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.
For those of you who have been looking for some of the teacher resources and student materials that I have used in my demonstration lessons, I’ve opted to try and put a collection of them all in one post… This collection of materials are intended for teaching place value, for use in lessons involving partitioning (addition, subtraction and multiplication), for comparing and ordering whole numbers as well as decimals, and for the teaching of fractions. As you’ve seen modelled in the lessons I’ve taught, these materials work best in concert with visuals (ten frames, base ten blocks, etc) and with plenty of opportunities for students to write equations, describe their thinking orally, build with models and create real-world situations to match.
The money and Cuisenaire Rods are best printed in colour, of course. I’d recommend sending the pdf’s to Staples.ca for printing. You can specify the weight of the paper (I like 80lb gloss cover) – and they’ll have the materials ready quickly for a reasonable price.
Consider putting magnetic tape on the back of these materials to allow them to be displayed on the white board. Check out the dispenser of magnetic tape available from Poster Pals. It’s great stuff!
I hope these prove helpful.
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.
Hello, my math friends!
I wanted to share something I put together not long ago to support students in understanding the value of the digits when we write decimal numbers. These decimal “tents” as I call them, are made from card stock and are folded in half to form a tent shape. Each one is cut so that the decimals on each card line up one under the other – but the digits themselves are still visible. It’s a bit hard to explain, I fear, but the following pictures should help…
This is what the cards look like, folded. I like to put a strip of magnetic tape on the back of each one so that I can stick them on the board, matching them to a model to show the same amount.
The cards are trimmed so that the decimal point falls at the same location on each of the “expanded” decimal number. On the decimal tents line master, this means you’ll slice off the light grey zeroes…
So when the cards are overlapped, the decimal number itself is clear, and made up of the parts.
It’s a powerful tool to use with students. Helping them to see that we can decompose a decimal number in the same way we do whole numbers is an important connection! This decimal tent set shows that 3 + 0.6 + 0.08 = 3.68.
Imagine a series of these tents strung along a string or wire in your classroom. Have students create a 3 digit decimal number, model it with materials and then order that number along the number line (that is, to hang their cards right on the wire!) placing it relative to the others. It’s a neat way to compare and order decimal numbers!