Focus on Math

Helping children become mathematicians!

Calgary City Teachers’ Convention 2017 Power Up your Problem Solving February 16, 2017

Filed under: General Math,Ideas from Carollee's Workshops — Focus on Math @ 7:59 pm

screen-shot-2017-02-16-at-7-42-50-pmOne of the best ways to begin improving problem solving in your math class is simply this: Just do it! Of course. you can learn some techniques for making that problem solving time more of a success than it would otherwise be. You can teach students some strategies for thinking, and help them to use mathematical tools (which I think of as anything concrete or pictorial that helps students build conceptual understanding), but ultimately problem solving is a skill that students master by engaging in it regularly.

Linda Gojak, past president of the NCTM, talks about using “rich tasks” in math lessons, and she defines a rich task in this way:

— A situation in which an appropriate path to a solution is not readily apparent
— Can be adapted to maintain high cognitive demand while meeting individual needs
— Requires students to do more than remember a fact or reproduce a skill
— Encourages investigations and deep thinking
— Has multiple entry points, solution paths and at times multiple solutions

I encourage you to look at the tasks you are asking students to do in your lessons and see how they stack up against such a criteria list.

For those attending the session tomorrow, I am not able right now to create a link for downloading the handout, but if you email me ( in the next 10 days I will see that you get a copy of it.

Mathematically yours,



BCTF New Teachers’ Conf: Seeing Dots February 27, 2016

100 dot array picI am delighted to be here in Richmond, BC, today presenting at the BCTF’s New Teachers’ Conference. I am doing a similar workshop to what I did at the Calgary City Teachers’ Convention two weeks ago, but it is well worth the repeat in this city!

I cannot say enough how important it is for students to be able to visualize and represent numbers in many forms. This tool, the 100-dot array, offers one tool for students to be able to use regularly and thus internalize the number relationships that can be seen when using it.

As before, I am making the handouts available here for downloading:

I will upload the extra large dot sheet (a quarter portion of the regular sized one) which can be made into a poster-sized array once I am home with access to my scanner. Watch for that in the next few days!

Let me know how things go with your students!

Mathematically yours,



Calgary City Teachers’ Convention: Seeing Dots February 10, 2016

100 dot array picThe 100 Dot Array remains one of my favourite tools for helping students visualize numbers. This session at the CCTC focuses mainly on its use with students in grades 2 and 3, although it can be used at many other grade levels. We will be talking about the best way to introduce the tool to students, showing an early activity to help with general number sense, and using the number in problem solving situations. A variety of problem are included to show its diverse use.

Here are the downloads available from the session:

Please let me know how it goes with using the 100 dot arrays with your students! I love to hear about kids using tools and strategies in math.

Mathematically yours,



Calgary City Teachers’ Convention: PS

It is my pleasure to present this session “Power Up Your Problem Solving” to the participants of this session.

Regular problem solving is a powerful way to help students develop conceptual understanding in the various strands of mathematics. Since there is a tradition in North America of “teaching by telling” (the “here’s-how-to-do-it-go-practice-50-of-these” method), it may take many weeks to develop a culture of deeper thinking in a classroom. Students need a variety of thinking tools and strategies to work with, as well as skills and practice in talking about math problems, but the time it takes to help students gain these needed things is time well spent. The payoff is huge!

I hope many of you will be encouraged to begin building a regular problem solving program with your students. It works at every grade level!

All the here are the downloads for the problem solving session:

I would love to hear from you how it goes in your classrooms!

Mathematically yours,



Making a Difference November 25, 2015

Filed under: General Math — Focus on Math @ 12:40 pm
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Screen Shot 2015-11-25 at 11.25.37 AMIt is always wonderful to hear when what you do makes a difference, and I wanted to share with my readers the wonderful email I recently received from a student who took a university course (Designs for Learning Mathematics: Elementary — a “how to teach math to kids” course) with me a few years back. I love the “ripple effect” that happens when I can help teachers and student teachers change their approach to teaching mathematics, which in turn can make a great change for how students understand mathematics!

Thank you, Laura, for taking time to share this! Here is Laura’s letter with only a couple of edits for clarification. Woohoo!

Hey Carollee,

Don’t know if you remember me, but I took your Simon Fraser University course a couple of years ago. My husband and I relocated to Ontario and I just started my first teaching contract 3 weeks ago in a grade 2/3 French immersion class. My students are very weak in math… but since I have  started teaching the way you taught me to, I can already see the ideas flowing in their heads! They are really starting to get it!!!

Two days ago we did our first word problem… they were blown away when I put the answer on the board and told them I didn’t care about the answer, but instead how they got to it! The first day they were a bit shy to try and fail, but by the 3rd day boy were they trying everything! number  lines, dot array, hundreds chart, blocks, pictures!!! I felt such joy!!!!

So… I guess  I just wanted to say thank you… and to let you know that  you are changing children’s understanding of math… EVERYDAY!


Laura Fusco


GAD Workshop, Surrey, BC October 23, 2015

learning to speak math picThanks to the teaching staff of GAD Elementary in Surrey, BC, for their warm welcome and heartfelt participation as we delved into problem solving, math tools and strategies, and math processes (especially communication). Changing our teaching practice is not an easy feat, but if we commit to some small changes, practice them regularly, add more changes, practice those regularly, and keep on going in that manner, we can end up making a significant and lasting change that will benefit students greatly.

Remember, “math talk” does not just happen. We have to plan ways to incorporate it into each math lesson. It is a good idea to create math partners so students are responsible to talk to someone about their math thinking. Modeling (letting students hear YOU talk through a demonstration problem) is always a good idea. Responding to students with proper math language/vocabulary (when they have not used such) is helpful. Posting “sentence stems” is a great way to give them an easier start in speaking math. Additionally, try creating a “math words” chart with the students that they can use as an on-going reference in both their speaking and writing (click here to see an example of a “math words” chart.)

As promised, I am adding links from this post to the handouts from today’s session (see bottom of the post) and some that we just talked about.

I would LOVE to hear from any of the GAD staff of how things go in your math lessons in the next weeks. You all listed something that you could begin to do right away in your classrooms, and I hope you will share what you are doing and the effect it is having on the students.

Remember, understanding “lives” in the processes! Reflect on your teaching regularly to see if you are embedding those processes into math classes. It will make a big difference in students’ understanding if they are immersed in the processes!

Mathematically yours,



Download materials here:

100 dot array (teacher size)

100 dot arrays 4 per page

100 dot arrays 6 per page

100 dot arrays 12 per page

break apart number sheet – 2’s

break apart number sheet – 3’s

problem solving assessment rubric

10 frames (teacher size)

10 frames (student size)

10 frames blank mini’s


Ten Things about Teaching Math I Wish I Had Known as a New Teacher September 22, 2015

Filed under: General Math — Focus on Math @ 6:09 pm
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Screen Shot 2015-09-22 at 6.10.24 PM Every teacher has a first year of teaching, one  which often seems overwhelming. Even the next few years can be taxing as one tries to deal with all the planning, the lessons, the assessment, the special needs, the routines, the supplies, the parents, the responsibilities, etc. Whoever says teaching is a piece of cake needs to step into the classroom for a while.

Besides spending years as a classroom teacher, I have been a math coach, a teacher of university math education courses, and a full time district math coach. My math journey has been exciting, but looking back I wish I had known in those early years of teaching some of what I know now.

Here are some thoughts along that line:

  1. My attitude toward mathematics matters. If I don’t like it, the students won’t either. If I love it, they will, too.
  1. Every child can learn math
  1. Concepts need to be developed beginning with concrete materials (manipulatives).
  1. It is important to use many kinds of visual/pictorial representations regularly.
  1. My students need my help to learn how to “talk math” and need time in my lessons to do it.
  1. There really are many ways to solve a problem, not just one “right way” (that was demonstrated by me, the teacher).
  1. It is better to do one problem five ways than five problems one way (Polya).
  1. Students need to develop strategies for solving problems, strategies that they understand and can explain.
  1. Adults use mathematical estimation daily. Kids need to practice it often.
  1. Doing algorithms requires no mathematical understanding, just a knowledge of how to follow rules.

What do you think? Let me know.

Mathematically yours,