I am immensely pleased to announce the release of my latest volume of problems for intermediate and middle school classrooms.
More Good Questions: A Year of Open Ended Math Problems for Grades 5-8 is exactly that — a series of 220 tasks to inspire thinking, connection-making and reasoning for today’s diverse math classrooms.
In this second volume of problems, students will engage with tasks involving the operations, proportional reasoning, measurement and patterns designed to promote mathematical capacity. Problems are structured in sets of 5, clustered by topic, strategy or big math idea. Each task is slightly more complex than the last to allow for conceptual development over the course of a week. Problem sets can also be used as an intact set of 5, allowing students to choose the problem that is just right for them.
Intended to be used daily, these problems are designed to promote mathematical curiosity and connection-making. The richness comes from the shared discussion and comparison of strategies. The more we share our thinking the smarter we all become!
Check it out at mindfull.ecwid.com.
Stay tuned for the Grades 2-4 version coming soon!
I am reaching out to let you know that I have just completed a new resource for intermediate and middle school teachers entitled Algebraic Thinking for Grades 5-9.
The resource focuses on the two important strands of algebraic thinking: patterns and relations and solving equations. Lessons include open-ended prompts, direct instruction and age-appropriate manipulatives use to promote the big ideas in algebraic thinking.
Content includes: increasing and decreasing patterns, generalizing from a T-table, describing and graphing linear relations in all 4 quadrants, explorations of slope (positive, negative, whole number and fractional) as well as y-intercept and the general form of a line, interpolation and extrapolation, operations on integers, solving equations, monomial and binomial multiplication using the distributive property, converting word problems to algebraic equations and more!
A range of strategies for developing mathematical language, for addressing diversity and for authentic assessment are featured in this 250 page teacher resource book. Algebra tiles, number balances and 4-pan algebra balances are used to model relations and to represent and solve advanced algebraic equations. Games, problems and levelled practice are included in each lesson, allowing for extensions and support as needed. Manageable and accessible digital scaffolds are highlighted, including virtual manipulatives and graphing tools.
This resource also features 23 embedded video clips — mini lessons on important algebraic concepts and demonstrations of how to use algebra tiles, colour tiles, the number balance and 4-pan algebra balance — as a way to support teachers and their students in grasping important algebraic ideas. These videos can be used by teachers to preview a lesson or by teachers and their students in a face-to-face or virtual setting.
Algebraic Thinking for Grades 5-9 is available from my online store for $50. Order now by visiting mindfull.ecwid.com — just in time for our return to school (in whatever form that takes!).
Thanks as always for your support.
Here’s to a new year…!
Happy Monday, all!
In a time when we find ourselves spending more time together, learning and thinking and playing together at home, I wanted to share a game that is appropriate for players of all ages. The game “Penguins!” is strategic and fun for the whole family!
To play you’ll need 2 regular 6-sided dice and some counters. They can be beans coloured on one side with a marker, or even some Cheerios and some Shreddies cereal. It’s a good idea to have a piece of paper and a pencil handy for calculations.
Here’s how to play (full instructions are included on the “Penguins!” game board):
Roll the dice. Look at the numbers.
Find the sum and write it down. (add the numbers)
Find the difference and write it down. (subtract one number from the other)
Find the product and write it down. (multiply the numbers)
Now decide which one of these answers (the sum, the difference or the product) you will use. You can only pick one! Cover that number in your colour. Let your partner have a turn. If your sum AND your difference AND your product are taken, you can cover a penguin instead! Three in a line in your colour wins the game.
Hello friends. I hope you’re well.
As we move into another week of “school at a distance”, I’d like to offer you a game for intermediate students. This is a game that requires a partner and a regular 6-sided die (although a 10-sided one will make things more interesting!).
Full instructions for play are on the Roll The Bigger Product game board, but the goal is to take turns placing numbers in each of the positions in the 2-digit factors to create the largest possible product. You get to discard 2 rolls — throwing them into the trashcan — to be even more strategic! When all 6 positions are filled, calculate the product and compare it to your partner’s. The larger product wins.
To add complexity to the game, try placing decimals between both double digit factors — or harder still, within just one of the 2 factors.
For more games like this and a set of fully fleshed out lessons, see my teaching resource “Multiplicative Thinking: From Skip Counting to Algebra for Grades 3 to 8” available from my online store.
My sincere appreciation to all of you who have waited for the publication of this book. As you know, I’ve had a pretty remarkable year. I hope you’ll forgive me, knowing that only good distractions delayed its completion!
But I am pleased as punch to announce the release of Place Value For Intermediate: Building Number Sense for Grades 3-5, available now from my online store for $50.
This resource for teachers of Grades 3 through 5 features lessons designed to support deep learning of number. A wide range of both open-ended and directed tasks focus on representing, describing, comparing and ordering numbers to 100 000, as well as explorations of decimal numbers to thousandths.
Measurement experiences make up a big part of this series of tasks. The metric system and all of its place value connections is featured in explorations of linear measurement (mm, cm, m, km), perimeter (cm, mm), area (square cm and square m), mass (g, kg) and capacity (mL, L).
Addition and subtraction of large numbers and decimals are also addressed in this volume. Lessons at the grades 4 and 5 level focus on multiplication of 1 by 2- and 3-digit factors as well as 2 by 2-digit factors using the distributive property (an area model).
Assessment tasks tap into students’ understandings of these numbers and their application in the real world. Being able to see and relate to big numbers and to very small ones, to understand their relative size and to capably use these numbers to estimate is the essence of number sense.
Set up in a developmental continuum intended to facilitate the teaching of combined grades, this 352 page volume is certain to contain material to meet the needs of all learners and to inspire fun and engagement with critically important place value concepts.
When you buy the book online, you also get access to almost 40 pages of digital files and resources, which will be emailed to you as a downloadable pdf!
Thanks for your continued support and inspiration…
Tonight we spoke about developing number sense in elementary – a series of tasks and games that can help children to make connections between important mathematical ideas.
Each one is an important precursor to the operations – and can help students to fill in the gaps in their learning around quantities and the relationships between them.
So – as promised, here are the number sense games and tasks that we played or talked about tonight. They make up the purposeful practice aspect of a balanced numeracy program! Click on each link to download the instructions and/or line masters needed to play the games. Enjoy – and feel free to share with your friends! See you in November….
Number sense tasks and games:
If you are interested [and have nothing better to do on a Friday night… 🙂 ] feel free to watch an archived webcast of the Elluminate Live sessions on math… You just have to click on this link then scroll down and find the January 14th or April 21st links.
In the second of these sessions, I addressed the mathematical processes of communication and connection-making… recognizing and assessing them across the grades. There are lots of problems to be solved and lots of student samples shared in the session. If you choose to watch this as a staff during a pro-d day, you can stop either session and allow time for discussion, then resume the webcast and continue learning together.
Here’s a pair of classics – and updated links for those of you who may have been frustrated with the blogroll…
These are Elementary School problems – great, open ended tasks for grades K-5 from the NCTM. They are often organized by theme, and have been archived for years… Of course many feature an American context, but there’s LOTS to choose from here!
The complement to these for our intermediate colleagues (grades 6-8) are the Middle School Problems. And these ones come with answers… 🙂
OK, it’s long past supper when I promised I would have this post on-line, but I have been perched on the windowsill waiting and waiting for the snow… Alas, it may not come until after I am asleep.
So – rather than watch the sky any longer, here are the names of the books I featured (and did not speak to, for lack of time) today.
Picnic Farm by Christine Morton
The Very Kind Rich Lady and her 100 Dogs by Chinlun Lee
Actual Size by Steve Jenkins
Prehistoric Actual Size by Steve Jenkins
Quack and Count by Keith Baker
A Frog in the Bog by Karma Wilson
Room on the Broom by Julia Donaldson
Counting Crocodiles by Judy Sierra
The teacher resource I would recommend is the Teaching Student Centered Mathematics, grades K-3 by John Van de Walle. It is a remarkable resource that outlines the big ideas behind the math we teach, and includes student tasks that are conceptually framed and open-ended, and structured in such a way that children in multi-aged classrooms can access the richness of them. It shows different ways to think about adding and subtracting as well as multiplication and division and goes into the reasoning for the changes in the way we are teaching these operations. I love it, and have great respect for the author’s work.
I know we began to talk about different ways to subtract today. If you scroll down in these posts you’ll find one entitled Chilliwack Foundations. In there is a link to some pdf files illustrating different ways to subtract featured in different countries around the world. Pretty neat stuff there – and likely something you’ve seen your students do spontaneously!
Hello again! How nice to have so many people come out to the Coffee and Conversation chat at McKinney today!!
Here are the pieces I promised you… to support your children in making connections between the mathematical ideas they are using at school. click here to download the line masters!
For a list of applets (on-line games and tasks) for your children to use to practice this kind of thinking, go here.
Hello to all the gang in Mission! I wanted to thank you for the opportunity to work with you all this evening. The more I work with teachers and administrators around instructional change, the clearer I am in my purpose and the more convinced I am we will get there.
I have attached some examples drawn from the resource called Lenses On Learning Instructional Leadership in Mathematics for you to look at. If you remember, we talked this evening about different strategies for thinking about addition, and I wanted to share strategies that are more sensible for thinking about subtraction (which, of course, I don’t believe we ever REALLY have to do… but I digress.) The pages I have attached are drawn from reproducible documents from the Lenses on Learning Module 1 for K-8 Administrators. The book and video are published by Dale Seymour Publications and are available through Pearson Professional Learning here in Canada.
Click below to open the file that outlines 6 different ways to subtract – each one explained, with references to the countries of origin…
I wanted to include a couple of links here that I like a lot.
The first connects to an interactive applet students can use to model double digit multiplication with arrays. A VERY powerful visual model that connects to the algorithm in meaningful ways.
The next is a link to a resource I am using a lot in my conversations with teachers. It’s the new Van de Walle eBook series – Teaching Student Centered Mathematics. The books come in grade bands – K-3, 3-5 and 5-8, which is great, but the best part is the media supports within the book itself. There are interviews with the author, small group and classroom episodes (Canadian classrooms!!) and snippets of workshops given by Van de Walle across Canada in the last 18 months. You can try the on-line demo here.
A project I am LOVING right now is the Tinkerplots project being carried out in one of my schools. This is a collaborative project involving students from Richmond BC and students in Montreal QC. The software we are piloting is called Tinkerplots – Dynamic Data Management Software from Key Curriculum. It is thoughtfully created and entices students in grades 4-8 to think deeply about data – to make inferences and to see relationships between attributes of a data set.
Student samples and a video of the Apple iBook lab being used to explore data can be found on the school’s website. The movie is big and takes a long time to load… be patient!
Teachers can download an evaluation copy of the software… I’d highly recommend it…!
Today I had the chance to work with a delightful group of teachers. throughout the course of the afternoon we re-examined each of the operations – addition, subtraction, multiplicaiton and division – and thought about each of them in a new way. For some, this was a way to re-connect to stategies they had been exposed to before, for others, it was all new.
It occurred to me as I left that in three short hours we had re-visited, re-vamped, and re-learned everything we spent our entire elementary school years learning in math class. No wonder they looked so spent! 🙂
I must apologise to this group (and perhaps that is why this post) for pushing their brains so hard in such a short time.
I guess I’m just searching for better, more sensible ways for students to think about math – and sometimes it gets the better of me…
So I spent some time last night surfing around, trying to find some good, THINKING tasks for supporting students with mastering the basic facts. Let me tell you, it was a bit of a challenge. So much of what is available is simply drill in disguise – and drill is not helpful until students have effective conceptual understanding of the operations and strategies to use to solve the problems. (and just memorizing doesn’t count!)
Last night’s surfing did yield some applets and visual demonstrations, as well as a few number puzzles that require strategic thinking – and I have included them in the file attached here: mastering the facts
If you know of a great link, please send it along! There’s got to be something out there…