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…!
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 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 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.