Wow. I have had the most extraordinary summer. Truly extraordinary. And somehow between engaging in a series of remarkable, life-affirming adventures I have managed to write another teacher resource book… 😊
It’s all about Place Value (as I’m sure you’ve figured out!) and is intended for teachers of kindergarten through grade 2, with special accommodations for those who teach in combined grades settings. There are 230 pages of developmentally framed lessons designed to address the diversity in our primary classrooms. Each one supports students to represent and describe quantity, to compare and order sets, to use referents to estimate and to skip count. Lessons devoted to measurement — an ideal practical application of place value in the world — are also featured. Whole class lessons, centres tasks and games for practice allow students to connect these important concepts in a seamless way, and can be used both as a unit or spread throughout the year to build and consolidate understanding.
(PS… A companion volume for Grades 2 to 4 is in the works – expect it later this fall!)
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 been busy writing this summer – putting together a volume devoted to teaching the operations in primary. And so, I am pleased to announce the publication of my latest teacher resource: Sums and Differences: Teaching Addition and Subtraction in Grades 1&2.
This resource includes a series of lesson sequences – open tasks, games, written practice, word problems and assessment support – for teaching the operations in a developmentally appropriate way. Beginning with place value explorations, these lessons increase in complexity while providing support for students across the grades. The lessons make explicit connections between concrete, pictorial and abstract representations of the math to ensure the operations are truly mastered.
The content in the book covers the grade 1 and 2 curricula and presents them in such a way that teachers of combined grades can use the lessons to work with their classes as a whole.
All the best!
I had the pleasure of working with K and K/1 teachers in Mission on Monday – a great group of teachers who somehow managed to summon up the energy to attend an after-school workshop with me this week!! Together we looked at ways to support their young students in subitizing and partitioning. Sounds complex, doesn’t it? 🙂 Truth is, children in early primary need opportunities to see numbers at a glance without counting (subtizing) and to recognize that we can break up sets and put them back together again and the set size is the same (partitioning). These concepts and skills are critically important for young children to develop – they underpin the ability to add and subtract, to multiply and divide…
Engaging young children in conversations about how they “see” sets of number is a great way to start. Present an arrangement of 5-8 objects in your daily opening activities, and ask children what they see and how they see it. Talk about the parts and label these smaller sets with numerals to make sense of the digits. Celebrate the fact that, no matter how you slice it, 7 is still 7!
Over time, you might want to make connections to the operations by using the attached “Missing Part Cards”. They include a numeral to indicate the set size, and then dots in familiar arrangements in the form of an equation. The important part of course is to cover up just one of the sets of dots before showing the missing part cards to the children! 🙂 A 6.5 cm x 6.5 cm square of thick paper (bond paper or construction paper – or even sticky notes doubled up) taped across the top creates a flap that will hide one of the parts from view, as indicated below.
Show the card and read it aloud with the children:
“Seven is the same as 4 and…?”
It’s a good idea to say “is the same as” and “and” for “equals” and “plus” here. “Equals” and “plus” are the names for the symbols and are less meaningful to learners than “is the same as” and “and” – which are words that describe what the symbols mean…
Have students say what they think is missing, and why they think so. You’ll be surprised at the strategies students will use to find the missing part! Older learners will benefit from seeing the equation written with a box to indicate the missing part – that is,
This is a great way to introduce algebraic thinking in a visual way!!
Feel free to download the Missing Part Cards for 5, Missing Part Cards for 6 and Missing Part Cards for 7 here. They are best printed in colour of course, and will hold up best if printed on card stock or bond paper. Credit for the idea goes to John Van de Walle, who first showed them to me years ago. A smart man, our John – and one I miss terribly.
PS – If you’re looking for more ideas like this for K and grade 1, consider purchasing a copy of my book: Number Sense – A Combined Grades Resource for K, K/1 and Grade 1 Math Classrooms. It’s set up to support teachers in addressing the number PLOs in mindful ways while keeping their Kindergarten and Grade 1 students together. Games, tasks, problems and meaningful practice opportunities are included in English and in French. To order online, click here.
It has been some time since I have made a post here, but fear not – I have been busy in the interim! 🙂
I am very pleased to announce the release of my new book, entitled NUMBER SENSE – A Combined Grades Resource for Kindergarten and Grade 1 Math Classrooms.
As the title suggests, it has been written in support of teachers of K/1 combined classes. The resource deals specifically with the number strand outcomes from the WNCP curriculum (the one currently in place in Canada), and does so in a way that keeps kindergarten and grade 1 learners together. The resource includes:
• line masters for all lessons
• practice opportuntities in the form of games, centres and additional tasks
• ideas for meaningful daily routines – an alternative to calendar!
• assessment tools – both formal and informal
The cost for the resource is $30 plus $4 shipping (for 3 or more copies, shipping costs will differ).
If you’d like to order a copy, please click here to purchase online.
Thanks so much for your support…
UPDATE: Thank you to all of those who have bought the book! A file of select line masters drawn from the resource is attached here. These are best printed and enjoyed in colour…