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.
For those who have been patiently waiting (and lovingly nagging!) I am happy to announce the publication of my newest math teaching resource: Proportional Reasoning in Intermediate for Grades 4-8, available now through my online store.
This resource for teachers of Grades 4 to 8 presents more than 250 pages of open-ended lessons, meaningful practice, games, literature connections and a wealth of problem-solving contexts for supporting students to make sense of fractions, decimals, percentages, ratios and proportions. Designed for today’s diverse classrooms, this resource offers a range of tasks to promote proportional thinking through intentional development of mathematical language and the use of key manipulatives. Colour tiles, Cuisenaire rods and tangrams are used to model and make connections within and between concepts.
In the first section of the resource, students will explore three models – set, area and linear – for representing and describing, comparing and ordering fractions. Students will learn to convert between fractions, decimals and percent and to apply these skills to problem situations, including measurement, tax, discounts and data management. Next, students learn to add and subtract fractions, to solve proportions using a range of strategies (involving both mental math and the appropriate use of technology) and then finally to multiply and divide fractions.
Assessment tools are threaded throughout the resource to allow teachers to keep track of student progress and to make instructional decisions.
Proportional reasoning IS the math we do every day. This resource provides an access point for all.
Finally … French translations of my latest books are now available!
Je viens de traduire mes deux ressources de bonnes questions — “A Year of Good Questions for Grades 2-4” et “A Year of Good Questions for grades 5-8” — afin que mes collègues d’immersion aient des ressources françaises avec lesquelles travailler. Merci pour vôtre patience!
In these new French translations of the English originals, you’ll find more than 200 open-ended and engaging problems for french immersion students from primary through middle school. All are posed in French and explore important mathematical concepts across the grades.
The first book: Bonnes Questions: Une année de bonnes tâches mathématiques pour les élèves de 2e à 4e is suitable for late primary students (grades 2-4) and features operational tasks, measurement tasks and pattern tasks of increasing complexity, posed in French.
The second volume: Bonnes Questions: Une année de bonnes tâches mathématiques pour les élèves de 5e à 8e is perfect for middle school immersion students (grades 5-8), with a focus on proportional reasoning, algebraic thinking as well as operations on integers, fractions and decimals to name a few.
Engaging problems and choice make these volumes the perfect conversation starter for our immersion classrooms, promoting oral language development and mathematical thinking …en même temps!
I am pleased to say that — beyond spending every day on the water this summer — I DID manage to create a new teacher resource for my intermediate colleagues.
This time, it’s a stand up calendar of problems — one for every day of the school year!
This compact but potent book comes with an easel so you can set it up on your desk and flip from one rich problem to the next, posing open-ended questions of your intermediate students.
Good Questions: A Year of Open-Ended Tasks is a problem-a-day resource that includes
rich tasks ideal for grades 5, 6, 7 and 8. Organized by topic and structured in problem sets of 5 or more, this simple to use teacher resource includes 210 mathematically important questions to engage your students in deep thinking. For only $25, it’s a perfect back-to-school gift for yourself!
Proportional reasoning, measurement, operations and algebra are featured in this calendar of problems. Each one engages students in thinking flexibly, critically and creatively in the face of important and challenging mathematics.
Let the problem-solving begin!
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…
I thought it was time to post another game for those of you who are looking to support your intermediate students. This is another classic game from BEAM. It’s called the Game of Remainders — but don’t be fooled! It’s about far more than simple division. There are connections to be made to skip counting and the multiples here that are worth talking about!
As a tool for thinking and for identifying the important patterns inherent in this game, consider giving students a hundred chart to begin. Have them shade or highlight all the multiples of 6 (6, 12, 18, 24, 30, 36, etc) before playing the game.
Then, as they land on a number in the wheel (like say 49), they can refer to the chart and see that the number 49 is not coloured, so it’s going to have a remainder. Looking further, the will notice that it is in fact one more than a multiple of 6, which means there will be 1 remainder.
Be sure students gave a chance to talk about what they’re noticing in the chart as they use it. The more we describe our thinking, the clearer it gets and the more connections we make!
I’ve made a few other versions of this game if you’re interested in downloading them. They follow the same format, but address divisibly of 3, 4 and 5.
All the best as we count down to summer!
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!
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 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…