Hello to the folks in the grade Math Makes Sense group! It was great to see you all yesterday. For those of you who weren’t able to attend, we talked a bit about the notion of integers and students’ experiences with modelling them on number lines. I described this particular applet to you, but thought it best if I sent it out for real… 🙂

Try the JUMPING NUMBER LINE. It asks students to arrive at a target number by “jumping” a certain distance in either a positive or negative direction… In this example I am aiming for the number 4. I have to use all four of the arrows. I must start at zero. Fortunately, I can reverse the direction of the bounce my clicking the direction button in the middle of the page…

This next applet uses green and blue bars to represent positive and negative integers. You create 2 bars of any length, then indicate by dragging dowon on a pull-down menu the operation that is happening between them. They are placed on a number line and you can choose to show the total or figure it out yourself. I liked this one… It’s simply called NUMBER LINE and require Flash Player to run… I had more success using Firefox with this one.

Here’s a screen shot of the game. I created 2 bars – one was -10, the other was +10. I chose the operation of subtraction, and asked that the answer be displayed…

Carole

I promised this to one of my friends in Salmon Arm some time ago and feel badly I haven’t come through.

Here are 7 lists of literature connections for teaching math in french immersion. They are organized by grade and are drawn from the Math Makes Sense (Chenelière mathématiques) program resources. I know more than one teacher-librarian in my district that has taken these lists and gone shopping… 😀

lit connections – maternelle
lit connections – 1ere
lit connections – 2e
lit connections – 3e
lit-connections-4e.pdf
lit connections – 5e
lit connections – 6e

For those of you who have downloaded and used the Math Tool Kits and assorted games in the past for supporting your students (grades 1-6) in mastering the facts, here is a treat for our immersion teachers! My friend Fiona took the time to translate the games into French for use with her grade 1/2 students, and has graciously invited me to share them with folks out there in the wide world. 😀 Check out the games here:

math tool kit games in french

As well, Fiona has created some lovely open-ended problems across the strands for children in immersion. The pages feature geometry, number and data questions in French, many based on frames from Good Questions for Math Teaching, grades K-6, a book we’ve put into each of our elementary schools, along with the grades 5-8 companion. Check the problems out here:

open-ended problems in french
Un grand merci à Fiona…
Enjoy!

Thanks to Lara, I have another way cool game to share for hooking into the visual aspect of thinking ten. 🙂

This game, called “The Complement of Ten” asks children to find the complement – or the other part – of ten using ten frames. Kids drag the images to fit the quantities together. It really relies on visualizing, and makes part-whole thinking more like a visual puzzle than number facts in isolation.

Thanks Lara!

Here’s a snapshot of elements of the game. See how the 2 is reversed to “fit” the 8?

ok, ok.
I know it shouldn’t be so high on my list, but today, my blog got its 10,000th hit.
😀
now THERE’S some place value for you! (har har har… :O)
Thanks for being here…
carole

Hello to all the patient folks in Coquitlam. My apologies for the traffic disaster this afternoon. Sigh. My kingdom for a transporter machine!

As promised, I typed up a list of the games that we played this afternoon at the workshop, that involved ten-frames for developing a sense of number to ten. These ten frames are mentioned explicitly in our new K-7 Math curriculum for BC and are a remarkable tool for supporting children in truly understanding the notion of 10-ness in all its parts and wholes. (for intermediate folks, think tenths and the tool becomes even more interesting!)

So… start saving those egg cartons! 🙂

Click on the link below to download the games and tasks in PDF form, as well as a set of coloured ten frames you can use to practice with.

Ten frame games and tasks for building number sense

Oh – and I managed to find one new on-line game for finding pairs of numbers. I don’t think it’s the game you mentioned today, but it invites kids to find pairs of numbers that add to a target sum. My son tried it today and gave it a 4 out of 5…

enjoy!
carole

Here are some resources put together by the Vancouver Island Net group of educators – documents that outline how you might use the Math Makes Sense resources you currently have to match the new K-7 IRP. They begin with the outcomes and then list the lessons that match – which is not to say that you ahve to teach the whole year in a different order, but rather it provides a cross correlation to the existing resources. Take a look… Despite the amount of time it took to create these cross correlations, the Island Net group is making these documents available to educators around the province for free – they are truly a collaborative group of teacher leaders.

Note – these are best printed in colour. 🙂
Carole

The English At-A-Glance documents

(note there is no grade 4 or 7 MMS correlation, since these grades have been re-written to match the new BC IRP and are available now. Grades K and 1 are also available, but a correlation document exists here.)

grade 1 MMS with BC IRP
grade 2 MMS with BC IRP
grade 3 MMS with BC IRP
grade 5 MMS with BC IRP
grade 6 MMS with BC IRP

and the french resources…

French Kindergarten MMS with BC IRP
French grade 1 MMS with BC IRP
French grade 2 MMS with BC IRP
French grade 3 MMS with BC IRP

wow….
I am sitting at the airport reeling after 2 days spent thinking and talking math! A huge thank you to my “hostess with the mostess” Sheri (mmmm – soup!) and to my friendly-neighbourhood stalker Jennifer. 😀

For those of you who worked with me today and yesterday, thanks for your patience and openness to new ideas. I think we managed to see a lot of amazing student work! I am attaching some of the forms we used today in our mental math lesson (called tools for thinking), as well as some I mentioned yesterday for using with early primary students (ten frames for adding). I like them both as tools for students to use to show their mathematical processes….

Amazing stuff too at the middle school where we manipulated growing patterns to develop understandings of the algebraic concepts of constant and variables. Check out this growiing pattern… Can you tell what’s changing and what’s staying the same as the man ages?

cheers!
carole

frog in the bog – counting system

Originally uploaded by mindfull

I love to start a math lesson with a story. Iread one of my favourite books, A Frog in the Bog by Karma Wilson to a group of grade one and 2 students, then asked them to find out how many insects were in the frog’s stomach in all.

This grade 1 student recorded her thinking in numbers and words, drew dots above the digits and then counted the dots to find the total.

frog in the bog – pyramid

Originally uploaded by mindfull

This child built a representation of the creatures using counters. Her arrangement clearly shows the growing pattern in the number of creatures the frog ate with each mouthful…

frog in the bog – making sets

Originally uploaded by mindfull

This child made sets to show the number of creatures, then counted to find the total. His counting system was really sophisticated. He found sets of fives on his page (1 and 4, 2 and 3, and 5) then counted them 5, 10, 15…. and did it all orally.

I was pleased to have been close enough to hear his solution, since no evidence of his developed number sense made it to the page – i have only this photo and that smug half grin to remind me of how clever he was. One reason I tote my digital camera about all the time…! 🙂

area of triangles challenge

Originally uploaded by mindfull

Here’s a great open-ended task. Have students build as many triangles as they can on a geoboard – with an area of 4 square units. This grade 8 student saw a pattern for finding tons of them!

So I was talking to my friend Bill today. We were chatting about the new K-7 math curriculum for BC – among other things (how decidedly academic of us! 🙂 ) and I brought up the mathematical processes that are featured in the new elementary curriculum. For those of you just cracking the cellophane on this newest curriculum, the processes are ways of approaching a mathematical situation – a way of processing the big math ideas and solving a problem.

The processes include:
communication
connections
mental math and estimation
visualizing
reasoning
problem-solving and
technology

Each of the PLOs in the new IRP has a mathematical process assigned to it – a way in which the prescribed learning outcome is to be approached. There are enormous implications for the way we teach embedded in these processes…. but I digress.

It was the last of the processes that got Bill and I talking. He asked if I had any new sites or software for integrating technology into mathematics teaching and learning… so I got thinking and wanted to share – both with him and with you – some sites that I think have potential.

check out the pattern generator applet. Students identify the pattern, then place missing elements into the pattern. This can be really tricky, though – especially when you change the difficulty level and you start into growing patterns!

tesselating tool – a simple and really effective tool for illustrating properties of tessellations. Look on the instructor tab for guiding questions to keep the classroom discussion happening.

and this last one made my sleep-deprived brain hurt. It’s an interactive attribute train. That is, you’re asked to identify which element of a pattern comes next, only you have to reason which of the attributes to pay attention to – colour, number or shape! YIKES! I have the feeling my son would be WAY better at this than me. :O

so. fun, yes, but there’s more…
The important thing about these sites is NOT that they will provide entertainment for students in the computer lab, but rather that they will initiate a conversation between classmates, be the visual manipulative for developing and consolidating a mathematical concept.

Let me know if any of you have found others you like!
Carole

Hello to all – and especially Sharon! 🙂

For any of you beginning to think about supporting your newly back to school child with mastering their multiplication facts, here are a few resources for you. First, a strategy for taking the fear and loathing out of the task, brought to you by John Van de Walle, called “Sort them as you do them“.

SORT THEM AS YOU DO THEM

Ask your child to cut apart the multiplication fact cards, and then to sort them into 2 piles – one pile for those that are easy and can be done without thinking, and another pile for those that are harder.

Immediately your child will see that there ARE some facts they already know – and what a relief THAT is!

Then begin to look at the facts that are more challenging. Sort those cards into piles and see if there are any sets. Do you see the 3x there? Are there some 7x? Now you can begin to work on developing strategies for the facts that are harder – and targetting NOT 100 discrete facts, but only those that require attention.

For a really great summary of the strategies drawn from Van de Walle’s work, check out this blog page by Amanda Waye of Newfoundland… Nice to know there are other “math chicks” out there!

Oh -and a multiplication chart is a really helpful tool as well. You can have your child cross off the facts they know in the multiplication chart and see the patterns both in what disappears and in the relationships between them.

enjoy!
Carole

So this week I shared a book called Equal Shmequal by Virginia Kroll – one I thought would be great fun for introducing notions of equivalence to our elementary aged students. With the new variables and equations strand in the BC Curriculum, we’ll be looking to collect books to share with our students on algebraic thinking… and this one’s fun! 🙂

The story is about a group of animals who explore whole issue of balance through a game of tug of war and then move to the seesaw to solve problems of equivalence. I’d suggest that the math in the book works for intermediate aged students as well…

And for fun, here’s a link to a game kids can play on-line to explore balance and equivalence. It’s available through the PBS site (we love PBS) and is connected to the show called “Jakers” – which I haven’t actually seen, but, well, what can I say?

Try out the game. It’s engaging (moo!) and there’s enough math to get the intermediate students thinking – especially if they play multiple screens and use deduction to solve for the weights of the anilmals…

Enjoy!
Carole

Seeing as how this is the beginning of a new year, it seems a good time to re-post the math word wall lists for you. Here they are, in English and French.

ENGLISH – PRIMARY
Kindergarten Math Word Wall Words
Grade 1 Math Word Wall Words
Grade 2 Math Word Wall Words

FRENCH
cheneliere-maths-1.pdf
cheneliere-maths-2.pdf
cheneliere-maths-3.pdf
cheneliere-maths-4.pdf
cheneliere-maths-5.pdf
cheneliere-maths-6.pdf
cheneliere-maths-7.pdf
cheneliere-maths-8.pdf

Here’s how I have used them in the past, in a grade 5/6 classroom displayed in a pocket chart…

Carole

As promised, I wanted to send along – or at least re-post – a mathematical process piece I mentioned in last week’s sessions.

The Strategies for Making Sense out of Mathematical Text are pasted below. The idea is that mathematical text can be a lot of things – a problem in the textbook, an equation to be decoded, a situational problem presented to a group of primary children, or a task to be solved involving number sense and the operations. When we engage with this kind of mathematical “text”, we use strategies that are similar to those we have been thinking about in literacy learning for a while now. (Think Faye Brownlie’s work, think SMART Reading…) The file is intended to mirror that for students, to remind them (and us! 🙂 ) that good thinking processes are good thinking processes, no matter what subject area we are dealing with.

The files are available in french and english, by clicking on the links below.

Strategies for Making Sense of Mathematical Text – English

Des stratégies pour aider la comprehension des situations mathématiques

And just to drive home the point, here is a summary of the mathematical processes drawn from our new BC Curriculum:

Mathematical Processes from the new BC IRP

plus ça change…
Carole

Well…
It must finally be summer. 8)

How do I know? I just read a book. Yes, cover to cover, and for pleasure.
(For those of you who know me well, this will come as a shock, I know.)

OK. So the fact that it was a MATH book affirms what people have suspected about me, and the reason that I have earned my nickname of Math Chick. The book is called “The Math Instinct – Why you’re a mathematical genius (along with lobsters, birds, cats and dogs)” by Keith Devlin.

Devlin is the National Public Radio’s “Math Guy” and has written several books. This one explores “natural math” – also called nature’s math – the math that has been programmed into us (and into dogs and lobsters, to name a few) through the course of evolution. Then he focuses on humans and their ability to mathematize – our innate capacity to estimate and design computational strategies that work for us. He uses compelling studies done in Brazil to compare street math and school math, and talks about meaning making and the essential role of context in developing mathematical understanding. He explores invented strategies, the problem with math tests, Fibonacci and shopping. He speaks to brain research and the role of first- and second-language in learning the facts.

Right until the last few pages of the last chapter I was grooving right along with him, seeing reasons for classroom experiences I have had, confirming for myself why we need to talk more in math class, celebrating the addition of visualizing, connection-making, mental math and estimation in our new curriculum in BC. The last few pages I will need to reassess though, since they seem at odds with Devlin’s earlier message of “meaning above all is what makes us a mathematical genius”. Guess I’ll just have to re-read. After all, what else have I got to do this summer besides counting the spirals on the pinecones dropping on the deck? (Data to date has been 8, 13, and 21…)

If you get a chance to pick up the book, do.
It’s worth a read.

Carole

Normally I hate pop-up flashing ads, but when this one appeared on-screen yesterday quoting statistics on how many girls drop out of math and science – because these subjects are not considered by girls to be something they can succeed at – I felt compelled to click and learn more.

Where I ended up was the Girls Go Tech site, compiled and supported by the american Girl Scout movement. I was impressed by the positive message and the friendliness of the site. They included a few on-line activities, talked about careers for women in the areas of math and science and technology and provided a link to a really great booklet to support parents in encouraging their girls to explore math, science and technology at home and outdoors.

Worth a read, me thinks.

Carole

I got wind of the following site from PBS today, and I wanted to share it. The site is aimed at parents, pre-school educators and early primary (grades 1 and 2) teachers. It outlines milestones with respect to mathematical thinking (number, geometry, etc) from ages 2 up, and presents some interesting games and – for the older children – on-line activities for developing these areas. Check it out!

Early Math

Hello to all the gang in Mission! I wanted to thank you for the opportunity to work with you all this evening. The more I work with teachers and administrators around instructional change, the clearer I am in my purpose and the more convinced I am we will get there.

I have attached some examples drawn from the resource called Lenses On Learning Instructional Leadership in Mathematics for you to look at. If you remember, we talked this evening about different strategies for thinking about addition, and I wanted to share strategies that are more sensible for thinking about subtraction (which, of course, I don’t believe we ever REALLY have to do… but I digress.) The pages I have attached are drawn from reproducible documents from the Lenses on Learning Module 1 for K-8 Administrators. The book and video are published by Dale Seymour Publications and are available through Pearson Professional Learning here in Canada.

Click below to open the file that outlines 6 different ways to subtract – each one explained, with references to the countries of origin…

6-ways-to-subtract.pdf

enjoy!

Carole