Focus on Math

Helping children become mathematicians!

SD #60’s 5th Annual Parent Conference March 20, 2012

Filed under: General Math,Parents — Focus on Math @ 3:44 pm

SD#60 (Fort St John, BC) will be hosting its Annual Parent Conference on April 21. The theme is “Your Amazing Child” and it looks to have lots of informational sessions. The really great part — it is FREE!! Woohoo!! Can’t beat that!

I am pleased to be presenting two different math session at this year’s conference. I am doing one session for parents of primary students (Session K) and another for parents of intermediate students (Session S), both with a focus on helping parents understand some of the different things that are happening in mathematics lessons these days. Parents will go away with a clearer understanding of why we are doing some things differently and of how to support their children’s math learning.

If you are in the area I hope you will join us for the conference. More information and registration can be found here:

I hope to see you there!
Mathematically yours,


Basic Facts: Mental Math as a Foundation for Multiplication Fact Strategies March 16, 2012

Basic Facts are still very important. Although newer curricula put a greater emphasis on problem solving, communication, reasoning, and representation of numbers, basic facts are still an integral part number sense in students. If a student is a good “memorizer”, then learning the multiplication facts will not be difficult. However, for many students the random bits information we call “facts” don’t stick well in the brain (the brain tends to remember information that is personally meaningful!), and thus it is important that we support those students in their learning by teaching and rehearsing thinking strategies.

Before we look at those particular strategies that are useful for learning the multiplication facts, there are some “prerequisites” to consider. Many of the strategies I will be suggesting use some kind of mental math to help students go from a known fact to an unknown fact.

The mantra for students is this: “Use something you KNOW to get to something you DON’T KNOW!” This is a comforting thing for students, particularly those who have struggled with learning their facts. They tend to feel that there is no hope for them. In some cases they have worked for a very long time, even several years, to memorize these facts, and at this point they feel like it is a hopeless task. We need to offer hope in the notion that they can begin their learning with things they do know, and build from there.

Consider working with your students to build these kinds of skills, remembering to tie them to concrete and/or visuals (such as ten frames or 100 dot arrays):
• Subtracting a single digit number from a multiple of ten (e.g., students use the known fact of 10 – 6 to solve 60 – 6. Tie into ten frames).
• Subtracting a double-digit number from a multiple of ten (e.g., build on the previous skill and have students solve 60 – 16 by subtracting first 10 and then 6.)
• Doubling any 2 digit number, using whole-part-part strategies if necessary. It may be easy to double 12 (think 10 + 10 + 2 + 2), but it will be harder to double 16. Students might consider 16 as 15 + 1, then double each of the two parts, and add back together (think 15 + 15 + 1 + 1 — look for “friendly numbers ending in 5’s or 0’s).
• Adding any single digit number to a double-digit number, particularly when the sum of the one’s place digits is greater than 10. E.g., 35 + 7 can be considered as 35 + 5 + 2; 48 + 6 can be considered as 48 + 2 + 6. (Pull apart the number to be added in a way that makes a group of ten.)
• Subtracting any single digit number from a double-digit number, particularly when “regrouping” would be required. E.g., 54 – 8 can be 54 – 4 – 4. (Again, break apart the number being subtracted into parts that make the work easier.)

It is well worth the time that you invest with students doing mental math. In As well as being a great life-skill, mental math allows students to be flexible with numbers and use powerful thinking strategies.

Mental Math and Basic Facts — don’t skip these important things!
Mathematically yours,


Pi Day Approaches! March 12, 2012

Mathematicians tend to celebrate 3/14 as Pi Day in honour of the important relationship that exists between the circumference and diameter of any circle. Historians note that at least 2000 BC humans had noticed the constant ratio between these two parts of any circle, but it was not until 1706 that the notation using the Greek letter π was introduced by a man named William Jones.

This site offers a whole host of ideas for exploring and celebrating Pi Day with students. Try singing this song (to the tune of Oh Christmas Tree) written by LaVern Christianson:


Oh Number PI

Oh, number Pi
Oh, number Pi
Your digits are unending,
Oh, number Pi
Oh, number Pi
No pattern are you sending.
You’re three point one four one five nine,
And even more if we had time,
Oh, number Pi
Oh, number Pi
For circle lengths unbending.

Oh, number Pi
Oh, number Pi
You are a number very sweet,
Oh, number Pi
Oh, number Pi
Your uses are so very neat.
There’s 2 Pi r and Pi r squared,
A half a circle and you’re there,
Oh, number Pi
Oh, number Pi
We know that Pi’s a tasty treat.

And here’s a quick video showing several approximations of pi:

Have fun, and enjoy a slice of Pi!
Mathematically yours,


North Central Zone Conference Sessions March 9, 2012

Thanks to all of you who participated in my two math sessions here in Prince George, BC, today as part of the Zone Conference. In spite of my sore throat, we covered a lot of ground about fractions, decimals, percents, integers, and algebra.

I promised some “clean copies” of the handouts, so here they are, ready for downloading:
balance scale (for doing algebra equations concretely)
percent circles
percent grids and blanks (see activity below)
mini 10 frames (for representing decimal tenths in adding, multiplying, etc.) 27 per page40 per page

Remember, the BC curricular documents stress over and over that students should demonstrate their mathematical understanding “concretely, pictorially, and symbolically”. We tend to not do enough of the concrete and pictorial parts, but hopefully after today’s session(s) you have a few more ideas of how you can fit those in to your lessons.

We did not do anything with the percent grids and blanks, so let me share an  activity you can do with those. Before photocopying to give to students, partially shade several of the “blank” squares. Don’t worry about shading in a particular manner, just draw a random closed curve in each square and shade it in. Ask the students to estimate the percentage of the square that is shaded, and then give each of them one of the little 100 grids copied onto acetate and cut out individually. Students can lay the acetate grid over the partially shaded square and count the number of little grid squares that are completely shaded. Then have them count all the little squares that are partially shaded (for instance, the curve goes through the square leaving part of the grid square shaded and part not shaded) and divide by two to average out the ones mostly shaded and mostly not shaded.

For a recap on what we talked about using the fraction pocket charts, check out the blog post called “Reasoning About Fractions Using Benchmarks”. That post goes over what we talked about today and includes directions for making the pocket charts as well.

If I have forgotten something, let me know and I will edit this post and add to it! I hope you try something from the workshop right away with your students!

Mathematically yours,


What Do I Do When My Kids Don’t Get the Math?

Thanks to all of the participants my session at the BCTF’s New Teachers’ Conference in Richmond, BC last weekend. The session, “What Do I Do When My Kids Don’t Get the Math?“, was all about helping kids make sense of mathematics by exploring and using a variety of strategies to do the four main math operations (addition, subtraction, multiplication, and division). Remember, it is not that the algorithms (or “standard” ways of doing things) are in and of themselves “bad”, it is just that students often do not make meaningful connections to the “why” of the underlying mathematics. They end up following rules that have no meaning and do not make sense (hmmmm… refer to my blog post about suspended sense making).

Understanding is all about meaningful connections, which I thought was depicted in the picture seen here. No, it is not some piece of modern art, but a picture of a section of the carpet of the Radisson Hotel there in Richmond where the conference was held last week. As I sat working at the table sponsored by the BC Association of Mathematics Teachers, I really looked at the floor and decided that the carpet gave a great visual representation of the dendritic connections in the brain that come into play when we understand something. This is what we need out students’ brains to be doing in math!!
Allow me “pitch” the mathematical processes again. I still believe that understanding “lives” in the processes, and that if we will engage students in these processes regularly, they cannot help but build mathematical understanding. Here in BC, the curriculum documents lists these seven processes and tie them to every single math outcome K-12!!

  • Communication
  • Connections (C)
  • Mental Math & Estimation (ME)
  • Problem Solving (PS)
  • Reasoning (R)
  • Technology (T)
  • Visualization (V)

If you live outside BC, then I recommend digging into the processes as listed in the documents of the National Council of Teachers of Mathematics (NCTM), which are these:

  • Communication
  • Connections
  • Problem Solving
  • Reasoning & Proof
  • Representation

So, if you construct learning experiences for your students that get them involved these processes, they will begin to build understanding! It won’t happen in a flash, but if you persist it will happen!

Mathematically yours,


Using a Rubric in Math Problem Solving March 3, 2012

Screen shot 2013-10-17 at 9.04.46 AM If we want students to become better problem solvers, not only must we provide situations where they can practice their problem solving skills, but we also need to make sure they are thinking meta-cognitively about the problem solving skills they are developing. One way to do that is to use a rubric with students.

Sandra Cushway, another teacher in my district, and I are presently in our 5th year of an action research project concerning teaching the whole curriculum through problem solving. As part of that project we developed a problem-solving rubric modeled somewhat after the rubrics developed by the BC Ministry of Education. Thus we chose to evaluate the same 4 aspects of mathematical thinking as those of the Ministry’s rubrics (namely, Concepts & Applications; Strategies and Approaches; Accuracy; and Representation & Communication), but we wrote the descriptors as “I statements” so students could self-assess. (Download our rubric here.)

The ministry’s rubrics were developed for specific grade levels (link here to see those) but Sandra and I and chose to make one rubric that was applicable to many grades.
For instance, if a student might choose this statement in the Strategies & Approaches aspect: “I chose a strategy that worked. It allowed me to get an answer but it took a long time, and was confusing in places.” That statement can apply to a primary student using strategies for double-digit addition as well as for a high school student looking to solve trig problems.

If you are new at using rubrics, may I suggest this: it is much better to begin the self-assessment process with a single aspect. In other words, choose one line from the rubric like “Strategies and Approaches” and only use that “strip” across the page with students. Talk about what the different levels mean and show samples of problem-solving work at each of the four levels. Have students work together to assess some work so they can get a feel for evaluating what good (and poor) strategies look like.

Let me know how the rubric works for you and your students! I know it can make a difference in the quality of work they do.

Mathematically yours,