Focus on Math

Helping children become mathematicians!

OLOL Problem Solving Workshp September 2, 2015

Filed under: General Math,Ideas from Carollee's Workshops — Focus on Math @ 10:19 am
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Screen Shot 2015-09-02 at 9.52.23 AMA big thanks to the staff of Our Lady of Lourdes in West Kelowna, BC for the attention, participation, and “buy-in” at the Problem Solving Workshop yesterday. I hope you went away inspired and equipped to do problem solving regularly with your students in this coming school year.

As promised, I am posting links to the items we discussed. Some of those are available elsewhere on the blog (and may have more explanation about using them in lessons) so you may want to use the “search” feature on the right side of the page to find other posts about particular resources. I certainly hope you will let me know how it is going in you classroom. Send me photos of your students’ work, your Tools and Strategies posters, your “sharing pages”. It’s going to be a great year!

Mathematically yours,


100 dot array large

100 dot array – 12 per page

100 dot array 6 per page

100 dot array 4 per page

student rubric for PS

ten frames – student

ten frames – teacher

mini blank ten frames

percent circles


“Number of the Day” Sheets: Choosing the Number January 5, 2015

Num of Day III eqn picI recently received an email from Stephanie, a grade 2 teacher in Newfoundland, inquiring about choosing the number for the Number of the Day sheets:

“I really love the Number of the Day sheets you have produced and the opportunities for differentiating the instruction. Just wondering how you set this up? Do children do this everyday or on designated days? How do you decide on the number for the day?”

I thought others might be asking this same question, so have decided to post an edited version of my response to Stephanie’s question:

As for setting up the Number of the Day sheets, things are really flexible. There is no one right way — you want what works best for your students and your time constraints. That being said, I have found that if you are able to have the kids do them really regularly (daily if possible) over a good number of weeks, the students are able to really get into the meat of them. By sharing about them after they have worked them, students get to hear what others have tried and will often stretch themselves to try to match what others are doing. They have a chance to really play and explore the number relationships that are brought out in the sheets’ activities.

The number can be picked in a variety of ways — everything from you choosing, a student choosing, drawing a number from a jar or dropping a bean on a 100 chart! Sometime I have chosen specific “repeats” (e.g., every number that week has a 9 in one’s place) sot the kids to see and compare what happens in such cases. What is the same as before? What is different? Or I might pick several numbers within a “decade” (e.g., 33, 37, 31, 35, 38) and again have students compare/contrast over those days.

No matter what number is chosen, one question that is really great to ask is “What do/did you notice?” When that is asked often in the math classroom, students get in the habit of paying attention to details, looking for patterns, making comparisons, and such.

I am happy with random numbers, too, but sometimes choosing numbers with a particular relationship is good so you can really draw out the depth of the relationship.

I hope you will try the Number of the Day sheet(s) with your students. More information about the sheets as well as the downloadable versions, can be found in the links below.

Mathematically yours,


Number of the Day Sheets to Download:

Level 1 (English and French)

Level 2  (English and French)

Level 3 (English and French)  (pictured above)





What’s Important to Have in a Grade 1 Classroom? October 2, 2014

Screen Shot 2014-10-02 at 10.02.55 AMI was recently contacted by a former colleague, Dawn, regarding what manipulatives a grade one classroom might need to have on hand to support effective learning math. It seems a friend of Dawn’s is in a classroom which really has nothing for the children to use for hands-on math learning and they were wondering what was needed.

First off the classroom needs counters — counters in different shapes, sizes, etc. They can be purchased ones (such as mini plastic teddy bears) or ones gathered from home (such as bread tags, but†ons, etc.). But the need to be abundant and available.

Students need a way to count efficiently, especially in tens and ones. Egg cartons cut down to 10 holes, blank 10-frames printed on paper or card stock, or commercially produced 10-frames can all be used. I even like using cookie sheets (non-aluminum) and marking them with coloured tape as a giant 10-frame for use with magnets.

Base 10 blocks are also great for young students. These a generally in the form of small 1 cm cubes for “ones”, sticks for the “tens”, and flats for the “100’s”. I do want to make a critical point here: students may be engaged in a game of trading 10 cubes for a stick, or 10 sticks for a flat with every appearance of understanding the “ten-ness” of our base-10 number system. But be careful here. Student can be following your rule of trading 10 for 1 without that understanding. They might be just as happy to trade 8 for 1 or 12 for 1. The manipulatives give a opportunity for students to develop that important base-10 understanding, but moving blocks around correctly does not necessarily indicate that the understanding has been built in the student’s mind.

I think a grade one classroom needs “pop cubes” (multi-link cubes) — those blocks about 1inch in each dimension that can be attached together. I like to store them sticks of 5. If students need a particular amount for an activity, say 18, we discuss how many sticks each student will need, and then go get them. I also use these in many quick number-sense building activities. If I have students hold up a certain number of blocks, I want them to do so to model a ten frame. If I ask for 9 blocks and a student were to hold up a single stick of 9, I, as the teacher, cannot tell from a distance if the student is holding 8, 9, 10, or 11 blocks. But if he holds up a five stick beside a four stick, I can tell at a glance that he has the correct number. Pop cubes can be used in a multitude of math activities and should be on-hand for regular use.

Another must-have in my book are pattern blocks. They are particularly great for patterning activities for exploring symmetry, not to mention the creativity factor! I love them!

There are a number of things that I think should be in the classroom that are “make-able” such as dot cards, dot plates, printed ten-frames, even printed dominoes (click for more info on these)— all useful in exploring numbers, in building number sense, and  in helping students develop the skill of subtilizing. Students need to SEE the numbers in math, and these materials can help develop that “seeing” in the children.

Of course there are many other things that are fun to have in the math classroom, such as dice, dominoes, blocks, playing cards, geoboards, plastic coins, bingo chips, square tiles, Cuisenaire rods, and two-colour counters, to name a few. But lots of math learning can take place with some thoughtfully crafted lessons and activities and just the basics.

I hope you will focus on the math understanding with whatever materials you have at your disposal!

Mathematically yours,


Number of the Day – Level II March 6, 2014

Numero du jour II picIn keeping with my belief that elementary school that students should be involved with numbers everyday in math time, I am posting my Number of the Day Level II sheet in English and French.

Today’s sheet is one to use primarily with numbers to 30. As in the Level I sheet, most of the components are self explanatory, and again the colouring on the 100 chart can be done either by colouring the individual number or by colouring all numbers up to and including the number of the day.

As mentioned before, breaking the number apart in different ways is an import thing for students to practice. As John Van de Walle wrote, “To conceptualize a number as being made up of two or more parts is the most important relationship that can be developed about numbers.” [Van de Walle, J. and Folk, S. (2005). Elementary and Middle School Mathematics: Teaching Developmentally (Canadian Edition). Pearson: Toronto.]

I am delighted to offer this sheet in a French version, as well. Merci to my friend and colleague Lynn St. Louis for her translation. number of the day II pic

Download the English version here.

Download the French version here.

I’d LOVE to hear from you if you try either version!

Mathematically yours,



Number of the Day – Level I March 5, 2014

Screen shot 2014-03-05 at 7.55.19 PMI have long believed that in elementary school that students should be involved with numbers everyday in math time. This may not always be the case — the teacher might be teaching a unit on pattering or geometry, for instance. While those are worthwhile concepts, I still remain convinced that students need some time each day to think about and work with numbers.

One way this can be accomplished is through the use of Number of the Day sheets. The idea of using such a sheet is not new – indeed, there are many versions available on the Internet.

I have added my own version of the Number of the Day sheet into the mix. In fact, I will be adding several versions over the next few days that are targeted at different levels of learners

The Number of the Day sheet I am posting today is one that can be used in Kindergarten classes, but it may be useful in Grade one classes early in the school year. The components are self-explanatory, although I did have one teacher who started using the sheet call me and ask about colouring on the 25 chart. She asked, “If the number of the day is 12, am I supposed to have students just find and colour the numeral 12, or are they supposed to colour all the boxes up to and including 12?” My response was, “Yes!” Either way is good, with each method focusing on something slightly different about the number 12.

Breaking the number apart in different ways is an import thing for students to practice. As John Van de Walle wrote, “To conceptualize a number as being made up of two or more parts is the most important relationship that can be developed about numbers.” [Van de Walle, J. and Folk, S. (2005). Elementary and Middle School Mathematics: Teaching Developmentally (Canadian Edition). Pearson: Toronto.]Screen shot 2014-03-05 at 7.55.36 PM

I am delighted to offer the sheet in a French version as well. Merci to my friend and colleague Lynn St. Louis for her translation.

Download the English version here.

Download the French version here.

Mathematically yours,



Calgary City Teachers’ Conf 2014 February 17, 2014

Screen shot 2014-02-17 at 9.04.21 AMIt was wonderful to share the Friday morning session at the Calgary City Teachers’ Conference with so many new friends! I hope you walked away with some ideas for helping your students understand mathematics is a deeper way. Congratulations to Shannon Muir who won the math coaching session in the draw!

If you remember one idea from the morning, I hope it is one about building understanding in math. Students need to make sense of the concepts using first concrete materials, then with pictorial representations, and then with symbolic (or numeric) representation. Rules for manipulating numbers are not remembered well if they are not based in meaning. Caine and Caine report from their brain research, “The brain resists meaninglessness.”

As promised, I am posting here the tools we used and referred to for your easy access.

100 dot arrays (1 large)

100 dot arrays (6 per page)

100 dot arrays (12 per page)

ten frames (teacher size)

ten frames (mini blank ones, 40 per page)

base 10 grid paper (enlarge as needed)

fraction & percent circles

fraction pocket chart    (link here for more discussion about these)

I think that is everything. If I have missed something let me know. And I would love to hear how this all makes a difference for your students!

Mathematically yours,


Screen shot 2014-02-17 at 11.27.57 AM


Building Numbers: A Kindergarten or Primary Activity January 23, 2014

building numbers chips 2

I visited Mrs. Merrill’s kindergarten class today. The focus of the math lesson was on building numbers to 10, we did this with a large organizing sheet (11” x 17”), some small dot cards (each student had a set of cards 1 to 10 — download below), and small bingo chips. Students were asked to place a dot card over each square on the paper, and then use the bingo chips to make another set the same size in each box.

Some students chose to lay their cards out in rank order, while others were happy to just lay the cards in any order they pulled the card out the small bag. We also noticed some students organizing and building left to right in the boxes, while others built randomly on the page.

building numbers chips 1

The organizing sheet is very “generic” on purpose allowing it to be used in a variety of ways. The number for building can be generated by a dot card, by rolling a die (or dice), by placing a number word card (e.g., “two”) over the square, by dropping a bean onto a 100 chart, etc. Students can build the number with counters, with little ten frames (I find children love to work with tiny things!), with base-10 blocks, etc.

building numbers 10 frames

I have not figured out how to put a large 11 x 17 paper into Dropbox, but if you will print out the template you want onto legal-sized paper, you can then enlarge at a copier 121% and it will fit the 11 x 17 page rather nicely.

I have created templates for building 8 different numbers as  well as for building 10 different numbers. The latter could be used for 100 Day activities by building 10 in each space for a total of 100.

Dot cards can be downloaded here as well.

I hope you are able to use the activity in one of its “versions” in your classroom!

Mathematically yours,