Here is another set of support materials for those wanting to play the “Roll and go game” from Math Makes Sense, Grade 3.

Click above for the instructions, which are drawn directly from the resource.

Try having your students record their patterns in 3 ways (and for a challenge, in 4) on the Number Pattern Three Ways form before exchanging their patterns with a friend.  Fold the bottom portion of the page back so that the pattern rule can’t be seen be the partner trying to guess it!  🙂

Alternately, the line master can be used simply to give students a place to practice representing patterns in multiple ways.  Hm… I wonder how we can get an action pattern in there??

Hello to the Whitehorse gang!

As promised, I have uploaded the line masters for the task we did today.  It is intended to tie together experiences of skip counting by a number (4, 8, 12, 16, etc), describing a pattern rule (we started at 9 and counted by threes) and using a hundreds chart as a tool for establishing and visualizing patterns.

So the job was to help me find the party at 35 “something” street – the name of the street was erased by the dog prints made by my puppy Porkchop who walked on the invitation.

Of course you are free to change the numbers in any of these scenarios to make the problem more or less difficult.  Remember that we are to use number patterns to 1000 in the new curriculum, so you might even consider a street in which the house numbers start at 200 and grow by 10 or 50 or even 100 each time as a more complex problem for later in the year…

To start, you’ll need houses.  Print (or draw) at least 6 for each street.  Number 4 of them (use sticky notes so you can change the “house numbers” for subsequent lessons) and leave 2 numberless to suggest that the numbers continue – just like the counting patterns we know…

tree

If you want to do the introductory tasks I modeled this morning, print off some trees.  Remember to leave 3 repeats of the pattern so that kids can predict the pattern rule for the street numbers before you cover a house-front or 2 with trees…

The invitation to the party is easily edited too, if you want to cover up the 35 and try another number instead.

Recall that the numbers I chose for the streets were:  

A STREET – 4, 8, 12, 16…

B STREET – 9, 12, 15, 18…

C STREET – 2, 5, 8, 11, …

and we were looking for the street that had the house number “35” on it.

Would make an interesting challenge to change the party house number to 48… then there’d be 2 possible streets where the party might be held! (ooo – I smell common multiples!!)

Enjoy!

Carole

Something I wanted to mention especially for my friends at early primary is this National Council of Teachers of Mathematics site. It’s a hundreds chart and a calculator applet – as you punch numbers and add to them, the corresponding numbers in the hundred’s chart are highlighted. it’s pretty cool – and very visual, which of course we all like…

Click here for the Hundreds Chart and Calculator applet.

Encourage your students to record their number patterns on the hundreds chart, then take a screen capture and print off their unique pattern.  Afterwards they can include a sentence describing their pattern rule.

it looks like this:

My pattern rule was fairly simple. Start at 2.  Add 2 each time.

Hm.  I wonder if I will hit 37? 54? 100??

🙂
Carole

OK, OK – I’d hate for you to feel left out!

For my colleagues who teach Intermediate Math, there are a ton of on-line resources to support you and your students.

Here are some of my new favourites:

Make 15 – You play against the computer, alternating you choice of numbers to create a set with a total of 15.  There’s GOT to be a way to win!

Math Search – You solve the equations (most with order of operations rules included) and then FIND the answer in a maze of digits.  It’s timed.  It make me a bit panicky playing, but I kinda like it.  :o)

Seesaw logic – oooo – I like this one.  For this game your task is to identify the heaviest object from a set on a number balance. It starts out easy and then you have to reason your way to a solution.  There are no weights or numbers indicated for the balances – just relative weights for the objects.  Neat!

Have fun!  Carole

I am always on the hunt for quality math games for our earliest learners – and am always pleased when I find some that DON’T require children to be readers!

These PBS games are a real find – A whole white board of tasks to use with students. Many are very very basic, and look at shapes and colours and patterns. Check out  Juggling George (pictured).

For a more challenging task (Grade 1/2), see Glass Palace.  George has to find the missing windows on a building with a front face reminiscent of a hundreds chart…

Juggling George

Hello to my K teaching friends in Kelowna!  I wanted to post some Kindergarten-relevant materials here, just for you…  All in one place and easy to find, as a follow up to our 2 days together.

Here goes:

Here is the line master for the book Five Black Dots:  (play around on your photocopier to have them come out right, back to back…!)

Five Black Dots

Here is the line master for the Roll It game (to practice one less than ideas… a precursor to subtraction).

ROLL IT

Here’s a book list of number sense related Math and literature connections for K and K/1.

Early Primary Number sense booklist

Here are a set of tasks and centres for K and K/1 classrooms – line masters, instructions, etc – and the Big Math Ideas to match!

big red bus

Take a Handful

spinners to 5

Take a Handful graphing grid

spinner to 2 & 5 frame

Odds and evens copy

Number 3 Ways

Number 3 Ways-five frame

Missing twos copy

Missing numbers2 copy

K_1 centres and BMIs

Enjoy!

Carole

So today I had the opportunity to talk with a group of educators – virtually – about the power of blogs in education.  Although we ended up cruising through my own blog specifically, there are some points to be made in general about blogs and their purpose and place in an educational setting…

First, the reason I blog is to communicate about mathematical thinking, best practice in numeracy and sound pedagogy with a wide and varied audience.  My site is visited by teachers, administrators, support staff, math coordinators, teacher educators, parents and students around BC and around the world.  It’s humbling to know that my words, ideas and beliefs are being broadcast so widely.  As a result, I feel a great responsibility to communicate and to share the best I can through this forum.  I know that the blog itself has been translated into other languages and is being read by many; perhaps even by people new to the education system in BC or in Canada, who are concerned with math teaching and learning… I hope that this window into what I believe mathematics could and should be – taught in a constructivist way, with open-ended tasks structured to address diversity and to challenge all learners – is illuminating, and that the tasks and links posted here are helpful in demonstrating the point.

And now for a little critical reflection… Truth is, I have learned a lot about myself as an educator by writing it all down here.  It’s interesting for me to trace back through the posts here and to see how my voice evolved over the last 2 years – how in establishing my purpose and my audience, I was able to focus the content and the message far more clearly.  I like my blog more now, and in reading through the statistics for the site, I can see exactly what it is that my readers/visitors like as well.  I know the kinds of posts that are most popular, the math games that get the most hits, and the numeracy topics that are most interesting to people.  I can also see what people are looking for in their “googling”; what terms they enter in a search engine to bring up the blog… fascinating reading for the insomniac among us…  :o)

I hope that some of you will consider blogging with your students, with your parents or in some educational forum.  For me it has rounded out my teaching – giving me a way to contact those with whom I work, to provide resources and a sounding board when needed, and to allow me a place to reflect on my own practice.  What could be better?

Feel free to add your comments below!

Carole

Hello to the gang at Beaver Creek – the first school with whom I have worked to have chosen Mental Math as an instructional focus for their school goal… wow!  You rock!  :o)

I have attached a fleshed out list of  mental math strategies for you.  As mentioned, they would be great to put on the wall with an illustration of each one…  Remember that think alouds will certainly help – as you model for the children, they will hear the language they need to describe their mental math strategies!

All the best,

Carole

OK, OK.

I never really understood what Pokémon were until I saw a young friend of mine playing the game – and watched him manipulating large numbers effortlessly…  So I decided to use the context of the game to help grades 2 and 3 students work with number sense and operations to 100 and to 1000.

Here’s what I did.

First I created some visuals for the kids.  I printed images found on the internet – some of the cutest of the Pokémon characters – and put them on the board. Then I attached prices to each of the characters: 17¢, 13¢, 20¢, 31¢ and 59¢.  I asked the kids which one they would like to buy, and everyone certainly had an opinion!  Next, I told the children that they had $1, or 100¢ to spend at my store, and that they could buy any Pokémon they wanted to – or even combinations of characters.  I asked them to find as many ways as they could to spend their money.

I laughed when I saw how energetically the children attacked the task, buying singles, combinations and multiples of the characters.  Some even volunteered how much money they had left after they had done their purchasing – a nice extension for those who are ready.

While we debriefed, we talked about their strategies for choosing and combining the prices.  There were many interesting ideas shared around adding tens then ones, and using doubles…

We also used this context to practice finding the difference or the missing part. I gave children 9¢ to spend at my store and told them they could choose any Pokémon character they wanted – IF they could tell me how much MORE money they needed to buy that particular one.  In effect, we were solving these problems: 9¢ + ∆ = 17¢, 9¢ + ∆ = 31, etc.  Children used number lines to show how much more they needed to get to the desired cost.  The idea of adding up through tens came across over and over…

For Grade 3’s, I worked with the 3-digit numbers. We assigned a point value to each of the Pokémon characters (either 250, 125, 75, 400 or 325) and I challenged the children to match – but to not exceed – my total of 1000 points using cards from their “deck”.  The strategies once again were great, and focussed largely on the 100’s – a brilliant use of front-end addition.

If you would like to download the pokemon images and the pokemon prices & points, feel free – there is a LOT that can be done with these materials, including comparing and ordering of the costs, etc…

Have fun!

Carole

PS – Thanks, Mason!

Check this out!  Reminds me of an electronic version of Tri-Ominoes from my youth!  Students arrange small triangles within a larger one to make sums of ten.  Strategic and challenging practice!

One Big Triangle

Carole

For my ever thought-full friends in the valley…  

Here are the shape and space/measurement tasks we did this evening, aimed at intermediate.

Thanks for keeping me company in the sunshine tonight!  

Click below for the full selection!

shape-and-space-tasks

Enjoy!   Carole

Math Central is an award winning site  maintained by faculty and students in Mathematics and Statistics and Mathematics Education at the University of Regina in Regina.  It exists in both English and French (and Spanish!!) and features famous mathematicians, teacher resources, even a problem of the week…

Enjoy!

Math Central

I stumbled upon some pre-school or Kindergarten appropriate links on the BBC website the other day that I thought I send along.  They are great for non-readers because all of the text is spoken aloud.  Each task can be adapted because there are different levels of difficulty.  The visuals are simple and the ideas are conceptual (subitizing, etc)….  In short, a gold-mine for pre-K and K teachers!  :o)

Enjoy!  Carole

Number Jacks (this asks kiddies to connect the shape of the numerals to examples from the environment…)

More Number Jacks (this is a set of different, very simple games – concentration, dominoes, etc)

Counting tasks(Talks you through the steps, different levels – encourages subitizing or recognition of sets…!)

Count the germs! (perfect for this flu season – really cute, and a bit challenging, too!  I got to level 3…)

When children make meaning of the operations they do so by modeling the action in the problem or situation they are given.  Sometimes that action is joining, sometimes it is separating and sometimes it involves comparing.

This week, I worked with students in grades 1 and 2 to explore 2 things – how the structure of the problem posed changes the strategy used, and how students’ strategies evolve depending on their developmental level.  All of this is drawn from the work of Fennema and Carpenter, who have written a book called Cognitively Guided Instruction.

The problems we used in grade 1 and 1/2 this week were based on this work, and set in the context of a story- Too many Frogs, by Sandy Asher, and I’m the Biggest Thing in the Ocean by Kevin  Sherry.  

I read the first book and asked children the following problem, a separate problem:

There are 8 frogs listening to the story.

Some went to the kitchen for snacks.

Five were left listening on the chair.

How many went for snacks?

I told the story problem at the board using simple pictures:

chair

fridge

frogs

The second problem involved measurement, and asked students to compare to find the answer.  It read:

Squid is 8 shells long.

Crab is 2 shells long.

How much longer is squid than crab?

I worked through how we might measure using “shells” – my own invented non-standard unit…!  :o)    Students modeled their thinking using unifix, having practiced with a similar task done earlier in the lesson…  The line master for that task is here: comparing handfuls.

Try these tasks with your children and observe carefully what they do.  I am curious what kinds of strategies you’ll see!  To read a summary of Fennema and Carpenter’s work, check out the Teaching Student Centered Mathematics grades K-3 book by John Van de Walle – it’s in chapter 3…

Carole

Here is the link I promised to the BEAM site, featuring the Math of the Month.  I love these games!  They are organized by strand, topic and age level, so they’re really easy to search.  WARNING:  The paper default size is A4 – be sure to set it to LETTER size if you don’t want to mess up your printer.  :o)

Carole

PS – Check out the Addem Cartoons as well!

I have been meaning to share this link for a while.  Clicking on it will take you to a page of resources produced through the Nova Scotia Department of Education.  It is a series of videos of classrooms in which early primary teachers (grades 1, 2 and 3) work on important mental math strategies with their students.  Each video is about 8-10 minutes and well worth a viewing.  They look to be producing videos for grades 4 and up as well, although the page has remained unchanged for the better part of a year, I am afraid.  

The Ministry of Ed in Nova Scotia has likewise produces a series of viewing guides, which I have “prettied up” and have attached for your use.  Each viewing guide is matched to each of the videos indicated above.  Perhaps your school staff or primary team could view the videos and have a collaborative chat about the strategies used…?  It’s ALWAYS best to learn these things together!

Enjoy.

Viewing Guides:

viewing guide 1 grades 1-2 introduce-make-ten-strategy

viewing guide 2-grades 1&2 reinforce-ten-frame-strategy

viewing guide 3 grades 1&2 assessing-students-strategy-selection

viewing guide 4 grades 2&3 near-doubles-strategy

viewing guide 5 grades 2&3 reinforce-make-ten-with-12-digits

Carole

This is a gift for Tamara and her amazing kids…

I put together some place value “tents” for modeling decimal numbers to 100ths, that I thought you might find useful.  They are, of course, untried, but if you do use them, let me know what you think and if they need tweaking.  These ones will nest in reverse – that is, i the number 3.21, the largest tent is the 0.01, the medium sized one is the 0.2 and the smallest is the 3. (3 and a decimal point with no numbers following… technically the decimal should not be there, but I THINK it makes sense conceptually when it’s modeled with the kids.)

carole

decimal-numbers-wholes

decimal-numbers-tenths

decimal-numbers-hundredths

Hello all…

I wanted to post the cards for creating nested 3-digit numbers – tents of paper that show, for example, how 357 is the same as 300 and 50 and 7…  Print the files below onto bond and cut them out, then fold them into tent shapes.  They’re a great resource for supporting children in understanding larger numbers – and REALLY making sense of the digits.  Clicking on each of the files below will give you enough cards for a class set – so check before you print then all!

place-value-numbers-100

place-value-numbers-10

place-value-numbers-1

Also, for Laura – some on-line games I thought you’d enjoy around developing place value understandings…  Have fun!

100 Hunt

Give the dog a bone

Woodcards

The Add 9 Fairy

For my friends…

I have attached some of the missing pieces you were looking for, namely, 

build-it-spinner

spinner-6-to-9-dots

good-questions-for-math-thinking

giant-ten-frames

doubles-snap

doubles-plus-one-snap

where-is-the-party

my-numbers-and-what-i-did

Big Red Bus

enjoy – let me know if i have forgotten anything…

carole

I made a set of images that people might like to use as models for thinking about the doubles facts.  The ideas come from the work of John Van de Walle – I just added the clip art!  Enjoy!

the-doubles

Carole

PS – The double nines are drawn from the image of an 18-wheeler… 2 wheels on the axel of the truck (under the cab), then 4 on the next axel and 4 on the next, then 4 and 4 more on the last 2 axels…  Tricky, but apparently THAT’S what makes an 18-wheeler an 18-wheeler!