For Tamara again…  🙂

There are things we have learned from literacy instruction – how to support students in getting meaning out of text – that apply to mathematics instruction.  When we talk in mathematics about the mathematical processes (ways of behaving like a mathematician) we consider the following:

COMMUNICATION
CONNECTION-MAKING
VISUALIZING
REASONING
PROBLEM-SOLVING
MENTAL MATH AND ESTIMATION
TECHNOLOGY

In literacy instruction we have accessed the work of experts to help us find ways to teach these sense-making strategies to students. I have borrowed from their work and put together my version of these strategies for sense-making in mathematics, or more particularly with mathematical text.  Try them out with your students and see what you think.  They are available in French and English, for Primary and Intermediate.

intermediate_strategies

intermediate strategies en français

primary strategies

primary strategies en français

Carole

Hello to the gang from Howe Sound…  For Tamara and Mary I am putting together a post with upper intermediate links and literature connections – easy to find and all in one place!  Whee!  :o)

First – Some FAB middle school links can be found at:

NCTM’s Illumination – Middle School On-Line Activities and applets for exploring math concepts. A complete searchable database of tasks…

The Figure This site is provides a selection of math tasks for families, but there are some great middle school math problems here….

Here’s a site that demonstrates the power of exponents – visually…

The nrich site is full of unusual, challenging problems – check out the weekly problem section…

Some books that are amazing for jump starting middle school math lessons – with math concepts complex enough to stimulate conversations at the upper grades are:

One Well – The Story of Water on Earth – Rochelle Strauss
decimals, percents, fractions, very small, very large numbers, data management

If the World Were A Village – David Smith
percent, decimals, fractions, data management, surveys, population

Uno’s Garden – Graeme Base patterns, series and sequence, increasing, decreasing patterns, relationships

Jayden’s Rescue – Vladimir Tumanov
non-routine problem-solving

The Number Devil – Hans Magnus Enzenberger
complex math topics – Pascal’s triangle, square numbers, triangular numbers, integers, permutations, etc etc

Flotsam – David Wiesner
magnification rates, relationships, hypothesis

Wild Fibonacci – Nature’s Secret Code Revealed by Joy N. Hulme 
Fibonacci in the natural world

A Very Improbable Story by Edward Einhorn
dependent, independent events, likelihood, complementary probability

365 Penguins by Jean-Luc Fromental
cubic numbers, factors, growing patterns, triangular numbers

The King’s Chessboard – David Burch
exponential growth patterns, very large numbers, scientific notation

A teacher resource book featuring lessons across the strands (geometry, number, pattern, probability and induction and reasoning) is Intermediate Investigations to Inspire – A Numeracy Resource for Grades 4-8 Classrooms. The lessons are classroom tested, feature student work, assessment rubrics, literature connections and on-line resources. You can purchase one for $18 by contacting me.

Carole

As promised, here are the pieces I mentioned yesterday during our demo teaching session. First, the list of fantastic new math and literature book titles – en français, naturellement – with ideas for how you might use them in your classrooms. (french-book-list)

For my friends in primary, I wanted to send along the support materials for the book we used in grade 1, Les bisous: the bisous lips (lips1), the list of characters in the story (characters) and the line master for student work (les-bisous1), as well as the mini penguins (penguins) for anyone who wants to use them in their exploration of the book 365 pingouins…

Enjoy!

Carole

Good morning to my friends in Campbell River!

What a treat to see you again this week. I have absolutely LOVED our course this year, and I have learned a great deal from our work together.  How fun that we’ll be continuing in the fall!  🙂

I thought I would send the Counting Crocodiles materials (a fun book by Judy Sierra) that we used for our lesson on Thursday, along with some photos of the kids’ problem-solving strategies as they worked to figure out how many crocodiles were in the Sillabobble Sea…

Download and print the pocket chart cards and the crocodile pictures for use in your own classroom.  Be sure to do more than needed, so that the kids have to think!!  :o)

I had magnetized all the crocodile pictures thinking they might be used by children on a whiteboard, but maybe you could shrink them down and have kids use them as counters, even gluing them down onto their papers in ten-frame arrangements…

Enjoy!  

The fun in doing this task is in watching the children strategize and use the idea of the complement of ten (ten partners, like 2 and 8, 3 and 7, for example) to calculate how many crocodiles are in the Sillabobble Sea. As usual, the answer is really not as interesting as the ways the children manipulate the numbers and reason through to a solution…

Cheers!

Carole

OK, OK. I know I am the only one thinking about math today, this, our first day of the March Break… BUT, I did want to share just one more thing today.It’s something Kate brought to our last workshop in Coquitlam, and I think it’s pretty cool. It’s a set of grids in a variety of shapes like this.  The idea is that you download and print or copy this sheet of hundreds chart puzzle pieces onto bond paper, laminate it, then cut out the little pieces. What you’ll end up with are a range of puzzle pieces to lay over top of a standard hundreds chart to block out some of the numbers. The job of the child then is to use an overhead pen (don’t they LOVE those?) to write down the missing digits – the ones that are covered.A great way to practice – and assess – understandings of the number system and patterns in the hundreds chart! Thanks Kate!Carole

Here’s another fun applet for identifying factors.  You can play against a friend or against the computer, a game of strategy and skill both.  I lost my first game against the computer – guess I should have read the instructions first.  :o)   Find it by clicking here!

Hey there!  I found these fun little games on the NCTM site – check them out! There are games to practice identifying numbers in a ten frame, finding the missing part, even adding on 2 ten frames. Check them out by clicking here

playing with ten frames:

adding:

Hello to my friends in Coquitlam!
I wanted to post some of the number sense games I mentioned  today – they come from BEAM and are available (among many many others) on the BEAM website, filed under Maths of the Month. Enjoy!

The games:
2s-and-5s.pdf
dolls
favourite-numbers.pdf
odds-and-evens.pdf
next-door-neighbours.pdf
very-odd.pdf
number-jigsaw.pdf
three-in-a-row.pdf
writing-numbers-3-dice.pdf

It was great to spend time together this year, playing and thinking mathematically…
Carole

Hello to the folks from West Vancouver! As promised, if not a bit delayed, I wanted to post the Numeracy IEP forms that I have been working on.  They are based on the notion that in order to support the creation of competent mathematicians, we must help children to develop confidence, hone their problem-solving strategies, foster fluency and the ability to communicate and represent mathematical thinking.  I hope these documents will prove helpful.  
Click here to download the Numeracy IEP forms.
Carole 

The book If  You Hopped like a Frog by David Schwartz is full of interesting facts that help students visualize and think about proportional reasoning.If you hopped like a frog, he says, you could jump from home plate to first base in a single bound…  Since frogs are able to jump 20 times their body length, so too would a human being.  He speaks about ants and snakes and other creatures in the same way, and uses proportional reasoning and amazing pictures to help students see what would happen if they too had the same abilities.

The discussions after reading this book are rich.  Having students create their own book or page like David Schwartz has done would be a great task to carry on from the conversation.  I have uploaded a selection of related problems (frog problems) that I found on the internet that I quite like, especially since they steer clear of the imperial system (which is featured in the story).  The problems are set out on a series of 20 cards – enough to share between 2 or so kids in an intermediate class.  I’d like to credit the author but can’t since there was not name on the problems, but you can find them and the whole document at this address
Carole

Hello to all my friends in Kelowna and Kamloops!  I wanted to send along the text & pictures you’ll need to try the Acrobats, Grandmas and Ivan problem with your students.  It’s a classic Marilyn Burns activity that I tried this last week in a grade 4/5 classroom with really cool results… I can see it playing out in a variety of ways at different age levels, perhaps even by partnering it with a read-aloud of the book Equal Shmequal by Virginia Kroll, a story in which forest animals take part in a tug of war with crazy outcomes!The Acrobats, Grandmas and Ivan task, with all its logical and algebraic thinking, presents a fun and engaging way to work with notions of equality and to explore many different ways to solve a problem.  If you’re looking for a task to encourage the mathematical process of reasoning, this one’s it! Click here for a pdf of the problem (Acrobats) including the pictures you’ll need to represent the first, second and final rounds of the tug of war contest…Carole 

Hello to my friends from Howe Sound! As promised, here are the instructions for the Geometry Tasks we played yesterday at our workshop. They all come from the Van de Walle resource mentioned below. These are the line masters for the shapes – remember it’s a good idea to print them all on one colour of bond paper…

Shape Sort Shapes

Click on the images below to access the tasks. They’ll open in another window and you can print them from there.

Hello all! Carly in Maple Ridge asked about how to find those great number balances that I have been carting all over the province…They are available from Spectrum Educational at a cost of $31.45. Here’s a picture from their 2007 Mathematics catalogue. They can be found on page 61 – if you click here you’ll go directly to that page in the catalogue.

The magnetic wand and counters are from Spectrum too. Here’s a snapshot of page 28. Click here to go directly to that page on line.

Oh – and you can get a great selection of dice from Spectrum as well. My favourites are the decadice with dot patterns on them. They help kids to see number in different ways, and to practice subitizing (seeing quantity without counting). If you get a good collection, these neat dice can make differentiating your lessons easy – simply by giving different children simpler or more complex dice to work with. They are on page 111 of the 2007 catalogue, found here in the on-line catalogue. Check these ones out:

Spectrum has a new catalogue out for 2008, if you’re looking for a hard copy in your school. It’s got three red dice on the cover… Call 1-800-668-0600 to order.

Carole

Hello to all the primary teachers who spent the day with me today.  Thank you all for opening yourselves to thinking about the operations in a new way, and to considering how having a range of strategies for finding the sum or difference will impact the students we work with and care for… I wanted to attach some materials for you – to make it easier to find what you came here for!  First, the Big Red Bus master can be downloaded by clicking here:  Big Red Bus. 

Spectrum is the place to go for the number balance and the magnetic counters. You’ll want to check out these personal strategies for subtraction, explained from Van de Walle and try some of the games from the Math Tool Kits (a great thing to send home with parents) to practice the basics and to promote the mathematical processes we discussed today.  

Once again, please remember that this pedagogical and content-based change is a journey and that we are embarking on it together, one small step at a time…Carole 

Hello all!  Welcome back to the new term!  
I hope everyone got some rest and some time with friends and family this holiday season…  Heaven knows we’ll all need it to keep up with our students!

I wanted to invite you to join me on-line for part one of a 2-part series of professional learning sessions devoted to promoting engagement – and deep learning – in the math classroom.  The session is being hosted by LearnNowBC and more specifically the Rural Schools Network of BC, as a follow-up to Faye Brownlie’s plenary at the Rural Schools Conference here in Richmond in October.  During the interactive session I’ll be connecting to Faye’s big ideas of the key elements of learning, namely connections, talk and engagement, and showing student samples from my work in the province.

 All are welcome to attend through the Elluminate Live service.  It allows you to text-chat, audio chat and use shared tools like a whiteboard to record your ideas and talk to others across BC. (pretty cool, huh?)  The session starts at 3:30 pm and runs to 5:00 pm on Monday, January 14th.  It’s a good idea to log in about 10 minutes early to get yourself configured and play around on the site.  There’s tech support that will help you before the session starts, too, so you can get a handle on the features.  Of course you are welcome to just sit and listen, but it’s always more fun to engage with the problems and ideas presented…  :o)

You can also view the archived sessions after the fact (along with those done by Lori Drussy on Talk in Language Arts, and the session hosted by Janice Novakowski – my colleague and friend – on Science and Inquiry) so if you can’t make the session, feel free to download it later!

Here’s the link to join the session.  

The site is open an hour beforehand.  
Hope to see you there!
Carole 

Thanks to Paul in Saltspring for this way cool link to games for practicing visualizing decimal relationships and operations with decimals.

check out DecimalSquares.
They work best on FireFox, and require a ShockWave plug-in… 
Carole

hello to my friends in Coquitlam…I wanted to share some things with you by way of follow up to last Friday’s workshop…  I know we experimented with a range of different strategies for subtraction, and we really didn’t have time to do them all justice.  I have attached some pieces drawn from the Teaching Student Centered Mathematics grades 3-5 book for you to look at, and hopefully it will help shed some light on the methods we played with.  click here to open a pdf of personal strategies for subtraction, explained 

The other thing that I wanted to share was a list of the big math ideas in elementary math – as outlined in our new IRP.  I’ve re-worded them to be more like enduring understandings than PLOs – and originally they were intended for parents, so feel free to share them.  The second page features questions to ask to get at the mathematical processes… let me know if they are helpful.  Download them at:  math for parents

Carole 

Hello to the fantastic parents and teachers at Eagle Harbour!  What a fun morning I had working with you and your children…  🙂

I am so pleased that we had the chance to talk about the changes in the new math curriculum and to watch how making sense of number and using strategies like “add tens, add ones” or “take from one and give to the other” can go a long way in supporting children in truly understanding what it means to join  groups…

I promised, in the last few rushed moments, to post some materials here for you to access and use with your children.  First, the Math Tool Kits and the games to play with your children can be found by clicking here.  They contain all the materials you need to support your elementary-aged child in mastering the facts in a visual way – they also help children to “see” how the strategies of “add ten and add ones” and “take from one and give to the other” work, when using the pink and blue ten frame cards.

 A couple of you asked for support materials to read to make sense of this for yourselves.  If you were up to reading a whole book (grin!  🙂  ) then one I would highly recommend are the resources by John Van de Walle, who has written Teaching Student Centered Mathematics, for Grades K-2, 3-5 and 5-8.  The books are available through Amazon.ca or through Chapters.ca.  If you’d prefer a small excerpt, here are 3 pages to read drawn from the grades 3-5 book, which describe what Van de Walle calls invented strategies for addition and subtraction.  These are the ones we modeled and talked about today – consider it a cheat sheet for helping your kids!

And for those of you who’d like to learn about what this looks like with long division, read on…

Division is about sharing.  The traditional algorithm focuses not on sharing but on numbers “going into” other numbers.  A strange thing even to visualize, no?  The new way of modeling and recording long division is based on the idea of sharing, and depends on a child knowing only the multiplication facts of 1, 2, 5, and 10… yes, the easy ones!!  🙂

Here’s how it goes. Imagine you have 359 candies on a table, and you have 16 children who want to share them.  How many would you give to each child to start? 1, 2, 5 or 10 each?  Most would say 10 each, just to make everyone happy. So if we give away ten each, that’s 16×10 or 160 candies that are gone.  (See below)

To figure out how many are left, we need to subtract 160 from 359 (or find the difference between them). We can do that by adjusting the top number – because if you were subtracting from 360 that would be so much easier…  To do that you have to add one to 359, find the difference   (360-160=200) and then take away that 1 you added before.  You now have 199 candies left, and the kids are still hungry, so you continue, giving away sets of candies to each child until there are too few to divide up.  What one does with the “remainder” in this case is a great conversation… Check out a full-sized illustration of this task by clicking here: long division – by sharing . 

Here’s another example, with larger numbers:  Van de Walle does another example using larger numbers (sharing in multiplies of 1, 2, 5, 10 and then 20, 50 and 100) in this excerpt from his book. As you can see, there are lots of ways of doing this – and many ways to be right.  What a relief!  🙂    Carole

Hey there…
I wanted to pass along 2 new applets (ok, new to me) for modelling fractions – both on a number line and using an array model.

The first is a game, in which you have to select a fraction that is equal to or less than the fraction you’re given, with a goal of moving all your sliders over to the far side of the screen – in as few moves as possible. My best score was 12 moves… 🙂 Try out out by clicking here… Here’s a game board:

The second applet asks you to create fractions equivalent to a given fraction on a number line. You have to slice a box into sections and then shade the correct number of sections in order to get the point to align on the number line. I like this one because there are lots of ways to do it… Check it out by clicking the link here!

A screen shot of the game…

By the way… I’m thinking that the rectangular array model is a far more powerful and visually meaninngful model than the “pie” model for representing fractions. Those pieces are so hard to slice, to draw and to compare that they seem more trouble than they’re worth. I get the whole pizza reference and all, but right now I am leaning towards square pizzas for the sake of conceptual understanding.

Carole