Hello Maths

Before the multiplication lessons for Year 7, I was able to go over some of the ideas with the AL and WC teachers in a Thursday afternoon session. I was asked at the time if we would have the same for the division lessons.  Unfortunately we haven’t had that opportunity, and so in this bulletin I am going to share some of the ideas behind the lessons that will be coming soon.

I would like to share some videos from the NCETM that I have used to inform my planning for the Division lessons in year 7.  They show the use of place value counters, which we used in our earlier lessons on addition and subtraction.

These videos (the red links) are from Year 4 lessons.  I think that they show the progression in ideas really well. The Year 7 lessons don’t go as far back as this, but the ideas will certainly be useful when students are receiving intervention, or if students are really struggling with the algorithm for division.

The teacher introduces division vocabulary.

Consider the high expectations in terms of using the correct vocabulary.

Using place value counters and recording division

Notice how the children work in pairs where one manipulates and the other records. They then swap roles.  This has proved to be an effective strategy to develop both reasoning and fluency in the use of the formal written method.

Division with remainders

Notice how the pupils’ estimating skills improve as they become familiar with the use of the place value counters for division.

The pupils recognise a problem in the tens column and suggest that they will need to “regroup”. What do you think they mean by this, and what does this indicate about their understanding of place value?

Division with exchange

Notice how a thorough understanding of the physical process of re-grouping and exchange enables the children to use the language of re-grouping when talking about the algorithm.

Finally, we move onto a lesson from KS3 on solving problems involving division.

Problems involving division

In this lesson, the girls work on a variety of problems involving division and multiplication. I got a bit irritated with the girl drawing on her whiteboard rubber at 5:38, but I think it shows some of the conversations that some of our students might have.

The division lessons for year 7 will be on the site this weekend.

In other news

You will have noticed that there is a new ‘Primary’ tab at the top of the page.  This page will share some of the work being done in Maths at Bluecoat Primary. It currently has  a few links for you to look at so you can learn about Maths No Problem, which is the excellent scheme they use for their Maths lessons.  Please do take the time to have a look.

Later on this term, Krissie Dickens, the Maths Lead, will use that page to showcase some of the work they are doing in Maths. I think you will find it really exciting  to see the work the children are involved with.

Have a great weekend everyone,

Matilde

Dear Maths

I’d like to start with a huge thank you to everyone for inputting all the data over the last two weeks.  In particular, the turnaround for the GCSE mock was fantastic. This means that Joel, Louise, Nick and myself are able to spend the afternoon analysing data and putting our intervention plans into place to maximise the amount of time between this mock and the next. The next mock is in the week before February half term.

As you will be aware, there are no grade boundaries available at the moment, so everyone around the country is struggling to make predictions. To help us make better predictions for the boundaries, I have been working with several schools from around the East Midlands to compare results. The boundaries we have agreed upon are these:

However, it must be remembered that these are at best an educated ‘guess’ and so students (and parents) should know they are not 100% reliable.

The Cambridgeshire Maths Hub have also been collating local results from all their schools who do AQA to set boundaries.  Their results are as follows:

As you can see they are very similar (which is a relief!). The only issue seems to be what will constitute a 5 on the Foundation paper. This obviously has implications for us when deciding on tiers of entry.  It may have been skewed due to schools being cautious and entering possible 5’s in Foundation rather than for Higher. This is an area I will be keeping a close eye on over the coming weeks and months.

KS3

I know that the year 7 and 8 lessons are taking quite a long time to get through, which is fine. I’ll be adding to the lessons this weekend so you have a while to look over the content beforehand so that you are well prepared for the lessons, and are able to make any changes as required. Please feel free to email me if you want me to go over any of the lessons with you – I can always arrange time to come and work with you in person too.

Have a great weekend everyone.

Matilde

Hi Maths

The Friday bulletin on a Friday! What a treat.

It has been a crazy week with the year 11 mock exams. Over here at BBA we have been delighted with how they have gone. The perseverance of some of our students on a very difficult paper (Higher paper 2) was amazing.

I sat down to write a model answer for this question yesterday as there was no-one in my class who scored more than 3 marks on it. It was on both the Foundation and Higher papers.

When marking the question it was apparent that it was the organisation of the work that caused most students problems, not the fact that they couldn’t do it. The students in my class kept making mistakes and then scribbling out their working, which meant they ran out of room.

When I wrote out my model answer, my first attempt didn’t fit in the space either! I had to redraft my working so that it could fit in the space but still include all my working in a way that clearly explained what I was doing.

Although I spend a lot of time in lessons on exam technique and how to answer non-routine questions, I know that I haven’t done much work with my year 11 classes in the past on drafting and redrafting work in exam conditions.  This is something I want to investigate further and will be working on over the next few weeks.

My favourite question on paper 2 was this one:

It requires knowledge of Venn diagrams, conditional probability and forming and solving quadratics. Lovely! I think our students will enjoy looking at how to answer these types of questions. The challenge for us is how do we include opportunities for such questions in our everyday teaching?

What was your favourite question? The geeks among you can answer in the comments section below!

On the subject of the mock exams, the East Midlands West Maths Hub are holding a Maths GCSE revision Teach Meet on 6th December from 4-6pm at George Spencer Academy. A flyer is attached here.  It is open to anyone who would like to attend.

The local Maths Hub events are always really good opportunities to keep up to date with the very latest news in maths education, as well as a great opportunity to form supportive networks with other maths teachers. We have two local hubs, East Midlands West and East Midlands East who both offer excellent opportunities.

East Midlands West  Bulletin November 2016

East Midlands East Newsletter November 2016

Just a final reminder that today is the deadline for data input for years 7-10 and that midday next Friday is the deadline for all year 11 marks to be in Go 4 Schools. Thank you to everyone who has input their data so far.

Matilde

Hello Maths

I hope you all had a great holiday and a good first week back.

A few deadlines are coming up over the next couple of weeks.  Please can you make sure that all data is in Go 4 Schools by the dates below. Thank you to those of you who have put theirs in so far. I hope you found the marking reasonable. Thank you to those who pointed out errors in my mark schemes. I think they have all been changed now ready for next year. Thank you also to Paul Dean at Aspley who has kindly offered to proof read future mark schemes.

Deadlines

Year 7 Prior knowledge audit – Friday 11th November

Years 7 – 10 test results – Friday 11th November

Year 11 mock results and QLA – Friday 18th November

Mock Exams

This is a very important exam for us in trying to determine predicted grades for the new GCSE, and to identify areas of weakness.

Please read the mark schemes carefully before you start your marking, familiarising yourselves with the codes in the glossary. Please don’t hesitate to ask if you are unsure. Joel, Louise and Nick will distribute the mark schemes for you next week, but they are available at All About Maths if you want to read ahead (you will need to register for a password if you don’t already have one).

There will be a very short QLA for you to fill in on Go 4 Schools.  For this first mock we will only be targeting 8 key questions from Higher and 8 key questions from Foundation. These will be taken from papers 1 and 2 only.  These will be the questions that we think all students should be able to answer, and the subsequent intervention will focus in depth on these topics over the next six weeks.

CPL

It was nice to see everyone from Aspley and Wollaton sites at the CPL on Thursday. Thank you to Louise for hosting us all.

The Powerpoint and documents are below.

Powerpoint
Video: Moving from Grid to a Column Method
Ofsted document: Good Practice in Primary Schools

I have also added the blank lattice templates to Year 7 lesson 2 as requested.

Geek fact of the week

Do you know what raising a number to a power of 4 is called?

Apparently 2⁴ can be read as “two  zenzizenic”, So 16 is the zenzizenic of 2.

This was coined by Robert Recorde (of the equals sign fame) as zenzizenzike in his 1557 mathematics book The Whetstone of Witte.

Unfortuantely the word is now obsolete, which is a shame, because I was looking forward to talking about the eighth power of a number as the zenzizenzizenzic, and the sixteenth power which is… you guessed it: zenzizenzizenzizenic.

Anyway, thought I’d share in case any of your year 8’s ask what the word is while they learn about indices this week. Thank you to Nick Wilson for introducing us to this great word!

Hello Maths,

The Friday bulletin seems to be becoming a Saturday Bulletin as the term moves on!

This week will be assessment week for lots of your classes.  Time to see if our little lovelies have learnt what we had intended them to.

Year 7 and 8 (and 9 at BBA)

Christa at BBA has decided to print out the record sheet on A5 separately to the test which is on A4. This would allow the students to stick it into their books without the hassle of rippring out the sheet, folding it over etc. This is such a common sense suggestion and one I wish I’d thought of. I will create them as separate documents for future assessments.

This weekend I will be making a Powerpoint that has each question on a slide with solutions so you can go over bits that are needed with your classes.  As it’s the first time that they will have filled in the record sheet, I will put instructions on the Powerpoint too.

A reminder about the marking: please NO numbers to be given out to students at all. I’ve copied the section about the marking of these tests from the document I sent out to everyone at the start of term here. Please do have a read.

Year 10 (and 9 at Aspley and Wollaton)

The point of the assessments is to check progress on what we have taught. Hopefully most misconceptions will have been picked up and addressed through formative assessment and AfL during lessons, with the only mistakes made being ‘slips’ rather than a lack of understanding.  However, we all know that however hard we try, there are some who slip beneath the radar in lessons. So, if there are any blank boxes in questions in the first column of any of the assessments for years 7 – 10, there will need to be some work to address these gaps.

The intervention we do has to be manageable and realistic. However, we can’t ignore any obvious gaps in our students’ knowledge.  The first wave of intervention should be by the class teacher. This can be during lessons – maybe through starters, re-teaching, guided practice on topics, etc. We have a generous allocation of maths lessons, so this doesn’t need to be after school or at lunchtime unless you personally choose to do that.

Out of class intervention is a finite resource, so we have to prioritise who will receive it. This year we have decided to use this intervention time for year 7 students who have any blanks in the first column in the hope that by the time they reach year 11, they won’t be caught up in the seemingly never-ending intervention cycle.  The year 7 intervention has been organised on each campus to take place away from lessons to supplement the work already being done in class.

We are in the fortunate position at Bluecoat to have Maths Coaches, a luxury that many schools don’t have.  We use our coaches for students who are falling way below what they are expected to achieve. They work on focused topics identified by assessments.  We are using our coaches solely for year 11. There are also further year 11 sessions being run at all campuses for year 11’s who aren’t being seen by coaches, but who need help.  These are being run in form time and after school

Next half term

The lessons should start going up early next week for years 7 and 8. As you can imagine, they do take a very long time to put together, so please be patient if the all of the lessons do not appear by the start of the half term. My hope is that the lessons will usually be at least three ahead of where you should be.

Year 7 will be starting ‘Numeracy Ninjas’ for the start of each of their lessons next half term. Details can be seen here.  Nick has been trialling it with his year 7 at BBA this half term as a settler for the first half term of every lesson.

Just a reminder that the objectives for year 9 (ALC/WPC) and year 10 are all on this site. All students should cover all of the objectives as far as possible as decisions about tier of entry won’t be made until we have more information about boundaries from the year 11 exams next summer.

Year 9 at Aspley/Wollaton and Year 10 at BBA will be on Handling Data. The objectives are on this page.

Year 10 at Aspley Wollaton will be on Graphs 1. The objectives are on this page

Have a great last week of half term. Only four teaching days to go…

Matilde

Hello Maths

I hope you’ve all had a great week!

I’ve really enjoyed teaching the negative number lessons to year 7 this week.  We’ve spent far longer than I intended on the lessons, but it really feels like the students are really understanding what is going on. Negative numbers was one of the topics that was rushed through in previous years, due to time constraints, which often resulted in an annoyingly poor use of negative numbers higher up the school, particularly when multiplying out double brackets in the simplifying stage, and in substitution questions.

My final lessons were taken from the classic Standards Units (N9 Evaluating Directed Number Statements), adapted to include only addition and subtraction for our scheme. We will come back to the other statements next half term.

The students have to separate cards into ‘always, sometimes, never’ categories.  We actually spent three lessons on this in the end because the students wanted to answer all of the cards.  Some used sandcastle diagrams, some used charges and some used thermometers to explain their reasoning. They challenged each other with well thought out arguments. I was so pleased with them all!

It turns out that there are no ‘never’ statements in the cards we use so a good challenge at the end is for the students to make their own ‘never’ statements, which they thought about really well.

In other news…

The new year 8 progress checker and the year 9 and 10 assessments will be uploaded this weekend. They all have the usual password.

The year 8 assessment takes the same form as year 7: simpler fluency questions followed by questions that require reasoning and non-routine questions.  Once again, no numerical grades should be given to the students. This front cover grid should be used to identify areas of weakness.  Any blanks in the first column would require some action on the part of the teacher, and more formal intervention should it remain a problem. This paper is a non-calculator paper.

The GCSE assessments have a similar format for questions, starting easier and building up to non-routine questions. As tiers of entry have not yet been decided for any group and all students have the same objectives, all students will sit the same test. This means that there may be a few questions at the end that some students may not be able to access. The grades for each assessment range from 9-1, which can be shared with students. The percentage from the test should be put into Go4Schools which will convert the percentage to a grade.

There is a record table on the front cover, similar to the year 7 and 8 progress checkers. For any blank boxes, students will be directed to a video from either www.corbettmaths.com or lesson powerpoints so that students can work on areas they are struggling with. Hopefully this will encourage students to take responsibility for their own learning first, before any intervention takes place.

Have a good weekend everyone, and see you all next week.

Hello Maths,

I’d like to start today’s bulletin by saying goodbye to Katie and wishing her a fantastic maternity leave.  Katie has been working hard over the past few weeks creating homeworks to accompany the year 7 and 8 schemes of work. Time to put your feet up now – see you soon!

It was great seeing everyone at Aspley for CPL on Thursday (Don’t worry BBA Maths, we will repeat the session at this week’s faculty meeting).  Thank you all for joining in with such good spirit. We’re very lucky to work at a place where people are happy to work together and discuss their subject with such enthusiasm.

Several of you have asked for the resources from the session, so the Powerpoint is attached here.

If any of you do develop any resources using the unit circle or the ratio tables, please do share them.  Some of you might like to develop something to go towards one of your appraisal targets, if it fits in with your development plans.

Upcoming events

The first set of mock exams for year 11 have been confirmed for the week starting 7th November at all campuses. The timing are slightly different at each though, so your DoL will let you know the details for your own school. We will be collating all results before setting boundaries, so will be setting a deadline for results to be in.  I’ll let you know the deadlines closer to the time.

That’s all this week as we had the CPL so most things were covered there.

Have a great weekend. See you all next week.

Matilde

Hello Maths,

The end of week 3! It’s seemed a very long one this week, possibly because of the recent open evenings. I hope you aren’t all too tired and are looking forward to a relaxing weekend.

I’ve managed to pop into a few more classrooms again this week.  Thank you for making me feel so welcome. I’ve loved seeing the KS3 lessons. The level of discussion and questioning that I have seen has been fantastic.  One class I saw at Wollaton who were working on the Cryparithms lesson in year 7 were so excited that they were begging to take the work home to finish!  I know some classes are finding the discussion based lessons difficult to keep concentration in.  Remember it is fine to supplement the lessons with consolidation/book work exercises if they need a break from all of the deep thinking!

CPL

For ALC and WPC CPL is joint faculty time from 2.30 – 4.00. I’ll let you know which campus on Monday. It is on the use of ratio tables and how they can be used in the GCSE as a tool for all students.

For BBA it is in the hall for Oracy Strategies.  This fits in very well with the work we are doing in KS3, so hopefully the maths department will have a lot to offer the session.

Deadlines

Hopefully the finalised year 7 intervention lists should be ready this week. Please make sure you have put your updated info onto Go 4 Schools.

KS3

Most people in year 7 are up to, or coming up to ‘Sandcastles’.

You may have wondered why on earth we are doing sandcastles followed by charges etc when lots of students can already ‘do’ negative numbers.

Negative numbers is one area that is full of misconceptions all the way up to GCSE.  Children are usually taught a several rules that many get confused about (how many times when simplifying -7x -6x do students say ‘13x, because two minuses make a plus’.  The idea here is to build up an understanding of negative numbers before diving straight into rules.

Please read this article from the ATM – MT217 that Lewis at Beechdale reminded me of this week.

The Sandcastles lesson isn’t a new one: the MrBartonMaths TES resource referenced in the article was made in 2007. We developed it in our department following a great CPL session by Richard Dunne. He talked about engaging learners through the systematic use of concrete objects, actions and language to make the abstract, symbolic language of mathematics accessible and enjoyable.  The current lesson uses an updated version of that resource.

Also, please read this  quick summary of Bruner’s Stages of Representation.  The lesson aims to follow the Enactive/ Iconic/Symbolic stages (although the students  aren’t actually building the sandcastles or digging the holes, the main idea is there).  This is sometimes also referred to as the Concrete/ Pictorial/Abstract, or CPA model , particularly when linked to maths education in Singapore.

Sandcastles and holes are things that are very familiar to children and are something they will recognise.  The ‘charges’ represent the sandcastles pictorially, and then students can move onto the actual calculations.

I think that this paragraph sums it up for me:

Furthermore, Bruner’s theory allows teachers to be able to engage all students in the learning process regardless of their cognitive level of the concept at the moment. While more advanced students may have a more well-developed symbolic system and can successfully be taught at the symbolic level, other students may need other representations of problems to grasp the material (Brahier, 2009, p. 54). In addition, by having all students go through each of the stages, it builds a foundation for which the student can fall back on if they forget or as they encounter increasingly difficult problems. For these reasons, it is essential that the teacher go through each of the stages with the whole class; however the time spent on each stage can and will vary depending on the student, topic, etc.

In year 8, there has been a lot of work using ratio tables this week.  Again, the idea for this is for all students to have the tools to be able to answer the many types of direct proportion questions. In faculty time on Thursday there will be a CPL session on the topic. Please bring your experiences (good or bad) to discuss at the session and any examples of student work that you have been pleased with.

GCSE

We are in the process of finalising the first set of mock exams for year 11. The intention is that they are in the week commencing 7^th November.  More information should be available in next week’s bulletin.

Hello Maths,

Thank you to everyone who has uploaded their year 7 intervention data. Your DoLs will let you know next steps for students on the list and will explain their plans for intervention. It will differ from campus to campus.  All intervention will continue until the progress check at the end of half term. The next phase of intervention will be planned based on the results of the progress check.

Deadlines:

None this week.

Curriculum Issues KS3:

Some questions that have come up this week.

• I’m struggling with the mixed ability classes.

This is a difficult one. Many of us have been teaching for a very long time in a strict setted environment so this is a huge shift in many ways.  The rationale for the mixed ability classes is to raise the aspirations and expectations of the students in the lower sets who historically make the least progress, while maintaining the challenge for the faster graspers.

The aim is that we teach to the top of the class so that students who would traditionally be in ‘bottom sets’ are exposed to the same content as everyone else. This gives them the opportunity to have good learning behaviours and habits modelled by students who have been more successful previously. It is important for students to see what other students of their age can do, and that actually, they can often succeed at the same things too.

As there is an open door policy across the trust, I would encourage you to work together and go and see each other teach the key stage 3 lessons.  I have a year 7 period 1 every day except for Wednesday, and anybody is more than welcome to come along to observe/help out/join in. Please let me know if you would be happy for others to come to your classes, and when those particular classes are.  I understand if you are happy for colleagues to see some classes and not others. Maybe we could make up a timetable of where mixed ability lessons are going on across BBA, ALC and WPC. Obviously, all visits are to be non-judgemental and for support and development reasons only.

• The lessons are really difficult and my class are struggling to access them.

The lessons were initially written for a mixed ability audience.  If you are teaching in sets, then the lessons will need to be modified.  It is absolutely fine to supplement lessons with a few consolidation lessons as your class requires.  Please don’t think you can’t have the odd quiet ‘death by worksheet lesson’ or other lessons that you have planned from teaching these topics previously.  Some of you have maths twice in one day, so you may well want to have the second lesson as a consolidation lesson. The discussion lessons can be exhausting for the students (and teachers!)

It is also important to note that the lesson plans are not intended to be scripts.  I started to write the lessons at my previous school as people were worried about planning for mixed ability classes.  I created the lessons to try and reduce time spent searching for resources, so that planning time could be spent concentrating on delivery and planning questions that would move the learning on for all students in the class.

I know that when I have used  Powerpoints or resources made by other people in the past, I have not always known what the intention behind the resource is. The lesson plans are how I would use the resources to teach the lessons. That doesn’t mean that it is necessarily how you would all teach the lessons. Please do use your professional judgement.

• Thank you once again to everyone who has sent in resources that they are using to supplement/differentiate the work. Please do send anything as it means people have a first port of call when looking for resources. I have been adding them to each lesson page as ‘supplementary resources’.

• Thank you for those of you who have been using the comments section. Please continue to use these, especially if your lesson has gone well, or if you have suggestions for improvements. Remember that our trainee teachers also use these resources, and may like to hear about things that made the lesson go well.

KS4:

We are in the process of organising intervention for year 11’s. Your DoL’s will let you know which students will be chosen and what they will be doing. For ALC and WPC, we will be using the Question Level Analysis from the PiXL Curve exams the students sat in June. The results are now out. Joel and Louise will share the results with you. They are in Go 4 Schools so you can check your class results.

We are hoping to have the first set of mock exams in the week starting 8^th November. More details to follow when the dates and times have been confirmed.

See you all soon,

Matilde