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!
I am truly excited to announce the release of my newest teacher resource book: Multiplicative Thinking: From Skip Counting to Algebra (Grades 3 to 8). This book is designed for teachers of the intermediate grades and is focused on the teaching and learning of multiplication. This resource addresses multiplication deeply — what it means to multiply, when to use multiplication in problem-solving situations, as well as how to manipulate whole number, fractional and decimal factors using strategies like the distributive property.
Lessons on skip counting, patterns in the multiples, factoring, and on prime and composite numbers are included in this 220 page teacher resource. Algebraic thinking is explored as well, from T-charts and input-output machines to solving equations, from graphing linear relations and extrapolation to finding the slope of a line. Students engage with visuals and real-world problems involving proportionality, rates, discounts and taxes to build their understanding of multiplicative thinking and see its very real application to their everyday lives.
Each of the 40 lessons features a connection to prior knowledge, whole class and small group explorations of the Big Math Ideas, guided conversations about the mathematics with key vocabulary, opportunities for meaningful practice, tasks for consolidation and customized assessment tools. Skill building lessons are interspersed throughout the book, ensuring students recall and continue to practice the essential skills needed to apply multiplicative ideas.
And of course literature links and games for practice are — as always — included!
Multiplicative Thinking: From Skip Counting to Algebra (Grades 3 to 8) is available for $40 + $10 expedited shipping. To order, click here or on the link at the right. From there you can also order other titles, including Mastering the Facts: Multiplication, a resource dedicated to the teaching and mastery of the critically important multiplication facts. It’s a perfect complement to this new volume and one that can be used in advance — or concurrently — to build a solid foundation.
Thank you for your support. All the best for a remarkable school year!
Why Multiplicative Thinking?
Multiplicative thinking plays an enormous role in elementary and middle school mathematics. So much bigger than simply knowing the facts — a critically important aspect — the ability to think multiplicatively is essential for success with almost every other mathematical concept, from ratio and proportionality to algebra. It is the operation most often used in “real life” to make sense of large quantities, of taxes and discounts, of income per hour and kilometres travelled. It’s the operation we use when we figure out how much paint or carpet to buy or what a tank of gas is going to cost; when we convert currency for a holiday away or sort out how much to tip on a meal. No matter where we look, multiplicative situations abound. We can’t spend too much time on the teaching and learning of these critical concepts!
In writing this resource, I have attempted to introduce multiplicative thinking — both the operation itself and the bigger concept of multiplicative reasoning — in a sense-making way. Through stories, models, pictures and words, students are introduced to the idea of multiplication as “groups of” and as “rows of”. Problems are posed to support learners in connecting what they know about patterns in the multiples to proportional situations. The associative and distributive properties are introduced and applied. Algebraic concepts — input and output machines, graphing and exploring the rate of change in linear relations — round out the topic and provide a preview for multiplicative reasoning at the middle and high-school levels.
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.
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!
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 all! I wanted to upload a couple of my new favourite games for developing fluency with the facts.
Once a strategy for recalling the facts has been learned, these games will help students to apply those strategies more fluently. It takes time and practice to master the facts – practice with the strategies and then practice using the strategies to recall the facts themselves… We all know the facts are critical to success with math. How we master them matters too.
So, first is the game from BEAM called Add Nines. It depends on knowing the strategy of “compensation”. Compensation is an algebraic idea, in which we “take from one number and give to the other”. This strategy works because in every case we make a ten (or another round number).
Think of it like this:
If we add 9 and 7, then we can take 1 from the 7 and give it to the nine, to make 10 and 6. And ten and 6 is easy… 16!
This game invites students to practice “taking one from one addend and giving it to the 9 to make ten and some more…” While this SOUNDS tricky, if you imagine the following images of 9 and 7, it’s pretty evident:
The next game is for mastering the 2 x facts and the 4 x facts. It’s my own (adapted from another BEAM game) but with numbers accessible to students learning these facts in 4th and 5th grade. It’s called Double or Double-Double. The goal of the game is to practice the strategy of doubling (multiplying by 2) or “double-doubling” (multiplying by four).
Think of it this way. Double 6 is 12. Double 12 is 24. So that means that double-double 6 is 24… Mathematically speaking, it’s the same as 2 x (2 x6) or 4 x 6. The idea of “double-doubling” works for all numbers, too. I like to call it the Tim Horton’s strategy. :o)
I hope these games prove fun for you and your children… More than that, I hope they will help your kids to truly master these important facts!