Number Sense Routines

I have two pre-school boys, 5 and 4. I noticed my five year old developing a lot of enthusiasm for numbers and I recognized his "number sense" was pretty good. I wanted to take a queue from his enthusiasm and help him develop that better so I got this book on number sense. Even before it arrived, I was reading the preview and was impressed with the Early Number Sense Learning Trajectory. Right away I recognized some things that could help both my boys. After I received the book, I've been reading through it and it's full of ideas that I can use for years to come. The book is helping me understand the learning process my boys are going through, and how to plan and implement routines that will help them develop an advanced sense of number.The book has useful ideas for pre-school through most of the elementary grades. The cover indicates K-3 but there's some 4th grade examples inside. More importantly, there's routines that will help people develop their number sense from wherever it's at now, no matter their age.My boys are examples of the early stages. My little one had some sense of magnitude, one-to-one correspondence in counting, and cardinality, but if you showed him four or five things he was still counting them. I started to work with him in subitizing with dot cards. In just a few days, he's gone from subitizing three up to six. We're making this a routine, for him with a single die (from a pair of six-sided dice), dot-pattern cards, and the dominoes whose two halves total to maybe 8. I'm using a ten wand and introducing ways to make a number. We also do choral counting as a family and we're starting to include him on counting around the circle.My older boy was excited about the dot patterns when I showed the kids the cards I had made. At first they just went up to six, but I told him I had some harder ones with more dots. Right away he tells me, "I know if it has five and five that's ten!" He was developing his sense of unitization.I had worked with him, introducing number lines, both in abstract, and as a thermometer, ruler, tape measure, weight scale, and the clock. I also showed him number circles on the circular clock, scale, thermometer dial, and a circular day of the week and month calendar I made. He could read any analog clock to the minute with or without numbers printed on it and had a pretty good grasp of modular arithmetic.For him, I brought out the dominoes that go up to 18 (two 9-dot patterns). I'm also using two dot-pattern cards or both dice at the same time. He's telling me things like, "I know this is 17 because nine and nine are eighteen but this one is missing one dot." He has good mastery of ten, ways to make ten, and factors of ten (he tells me that he knows 80 and 80 is 160 because he knows that 8 and 8 is sixteen). He also counts into the thousands, races through backward counting by one from 100, and skip counts by two and ten. He's developing a better sense of compensation, and I think he will also get better at mental math with numbers other than factors of 2, 5 and 10. I really look forward to having more in-depth discussion with him about things like ways to make a number, and having him explain his thinking in addition to the answer.In recollecting my own education in math, I distinctly remember a decisive turning point during the 4th grade. In 3rd grade I was loving it and excelling at the level of adding and subtracting fractions. By 4th, math became algorithmic, tedious, and I began to struggle. The only time I really enjoyed math after that was when I discovered Euclidean geometry. What I was missing was the kind of number sense the routines in this book help to develop when they're practiced daily. Because of that, the only strategies I had for problem solving were inefficient, tedious, and algorithmic. If you think about it, a long-division problem is whole bunch of simple subtraction and multiplication problems bundled into an algorithm. If you have strong metal math skills and the ability to pick efficient strategies to solve the component problems, everything will go well. If not, a whole sheet of long division problems is tedium beyond what one can bear. It's the same thing with quadractic equations and polynomials. Unfortunately my own educators focused on explaining the algorithms without recognizing the gaps in my skills and number sense. I believe this happened because they simply didn't know what to do about that anyway. This book has the answers.

I was a classroom teacher for 5 years and I am currently in my second year as a math interventionist. I bought this book a year ago and finally have had a chance to sit down and read it. I have to say it is a fabulous book! It is such a reader friendly book and a quick read as it is engaging as well. As I read the book, I get excited to plan for my small groups, especially with a better understanding of some terminology that is thrown around, yet I don't have a full understanding of the meaning. If you are an experienced teacher/interventionist, you may already know much of what is in the book, but regardless I recommend it.

This book is a great resource for early childhood math teachers, there a great ideas for building number sense and so many wonderful ways to incorporate through your day. Some of these activities are things I already do so that helped me feel validated in what I am already doing, and there were so many new ideas. This was a very easy read, because I was very interested in the topic, if becoming a better math teacher is not your goal I wouldn't suggest this book, otherwise it is a must need resource for your classroom.

This book is a powerful resource for any math teacher at any grade level to have on their shelf. This is not a book that you need to read in order or cover to cover. It is a resources that can be pulled to get powerful strategies that all aim to build solid mathematical number sense in students. This book lays out many visual routines that can be used to help implement routines into the classroom and deepen their understanding of how numbers work. Subitizing is gaining traction in the world of math education and all the strategies aiming to help students "see" numbers is getting at that subitizing skill. This book is an easy read and you will be able to implement strategies as you read them and make a positive impact on your students right away. This would be a great book to use as part of a PLC or book study!

This book is solely to help improve numerical fluency solely in warmup situations. It does provide helpful strategies, some of which I intend to use next school year.

This book is so many things I've been looking for all in one place. It is a goldmine, a bank of powerful strategies, which are critical for building number sense (the foundation of all mathematics). I especially love the visual routines. These help students "see" numbers and deepen their understanding of how numbers work (how they can be flexible by decomposing them). This understanding makes their learning so much more meaningful and practical when it is transferred to "mental math", which is used daily in the real world. As I was reading this, I eagerly implemented what I was reading and used many of the resources before I even finished the book! I teach third grade math and found many great ideas for differentiating my instruction-for my remedial groups all the way to modifications of the strategies to challenge my high performers. Reading this book inspired me to start a "vertical team" book study, open to any interested K-5 math teachers (gen ed and ESE) at my school. I can't wait to see the effects of the great conversations we've been having!

Good book; what I expected. Good delivery time.

I continue to get good ideas from this book! I have used it for 3 years and keep returning to it.

Clear ,simple and do- able immediately - really opens up thinking and dialogue with my learners!

Easy to read and usable content

It's a fantastic resource for teaching math!