I am reaching out to let you know that I have just completed a new resource for intermediate and middle school teachers entitled Algebraic Thinking for Grades 5-9.
The resource focuses on the two important strands of algebraic thinking: patterns and relations and solving equations. Lessons include open-ended prompts, direct instruction and age-appropriate manipulatives use to promote the big ideas in algebraic thinking.
Content includes: increasing and decreasing patterns, generalizing from a T-table, describing and graphing linear relations in all 4 quadrants, explorations of slope (positive, negative, whole number and fractional) as well as y-intercept and the general form of a line, interpolation and extrapolation, operations on integers, solving equations, monomial and binomial multiplication using the distributive property, converting word problems to algebraic equations and more!
A range of strategies for developing mathematical language, for addressing diversity and for authentic assessment are featured in this 250 page teacher resource book. Algebra tiles, number balances and 4-pan algebra balances are used to model relations and to represent and solve advanced algebraic equations. Games, problems and levelled practice are included in each lesson, allowing for extensions and support as needed. Manageable and accessible digital scaffolds are highlighted, including virtual manipulatives and graphing tools.
This resource also features 23 embedded video clips — mini lessons on important algebraic concepts and demonstrations of how to use algebra tiles, colour tiles, the number balance and 4-pan algebra balance — as a way to support teachers and their students in grasping important algebraic ideas. These videos can be used by teachers to preview a lesson or by teachers and their students in a face-to-face or virtual setting.
Algebraic Thinking for Grades 5-9 is available from my online store for $50. Order now by visiting mindfull.ecwid.com — just in time for our return to school (in whatever form that takes!).
Thanks as always for your support.
Here’s to a new year…!
Today marks the beginning of a new kind of school — the stay-at-home kind. More than ever we are going to need to be flexible and patient and kind to our kids, their parents and our teacher colleagues. We are in uncharted waters… but not without good will!
I wanted to offer up a couple of simple dice games for you to play at home, to build number sense and computational fluency while having fun…
For more games like these, check out my resources entitled: Mastering the Facts Addition (2nd Edition) , Mastering the Facts Subtraction and Mastering the Facts Multiplication (2nd Edition) available from my online store.
Stay safe. Be kind.
Reach for the Top You can play this game alone, with a partner or against a partner. Print a copy of the Reach for the Top grid available here.
Order of Operations Bowling: You can play this game alone, with a partner or against a partner. You need one 6-sided die and the optional Bowling Pin recording sheet attached. The object of the game is to “knock down” all the bowling pins from 1 to 10.
How to play: Roll the die 3 times. Record the 3 numbers. Use these three numbers — in any order — to create an equation with an answer of 1. You must use all three numbers. Once you’ve found an equation (or 2 or 3!) with an answer of 1, cross off the bowling pin with the number 1 on it. Now move on to the number 2, then 3, then 4… until you have created equations with all the answers from 1 to 10. Each time you find an equation, you can knock down the pin with that number on it.
If you can knock down all 10 bowling pins with one set of numbers, you get a “strike”. If not, roll the dice 3 more times to get a new set of numbers and continue. Two sets of numbers earns you a “spare”. How many different operations can you use?
In the sample round below, Player A rolled a 1, a 5 and a 6. She used all 3 numbers to create equations (a whole bunch of them!) with an answer of 1. She chooses one of the equations and knocks down the 1 pin. She then moves on to create equations with an answer of 2.
I am pleased to say that — beyond spending every day on the water this summer — I DID manage to create a new teacher resource for my intermediate colleagues.
This time, it’s a stand up calendar of problems — one for every day of the school year!
This compact but potent book comes with an easel so you can set it up on your desk and flip from one rich problem to the next, posing open-ended questions of your intermediate students.
Good Questions: A Year of Open-Ended Tasks is a problem-a-day resource that includes
rich tasks ideal for grades 5, 6, 7 and 8. Organized by topic and structured in problem sets of 5 or more, this simple to use teacher resource includes 210 mathematically important questions to engage your students in deep thinking. For only $25, it’s a perfect back-to-school gift for yourself!
Proportional reasoning, measurement, operations and algebra are featured in this calendar of problems. Each one engages students in thinking flexibly, critically and creatively in the face of important and challenging mathematics.
Let the problem-solving begin!
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.