Tag Archives: operations on fractions

Another New Resource! Multiplicative Thinking – From Skip Counting to Algebra (Grades 3 to 8)

cover Multiplicative bookFor those of you about to return to another school year, welcome back!

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.