# Place Value in Primary: Developing Number Sense

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.

Place Value in Primary: Developing Number Sense is available from my online store for \$40 plus shipping. I hope you enjoy it!

Carole

(PS… A companion volume for Grades 2 to 4 is in the works – expect it later this fall!)

# A fun and thought-full division game…

Hello all.

I thought it was time to post another game for those of you who are looking to support your intermediate students. This is another classic game from BEAM. It’s called the Game of Remainders — but don’t be fooled! It’s about far more than simple division. There are connections to be made to skip counting and the multiples here that are worth talking about!

Remainders division game (6)

As a tool for thinking and for identifying the important patterns inherent in this game, consider giving students a hundred chart to begin. Have them shade or highlight all the multiples of 6 (6, 12, 18, 24, 30, 36, etc) before playing the game.

Then, as they land on a number in the wheel (like say 49), they can refer to the chart and see that the number 49 is not coloured, so it’s going to have a remainder.  Looking further, the will notice that it is in fact one more than a multiple of 6, which means there will be 1 remainder.

Fun, right?

Be sure students gave a chance to talk about what they’re noticing in the chart as they use it. The more we describe our thinking, the clearer it gets and the more connections we make!

Three in a line – remainders game – 3

Three in a line – remainders game – 4

Three in a line – remainders game – 5

And, if you’re looking for a resource to help you in your teaching of division, consider this one: Fair Shares – Teaching Division in Grades 4-7.  It’s available from my on-line store.

All the best as we count down to summer!

Carole

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

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!

Carole

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.

Happy New Year, Everyone!

The resource includes all the line masters, game boards, written practice and teaching materials required to support your students in becoming proficient with addition and subtraction in ways that are consistent with the curriculum and which promote number sense.

This 220 page resource is just \$40 plus shipping. Click here to order!

PS – The companion resource for grades 1&2 is also available for purchase. Read about it by clicking here.

PPS – My sincere apologies.  I have discovered 2 errors in the book. One comes on page 167, in the game called “Three in a Line – Subtracting hundreds, tens and ones”.  The wheel at the top of the page and the differences below don’t match. 😦  I’ve attached the replacement game here for you.

Three in a line HTO game NEW

Likewise, I’ve had some feedback about the “I have…, Who has…?” game in the early pages of the resource.  I’ve re-created it and uploaded the replacement here.

“I have, who has” game NEW

Thanks for your patience and understanding…

Carole

# Fair Shares – Teaching Division in Grades 4-7

Hello, all…

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.

Carole

# New Resource! Mastering the Facts – Subtraction

You know, some people holiday over the summer.  Me, I seem to write teacher resources.  :o)

I am very pleased to announce the release of my newest resource called Mastering the Facts – Subtraction: Lessons for Making Sense of Subtraction for grades 1 to 3. This teacher book includes 17 complete lessons aimed at supporting primary aged students in mastering the subtraction facts to 20. Each strategy-based lesson features:

• a 3-part direct instruction lesson
• a task for guided practice
• games and worksheets for independent practice
• open-ended story problems
• targeted fluency building opportunities
• an assessment task customized to match the facts learned

All the lines masters for games, written practice, flash cards, teacher materials and other instructional support are included in this 185 page resource. Organized by strategy, these lessons are designed to promote mastery of the facts, not just memorization!  Teacher tips for using and organizing manipulatives, for supporting students who struggle and for working in a combined grades setting are also included.

Matched to the WNCP and BC math curricula, this book is designed for classroom teachers of grades 1 to 3 and primary resource teachers. Select lessons are suitable for kindergarten students as well.

Cost for the resource is \$40 plus shipping.

Carole

PS – Please click below to download select colour line masters drawn from the resource.  All other line masters are included and are to be copied onto black and white, but these ones deserved a little colour…!

rocket ship

Houses for number lines extra large

# Addressing Diversity in Math with Open Ended Questions

Our math classrooms are more and more diverse each year. Learners come to us with a range of different experiences and levels of understanding of the mathematics that’s important to know. Meeting the needs can prove challenging. Dr. Marian Small’s book called Good Questions: Great Ways to Differentiate Mathematics Instruction is an excellent resource for learning how to craft questions to make the math accessible to all – challenging for those who need it, and simplified for others. Check it out for more rich and open tasks to engage children in thinking mathematically across the grades!

This is an incredibly useful teacher resource book. In it, Dr. Small poses open-ended questions across the strands as well as what she terms “parallel tasks”, which present the same math concept at 2 different levels of complexity. It’s a very clever way to include everyone in the mathematical discussion, and can really help when we’re planning for instruction in a combined grade setting. Oh – and did I mention that Marian Small is Canadian?? 🙂 Her work is in line with the WNCP math curriculum and so makes a great match for anyone teaching math here in Canada.

This selection of questions from Dr. Marian Small’s book are ideal for combined grades settings, since they address big math ideas that are common to side-by-side curricula. Invite your students to represent their thinking with models, pictures and words, and to share what they know with a peer, a small group and/or the class. These questions lend themselves to rich classroom discussions, and can give you as a teacher important assessment data to inform your planning.
Enjoy!
Carole

PS – Marian Small has also authored a companion book for secondary math that’s well worth checking out: MORE Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction.