The NCTM (National Council of Teachers of Mathematics) has a set of online math resources worth looking into. Check out Calculation Nation (calculationnation.nctm.org/) for a series of challenging and engaging games for students in grades 3-9. Students will explore factors, prime and composite numbers, multiplication, area and perimeter, operations on fractions, solving algebraic equations and geometric concepts like tessellations and symmetry. Students can play these games against the computer or even against another player somewhere else in the world!
A simple log in is all that’s required in order to play.
I’m sure you’ll find some worthwhile tasks in this set of carefully crafted materials. Enjoy!
Sandra Ball and I have been at it again!
We have just put the finishing touches on another assessment tool for use in fall of the year. It’s a companion to the other “What Do They Know” assessments featured above, but are designed for students in grade 2 and 3.
Focussed on place value, partitioning and skip counting, this tool highlights number sense and the operations. The tool is administered by the classroom teacher and involves the whole class and small groups.
If you’re interested in piloting these materials, please feel free to contact me for the password using the form below. The Teacher’s Guide and support materials are available for download by clicking on the link above.
I hope it proves helpful to you in getting to know your learners and what they’re truly capable of!
Sandra Ball and I are pleased to announce the release of our newest collaboration, entitled Daily Math Investigations: Meaningful Math Routines. The resource is intended to present alternatives to a traditional calendar time – ways to keep our students actively engaged in the learning of mathematics in meaningful, hands-on and developmentally appropriate ways.
In the resource, you’ll find a set of thoughtful tasks that promote visual spatial capacity, number sense, operational sense, data and measurement concepts. Each is presented in the form of both entry tasks and rich routines, intended to keep your youngest students thinking and reasoning mathematically. The complete resource, including a selection of classroom-ready line masters, is available to download for free, by clicking on the tab above. That said, the post is password protected, so please complete the form below to contact Carole for the password!
We sincerely hope that this resource provides you with practical, fun and engaging ideas for use your primary classroom – ways to ensure all students are doing math every day!
Carole and Sandra
Between holidaying in the Maritimes and gardening in Montreal, I have been busy writing this summer – putting together a volume devoted to teaching the operations in primary. And so, I am pleased to announce the publication of my latest teacher resource: Sums and Differences: Teaching Addition and Subtraction in Grades 1&2.
This resource includes a series of lesson sequences – open tasks, games, written practice, word problems and assessment support – for teaching the operations in a developmentally appropriate way. Beginning with place value explorations, these lessons increase in complexity while providing support for students across the grades. The lessons make explicit connections between concrete, pictorial and abstract representations of the math to ensure the operations are truly mastered.
The content in the book covers the grade 1 and 2 curricula and presents them in such a way that teachers of combined grades can use the lessons to work with their classes as a whole.
All the best!
Who knew it could happen.
My little blog has been clicked on, read, shared and accessed 500,000 times since its inception 6 years ago.
It freaks me out just a little, and makes me immensely proud at the same time.
A half a million anything is a lot – almost beyond comprehension. So the mathematician in me did a little searching. You should know that…
- 500,000 is a little less than the number of minutes in a year.
- If you started today and counted to 500,000, you’d finish about 2 weeks from now.
- 500,000 is the number of times you’ll blink in the next month.
- If you made a stack of $500,000 in $100 bills, the pile would be almost 60 cm tall.
To all of you from around the globe who have visited, my sincere thanks for stopping by.
…and come again. :)
I have attached a short list of some of my favourite math and literature connections for intermediate and secondary classes. It follows on the heels of a workshop I gave yesterday in Maple Ridge, in which we explored important mathematical concepts in a series of engaging reads. There is so much math potential in each of these stories that they can easily be shared with learners across the grades – either as a way to introduce a new topic or to present a context for a meaningful mathematical exploration.
I hope you find these titles - and links to the mathematical concepts they address – helpful.
I am pleased to announce the publication of my latest teacher resource book called Fair Shares – Teaching Division in Grades 4-7. The book features tasks, games and problems for intermediate aged students focussed on making sense of division.
Through stories, models, pictures and words, students are introduced to the idea of division as sharing and division as grouping. Lessons include opportunities for talk, for exploration and for practice in the form of games and engaging tasks across the grades. The lesson sequences are designed to address division of whole numbers and decimal numbers, to make meaningful connections to fractions and decimals in context and to support students in seeing patterns in quotients. Lessons map out how to use manipulatives to model division situations, and literature connections to introduce great division contexts. Match to the WNCP curriculum, Fair Shares – Teaching Division in Grades 4-7 outlines a range of assessment tools to allow teachers to gather evidence – quickly and without stress on the part of the students – to show what their learners know and can do.
Thank you, as always, for your support.
I discovered this engaging game a week or so ago and wanted to share. It’s called Deep Sea Duel. In the game, you match wits with the computer in the form of an octopus called Okta. (She’s the same character as in the iPad game called Pick-a-Path, below). When you square off against Okta, you can choose the level of difficulty and her level of “nastiness”. Good thing too. It took me a while to sort out a strategy for winning when things were too easy, and I had to crank up the nastiness in order to really understand the game and its complexity. The thing that I hadn’t considered was that Okta could win with ANY of her 3 (4) cards – not just the first 3 – if that makes any sense.
The goal of the game is to reach a target number by adding a set of cards together. You and Okta take turns. As you play, keep track of both your score and Okta’s to be able to block her attempts to collect three (or 4) cards with the specified total before you can! There’s a ton of mental math going on in this game – and, if you’re up for it, you can move into decimal numbers too…!!
Enjoy…! More games and links like these can be found on the NCTM Illuminations webpage.
I thought I’d post an autumn-themed game on the blog this week for my colleagues in kindergarten. The game is called Falling Leaves, and it’s based on a game from the BEAM website. In my version of the game, students start with 15 unifix or stacking cubes in their own colour. To begin, Player 1 rolls a regular 6-sided die and puts a cube on the leaf with that numeral. Then Player 2 has a turn. If there is already a cube in that leaf, students stack their cube on top of the one that’s there, to make a tower.
At the end of the game (when all of the cubes are used up), players scan to see which of the towers has their colour on the top. Those towers are collected and snapped together. The player with the tallest tower wins!
In this game, pink is playing green. Green collects all the towers with green on top. Pink collects all of the towers with pink on top.
Stacked together, it’s clear to see that pink wins!
Enjoy… And happy fall!
I wanted to follow up with my colleagues who attended the k and k/1 sessions in Langley on Friday. I showed some materials that I then promised to upload to the blog – and then promptly forgot! Here are the files… :)
For those of you who were not in attendance, the idea is simple. Young children need the opportunity to represent number in many ways to truly make sense of it. Our youngest learners need more than most to make sense of the squiggles we call digits by building, comparing, partitioning and learning to subitize amounts to five – and then from 5 through ten. Consider these cards, images and frames for representing number as part of your opening activities, a centre or as meaningful practice following on from a lesson. Students love the chance to roll a die and say how many – and then to build and record what happened! The files are below – and are included in French as well.
PS – Use the “finger cards” to create sets that make five like in the Room on the Broom task, below. Copy the cards, cut them out and then distribute them in pairs so that you know that every child in the room will be able to find their missing part (ie, be sire to hand out a 2 and a 3, a 4 and a 1, and a 5 and a zero…). You might consider NOT using the 5 and zero pairing – seems sort of unkind to leave a child with nothing in front of them!!
I wanted to send along a list of spooky books for math investigations for spreading the Hallowe’en math love. I hope you can find some or all of these in your school libraries… There are so many fun contexts to explore around this season – from notions of pumpkin circumference to skip counting, from growing patterns to playing with the operations and the complements of 5 and 10.
One of my favourite contexts for thinking about parts of 5 stems from a story called Room on the Broom. Just this week I worked in a K/1 classroom and explored the missing part – or complement – of 5. Then we read the book by Julia Donaldson, in which a witch and her friends fly about on a broomstick – adding a friend until there are 5 on the broomstick in all. We “built” some of the book’s illustrations in egg carton 5-frames, and talked about how much room was still left on our broom, if our brooms, like hers, had 5 seats.
Next, I whispered a number from 1-4 in each child’s ear (I left off zero and five for this initial exploration…) and had them build that number in their 5-frame broomstick. Then I asked the children “How much room is on your broom?”. The K/1 kids then had to find the person whose broom “completed” their’s… Click to take a look in the pictures below:
a child with 2 on his broom finds a child with three on her broom:
3 and 2
and they put their brooms together (one on top of the other) to fill it up.
The egg cartons I like best are clear plastic ones – and you can see why… looking through one 5-frame to the other is a powerful way to see the parts of 5!
After a couple of turns with this game, I asked children to record what they did and how they filled up the room on their broom with their partner. You are welcome to use the There’s More Room on my Broom! line master to try this with your students as well. In this photo, you can see see one of the grade 1 students working to show her thinking on the form…
Have a fun and spooky mathy season!
Here’s a fun little game for primary classrooms… The Magic Squares game provides students with a total for each row and column, as well as a few key starting numbers. Use the magic wand to place the correct digits from the set of numbers at the bottom of the screen. Double click to grab and then place the correct numerals in the grid.
Each game sets a different total for the rows and columns, so students can choose a number that makes sense for them before beginning.
The challenge of finding a sum for 3 addends is a good one for late grade 1 (when the digits without images to accompany them make sense) through grades 3.
I came across an interesting game today in my perpetual on-line search for quality math games that promote thinking. It’s called Mission 211 – Mental Maths.
A video transmission from mission control’s Caleb explains the tasks at hand. You must answer mental math questions as quickly as you can in order to collect biofuel rods and foil the evil roboids..!! Best of all, Caleb provides strategies for solving the problems, if you need his help. The strategies include “counting on”, “breaking down numbers” and “rounding” – what we might call compensation or friendly numbers.
The music and the heartbeat in the background (yes, really!) create a sense of urgency, and encourage you to complete the questions as quickly as you can. If you need help, pressing the “HINT” button produces a mental math strategy to one side of the screen. It’s a super helpful scaffold, and one that helps to make the numbers meaningful. As you progress through the game, there are true or false multiplication and division questions as well – a nice blend of methods and ways of presenting content.
I like it!
Now – back to the game. I’ve got some evil roboids to destroy. :)
PS – Play the game in FULL SCREEN MODE to avoid silly advertising…
The iPad sensation is truly wild. I have one (of course) and use it often to present mathematical ideas and problems, stories with a mathy context and visual manipulatives to my students while I teach in classrooms around the province and territory. What I struggle with is the never-ending search for quality math games for the iPad that amount to more than digital drill… :oP Surely the technology can offer up something more thought-full??
I found an app this week that is worth sharing, called Pick-A-Path. It was released by the NCTM (National Council of Teachers of Mathematics) and features a number-puzzle for students to solve. The goal of the game is to navigate a maze, moving an octopus (Okta) through a series of numbers and operations, trying to create a maximum or exact amount. In the different levels, students use whole numbers, powers of ten, integers, fractions, exponents and decimals to solve the puzzles, gaining “starfish” as prizes. It had me hooked! Because for the different levels, I can see it being used from grades 2/3 through grade 9 — if you want to stick to the curriculum precisely — and beyond that, if you’re looking for a challenging game. Oh – and it’s free!
I just had to share! Here’s a game drawn from my new Mastering the Facts: Subtraction resource, called Lucky Ducky!
Before they start playing, children decide who will be the odd numbers and who will be the evens…
Each player subtracts from 18 on their turn.
Player A rolls the die and reads the number. She subtracts this number from 18 and puts a counter on the difference.
Player B has their turn, and play continues until all the counters are used up.
The player who is “Odds” collects all the counters that have been placed on odd differences on the board (9, 11, 13, 15, etc). The player who is “Evens” collects all the counters placed on the even differences (10, 12, 14, 16, etc).
The player with the most counters at the end of the game is the winner!
PS – This game was drawn from my Mastering the Facts – Subtraction resource. To order online, click here.
Hard to believe the summer has flown by so fast. In the spirit of the season (new classes and freshly sharpened pencils and all that) I wanted to share a game that I put together last spring. It’s appropriate for students in late grade 1 (skip counting from zero) through grade 5-6 (using multiples).
To play, students pair up and each one chooses a colour of counter to play with. Player A spins the spinner (use a paperclip and a downward pointed pencil as a spinner) to find out what number she must count by. Player A puts a counter in her colour on any number in the lily pad grid that is a multiple of that number. So if Player A spins a 2, she can cover a 2, 4, 6, 8, 10, etc – but NOT a 5 or a 15… Then Player B has a turn.
Three in a row in one colour wins the game.
Oh – and if you spin a lily pad, you can put your counter anywhere at all!
Consider using this game as a beginning of the year start up task. Observe your students as they play and listen to their strategies. Chances are you’ll learn something new about your kids….
Hello to my colleagues and friends…
Last spring, Sandra Ball (Surrey School District) and I crafted an assessment and instructional resource for kindergarten and K/1 classrooms. Focussed on subitizing, partitioning and patterning, this tool is designed to be administered in the fall and again in the spring of the year. Teachers wirk with the whole class or with small groups when performing the assessment. The tasks are drawn from story contexts to make them connected and authentic. Kids have fun showing what they know and can do! Hence the name – The “What Do They Know” Assessment. :o)
THIS spring, Sandra and I put together the companion resource for grade 1 and 2 classrooms. Again, we focus on subitizing and partitioning, but now we extend notions of patterning to include skip counting.
Best of all, an instructional component accompanies both the K/1 and Grades 1/2 resources, to help guide your teaching between assessments!
Sandra and I would like to invite you to download and use these assessments with your students this fall. They can be found by clicking on the tab(s) in the upper right hand corner of the blog. The files are password protected, but if you’re interested in them, please email me at mindfull (dot) consulting (at) gmail (dot com and I’ll be happy to share.
Have an amazing year! Enjoy every minute.
Carole (and Sandra!)
To learn more about the K/1 resource, its design and intent, please click here to read an article from the September 2011 edition of the BC Association of Mathematics Teachers’ journal, Vector.
You know, some people holiday over the summer. Me, I seem to write teacher resources. :o)
I am very pleased to announce the release of my newest resource called Mastering the Facts – Subtraction: Lessons for Making Sense of Subtraction for grades 1 to 3. This teacher book includes 17 complete lessons aimed at supporting primary aged students in mastering the subtraction facts to 20. Each strategy-based lesson features:
- a 3-part direct instruction lesson
- a task for guided practice
- games and worksheets for independent practice
- open-ended story problems
- targeted fluency building opportunities
- an assessment task customized to match the facts learned
All the lines masters for games, written practice, flash cards, teacher materials and other instructional support are included in this 185 page resource. Organized by strategy, these lessons are designed to promote mastery of the facts, not just memorization! Teacher tips for using and organizing manipulatives, for supporting students who struggle and for working in a combined grades setting are also included.
Matched to the WNCP and BC math curricula, this book is designed for classroom teachers of grades 1 to 3 and primary resource teachers. Select lessons are suitable for kindergarten students as well.
Cost for the resource is $40 plus $10 express shipping.
If you’re interested in getting your hands on a copy, click here to fill out the online form. I’ll get back to you with shipping costs and payment details.
Thanks for your ongoing support. I hope the book proves helpful.
PS – Please click below to download select colour line masters drawn from the resource. All other line masters are included and are to be copied onto black and white, but these ones deserved a little colour…!
I had the pleasure of working with K and K/1 teachers in Mission on Monday – a great group of teachers who somehow managed to summon up the energy to attend an after-school workshop with me this week!! Together we looked at ways to support their young students in subitizing and partitioning. Sounds complex, doesn’t it? :) Truth is, children in early primary need opportunities to see numbers at a glance without counting (subtizing) and to recognize that we can break up sets and put them back together again and the set size is the same (partitioning). These concepts and skills are critically important for young children to develop – they underpin the ability to add and subtract, to multiply and divide…
Engaging young children in conversations about how they “see” sets of number is a great way to start. Present an arrangement of 5-8 objects in your daily opening activities, and ask children what they see and how they see it. Talk about the parts and label these smaller sets with numerals to make sense of the digits. Celebrate the fact that, no matter how you slice it, 7 is still 7!
Over time, you might want to make connections to the operations by using the attached “Missing Part Cards”. They include a numeral to indicate the set size, and then dots in familiar arrangements in the form of an equation. The important part of course is to cover up just one of the sets of dots before showing the missing part cards to the children! :) A 6.5 cm x 6.5 cm square of thick paper (bond paper or construction paper – or even sticky notes doubled up) taped across the top creates a flap that will hide one of the parts from view, as indicated below.
Show the card and read it aloud with the children:
“Seven is the same as 4 and…?”
It’s a good idea to say “is the same as” and “and” for “equals” and “plus” here. ”Equals” and “plus” are the names for the symbols and are less meaningful to learners than “is the same as” and “and” – which are words that describe what the symbols mean…
Have students say what they think is missing, and why they think so. You’ll be surprised at the strategies students will use to find the missing part! Older learners will benefit from seeing the equation written with a box to indicate the missing part – that is,
This is a great way to introduce algebraic thinking in a visual way!!
Feel free to download the Missing Part Cards for 5, Missing Part Cards for 6 and Missing Part Cards for 7 here. They are best printed in colour of course, and will hold up best if printed on card stock or bond paper. Credit for the idea goes to John Van de Walle, who first showed them to me years ago. A smart man, our John – and one I miss terribly.
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.