Focus on Math

Helping children become mathematicians!

Breaking Apart Numbers: Practice Sheets May 27, 2014

Screen shot 2014-05-27 at 10.57.33 AMI have mentioned before about the importance of breaking numbers apart, of having students understand that every number can be broken into smaller numbers. I have included this practice on all of the Number of the Day sheets (level l, level ll, level lll) that I have posted, but it warrants adding these other sheets that focus on this Whole-Part-Part number relationship.

Regularly practicing this skill can change students’ thinking. They will be much more likely, in any given situation involving numbers, to look for alternative ways of thinking if they have spent time pulling numbers apart in many ways.

Remember, the students are not starting with a new number in every circle. Rather they are using one particular number for a line or for the whole page! In different situations it may be more beneficial to break a number apart in one way than it is in another way.

Mathematically yours,


download the breaking into two parts sheet here

download the breaking into three parts sheet here

Screen shot 2014-05-27 at 10.57.53 AM


Mathematics is Much More than Numbers on a Page May 22, 2014

Filed under: General Math — Focus on Math @ 11:34 am
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Screen shot 2014-05-22 at 11.27.16 AM One of my favourite quotes about mathematics: “Mathematical notation no more is mathematics than musical notation is music. A page of sheet music represents a piece of music, but the notation and the music are not the same; the music itself happens when the notes on the page are sung or performed on a musical instrument. It is in its performance that the music comes alive; it exists not on the page but in our minds. The same is true for mathematics.” — Keith Delvin

Are your students really DOING mathematics, or just working with notations on a page?

Mathematically yours,



Carollee is Retiring –from SD#60 but NOT from math!! May 21, 2014

Filed under: General Math — Focus on Math @ 2:10 pm

Screen shot 2014-05-21 at 1.52.20 PMIt is with great delight that I let you all know that I am retiring from my position here at School District #60 Peace River North. I am off to live in Comox, BC, on Vancouver Island, near my daughter and her family. I will be leaving The North in just a couple of weeks after being here for many, many years.

I will NOT, however, be retiring from MATH! I will certainly continue with this blog, and I will continue to work with schools and districts to work toward better math instruction and learning. My time for such involvements will be much more flexible and I am looking forward to new endeavours.

If I have had an impact on YOUR teaching, thinking, etc., or if you are just wanting to send good wishes, feel free to contribute to the google presentation that will be shown at the retirement tea on June 3. (I am under strict orders to NOT visit that site so as to be surprised at the tea itself!)

The google presentation site is this:    (You will have to copy and paste this one as I do not want to open the link myself LOL).

This has been a great journey, but it is time for a new chapter.

Mathematically yours,


PS: The poster is the handiwork of my colleague and friend Toni Thompson.


Ecole Muheim Elementary, Smithers, BC: Math Week May 20, 2014

Math week picMy appreciation to the staff at Ecole Muheim Elementary in Smithers, BC, for your great participation in the workshop last Friday! With the weather as beautiful as it was, and the fact that it was the beginning of the Victoria Day long weekend, your focus and participation is doubly appreciated!

One of the things we talked about at the session was the idea of breaking away from the traditional focus of teaching mathematics in units that are seldom revisited. You know, the three-week unit on fractions, after which we do very little with fractions for the remainder of the school year. I showed you the “math week” I worked with as a classroom teacher, and promised I would post a copy of that.

Please note that the main focus everyday was on number and operations. I think particularly in elementary school that this is often neglected. We will do units on patterning, on geometry, and such (which, of course, are valid topics in mathematics!) that go for weeks at a time while leaving behind number. I personally believe that this is not the best way to cover the topics, and so propose a weekly plan where the other strands/topics are addressed in mini-lessons.

I have had teachers tell me that the idea of juggling all of the different topics at once was overwhelming – and to that I offer the plan of keeping the mini-lessons the same for a week or two. Even doing that you will be covering all of the topics each grading term, which I believe is a very good thing.

You do not need to re-invent the wheel so to speak when it comes to the mini-lessons. For example, as you consider what you will do in the patterns & relations mini-lessons, you can go to your regular textbook source and use lesson ideas from there – you will just chunk the lessons into smaller bits and do them in successive lessons.

I coached one teacher regarding the Math Week system, and she created for herself a series of thin binders to keep track. Her Monday binder had the unit content photocopied for the topic for each Monday mini-lesson, and she just highlighted the chunks she was going to do and numbered them in the order she was going to do them, and thus in one planning sitting she laid out for herself the next 8-10 mini-lessons on that topic. She did this same thing for each of the days of week. The system worked very well for her in that manner.

Download the Math Week sheet here.

For the Muheim folks I will add links here to a number of the handouts we used so you have access to clean copies of those:

–100 dot arrays (1 large)

–100 dot arrays (4 per page)

–100 dot arrays (6 per page)

–100 dot arrays (12 per page)

–number of the day level 1 (English)

–number of the day level 1 (French)

–number of the day level 2 (English)

–number of the day level 2 (French)

–number of the day level 3 (English)

–number of the day level 3 (French)

–base 10 grid paper (larger)

–percent circles


I would love to hear about the ideas you are trying in your classrooms! Please comment on the blog or send me an email!

Mathematically yours,



Early Counting: the Foundation of Math May 12, 2014

Screen shot 2014-05-12 at 9.55.18 AMThe meaning attached to counting is the most important idea on which all other number concepts are developed.

Counting Involves at Least Two Separate Skills:

  • A child must be able to produce the standard list of counting words in order: “one, two, three, etc.” This must be learned by rote memory.
  • The child must be able to connect this sequence in a one-to-one manner with the items in the set being counted. In other words, each item must get one and only one count. This important understanding is called one-to-one correspondence.

Meaning Attached to Counting:

There is a difference between being able to count as explained above and knowing what the counting means. When we count a set, the last number word used represents the magnitude or the cardinality of the set. When children understand that the last count word names the quantity of the set, they are said to have the cardinality principle.

Give a child a set of objects and ask, “How many”? After counting, if the child does not name how many are there (as, “There are 7 of them,”), then ask again, “How many?” If a child can answer without recounting, it is clear he or she is using the cardinal meaning of the counting word. Recounting the entire set again usually means that the child interprets the question “How many?” as a command to count.

Almost any counting activity will help children develop cardinality.

  • Have the child count several sets where the number of objects is the same but the objects are very different in size. Ask the child to talk about this.
  • Have the child count a set of objects, and them rearrange the objects. Ask, “How many now?” (If the child sees no reason to count again, likely the child has a good sense of number and has developed cardinality.)

Happy counting!

Mathematically yours,



Notre Dame School, Dawson Creek, BC May 2, 2014

Filed under: General Math — Focus on Math @ 4:19 pm

Screen shot 2014-04-23 at 2.44.48 PMA big shout out to the staff of Notre Dame School in Dawson Creek, BC! The session last week , focusing on Number Sense, was designed to help you take positive steps in your classroom. Thank you for your enthusiastic participation!

Hilde Howden’s definition of number sense is still my favourite of all the ones I have come across. Read it through and decide which are the 3 most important words in it. I’d love to hear your choices!

Students build number sense mainly as a result of the math experiences we offer them, and so it is critical that we make sure to provide a rich mathematical environment. Talking about and working with number relationships is worthwhile. Additionally, making sure students have lots of concrete materials and visual representations will help them build a better understanding of numbers.

Remember, math is supposed to make sense for EVERY student EVERY day!

Mathematically yours,