Bar Logik

 

A practice app for learners at key stage 2 to 3 to be introduced to the bar model format in an engaging and challenging way.

The classic bar logik title has now been complemented by PROPORTIONAL logik with soon to be available further titles including fractional logik.  

Learners at each level are asked to find the missing value

Starting at basic additive model 

BL1

through increasingly complex challenges which learners can unlock

BL2

 

the multiplicative model is introduced which offers mental tables practice

BL3

but can also be linked to ratio, fractional & proportion problem solving.

BL4

The higher levels challenge mental agility as well as familiarisation of key concept models.

BL5

To further challenge and encourage practice for fluency, each level has a timed challenge.

BL6

Teachers can track learners progress at each level and are encouraged to offer suggestions for further development of the series. 

Try the free demo at https://platform.westudysmart.com/login

Username: DemoUser

Password: smartpasswordmaths

We suggest choosing student demo and select topics to access Bar Logik and Proportion Logik

For further details see the westudysmart webpage https://www.westudysmart.com/bar-modelling/

 

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Using technology

Whilst this is a very open ended title , this section is going to focus on using technology to support looking at different mathematical structures, to hopefully support or reveal a deeper understanding.. These will largely be self created and either use excel spreadsheets or geogebra (which I'm only just starting to get the hang of). The resources described by me at the White Rose Maths Hub conference on bar modelling can be found here.

Power point presentation.

PDF of presentation at White Rose Bar Model conference, Salford (Feb 2017).

Spreadsheets

10 Bar random sums <10 illustrated on a bar model (any part of the number sentence can be hidden)

10Bar1

NB comparative bars & subtraction are also available on the same file

 

Fraction as a number a mixture of random and self-input fractions showing equivalence in different denominations and mixed number & vulgar fractions  

frac1frac2

Fractions "of" & ratio 

frac3frac4

frac5

NB- Values of parts or ratios can be selected to be shown or not

 

Geogebra

10 Bar interactive model of x+y=10 as a bar and as a line graph

geo1

 

x-squared interactive model of y=xshown as bars and as a point on graph

Geo2

 

Circle thoerems: a series of simple geogebra files to allow interactive investigation of theorems

cyclic quadrilaterals

same chord

angle at centre double

geo3geo4geo6

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Mathematical Structures

Representing the structure behind mathematics can help develop an understanding of arithmetic and/or algebra. This can also be linked with multiple representations of a concept as each of the illustrations below can be shown in alternative ways including number lines, sets & arrays of counters amongst others.

These are intended to provoke discussion amongst colleagues rather than to be used without thought or reflection with learners but SYMH would be happy to hear of colleagues' thoughts on these and if they have used any or similar models with learners to good effect.  

You can also find here a series of resources that can be used with colleagues to discuss conceptual development and structures underlying some of the common techniques taught in niumber and algebra.

Feel free to use these resources as a catalyst for professional dialogue - should you wish a professional development session to be facilitated in your school, feel free to contact This email address is being protected from spambots. You need JavaScript enabled to view it.

Click on each below link to download PDF

Additive structures

Multiplicative Structures

Linear equations as bar models

Simultaneous (linear) equations as bar models

mr1

 

mr02

 

MR03

 

mr04

 

mr06

 

mr07

 

mr08

 

mr09

 

mr10

 

mr11

 

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Modelling negatives

 

Just a few images that some may find helpful when describing calculations with negatives

aneg1

aneg2

aneg3

 

 

 aneg4

 

Multiplying involves the concept of an "enlargement" operation.

amneg1

 

Then the distinction between the multiplying effect of 1 (stays the same) and -1 (flips it over)

amneg2

 

Which also works on negatives

amneg3

...and so we can multiply by any sized positive or negative number.

amneg4

amneg5

Now I know I haven't included "taking away" negatives but my explanation takes more than one image to explain - so will upload later.

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Calculn policies

Each school has it's own emphasis and use of a calculation policy and there are lots of ideas that I feel we would benefit from sharing across the SYMH region.

The NCETM have published a Calculation Guidance document and I invite schools and colleagues to not only share their current working documentation but also their thoughts about how these can be best and most effectively used. 

https://www.ncetm.org.uk/public/files/25120980/NCETM+Calculation+Guidance+October+2015.pdf

 

To comment or share any resources or thoughts for the SYMH website please email Pete Sides at This email address is being protected from spambots. You need JavaScript enabled to view it.

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Mental Agility & Subitising Research

Work groups have run for two years on this aspect and we encourage all schools to engage in some way.

Subitising can be defined as ‘the ability to recognise the numerosity of a small number of objects without counting’ or ‘instantly seeing how many’. Research shows that it is closely linked to number sense and is important in helping children develop mental imagery. Douglas H Clements (Professor of Early Childhood Learning, University of Denver) proposes that there are two types of subitising: perceptual (instantly knowing the amount) and conceptual (involving some form of calculation). See Research Article or upload from the bottom of this page. Through the development of resources and the trialling of these within classrooms, the workgroup led by Judith Copley in 2015/6 aimed to consider some questions regarding subitising, for example:

  • Do children have to be able to count in order to subitise?
  • Is the matching of patterns, subitising?
  • What skills should be developed in conceptual subitising?
  • What is the value of using random patterns?
  • Does subitising in regular patterns develop number bonds?

Underpnning all of these questions is: ‘Does subitising in any form aid the development of number skills in young children?’

Following an initial launch meeting, 23 schools signed up to the group which culminated in presentations of findings at the end of the academic year. Copies of schools' presentations and their reports can be uploaded from the bottom of this page.

How does my school benefit from this?

SYMH is encouraging all schools to participate in a repeat of last year's activities. See this message from Judith.

Dear colleague,

Further to our successful work last year, there will be another work group funded by the South Yorkshire Maths Hub in 2016-17 to extend involvement in subitising (recognising amounts without counting) to more schools. This will be a chance for those which were not involved to learn from last year’s work and try out some of the activities / approaches. Schools who participated last year could further develop their work by attending sessions, sending new staff, or simply continuing to develop and roll out the approach within their setting without attending, however there are further opportunities for you (see the next email).

If you would like to be involved, there will be an introductory session on Wednesday 5th October at The Unity Centre, St Leonard’s Road, Rotherham, S65 1PD from 1.15 to 3.30pm. This session will share research, resources and suggestions for you to try out. Most schools last year worked with EYFS to Y2, but this could be appropriate for Y3 also, depending on ability. There will then be a small number of half day/twilight sessions during the year where we can share resources and ideas, culminating in a final session where we would share findings, resources which have worked well and some case studies. However, most of the work will take place within your school, with your pupils as you try and develop resources and strategies.

The focus will be on encouraging young children to recognise patterns of amounts without counting and explain what they see. We will focus on regular patterns and move to irregular. Participants last year found that this increased children’s ability to look for patterns and visualise numbers and number bonds but also had a positive impact on their confidence, enjoyment and ability in using numbers and amounts.

I would recommend involving two teachers, as they can share ideas within school.

Please email me to express your interest and to let me know how many people will be attending on 5th October, their names and roles.

I look forward to working with you.

Kind regards,

Judith

Schools wishing to contact Judith who will continue as work group leader can do so by email This email address is being protected from spambots. You need JavaScript enabled to view it.

Additionally, in time there will be suggested activities and examples of materials in use made available through IRIS Connect   

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Rainbow Arithmetic Scheme

A little and often

The strategy of focusing on arithmetic skills throughout Key Stages 2 & 3 by addressing and practising skills in the first few minutes of each lesson is being used to good effect in a number of the region’s schools.

But Rainbow Arithmetic is more than just a set of FREE resources that enables teachers to do this. At its heart is a set of principles that have a lot in common with the "teaching for mastery" style of learning that many colleagues are developing as they are getting to grips with the new National Curriculum.

Additionally as schools are being encouraged to consider the benefit of using a common approach to the development of arithmetic skills, ideally in coordination within a primary/secondary pyramid the Rainbow scheme can provide the scaffold within which clusters of schools can collaborate.

 

How can my school benefit from this?

This work group is sub-part of the "Development of Secondary Teaching & Curriculum Resources" work group. Schools have been able to access the teaching materials free of charge for a number of years, but a number of schools have not known how to use them appropriately and effectively. This year a set of exemplar resources will be produced to allow schools to see the scheme in action along with professional development materials that can be used to introduce and embed the scheme into key stage 3 curriculum and practice.

These professional development materials can be accessed FREE through IRIS Connect and additional face to face support is available including a FREE presentation to local maths department at a mutually convenient after school meeting. 

 

How it began

The Rainbow strategy came about as a result of looking for resources that regularly gave practice of a variety of the basic arithmetic skills. Since none were readily available at that time, in-house worksheets were developed. These were either used once a week in either a practice lesson or given for homework.

Despite KS3 being supposedly "setted" for ability it became apparent that there was a wide range of students' capabilities that quickly resulted in differentiated resources being required to cater for the varied needs. Hence a colour system that started with Red (easiest) to Ultra-Violet (hardest)

More than just practice

Once a week gave way to regular "start of lesson" practice interspersed with short episodes of learning that addressed misconceptions and procedural errors. The use of mini-whiteboards became an essential feature of these explanatory sessions that focussed on a single conceptual element or arithmetic skill.

The practice element continued in intervening sessions either focussing on a single aspect just covered or back to a mix of skills appropriate to the level of the students.

The importance of written solutions

Homework then became a different type of practice. Over time the emphasis of homework focused on presentation and clear explanation of working. So the scheme incorporated quick-fire practice at the start of lessons and more considered application of skills at home.

Randomised questions & on-line support

The need to quickly produce a large number of questions for students to tackle prompted a greater use of the random function of spreadsheets. These could be used to easily create a starter or a practice homework which many teachers found an invaluable tool.

On-line support for students ranged from VLE based explanations to Youtube videos and a structure of learning objectives was created mostly in-line with the National Curriculum that gave students clear targets to achieve before moving to the next colour. The next step is to develop on-line resources that use iconic structure to support conceptual understanding.

Targeted feedback and problem solving

The strategy of using Rainbow starters for either practice or focussed learning has been consistent, but the development of the use of homework to develop multi-step skills and "follow-up" homework to address individual students' needs took the homework to the next level.

The practice of fortnightly individualised follow up homework based on a student’s previous submitted work has greatly helped target individual progress.

The practice of setting problems using skills from a previous level has also allowed students to tackle more confidently the unfamiliar or applied aspect of problem solving.

Want to find out more?

This overview can in no way satisfactorily describe the Rainbow pedagogy but colleagues are encouraged to examine the resources available and consider the face to face professional development support available to schools.

Schools with access to IRIS Connect (freely available for all South Yorkshire schools) will soon be able to see exemplar videos of the whole programme in action.

If you would like to discuss a presentation for your school please contact This email address is being protected from spambots. You need JavaScript enabled to view it. 

FREE resources: Click on pictures to open

Feel free to use these and distribute and share with others. You may not sell these resources and it would be appreciated if you acknowledged the contribution of the Notre Dame maths department in their development. Please note spreadsheet erquire macros to be enabled to work correctly.

Starters

The interactive spreadsheets that make up the question bank is the core resource used by teachers in the Rainbow strategy in the classroom. The questions are sub-divided by colour and strand and can easily be edited to create a bespoke resource to meet the needs of a particular group. 

Randomised spreadsheet starters with preset challenges for a variety of levels, use bottom tabs to select different ones

Rainbowchallengeexample

 

Question bank of over 200 different randomised questions classified into type and level - from which bespoke challenges can be created

Rainbowquestionbankexample

Level Descriptors

You will notice that each colour/level is sub-divided into strands and each has a short description of the "skill/concept" being targeted for development.

These are NOT strictly along national curriculum lines but for approximate comparison BLUE is in line with the expectation of Y6. The strategy is aimed at practising & developing skills in KS2 & 3 so not directly relevant for KS1.

However aspirationally KS1 = Red, Orange = Y3, Yellow = Y4, Green = Y5, Blue = Y6, Indigo = Y7

 Rainbowleveldescriptors

Start of Y7 Assessment

This is used at ND in the first week, teachers are encouraged to adapt something similar for their own purposes as they know their students best.

For obvious reasons we do not make this assessment freely available via the website but please email This email address is being protected from spambots. You need JavaScript enabled to view it. to request a copy

 

Homework Sheets

For those of you familiar with the older resources you will notice a slight shift of emphasis towards a balance between the straightforward computational questions and multi-step problems. This suits the ND version of Rainbow however it is now much easier to create your own set of homework or independent study sheets.

Rainbowhmwkexample

There are over 50 pre-written homeworks across the range of levels which cannot be uploaded to this site

- if you would like more examples or the full set please contact This email address is being protected from spambots. You need JavaScript enabled to view it. 

So much more than just a set of resources

The 4 rules practice spreadsheet is an example of just one resource amongst many available that can be used to practice. However what is ESSENTIAL for teachers to understand is that this resource as well as all the Rainbow resources are only effective if they are used effectively. The success of Rainbow as a strategy is HOW it has been used in schools as a developmental tool to support teachers TEACH procedural techniques alongside conceptual understanding AND allow students to PRACTICE without requiring an over burdensome amount of preparation.

 Rainbow4rulespractice

For more details about the Rainbow strategy feel free to contact the South Yorkshire Maths Hub at This email address is being protected from spambots. You need JavaScript enabled to view it. 

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Developing Number Sense

Associated work groups

KS1 mental agility development & subitising research

KS3 Rainbow Arithmetic Scheme

 

Procedural competence is not enough.

Mathematics is so much more than just about numbers but crucial to children's success and confidence in maths is their ability to understand and manipulate the number system in arithmetic and subsequently algebra. Establishing number sense and understanding the structures that underpin arithmetic are essential for a pupil's progress and the principles of teaching for mastery underline the importance of getting the basics right at whatever stage before moving on prematurely to more complex aspects.

This is not just relevant for younger children and many teachers will recognise the issue of re-teaching the basics to older students because they haven't mastered the fundamentals. This problem will not go away quickly and despite the introduction of a teaching for mastery strategy in some schools, as a country we are many years away from establishing satisfactory progress and true understanding for all our children. Even those schools who have adopted the teaching for mastery principles will take time to fully develop their practices and in many schools where progress has apparently been outstanding the bar of our expectation must be raised such that procedural competence is not enough but fluency and mastery are the goals we as professionals should be seeking to develop in our students.

This section of the website focuses on issues around developing number sense and basic arithmetic skills at all levels and ages. The South Yorkshire Maths Hub aims to support teachers and schools to reflect on their current practices and develop a teaching for mastery strategy that works for their students. SYMH encourages feeder primary schools and secondaries to work closely together as well as clusters and alliances of schools. Through this website and the IRIS Connect platform SYMH will endeavour to share best practice and resources but encourages colleagues to contribute to this local collaboration by sharing experiences within schools and across the region.

Case studies

We hope to be able to bring to your attention case studies and exemplar material

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Bar Logik

12-03-2017 Hits:395

  A practice app for learners at key stage 2 to 3 to be introduced to the bar model format in an engaging and challenging way. The classic bar logik title has...

Read more

Using technology

15-02-2017 Hits:357

Whilst this is a very open ended title , this section is going to focus on using technology to support looking at different mathematical structures, to hopefully support or reveal...

Read more

Mathematical Structures

08-11-2016 Hits:334

Representing the structure behind mathematics can help develop an understanding of arithmetic and/or algebra. This can also be linked with multiple representations of a concept as each of the illustrations...

Read more

Modelling negatives

03-11-2016 Hits:325

  Just a few images that some may find helpful when describing calculations with negatives         Multiplying involves the concept of an "enlargement" operation.   Then the distinction between the multiplying effect of 1 (stays...

Read more

Calculn policies

09-02-2016 Hits:716

Each school has it's own emphasis and use of a calculation policy and there are lots of ideas that I feel we would benefit from sharing across the SYMH region. The...

Read more

Mental Agility & Subitising Research

27-08-2015 Hits:2521

Work groups have run for two years on this aspect and we encourage all schools to engage in some way. Subitising can be defined as ‘the ability to recognise the numerosity...

Read more

Rainbow Arithmetic Scheme

19-08-2015 Hits:1193

A little and often The strategy of focusing on arithmetic skills throughout Key Stages 2 & 3 by addressing and practising skills in the first few minutes of each lesson is being...

Read more

Developing Number Sense

30-12-2014 Hits:3296

Associated work groups KS1 mental agility development & subitising research KS3 Rainbow Arithmetic Scheme   Procedural competence is not enough. Mathematics is so much more than just about numbers but crucial to children's success and...

Read more

Universities

Sheffield Hallam University
University of Sheffield
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

FE Colleges

Barnsley College
Doncaster College
Rotherham College of Arts & Technology
Sheffield College
 
 
 
 
 
 
 
 
 
 

Alliances

United Learning
Navigate Trust