and Activity: LA – Level Up 4-6, page 136, Why are estimate WILF: question 4 on to page 137. imperial • Select and use Reinforce and Using examples, LA - as LA – reinforce units still standard metric secure pupils to explain yesterday. yesterday. MA – Level Up 5-7, page 214. learnt? units of measure calculation the necessary MA/HA – Some and convert methods related methods. MA/HA – 5 miles = 8 km HA - Level Up 5-7, page 215. countries between units to addition and Use large Understand how 1 mile=___km? still use using decimals to subtraction, numbers close to convert metric (8÷5) H/W – Myimaths, Shape, them! two places (e.g. using multi- and not close measurements 2.5 miles etc? Converting Units, Metric change 2.75 litres digit, decimals together, to imperial and conversion and Converting to 2750 ml, or and fractions. improper fractions vice versa. Measures. vice versa) and mixed numbers and I can convert decimals that do measures between units and do not have a including unit. decimals Wed WALT: Activity: WALT and Activity: LA - Pupils use with netbooks. Why do WILF: Generate own and take turns to scales with read from the various scales that different • Read and As yesterday Use written LA/MA - Pupils http://www.teache interpret scales the website produces. amounts but with questions on the can accurately rled.com/resource on a range of present multiplication board but also determine the s/dials/dialsload.h measuring MA – Mymaths website, Shape, exist? and division, provide size of the tml instruments, Scale and Similarity, Scale exploring as opportunities to intervals on recognising that Drawing and Map Scales. Lateral many different use in oral and different scales Using the the measurement thinking, methods and application and accurately smartboard, begin made is HA – Level Up 5-7, page 268. would you strategies as questions i.e. read values. with whole class approximate and use the recording results possible. practical to ensure same to a required situations. HA – Read and understanding. device to degree of Holiday costs use map scales. Students to take measure accuracy; $750, 20% turns reading the the mass of compare readings reduction, what is scales produced. a mouse on different new cost? and an scales, for example when elephant, using different why? instruments Thur WALT: Activity: WALT and Activity: LA – Mymaths website, Shape, How has s WILF: Scale and Similarity, Scale learning I can read and Drawing and Map Scales. about Apply Mental maths LA/MA - Pupils LA - As yesterday. answer questions decimal understanding practice SATs test. can accurately about scales and MA – Level Up 5-7, page 268. places in of concepts determine the Convert distances write down my previous quickly and size of the on the class world answer as HA – Level Up 5-7, page 269. weeks accurately as the accurately to intervals on map using the enabled or question requires mental recall different scales scale it has. H/W – Myimaths, Data, enhanced and use of and accurately Processing Data, Mean and our ability count, tally, I can compare questions. read values. Mode, Median and Range. to record sort, vote readings from and convert survey, different scales HA – Read and between questionnair use map scales. different e • Describe and units of data, predict outcomes measureme database from data using nt e.g. g, graph, block the language of kg. graph, line chance or graph likelihood pictogram, Fri LA – Level Up 4-6, page 70. Ext, What is the represent I can use data to WALT: Activity: WALT and Activity: work out WILF: page 72. purpose of each and problems about Perform two In preparation of LA - Develop Students to recall MA – Mymaths, Data, Processing how do they chance calculation determining understanding of their Data, Mean and Mode, Median each help tasks involving mean, students to and use mean. understanding of and Range. us to • Construct and 1, 2 and 3 digit perform mental these averages interpret understand numbers. tasks involving MA/HA – Use and how they are frequency tables, HA – Level Up 5-7, page 190. Ext, the results two operations: mean, median determined. bar charts with page 192. in greater add 5 numbers and mode with Use examples, grouped discrete detail? below 30 and sets of results. making sure the data, and line group, set multiply by 3 etc. results are graphs; interpret list, chart, Record on pupil ordered before pie charts line chart w/boards. the averages are table, I can represent determined. frequency data in different table ways and understand its label, title, meaning axis, axes diagram • Describe and most interpret results popular, Mon LA – Level Up 4-6, page 126. Students to and solutions to WALT: Activity: WALT and Activity: most explain problems using WILF: common MA – Level Up 5-7, pages 196-7. succinctly, the mode, range, Develop the Use the S.O.D.A Pupils are to Discuss and least using median and mean ability to apply activity of the day know how the explore how 360° popular, HA – Myimaths, Shape, Presenting mathematic the knowledge to reinforce quick 360° of a pie is divided least Data, Drawing Pie Charts. (L6) al I can solve and mental recall, chart is appropriately by common vocabulary, problems using understanding calculation and accurately the number of mode, mode, range, their that has problem solving divided to results collected range, median and mean understandi accumulated skills. convey results and then mean, ng of thus far to that have been multiplied by the average, • Use a calculator constructing mental problem collected. amount in each median to solve problems a pie chart. involving multi- contexts. group. statistics, step calculations Pupils will distribution produce their Using the I can use a own pie charts ‘interpreting pie maximum/ calculator to using this chart’ document, minimum solve problems understanding. examine the value involving more numbers in each classify, than one step section by outcome observing the • Use a range of area each oral techniques to occupies in the present pie. persuasive Answer the argument attached I can present a questions persuasive together as class argument to and ensure all others understand.

Tues WALT: Activity: WALT and Activity: LA – Myimaths, Shape, Presenting What is the WILF: Data, Reading Pie Charts. (L5) purpose of pie charts? Use numbers to Use five digit Be able to Reinforce method MA – Complete yesterday’s pages. Why do we three decimal numbers, three of construct pie of pie Ext - Level Up 4-6, page 234. (L5 use them? places those digits to the charts by using construction, as and 6 tasks). understanding right of the knowledge of yesterday. Use the positional decimal point e.g. how to divide examples. HA - Level Up 5-7, pages 196-7. term for each 12.345, and 360° by the Ext page 294. digit and the identify which number of base ten column each digit results. H/W – Data, Presenting Data, relationship is in and how to Reading Pie Charts, Drawing between digits move from Create and Pie Charts. in different thousandths to analyse complex columns. hundredths etc. pie charts.

Wed WALT: Activity: WALT and Activity: LA – Level Up 4-6. Page 74 and What WILF: 75, to question 4. (L5) understandi ng has been Reinforce Using knowledge Be able to read Using the MA – Level Up 4-6. Page 74 and acquired or equivalent from number lines and analyse data designated 75. (L5 and 6) developed amounts constructed, from a textbook, perform of this between convert between conversion/line questions HA – Level Up 5-7, pages 194-5. graph? fractions, the three systems. graph by together to

decimals and accurately ensure fair, unfair percentages. examining understanding of likely, values along the concepts unlikely, each axis. involved. likelihood, equally Thur WALT: Activity: WALT and Activity: LA – Complete yesterday’s Discuss how likely s WILF: activity. conversion certain, Ext, L6 questions, page 75. graphs are uncertain Apply Mental maths Be able to read Using the helpful probable, understanding practice SATs test. and analyse data designated MA – Complete yesterday’s when possible, of concepts from a textbook, perform activity. comparing impossible quickly and conversion/line questions Ext, Level Up 5-7, pages 194-5. different chance, accurately to graph by together to units of good mental recall accurately ensure HA – Complete yesterday’s measureme chance, and use of examining understanding of activity. nt e.g. miles poor questions. values along the concepts Ext, Level Up 5-7, page 294. and chance, no each axis. involved. kilometres. chance H/W – Myimaths, Data, equal Presenting Data, Grouping chance, data. even Fri WALT: Activity: WALT and Activity: LA - Level Up 4-6, pages 76 and Discuss chance, WILF: 77. further fifty-fifty probabilities chance Develop the Use the S.O.D.A Use vocabulary Mymaths website; MA – Level Up 4-6, pages 78 and of events as risk, doubt ability to apply activity of the day associated with Data, Probability, 79. a class; biased, the knowledge to reinforce quick probability. Probability intro Taking a random and mental recall, or Simple HA – Myimaths, Data, Probability, heart from a understanding calculation and Determine the probability. Listing Outcomes. pack of that has problem solving outcome of cards, a accumulated skills. events related to heart or thus far to the likelihood of spade… mental problem them occurring. contexts.

Evaluation notes

Term 3 20012-13

Week 1 2 3 4 5 6 7 8 9 10 11 12 13 Date 31 6 14 21 28 5 13 19 26 2 10 16 23 Mar Apr Apr Apr Apr May May May May June June June June Maths Unit 3A3 3A3 3B3 3B3 3B3 3C3 3C3 3D3 3D3 Optional 3E3 3E3 3E3 Tests Assessment Rounding 2,3,4,5,6,1 Problem Proper Describe Choosing Reading Multiply Identify and Identifying Identify 2,3,4,5,6, for 2 and 3 0 times solving fractions – and sort suitable scales and divide compare patterns and 10 times digit tables using identifying 2D and units to Tally a 2digit angles involving recognise tables Learning numbers Multiples money, and 3D measure charts – number by Read numbers fractions Multiples (Ongoing, to 10 and of 2,5, 10 measures, estimating shapes. interpreting 1 digit analogue of 2,5, 10 formative) 100 up to 1000 time Compare data and digital up to angles clocks 1000 Assessment #4 of Maths end of year test Learning QCA (Snapshot, optional test summative)

Assessment for Learning (Ongoing, formative) Assessment for Learning is the process of seeking and interpreting evidence for use by learners and their teachers to decide where the learners are in their learning, where they need to go and how best to get there

Assessment of Learning (Snapshot, summative) Assessment of learning is any assessment that summarises where learners are at a given point in time – it provides a snapshot of what has been learned (in terms of both attainment and achievement)

Five key factors that improve learning through assessment:

 Providing effective feedback to children  Actively involving children in their own learning  Adjusting teaching to take account of the results of assessment  Recognising the profound influence assessment has on the motivation and self-esteem of children, both of which are crucial to learning  Considering the need for children to be able to assess themselves and to understand how to improve.