Place value game - includes decimals

 Here is a box link for downloading the MS Word file.  
It includes the instructions, game board and cards.

Place value and decimal fractions feature large in the South African Grade 6 curriculum. This is a game I made to help learners become more familiar with place value, and how numbers change when we multiply or divide them with 10, or multiples of 10.

In particular I'm using this game as a springboard to get learners to think about shifting the digits to different place values, rather than blindly adding zeroes/moving the decimal point.

BASIC IDEA
Learners work in groups, each group has a 'place value board' and a marker with a single digit, which starts in the Units place, and can move towards the left or right through different place values.

Teams elect to draw a yellow or red card, which will instruct them to multiply or divide by a multiple of ten - effectively, shift the digit along the board. Red cards say multiply or divide by 1000 or even 10 000; yellow cards only have 1, 10 or 100. Depending on their choice of colour and the operation on the card, they will shift their marker and write the resultant 'new total' on the card, before choosing a new one.

The first team to make it 'off the chart' on the left hand side wins. Going 'off the chart' on the right has a penalty e.g. temporary suspension from the game.

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I've tried it out once, last week.

What went well:
My girls understood what to do, got going, and all too soon one team had won.
They enjoyed the game.
When we had to do similar operations later in the week, I could remind them of the game, and they'd find their feet.

What could have been better:
I did not shuffle the cards well enough, so there were too many multiplications coming up, too few divisions. This meant one team won rather quickly.
I should have left more time for the game, perhaps: 10 minutes for getting into groups, intro, distributing stuff; 15-20 minutes for playing, 10-15 minutes for an individual activity answering problems like the ones that come up in the game.

A note on the document (see link at the top). Here in South Africa we use a comma to indicate the decimal point - mainly at school (eccentric, I know).  We leave spaces between sets of three place values. I've adapted the Word document to follow the US convention, but anyone can change it.

MISTAKES/SUGGESTIONS
This was a first try. I'm new at this and open to corrections or suggestions!

Sunday Funday - Homework policy

It's our school policy that learners should get Maths and English homework every day Monday to Thursday. Homework should help them develop/practice skills but should not take too long - many learners travel long distances and get home tired in the late afternoon.

We've also been seeing poor compliance with homework.

The solution we've come up with (actually my Maths HoD's idea) is to create a weekly homework sheet for Maths and English classes. This gets glued into special 'Homework Books' (notebooks) on Mondays and we encourage parents to check and sign these sheets daily.  The homework on the sheet gets done in the Homework Book for the subject, which makes quick correction at the start of the lesson easy.

It's a challenge to have the sheets ready every Monday but so worth it to avoid power struggles around getting homework noted down in diaries. When parents come on board, and many have, it makes a huge difference and even former reluctant 'homeworkers' start taking pride in their consistent efforts.


The homework sheet differs from teacher to teacher - many just highlight upcoming tests and quizzes and indicate the textbook exercises to be done for each day. I usually add some custom excercises and use the back to print a worksheet. 

Learners earn stars or stickers for homework assignments completed neatly and without errors, these  eventually add up to Merits. Homework repeatedly not done can lead to a detention.

That's it, it's been working for us. 

Sleep and the female teacher

Julie at I Speak Math named sleep her favourite thing of the week. This reminded me that my biggest personal challenge to myself this year was getting enough sleep. Can't say I've done well at it.

I normally go to bed at 10 with my husband but I'm no good at working at night so get up at 3 most days to do marking and prep. Five hours is not enough and definitely does not constitute 'beauty sleep'. Something's gotta give somewhere because besides being bad for my complexion, lack of sleep
- makes me crabby and less able to handle the ups and downs of a school day (and be a good teacher)
- my mom had breast cancer (which she fortunately survived brilliantly) but I've been trying to find out what might have triggered it.
She was always up well before the rest of the family (though not as early as I'm getting up now).

This is what I've found out:
1. Continued lack of sleep contributes significantly to breast cancer risk. (Read here.)
2. The California Teacher's Study investigated health trends among more than 130 000 female teachers and school administrators. Female teachers had a higher risk of breast cancer than the average population.
Are there some dots to connect here?

I'm not writing this to scare anyone but to motivate myself and others to look after ourselves. Which comes at the end of the list much too often.

P.S. Bit of good news: us female teachers are less likely to get lung or cervical cancer. Less living on the wild side, I guess.

Also kinda good, among the many negative health impacts of not sleeping enough is obesity. So I'm hoping I can sleep myself thin :)

Yes! Brilliant & Boy-friendly resources

From Borscht with Anna's blogroll I found To infinity... and beyond
I'm guessing Mr Taylor must be teaching at a boys' school
His resources are INSANELY boy-friendly
Sports, missiles, humour, puzzles, exciting graphics and font...
THANK YOU

Boy Maths - any ideas?

Since July this year, we've split our classes (from Grade 5 up) into separate boy and girl classes. In our tiny school, that translates to one class for each gender per grade, about 30 kids per class.

So, the girls have been taking off like a bunch of rockets, or maybe racing cars that have been revving their engines and are finally given green for go. They help each other, compete with each other, pay attention in class (most days), do their best and are seeing improved results.

For the boys, things have not been going that well. There have been a few lessons where early finishers on a task have moved around helping others, everyone liked that. But they have hardly any tolerance for me standing  up in front explaining a concept, even interactively - and I'm not yet sure how to teach maths without a bit of explanation at the start of the lesson, before they dive in to the set activities.

Their restlessness tends to draw out the amount of time it takes me to do the introduction/explanation - a vicious circle. Yesterday I felt some real despair at the way their marks are going down. There is little of the group-wide sense of competition and pride that exists among the girls (although a handful of boys are keeping their inner motivation alive).

Unfortunately this is also a group with a long history of poor behaviour, so class disturbance and poor performance are in a way behaviours that feel 'familiar', even 'safe' to them.

So, here is a major mind-body-maths challenge. Teaching boys in a way that works for them, that engages them. I know nothing will come right until I crack this.

One of the hardest parts is trying to get this right at the same time as being under huge pressure to finish most of the curriculum over the next few weeks AND prepare them for the kind of questions that come up in our Annual National Assessment. The results of which, I've only recently found out, determines the reputation of our school.... (this is my first year in the government school system).

What I HAVE been doing...
- starting each concept on a back-to-basics, very simple level, working on the basic concepts before getting into solving more complex problems
- using manipulatives where possible
- occasional games/challenges - these work if VERY simple, otherwise tend to break down into chaos with the boys
- using worksheets rather than having them copy work from the board - though this brings another horror as they have to glue the sheets into their classwork books - gluing in one sheet can take 5 minutes of disorder
- Currently my learners are sitting two to a desk, facing the front. Group seating earlier in the year led to too much inappropriate interactions, and I like to work with individual and pair activities most of the time.

Anybody else teaching maths to boy classes? What has worked for you?

Term 1 Take-Aways

Well, it's all over. The first term, the "big test" referred to in my previous post... reports have been handed out and what's done is done. What sticks out most: my marks were 'much too high' and the learners now all love  Maths and almost all of them feel confident or very confident. Are these first steps to success or disaster?????

I'll jot down some quick notes on how the final test went, and then write about my own 'big questions' for next term.

Test and final results - confidence building, standards, and challenge

In the end I took some of my own advice and scheduled an extra lesson before the test, AND made a colourful foldable summary of everything we've learnt about fractions. I'm sure it's better if learners make this kind of thing themselves,  but there wasn't time, and my trifold pamphlet-style summary was useful during a revision lesson.

I made the test too easy (by any normal standard), scared of damaging the learners' fragile and (for many) newfound confidence.

In the end my maths term marks were over-the-top high. This was a result of the non-challenging final test, and because the rest of the mark consisted of skill-by-skill assessments. I also allowed learners to re-take the smaller tests and so improve their marks. This seems all very well but in South Africa a grade average of 78%  means you're doing something wrong.  (Pass is 40%, grade average usually around 60 or 65.)

My HOD first asked if there was any way we could weight marks differently, so as to reduce them. In the end I managed to convince her and the principal to keep the marks. I sent a letter out with the reports, explaining that the first term's focus had been on foundation skills and confidence building, and that the pace and level of challenge will now be picking up. I'm happy with this.

Questions for next term

1. Can I sustainably use the JUMP Math methodology without the workbooks? The Teacher's Guide is pretty explicit but I found the way activities are laid out in the Introduction Unit Using Fractions really helpful to learners - and I'm not sure I can replicate this.

2. We've been given some excellent, full-colour workbooks provided by the goverment to all state schools (see further note on these, below). However, I'm worried about integrating these additional activities without
 shifting too far from a JUMP Math methodology. 

3. Providing enough challenge for the high-performing learners. Some of them simply zoom through any extension activities I include in the daily work, so I'm thinking of compiling a booklet they may work on, and providing some answer sheets they can access by themselves.

4. Limiting the time spent on marking homework (will try again to get overhead projector working - beamer is a distant dream); finding time for 'mental and oral' work on which we are supposed to spend 30-60 minutes per week.

5. Getting through the curriculum! I'm already behind my own plan...Perhaps the truth is that I'll need to identify some topics where we work more superficially. My preference would be to build really strong skills in the most important areas... once I've identified those :)

6. Finding a new balance between confidence building, meeting standards and providing challenge - hopefully without losing the confidence and enthusiasm I've just invested so much in.

Government issue Math workbooks
This is a MAJOR good deed by our government - imagine children in distant villages and shack settlements receiving these. They are supplied for Mathematics and Home Language. There's plenty  of use of colour graphics, and even cut-out manipulatives  in the back, suggestions for games, etc. What makes them a bit tricky to work with is that their approach is to go through almost all the topics in our curriculum every term (4 terms per year), increasing the level each time. I'm not used to this 'bitty' approach and feel insecure about using it. Nevertheless, now that we have them, one option I have is to abandon JUMP Maths and simply follow the workbook.

consolidating?

Wrote this post a while ago, and then forgot to publish... so it's a bit out of date but a record I want to keep.

We are now approaching our 'big' maths test of the term, and I have some concerns
(The test will include early number systems, adding and subtracting fractions (same or different denominators), reducing fractions, and some work with proper/improper fractions - further work with fractions and decimals comes later in the year; also number sequences.)

1. There are a few learners who never got adding fractions with different denominators right. I hoped to do remedial work with them during this last week but the timing didn't work out.
2. A small group are also struggling with reducing fractions, and changing mixed to improper fractions (and linking those terms to what they stand for).
3. We have to write the test at the very latest on Friday.
4. In the meantime, we have to continue with our new module on number patterns and sequences.
5. While I can do some whole-class revision of the problem concepts, there isn't time for enough, nor would the learners (majority) who are doing well with them, tolerate that.

So far I'm thinking:

• I really should have caught up with the first problems a while ago, and in future I need to make sure to respond quickly to any problems.
• Whole class revision: maybe creating a colourful foldable or summary sheet together will be interesting for the class and of use to those who need it.
• It would be a good idea to schedule a special lesson in my extra maths time slot, to work with learners who need it. It is on Tuesday. I'd then still need to set them a small number of revision exercises to maintain/consolidate their knowledge leading up to the test. 

Problems I've encountered in teaching the fractions unit:

- To start with, the learners had a weak foundational concept of what fractions even are, and what fraction notation represents
- Though we did some good cutting and pasting activities to understand equivalent fractions, we really needed to do some more manipulatives work when it came to mixed/improper fractons. I'm only realising this now, though time would have been a problem anyway.
- What conceptual understanding learners have of fractions, tend to get clouded by confusion over computational strategies (where and how to multiply and divide, add and subtract - to find equivalent fractions we multiply or divide both the numerator and the denominator, but when to use which? Depending on the operation, there are different methods to determine what to multiply or divide by...) and perhaps we learnt these too much by rote, without understanding WHY. This could be a weakness in the Jump Math programme, or else in my interpretation of it.

While a week ago I had a class of mostly positive, achieving learners, more of us now seem to be on morassy ground... and I would hate to end what was meant to be a confidence building phase, with some learners drowning while others are rearing to go for the mountains and frustrated at our pace.

Mat routine versus trapeze

OK the honeymoon is over and right now I'm seriously challenged by managing my two very unruly classes (though as usual, the problem is down to a minority of individuals).

As a result I'm not making as much progress as I'd hoped, though this is more pronounced in English than Maths. I think the predictability of what happens in Maths suits many of the learners (is that an indictment of me?) and the language barrier many experience in English is less of an issue.

Though on the slow side, the progress we have made so far is pretty solid, thanks to the Jump Math material I'm using. Most of the kids who'd been close to failing are shining and very proud of themselves, so that's a big thing to feel happy about. On the downside, while giving attention to those whom I know needed it... I missed out on a few others who've 'fallen by the wayside' as revealed by a recent quiz. Though I feel responsible for not having noticed, fortunately I can help them back on track before our major test for the term.

I'm still figuring out how to keep track of the progress of 30 children per class, at a time, without completely killing myself with over-frequent marking. While I usually get around to helping those who ask, others have been quietly messing up.

What to do?

Ideas so far:
- compile a more comprehensive list of learners to keep an eye on
- mark smaller sections more often
- form quick study groups within class (I have no idea of how to make this work!) rather than helping learners one by one and missing out on some

A final word on Jump Math. It's been a really good feeling for myself and the learners, never to have felt that quicksand-feeling of half-formed ideas and misconceptions under their feet as they try to get to the other side of a task. Our feet have been firmly on solid ground. But the last two days I deviated from the material, mostly to speed up and finish an overdue unit.

Without the careful scaffolding we've been used to, suddenly a bunch of the kids looked like worried trapeze artists again.

I wonder whether I'm coddling the most able students too much, perhaps undermining their belief in their own ability to struggle through and figure things out. On the other hand, the sense of ability most formerly-struggling learners are glowing with is hard to pass up.

I guess there's always differentiation. Anyone got a link to good 6th grade enrichment material?

Out of the starting blocks

It's hard to believe I'm through four full weeks of teaching this year (first two weeks of school were orientation and camp).

Maths teaching & methods

I spent ages in the December holidays reading on the web about maths teaching methodology & thought, and working to integrate the materials available in our textbook and state-provided teaching materials into a programme of work for the year. The Foundations for Learning material contains lots of good teaching ideas, though the way it jumps around topics and the pace in general seems unrealistic. Our textbook, Classroom Mathematics, also has (what seemed) a good emphasis on discovery, problem solving, recognising more than one way to get to an answer, and real life applications.

But.... our baseline assessment at the start of the year showed a huge gap between a bunch of star performers and another bunch of kids who are drowning at sea. (Sound familiar anyone?) There are also some topics that are weak across the group (long division, column multiplication, ratio among them). I kicked off with my planned lessons on calculator skills, some review of Grade 5 skills and problem solving as per the textbook....and we were immediately in trouble.  Most of the problems set by the textbook assumed skills which many of the learners couldn't bring to the party, and they were immediately floundering. I won't go into the details, but it was scary.

The good news: right at that time two Jump Math webinar's I'd booked during the holidays came up. You can read all about Jump Maths here if you haven't yet, but the parts that I really like are the way each component skill of a higher level operation is properly put into place, before it is taught or attempted. Learning and embedding small steps of skills also builds confidence - a major problem among the 30% of my learners who have regularly been getting awful grades for Maths.

So, two weeks ago we started off on our journey with Jump Maths, an inexperienced maths teacher, two challenging classes, and some promising material off the web. My HoD said anything that works as long as it covers the curriculum. I took a deep breath and suppressed my worries about losing the plot...

We started off with the Introductory Unit Using Fractions, which is intended to cement some basic operations skills and knowledge, while developing confidence and making a good start on an important (and often troublesome) part of the curriculum.

On the positive side, as per the testimonials on the Jump Math website, my 'weaker' learners are charging successfully through the work, and the boy who said at the outset, "I can't do fractions," is smiling all the way. Overall most of the learners in the class are enjoying the work and the safety of learning incrementally rather than trying to make some kind of trapeze leap with weak equipment. I'm assessing what they've learnt to far on Monday, and am feeling hopeful.

What I'll need to figure out:

• I'm working hard at trying to match up Jump Math units and lessons with our curriculum. There are more lessons than I can fit in, and the curricula are not a perfect match. I'm also concerned that we'll move a bit more slowly than necessary to get through all the required topics.
• Bringing in other resources and ideas. I'm never someone to rely completely on a given set of resources. Part of my prep will need to be seeing where I think some of my own/other resources are necessary to add local relevance, deepen conceptual understanding, or develop specific skills. 
• Differentiation. Some of the children who are way 'ahead of the pack' are zooming through the Jump Math work as well as extension and bonus questions provided by the text, and more provided by me. They are looking a bit skeptical and the fact is they like a challenge, and are not getting enough of that. I think what I need is good quality extension material they can work on by themselves when they have free time. I'd want something with answer sheets so they can get these from me to correct their own work, and only consult me if they are completely stuck.  Any suggestions?
• Conversely, the little mental maths/maths facts workbook we are provided with and have to work through (as homework), is pitched at too high a level for some learners. I'll need to give them different or additional homework to practice more basic skills - but manage this without making them feel inferior. Perhaps I can simply leave the choice to them.

I still wanted to write a bit about classroom management issues but this post is already long and it will have to wait. Happy Maths teaching and please let me know if you have any advice, suggestions, or experience of using Jump Math material.

Eye on the child - checklist

It would be nice to have a daily checklist to help me reflect on how I can keep my 'eye on the child' - or whether I managed to do so.

Any ideas for checklist items?

I'll put some down as I think of them.

1. Did I ask lots of questions, or just tell?

2. Did learners ask questions? To each other, to me? If not, why not?

The issue of questions is much on my mind, as I've recently re-read the immortal poem about teaching "The Question" .... (I meant to link to it here, but can't find it again on the huge web - let me know if you know where it is, please!)

3. During the lesson, who's doing the work? Are the children active, or am I doing a 'star performance' while they doze?

4. Are there children who remain inactive, even while others are participating?


5. Do the children feel like they are learning something (How would I know this? How would THEY know this? )

The questions above aren't my own creations but based on the materials I've been studying, from across the web. Thank goodness for others' wisdom and perspective!

First look

OK, it's three weeks into the school term but the first half week was in-school orientation, then there was a week of camp, so really I'm about six days into teaching at my new home.

It's government bureaucracy crunch time with a deluge of files, schedules and plans to be filled out and submitted. Year plans, lesson plans, assessment plans, week plans, day plans...Sorry about grumbling but had to get it out. One kid's dad already phoned and asked why I've done so little marking of their exercise books.


Now, moaning aside, here's what I've noticed about my learners and myself so far:

1. There is a huge range in their abilities, in fact, two thirds of the learners are performing average to well, and very well. This is a big deal in South Africa, where our national performance in mathematics is abysmal. Nevertheless 10 out of 60 children are in serious danger of failing, and so, as in many classrooms around the world, there is a long bridge to cross, or maybe construct, in every lesson.

2. More than half the children are well-behaved and make an effort, but a significant group can be rowdy and resist doing homework. A few are disruptive and one child seems completely unable to control his own behaviour. I really feel the need to connect with the children who are on board, and avoid giving the bulk of my attention to the 'misbehavers'. I find this difficult. The school's existing disciplinary system is very 'gentle'

3. I do like children and I'm finding it easy enough to focus on their needs rather than on the 'needs' of the subject. Actually, having written that, I'm not so sure. I don't have any cleaer idea of what it feels like to be an 11 year old on the receiving end of my lessons, and I need to find out more about this, as well as ways to measure responses and progress.

Keep your eye on the... child

This post is a touchstone to remind me that children learn with their whole selves (hence the name of the blog).

More specifically, that my focus needs to be on the learners. Not on myself, and not, in the first place, on the wonderful world of mathematics, but:
on what children are busy learning about themselves, and maths, and about how they are able to engage with it. Any clever ideas are only good, if they make learning more accessible and healthy for the particular group of children in my class.

I worked with a teacher at the school I've just left, who repeatedly taught me this by example. She would challenge her learners, but only after ensuring they had a solid foundation in place. I'd always run my tests by her for editing - she has a special skill in phrasing questions and assignments in such a way that they are crystal clear and non-threatening, without lowering the standard of work.

Thank you, Birgit!