Mathematics Course – Year 5 teachers

Buckinghamshire School Improvement Service

Mathematics Course – Year 5 teachers

Becky Ellers (Maths)

[email protected]

Cathy Tracy (SCC)

[email protected]

Progression in Mental Calculations- reasoning and mathematical language

• Mirrors the Year 1 teachers course

• Runs alongside the Headteacher course

• Day 2 (9th Jan 08)– AFL – Using the renewed framework to embed day-to-day assessment

Aims of day 1

• Build subject knowledge

• Build a clear understanding of progression within and beyond year 5

• Broaden your repertoire of teaching approaches

• Develop children’s reasoning skills

Session 1

• To consider the prerequisites for an aspect of calculation from Year 5

• To further your understanding of important aspects of mathematics that children need in order to develop mental calculation

The importance of Progression in calculation• Look at the ‘Yearly Overviews’.

• Sort the year groups into the correct order.

222 ÷ 3 =

What knowledge, skills and concepts would children need in order to be able to do this

calculation?

Show the person next to you how you currently teach your Year 5 children to carry out this

calculation.

Methods

• Chunking

• Number line

• Short division

What is the difference between three hundred and ninety-five and five hundred

and one?-Taken from mental maths paper (15secs)

What knowledge, skills and concepts would children need in order to be able to do this

calculation?

Show the person next to you how you would teach Year 5 children to carry out this

calculation.

Methods

The use of the number line

How do we develop children’s mental calculation skills using a number line?

Prerequisites for using an empty number line• Position a number on a number line• Jump to a number from zero• Add /subtract a multiple of 10 to/from any 2 digit number (without

crossing 100)• Recall addition and subtraction facts for all numbers to at least 10 • Use this knowledge to add / subtract a single digit number to or

from a two-digit number, without crossing the tens boundary• Bridge through 10 • Use this strategy to add / subtract a single digit number to or from

a two-digit number, crossing the tens boundary)• Know the complement to the next multiple of 10 for any two-digit

number• Use knowledge of place value to add a single digit number to a

multiple of 10

When might you use number lines?

Resources

• Bead strings

• Counting sticks

• Printed number lines and tracks

• ICT – Excel counting stick

Session 2

• To consider key characteristics of good mathematics teaching

• To identify teaching approaches, including the use of ICT, that support the development of reasoning

• To identify teaching approaches that support the development of mathematical language

What makes a good maths teacher?

• A good subject knowledge

• An understanding of progression in the curriculum being taught

• Recognition that some teaching approaches are better suited to promote particular learning and outcomes

• Enthusiasm!

In summary, mathematics teaching should: • provide children with a balance of exploration, acquisition, consolidation and application • ensure that children experience the excitement of learning mathematics • direct and steer children to explore, identify and use rules, patterns and properties and model this process • build in frequent short and sharp periods of practice and consolidation • engage with children’s thinking, giving sufficient time for dialogue and discussion and space to think • demonstrate the correct use of mathematical vocabulary, language and symbols, images, diagrams and models as tools to support and extend thinking • give well-directed opportunities for children to use and apply their learning • teach children how to evaluate solutions and analyse methods and understand why some methods are more efficient than others • pause and take stock to review children’s learning with them • model with children how they identify their learning skills, and manage and review their own learning.

Teaching Styles

• Direct – teaching tables (number dials, IWB Number dials, counting stick, hundred square)

• Instructive – Using compensation

• Inductive – Multiplication excel grid

• Applicable – Flexible line graph

• Exploratory – Ball of Wool

• Reflective - Fractions

(Planning Cycle )

Models and Images

• Models and Images charts

Year 5Mental Calculation

Session 3Review and Planning

Buckinghamshire School Improvement Service

How to plan a block.

(In 3 easy steps!)

A Suggested Planning Process

Summary

1. Read/Check Prior Learning

2. Read and organise the Objectives

3. Plan first 3 days of work using available resources

The teaching Sequence

When planning a UNIT of 2 or 3 weeks of work, the structure of the teaching sequence requires thought to ensure that children get the opportunity to consolidate, secure and extend their learning through practice and application of their learning.

The Teaching and Learning Cycle

Review – Teach – Practise – Apply – Review

The cycle constitutes four teaching and learning foci:• Focus A: Review prior learning and introduce new learning• Focus B: Practise and Consolidate learning• Focus C: Apply, secure and extend learning• Focus D: Review and evaluate progress in learning

Examples of teaching sequences over a Unit (10 lessons)

Focus AReview prior learning/ introduce new learning

(2 lessons)

Focus BPractise and Consolidate

(2 Lessons)

Focus CApply, secure and extend learning

(3 Lessons)

Focus DReview and evaluate progress in learning

(1 Lesson)

Foci B, C

(1 Lesson)


(1 Lesson)

Focus AReview prior learning/ introduce new learning

(1 lesson)


(2 Lessons)


(4 Lessons)


(1 Lesson)


(1 Lesson)


(1 Lesson)

or

Modelling the Planning Process

• Year 5, Block D, Unit 1

Step one - Prior Learning

Mathematics

Planning

Year 5

Block D

Prior Learning

Step one - Prior LearningYear 5 Block D - Calculating, measuring and understanding shapeBuilding on previous learningCheck that children can already:• talk about their methods and solutions to one- and two-step problems • partition, round and order four-digit whole numbers and decimals to two places, and use

decimal notation to record measurements, e.g. 1.3m or 0.6kg • multiply and divide numbers to 1000 by 10 and 100 (whole-number answers) • use written methods to add and subtract two- and three-digit whole numbers and .p, and to

multiply and divide two-digit numbers by a one-digit number, including division with remainders, e.g. 15 9, 98 6

• know that addition is the inverse of subtraction and that multiplication is the inverse of division, and vice versa

• use a calculator to carry out one- and two-step calculations involving all four operations • know that angles are measured in degrees and that one whole turn is 360 • read scales to the nearest tenth of a unit • measure and calculate perimeters of rectangles and find the area of shapes drawn on a

square grid by counting squares • read time to the nearest minute; use am, pm and 12-hour clock notation, and calculate time

intervals from clocks and timetables

How might the use of the Prior learning prompts in a block be built into the

teaching and learning cycle?

Step 2 Make sense of the objectivesLearning Objectives for Unit 5D1:1. Solve one-step and two-step problems 2. Use understanding of place value to multiply and divide whole numbers and decimals

by 10, 100 or 10003. Use a calculator to solve problems, (including decimals or fractions), interpret display4. Read and plot coordinates in the first quadrant; recognise parallel and perpendicular

lines in grids and shapes; use a set-square and ruler to draw shapes with perpendicular or parallel sides

5. Read, choose, use and record standard metric units to estimate and measure length, weight and capacity to a suitable degree of accuracy (e.g. the nearest centimetre); convert larger to smaller units using decimals to one place (e.g. change 2.6 kg to 2600 g)

6. Interpret a reading that lies between two unnumbered divisions on a scale7. Draw and measure lines to the nearest millimetre; measure and calculate the

perimeter of regular and irregular polygons; use the formula for the area of a rectangle to calculate the rectangle’s area

8. Read timetables and time using 24-hour clock notation; use a calendar to calculate time intervals

Step 2 - Making sense of the objectives-Beginning to group the objectives

Mental Skills: Use understanding of place value to multiply/divide whole numbers and decimals by 10,100,1000 Interpret a reading that lies between two unnumbered divisions on a scale Read timetables and time using 24-hour clock notation; use a calendar to calculate time intervals

Length: Read, choose, use and record standard metric units to estimate and measure length, convert

larger to smaller units using decimals to one place (e.g. change 2.6 kg to 2600 g) Draw and measure lines to the nearest millimetre; measure and calculate the perimeter of regular

and irregular polygons; use the formula for the area of a rectangle to calculate the rectangle’s area Solve one-step and two-step problems Use a calculator to solve problems, (including decimals or fractions), interpret display

Coordinates: Read and plot coordinates in the first quadrant; recognise parallel and perpendicular lines in grids

and shapes; use a set-square and ruler to draw shapes with perpendicular or parallel sides

Time: Read timetables and time using 24-hour clock notation; use a calendar to calculate time intervals Solve one-step and two-step problems

Outcome:Solve one-step and two-step problems (Mixed)

Step 3• Plan the 10 lessons in outline• You don’t have to teach the objectives in any set order • Have you previously taught lessons on these topics which have gone well in terms

of children’s learning? (including Unit plans). You could incorporate and adapt these

• Keep in mind the appropriate teaching focus – Review / Teach / Practise / Apply

• Whole class work on reviewing prior learning must be limited to the items you know the majority of children still have difficulty with. Small amounts of prior learning should be dealt with at the beginning of the relevant lesson and specific individual or group needs through differentiation

• Make sure you include opportunities for:- – the children to use ICT– assessment– AT1– links to other subjects

A Suggested Planning Process

Summary

1. Read/Check Prior Learning

2. Read and organise the Objectives

3. Plan first 3 days of work using available resources

Questioning for assessment

Questions can be used to assess:• Children’s knowledge• Children’s use of mathematical

language• Children’s use of models• Children’s methods and strategies• Children’s reasoning• Children’s understanding

AFL questions in the learning objective section

Key Messages• The learning objectives in the Primary Framework set out

the essential learning steps for children to make effective progress in mathematics

• Looking at the objectives across two year groups highlights the ‘bigger picture’ for the year group and helps to identify the prior learning at the start of the year

• The learning overviews for the year and for a Unit provide more detail to inform long-term and short-term planning

• Building on prior learning requires some flexibility in planning; planning assessment questions helps to monitor children’s learning over a Unit

Year 1, 3 and 5School-based activity

Session 4Review and Progression

Aims of the session

• To explain how teachers’ CPD and Head teachers’ CPD fit together

• To provide guidance on the CPD models • To identify the contribution the school-based activity

makes to school improvement• To provide guidance on the school-based activity• To discuss how outcomes of school-based activity

will be fed into Day 2

Structure of the session

Context of the Teachers’ and Head teachers’ CPD

Supporting the activity back in school

1. Discussion with the head and school subject leader about how Day 1 will be fed back to all staff

2. Preparing for the collaborative tasks3. Preparing for the diagnostic tasks

Feedback into Day 2

1.Discussion with the head and school subject leader about how Day 1 will be fed back to all staff

• Methods of calculation• Exploring prerequisite skills• Teaching styles• Using the renewed framework to support planning

(teachers knowledge of progression through the prior learning)

How will you move forward with these areas?

2. Preparing for the collaborative tasks

In groups decide:• which of the three models would be most beneficial

to your own professional development• the focus that the collaborative work will take • how the collaborative work will be organised and

who will be involved• the actions that need to take to ensure that it can

take place successfully for them.

3. Preparing for the diagnostic tasks

In your own class,• Identify 3 children (1L/A, 1 M/A & 1 H/A)

• Ask the children to complete the questions on handout 4.1

• Talk with the children (1:1) about barriers, challenges, next steps.

• Develop a teaching activity to help move the children on and consider the teaching style which would be most appropriate.

Feedback expectations

Prepare a short presentation on the outcomes of the follow up work you have carried out in school.

Structure1. How did you feedback from day 1 to the

SMT/whole school? Impact?2. What models of CPD did the school use to

support staff? Impact?3. Briefly explain the outcomes of the

diagnostic maths task carried out on 3 children in you class. Impact?

Dates

• Day 2 – Jan 9th 2008

Documents

Mathematics Course – Year 5 teachers