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.
Hello to my friends near and far… It has been a long time since I have posted anything to my blog, and for that I am truly sorry. To my faithful visitors, I offer you my thanks. I hope this latest instalment has been worth the wait!
My newest collaboration — as always, co-created with the inimitable Sandra Ball — is entitled Financial Literacy In Primary: Thinking About Money in the Canadian Classroom. This full-colour, 50 page resource is free to download – but you’ll need a password to access it. Please use the form below to contact me for the secret code. Read on to learn more. Enjoy! Carole
Financial Literacy — An Important Aspect of Numeracy
Beginning in the fall of 2016, concepts addressing financial literacy are being introduced to the Western Canadian mathematics curriculum. Although they have been included at the middle school level for a number of years, this is the first time that financial literacy as been highlighted in elementary — and most notably at the primary level. This raises some important questions. What is financial literacy at the primary level anyway? Certainly it is more than recognizing and naming Canadian coins! Structured instead around notions of earning, saving and spending and giving money, curricular outcomes dedicated to financial literacy are intended to look more deeply at what it means to be financially responsible.
Our youngest learners need support and explicit teaching to reach these goals. Engaging, authentic and meaningful tasks are critically important. Learning about money should be fun, of course, but should include notions of social responsibility — earning, saving and giving — as well as spending!
Playing with Money: Connecting to Number Sense
In this new resource, Sandra and I have crafted a series of lessons to support teachers in introducing and developing ideas around financial literacy in Kindergarten through Grade 3. Currently there are few — if any — resources devoted to these ideas for primary students. We are hopeful this resource will fill that need!
Rich tasks, literature connections and games for practice in this resource are laid out along a continuum and are intended to be used across grades. In alignment with our new curriculum, these lessons are connected to both the core competencies (Thinking, Communicating and Personal and Social Responsibility) as well as to the curricular competenciesfor mathematics. By integrating financial literacy into our math program in primary, we create meaningful contexts for the math we are learning.
Think of the mathematical expertise our students will build as we represent and describe money amounts, compare and order values, skip count with coins and bills, use place value understandings and add and subtract dollar amounts!
The Math Big Ideas for Financial Literacy
This teacher resource is structured around a set of Big Math Ideas for earning money, saving money and spending and giving money. These enduring understandings apply across the primary grades and beyond. By addressing these Big Math Ideas in developmentally appropriate and engaging ways we can ensure students have fun while they lay the foundations for ensuring financially responsible decision-making.
Sandra and I hope that this resource proves useful to you and fun for your students!
To download the materials, visit my online store (https://mindfull.ecwid.com) and click on the FREE DOWNLOADS icon.
My colleague Sandra Ball and I have completed another resource for primary teachers!
Read A Story: Explore The Math promotes the teaching of important math concepts through the context of great children’s books… The lessons span K-3 and some are even appropriate for grades 3/4 classrooms. Lessons involving number sense and operations, data management, measurement and more are included in this 65 page resource. Scan through the list of titles and corresponding math concepts to sort out which children’s books would be a best fit for you and your students. The complete set of ISBN numbers for each of the stories is included so you can easily share ordering information with your teacher librarian…!
To download, please visit my online store (https://mindfull.ecwid.com) and click on the FREE DOWNLOADS icon.
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 wanted to send along a list of spooky books for math investigations for spreading the Hallowe’en math love. I hope you can find some or all of these in your school libraries… There are so many fun contexts to explore around this season – from notions of pumpkin circumference to skip counting, from growing patterns to playing with the operations and the complements of 5 and 10.
One of my favourite contexts for thinking about parts of 5 stems from a story called Room on the Broom. Just this week I worked in a K/1 classroom and explored the missing part – or complement – of 5. Then we read the book by Julia Donaldson, in which a witch and her friends fly about on a broomstick – adding a friend until there are 5 on the broomstick in all. We “built” some of the book’s illustrations in egg carton 5-frames, and talked about how much room was still left on our broom, if our brooms, like hers, had 5 seats.
Next, I whispered a number from 1-4 in each child’s ear (I left off zero and five for this initial exploration…) and had them build that number in their 5-frame broomstick. Then I asked the children “How much room is on your broom?”. The K/1 kids then had to find the person whose broom “completed” their’s… Click to take a look in the pictures below:
a child with 2 on his broom finds a child with three on her broom:
3 and 2
and they put their brooms together (one on top of the other) to fill it up.
The egg cartons I like best are clear plastic ones – and you can see why… looking through one 5-frame to the other is a powerful way to see the parts of 5!
After a couple of turns with this game, I asked children to record what they did and how they filled up the room on their broom with their partner. You are welcome to use the There’s More Room on my Broom! line master to try this with your students as well. In this photo, you can see see one of the grade 1 students working to show her thinking on the form…
Have a fun and spooky mathy season!
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!
Today I had a lovely time at Hillcrest Elementary working with some awesome kids in grades 1, 2 and 3. Our mathematical tasks grew out of the book “365 Penguins” by Jean-Luc Fromental (which is, of course, available in French as well!). Together we added flocks of penguins and created arrangements of penguins, exploring mental math strategies as well as multiplication and division!