Math and The Holidays December 14, 2009

Happy holidays, everyone!

As someone who – this year – will celebrate both Hanukkah and Christmas, I wanted to re-post a couple of seasonal problems for you…  There is math everywhere!

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

Protected: Grade 9 Math – Circle Properties November 30, 2009

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More primary games for developing number sense! November 23, 2009

Thank you for coming this evening in such numbers to play and talk math!  It is so important that we work conscientiously on developing number sense in our students – the ability to compare sets, to build and represent number in many ways, to partition and decompose number – in advance of working with the operations…  Laying these foundations is so critical to success…

For those of you who did not get a handout this evening (whew! 32 more than I expected!), click here to download the games for k-3 number sense.

And, as an added treat, Jennifer passed along this HIGHLY addictive game for finding the complements to ten called math lines.  If you can get past the ads on the host page and focus on the math, it’s really fun – an JUST like a game called Zuma that I have on my iPhone…  :)

Enjoy!

Carole

On-line applets for Grade 9 Algebraic Thinking October 28, 2009

 

2x squared plus 7x plus 4

Hello to all those exploring the new Grade 9 Math curriculum!  The new prescribed learning outcomes for this curriculum are very clear – students need to model and solve linear equations in various forms, and apply the operations to polynomial expressions concretely, pictorially and abstractly.

 

So – sounds like we’ll need some tools to do this justice, right?

Here are some of my new favourite on-line applets for exploring these big ideas in the curriculum.

First, the National Library of Virtual Manipulatives, which is a treasure trove of materials.  They can be used on a Smartboard or on a laptop projected onto a screen in your classroom.  You can even suggest students use these free materials to support them with their homework and access the links at home!

National Library of Virtual Manipulatives – materials across the grades and across the strands

Algebra Tiles – for modeling and solving equations.  This includes the Guiding Tiles tray, and a “y” tile for later explorations.

Algebra Balance Scales – for positive integers

Negative Algebra Balance Scales – for negative integers

Virtual Pattern Blocks – for increasing patterns, for tessellations, for exploring operations with fractions

Rectangle Multiplication – using an area model to look at multiplication

Area model for multiplying integers – based on the 4 quadrants on the Cartesian plane

Hope these are helpful…

Carole

Protected: Grade 9 – Algebraic Thinking Tasks October 28, 2009

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Grade 9 Circle Properties… on YouTube! October 21, 2009

OK.  I gotta get me a TV.

I was working through some of the content for the Grade 9 curriculum and stumbled upon some YouTube videos that might be helpful.  The teacher who does the demonstrations is lovely, although the comments below her vids aren’t particularly kind.  If you show these to your students, consider using a full screen mode so they don’t see the nasty comments…. )

Try these instructional videos:  

What’s a Tangent?

Arcs and Chords – problem solving to find the radius

Tangents and circles – problem solving

Inscribed angles problem-solving (quadrilaterals)

And for a lark, check out this “music video” that reviews the important parts of a circle (diameter, radius, pi, circumference, etc…).  Hey – I’ll try anything at this point!

If anyone out there has any gems to share in the way of interactive applets to demonstrate the circle properties (tangent to a circle, inscribed angles, bisected chord, angles in an inscribed quadrilateral) I’d be most grateful!

Carole

Pythagoras was here… a cool interactive applet… October 21, 2009

Check this out!

My tech-savvy husband Tom put me onto a great free and open-source application called GeoNext.  It is powerful and intuitive software for creating and demonstrating geometric principles and properties.  The link below takes you to a site that makes use of the software for demonstration purposes, but also poses a range of problems for students to explore while using GeoNext.  The problems are in French, but the software can be downloaded and used for free by anyone.

Take a look at this really neat visual representation of Pythagorean theorem…  Try moving point C…. This demonstration makes the theorem VERY visually clear.

GeoNext demonstration of Pythagorus

OK, so if you want to watch some You Tube demos of Pythagorus, check these out!

The Math Lady solves a simple right angled triangle problem, and explains step-by-step how to do it…

and a bonus video on Pythagorus  - a ladder problem explained

Carole

Grade 9 tasks and games – number October 21, 2009

Hello to the gang in Campbell River!

As promised, I have posted some of the tasks we did together last night that touch the grade 9 curriculum – and other grades too, depending on how they are used…

Click below to download select slides from the presentation last evening:

Rich tasks for Grade 9 – Games and Good questions

Check out my next post for a really cool on-line connection to Pythagorus!

Carole

The big math ideas – grade 2/3 October 21, 2009

Hello to my friends in Coquitlam!  Here are the slides you were looking for, outlining the Big Math Ideas for grade 2/3 math – or at least for the first part of the year!  Remember that in teaching in the way (considering the enduing understandings) it is far easier to stay sane as a combined grades teacher!  :)  If we find the commonalities and focus on them, we can teach to the whole class, rather than splitting them up!  Phew!  I feel saner already!

Here are some supports for you:

First, the document from the Island Net Group – the At-a-Glance form that looks at combined grades and how the PLOs connect across side-by-side grade levels.

Grade 2 and 3 PLOs at-a-a-glance

The big ideas in Patterning and Number Concepts for Grades 2&3

Ordering information for Pearson’s Math Makes Sense Combined Grades resources, which take a day-by-day approach to planning, connecting lessons at side-by-side grades using the new WNCP versions of the Math Makes Sense program.  These documents exist for every grade combination from 1/2 to 7/8, with some available immediately and others coming December, 2009.

Enjoy!

Carole

100,000 hits! October 9, 2009

Holy cow!  Math education is alive and well….!  

Yesterday marked the 100,000th hit on this blog!

I credit my husband Tom who encouraged me (ok, TAUGHT me how) to set up a blog in the first place, and you, the people who read the posts and access materials to support your students.  We hail from all over the world (check out the map on the right hand side!) Yay us!

Happy Thanksgiving, all!

Carole Fullerton

(formerly Saundry)

Printable Games for Grade 3 Number sense September 28, 2009

One more thing to share this evening for the gang in Whitehorse!

As promised, I wanted to post the games for practicing number sense and operations as connected to our Grade 3 math curriculum.  There are many more tasks where these came from – and they are available for students as young as 3 years of age – so do explore on your own if you have time.  Consider the range of learners in classrooms and how we could support them in coming to real conceptual understanding by using games as the medium!!

Download the Grade 3 Number sense package here.

Then try exploring the BEAM Maths of the Month site for more tasks!

Enjoy…

Carole

Number Patterns for Grade 3 – Pattern 3 Ways September 28, 2009

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??

Where’s the party? Number Patterns for Grade 3 September 28, 2009

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

Hundreds chart and calculator applet! September 27, 2009

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

Intermediate on-line math games September 26, 2009

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

Pre-school and early primary on-line math games September 24, 2009

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

Kindergarten Math Materials September 3, 2009

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

Reflecting – critically – on blogging in education August 25, 2009

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

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!