Grade 10 Math tasks
Hello to all the Grade 10 teachers who spent the day with me today, planning the first couple of units for next year’s new grade 10 courses.
As promised, I am sending along some of the tasks and links we explored today. I hope they prove helpful as you plan your instructional flow for the new year… I am looking forward to meeting with you again in the fall, and to continuing the conversation as you implement the new curriculum.
grade 10 tasks for CR – follow up
In addition, I wanted you to have access to some of the e-demos and applets that I showed today. I know they will help to model the important math concepts you’re addressing with your students.
All the best!
Carole
http://tinyurl.com/polyhedra-unfolder
http://tinyurl.com/surface-area-cylinder
http://tinyurl.com/volume-of-a-sphere
Ten Frames for the SmartBoard
If you are looking for a way to digitally manipulate ten frames on your classroom SmartBoard, then please help yourself to the file I worked on… It’s appropriate for whole number or for decimal number explorations. Games and tasks are suggested on the notebook pages, and regardless of whether you’re using the materials in primary or intermediate, they address the same concepts of part-whole or partitioning…
Because wordpress would not allow me to upload this file format, a colleague has graciously posted the file for me.
My thanks to Anita Strang of Coquitlam for including this file in her district storehouse of SmartBoard ready math resources… The file is called “Ten Frames basic” and was created in April 2010. And while you’re there, you should really check out other items on the list – you’ll even find some of my favourite primary math games from BEAM made into SmartBoard enabled files!
Carole
The game of remainders
Hello all!
I wanted to post the instructions for one of my favourite hands-on division games, called The Game of Remainders. Each pair of students needs 15 counters, 6 small paper plates and a die, as well as a piece of paper and a pencil. The instructions can be downloaded by clicking on this link: game of remainders.
The big Math Ideas include:
When we divide, we share into equal parts. Division sentences describe the action of sharing.
When we divide, most often there is a remainder.
What we do with that remainder counts.
Played strategically this game can address notions of prime and composite numbers and can support students in connecting multiplication with division… My thanks to Marilyn Burns fo this engaging task!
Enjoy!
Measurement in Primary – The Big Ideas
For my colleagues in Coquitlam, with apologies for the delay!
I wanted to send along a list of the “big ideas” in measurement for primary grades. As you recall from our conversations, the primary curriculum has changed with respect to the measurement strand. The learning outcomes promote exploration and comparison in a developmental way through grade 3, when we introduce standard units of measure like cm and m.. In considering lessons for primary then, it’s a good idea to construct experiences around the big ideas, such as the following…
• When we measure, we compare.
• When we measure, it’s a good idea to line things up – to use a common baseline.
• When we measure it’s important to use the same units (all unifix or all straws for example and not a mixture of them)
• Mathematicians know that when we change the size of units we use, we get a different measurement for our object.
• There are many aspects we can measure. (height, mass, capacity)
• It’s a good idea to choose big units to measure big things and small units to measure little things.
• When we can’t bring 2 things together to compare them – like a door and a window – or when something is curved, we can use another object as a measurement tool (like a piece of string). Mathematicians call this indirect comparison.
• We can measure how many units it takes to cover an object – to see how much space it takes up.
• Mathematicians use personal referents when they think about standard measures – like the width of a finger (1 cm) or the length of a giant step (1 m).
I hope this list proves helpful.
Carole
Fun online game – working with doubles
I was cruising around this morning and came across some of my favourite games for practicing mental math strategies. Check out this cool game called dinosaur dentist… It asks kids to find the double fact that matches the number of teeth in the dinosaur’s mouth, then to subtract one tooth (the black one) to find the doubles less one fact! The pain-free dino does a dance to celebrate afterwards. Very cute!
The next game is called Woodcards. It uses the idea of partitioning to help kids see how they can apply doubles strategies to much larger numbers. The cards with the digits printed on them slide apart to help students remember they are talking about tens and ones! It pairs the numbers with abacus sets to represent the values. This is a good game for late grade 2 or grade 3.
They are part of the most amazing and conceptually grounded sets of games for developing number and operational sense in primary students. They are really fun (yes, even for me!) and the graphics are great too. Check them all out at ICT Numeracy Games. Developed by James Barrett to match the very evolved British curriculum, they are focussed on mental math strategies and help target those ideas in early learners.
Have fun!
2010 Olympic Data – A rich interactive site!
For those of you who just can’t get enough of the Olympic Games, here’s a remarkable site hosted by Vancouver 2010 that is well worth checking out. In this interactive Java applet, the results of the Olympic games are stored, sorted and available for manipulation by your students in a really accessible graphic form. Selecting different attributes like “number of gold medals”, “number of male athletes” or even a specific event changes the size of the green dot for each country on the world map.
Hovering over the dot gives you numeric information, and clicking on it expands the window to get a closer look by country.
There’s way more to explore and compare – take some time with your students and have them investigate their questions. They can even go back in time to 1924 and look for trends in the data throughout history…
Enjoy!
Carole
Kindergarten & Grade 1 math games – mastering fives & tens
I am, as many of you know, a great fan of the games produced by the good folks at BEAM. They are conceptual, strategic and focus on the big math ideas across the grades. One of my favourites is “Totally Ten Snake”, in which two players take turns covering pairs of digits that add to 10 along a “snake” of numbers. When all the digits are covered – each player using his or her own coloured counters – the winner is the one with the longest string of digits covered in their colour. In the example below, red wins, with 4 in a row at the end of the game against purple:
Well, I love this game a lot, and when played strategically it can engage kids across the grades (and even adults at my workshops!). That said, I thought it was worth re-jigging the game for children who are younger, and for those who need support to focus on quantity rather than on the digits as set out in the original BEAM game.
These edited games are geared towards understandings of 5-ness and ten-ness, and use dots in place of digits. The rules are the same as in the original. You can download your own version of Terrific Ten Snake or the easier ten frame 10 snake and/or the Fabulous Five Worm by clicking on their names…
Enjoy! Carole
PS – If you’re looking for more ideas like this for K and grade 1, consider purchasing a copy of my book: Number Sense – A Combined Grades Resource for K, K/1 and Grade 1 Math Classrooms. It’s set up to support teachers in addressing the number PLOs in mindful ways while keeping their Kindergarten and Grade 1 students together. Games, tasks, problems and meaningful practice opportunities are included in English and in French. To order online, click here.
Explaining the derivation of the Area of a Circle – Grade 7
So… we all know that the formula of the area of a circle is 
.
But have you ever considered why? Students in Grade 7 need to understand the derivation of this formula and apply it to different situations. My husband sent me these awesome on-line demonstrations of how the area of s circle is derived, using what we know about triangles. Consider these images and what they show. First, the circle is chopped up into roughly triangular segments.
They are put together to form a parallelogram, in which the base is 1/2 of the circumference of the original circle.
The height of the parallelogram is the same as the radius of the circle (since each of the triangles is a section of the original circle).
To find the area of the parallelogram, we multiply the base times the height, or 1/2 of the circumference of the circle x the radius of the circle. Consider it in this more abstract language:
1/2 ( 
) r which simplifies to
Cool, huh?
It’s WAY more effective to watch the video of the event. Check it out here!
Carole
PS – There’s another derivation that draws on the area of a triangle… I won’t wreck it for you, but consider this… The base of the large triangle here is the whole circumference of the circle, or 2πr. Each of the little triangles that make it has a height the same as the radius of the original circle. So that means that the area of this large circle is 1/2 base x height, or 1/2 (2πr) x radius/ Familiar?
Olympic Fever! Primary Math tasks around the 2010 games…
My apologies to my colleagues in Coquitlam – I promised to post this over the weekend, but ended up riding my bike to the Olympic sites downtown – and was completely overwhelmed by the celebrations…
The 2010 Olympic Games are in full force here in Vancouver, and I for one couldn’t be more excited – or more proud – to live in this city! Kids everywhere are getting right into the games and patriotism is at an unprecedented high. So, with that in mind, I structured a math lesson with an Olympic spin for primary classrooms. The big math ideas of this lesson highlight 2 things: “We can find the sum using 3 addends”, and “We can make ten in many ways.”
I had a great time engaging with students in Kindergarten with this task – but I’d suggest there are ways to extend it all the way through Grade 2, depending on the questions you ask. Here’s what we did.
I told the kinders that I was a volunteer with the Olympics and that my job was to figure out for each event who had won and how many medals each country had in all. I told them that I had to produce a report for the Olympic Committee to show how I had figured it all out. I began by talking about the different kinds of medals we could win, then told them the names of the 3 countries I would be comparing – China, the US and Canada. We modelled a possible solution for one event (the speed-skating event) and figured out a way to record and compare the results.
Students went to tables and, working in partners and alone, modelled and recorded solutions for each of the sports that I was in charge of – namely Snowboarding, Bobsledding, Curling, Skiing and Figure Skating. They were VERY excited to discover that Canada had won each event… With a coincidental score of 10 medals for each and every event! 🙂
Next, we compared the different ways we can make 10 (1+8+1; 3+3+4, 5+3+2, etc) and focussed on how each set made ten, no matter how we added them – a big concept for the primary grades.
To take this context and the math even further, students could compare the number of medals earned by each country and calculate the difference between each country’s total. At later grades, students could sort out how many gold, silver and bronze medals were handed out, and then how many medals were awarded in all.
Hopefully there’s something helpful in these materials for you to use in the next while. Get the results by country and by sports, images of the medals and an image to match each sport here…
Go Canada!
Carole
Decimal games for Grade 4
This one’s for Duncan… 🙂 
After woking in West Vancouver yesterday, introducing addition and subtraction of decimal numbers to Grade 4 students, I was encouraged to edit a game originally designed for basic place value in primary to be applicable to decimals (to tenths).
You can download the Closest to 10.0 – decimal game instructions and game cards here.
The idea is that students choose 2 decimal numbers from the set that will get them closest to 10.0 when added together. The closer sum wins, and play continues until all the cards are used up.
The more interesting tool to accompany this game is the Decimal “Hundreds” Chart. Although there are indeed 100 numerals on the chart, they largest is 10.0, not 100. The purpose of this tool is to explore patterns in increasing decimal numbers, and to explore adding and subtracting whole numbers and tenths. Have students place a counter on 0.1, then roll a die with the following faces:
+ 1.0, +1.0, -1.0, +0.1, +o.1 and -0.1
With each roll, students move their counter according to the instructions, racing against a partner to “Get to 10.0”. It’s a simple game, but reinforces what happens when we increase or decrease a number by tenths and whole numbers. Once students are familiar with this pattern (down a row is like adding 1.0, to the left one is like subtracting 0.1… etc.) they can use the hundreds chart to add larger numbers and to find the difference between decimal numbers (ie: adding 2.3 is like moving down 2 rows then to the right 3…).
Have fun!
Carole
More primary games for developing number sense!
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
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
Grade 9 – Algebraic Thinking Tasks
Hello to the hard-working and deep-thinking teachers of Coquitlam!
I have attached select slides from today’s presentation on algebraic thinking, to remind you of the tasks that we did as a group, their purpose and how they connect to the PLOs for the Grade 9 Patterns and the Grade 9 Variables and Equations strands. Remember that the curriculum is very clear that students must model their algebraic thought – and we can do so with materials like pattern blocks (the shapes you used today to make your growing patterns and tessellations), base ten blocks, colour tiles, two-colour counters and algebra tiles.
Each of these materials is available through Spectrumed.com. The selection and rates are better if you access through the elementary math catalogue rather than the secondary one…
Enjoy!
Carole
Grade 9 Circle Properties… on YouTube!
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…. :o)
Try these instructional videos: 
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…
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
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
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!
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
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
Mathematical Thinking 