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’ve said it before… Cuisenaire rods rock. I was first introduced to Cuisenaire rods in 2006 by my dear friend and mentor John Van de Walle. In February of that year I was invited to join him in Spokane, Washington and to observe as he did demonstration lessons in primary and intermediate classrooms. His problem-based lessons featured Cuisenaire rods, and while I watched the students responding to the openness of the tasks and the richness of the manipulatives I knew I was witnessing something powerful. The proportional relationships between the pieces and the colour wheel connections make Cuisenaire rods both aesthetically pleasing and mathematically significant. I was hooked. It took some time and experimentation to figure out how to best introduce the materials and to sort out what tasks and questions would promote thinking across the grades. But in the end, I’ve managed to compile a series of open-ended tasks, games, lessons and practice opportunities that are developmentally sequenced and laid out from Kindergarten to grade 7. I’ve compiled these lessons in 2 full-colour volumes – a primary resource (grades K-3) and an intermediate resource (grades 4-7). All of the tasks have been tested and refined to ensure they are classroom-ready and engaging for all! So it is with great humility (and no small sense of accomplishment!) that I announce the release of my latest resources – Remarkable Cuisenaire Rods: Mathematical Tasks for Primary Classrooms and Cuisenaire Rods Rock: Exploring Multiplication and Proportionality in Grades 4-7. These resources would not exist if it weren’t for the mentorship of John Van de Walle. He shaped my mathematical practice more than he knew in his all-too-short lifetime. And so I dedicate my student-centered and pedagogically grounded efforts to his memory. I hope you will enjoy the tasks and games, the investigations and the open-ended problems posed in these resources. They are intended to promote big thinking in elementary – from addition and subtraction to skip counting and multiplication, from fractions to division and more… The full colour primary resource, Remarkable Cuisenaire Rods: Mathematical Tasks for Primary Classrooms is intended for Kindergarten through Grade 3 can be ordered by clicking here or on the image on the left. The resource is $40 plus shipping. Click on the link below to preview lesson titles and the intended grade levels for the tasks. Cuisenaire Rod Resource K-3 Table of Contents The full colour intermediate resource, Cuisenaire Rods Rock! Exploring Multiplication and Proportionality in Grades 4-7 is designed for intermediate students and can be ordered by clicking here or on the image at the right. This resource is $50 plus shipping. Click on the link below to preview lesson titles and the intended grade levels for the tasks. Cuisenaire Rod Resource 4-7 Table of Contents As always, thank you for your support! Carole
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.
One of my all time favourite stories for introducing division is “Bean Thirteen” by Matthew McElligott. He is a mathematically clever author whose stories play with important concepts in accessible ways. “Bean Thirteen” is a story about 2 crickets who gather beans to eat, but find that, no matter how they share them, or with how many friends, there is always one left over! The story makes an excellent read aloud, and the pictures are worth sharing with students of all ages. I ask that learners copy the pictures on key pages, then record what a mathematician would write for that particular image. It inspires interesting conversations about doubles, groups of and division with remainders…
The next post contains some of the key images from the book so you can project them for your students to view and discuss.
Don’t forget to play “The Game of Remainders” as follow up! Rules can be found by clicking here:
PS – For another, more advanced look at division and sharing, consider “The Lion’s Share”, also by Matthew McElligott. In it, creatures share a single cake into increasingly small fractional pieces… Smart – and visually appealing for kids looking to truly understand multiplication by fractions!