Mental Math Strategies June 1, 2009

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

Pokémon math! June 1, 2009

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!

Cool game for make tens strategy – primary April 16, 2009

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

Shape and Space Tasks April 6, 2009

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

Great bilingual site for teachers and students… Check it out! March 29, 2009

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

More on-line applications for early primary March 29, 2009

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…)

Frogs, Snacks and Squids – Modeling the operations in grade 1/2 January 18, 2009

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

50,000 hits!! December 16, 2008

Oh, but my mathematical soul is bursting…!  Today this blog hit 50,000 hits!!!

In the last 2 years, teachers, parents, students and others have clicked on this blog fifty-thousand times to explore mathematical ideas and to share what they are doing in their own classrooms.

whoa. My head is spinning.  :)

 

As a holiday gift (to thank you for 50,000 hits to my self esteem!), I’ve put 2 seasonal problems out there for you…

 

The first:

There are 8 days of Hanukkah. For each of the 8 days, a candle is lit and placed in the menorah – one on the first day, 2 on the second day etc.  Sounds simple, right?  Well, yes and no.  Understand that by the end of each day, these candles burn out and have to be replaced.  AND these candles are lit by another candle, called the shamash.    

So.  If you had to buy enough candles for this year’s menorah, how many would you buy in all?  

 

 

And another problem…

 

There are twelve days of Christmas.  And according to the song, there were a lot of gifts given over those 12 days.

Tamara shared this awesome website with current prices for the items given over the 2 days – including shipping and handling changes – so that you too can figure out what it would cost to give 5 gold rings, 4 calling birds, 3 french hens, 2 turtledoves and a partridge in a pear tree… let alone financing the maids a-milkin’!

Happy Hanukkah Ho Hos!

Carole

BEAM maths of the month -Games for preschool to grade 7 December 8, 2008

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!

Mental Math in Primary – Videos & Viewing Guides November 30, 2008

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

 

Place Value – decimals November 26, 2008

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

Place Value Materials November 24, 2008

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

Primary games – spinners and more November 19, 2008

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

The doubles… November 13, 2008

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!

the new math curriculum documents November 10, 2008

For those of you (like Sylvia) who are looking to find the Prescribed Learning Outcomes (PLOs) and Achievement Indicators for the new math curriculum related to your particular grade level, here they are!  :) You can print off the whole package (K-7) or just the grade(s) you teach.

ministry of education – math irps

Carole

De-mystifying the multiplication chart November 9, 2008

Here is a post for Hilde and friends…  

I promised to send along my powerpoint slide with the animations to show how the multiplication chart is full of patterns – and how learning strategies for mastering the facts makes it manageable. 

hope it’s helpful.

demystifying the multiplication chart powerpoint

The Order of Operations Bowling Game November 6, 2008

Here’s a game we played today in grade 7, to practice and apply the notion of order of operations – that when you have a string of operations to perform, it matters in what order you apply those operations.  It’s a bowling game. The goal of the game is to “knock down” as many of the 10 bowling pins as you can, by creating number sentences from 3 digits rolled at random by the kids.  Students can use any operation, even exponents and brackets to create a true statement for each of the numbers.  This is a fun and engaging game – and students will work hard to practice and apply their understandings of “BEDMAS” or “PEDMAS” to get a “strike”… We did today – knocking down all ten pins with equations created with only the digits 1, 2 and 5!

order-of-operations-bowling-game

The game comes from Marilyn Burns’ website (www.mathsolutions.com) where she features sample lessons drawn from her extensive collection of teacher resource books – all free.  The tasks range from k-8 or 9 and are conceptual and fun.  Check them out at her site: Lessons from the Classroom

Enjoy!

Carole

Magnetic Tape November 2, 2008

Doesn’t SOUND like a math post, does it?  Except that I have shown this stuff off at so many workshops lately and feel compelled to share what this extremely useful tape looks like….

I have been buying Modern Craft Magnetic Tape on a tape dispenser at my local dollar store (Richmond, BC).  I stick it onto the back of all sorts of printed images (penguins, lips, red and yellow apples…) to model children’s solutions to open-ended math problems.  When a child tells me that there were 13 apples in a bag, and that 6 of them were yellow and 7 were red, I like to be able to model that solution so we can “check it” as a class.  Using magnetic tape on the back of a simple image (clip art is magic…) allows children to move the pictures and re-create their thinking on the white board in front of their peers in a representation all can understand – and see – from the back of the room!

Carole

fun in coquitlam! October 30, 2008

Wow… I LOVE working with you folks.  :)

OK – I am taking care of my to do list… Here is the stuff I promised you.

The labels for the wooden dice are here, so you can play “tens and ones” on the hundreds chart:  

tens-and-ones-dice-labels3

ten-and-ones-game

 

 

 

The instructions – and game cards – for the game “Get to a 100″ are here:

get-to-100-instructions

get-to-100-number-cards

I know I promised you more, but I can”t remember what!!  eek!  send me a message here if YOU remember what I cannot right now…

Carole

Integer Magic Square! October 29, 2008

oooo – This one’s tricky!  Just ask the students at Whitehorse Elementary!

Get your students to cut apart the number cards (digits ranging from -3 to +5) and have them place them in the magic square cells so that each column, row and diagonal has the same sum.  

What’s the sum? Well, there are MANY ways to do this puzzle, so that’s negotiable!  This is best done in partners, since two brains are better than one…

A hint?  

Order your digit cards.  What do you notice about the number in the middle?

Does that help??

enjoy!

integer-magic-square

Carole