Focus on Math

Helping children become mathematicians!

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,



Math Toolkits for Students — More Stuff to Add (part 3) May 19, 2011

There are more items that can be added to the toolkits for students, but these I will separate by primary (gr 1-3) and intermediate (gr 4-7) levels. Again, it is hard to just mention the contents without going into activities that use the tools to help students build mathematical understanding. Hopefully the tool itself will prompt you to think about some ways to use it.

Primary Tools:

  • 25 chart, laminated (usually created in 5 rows of 5)
  • blank 5-frame (with spaces big enough to put counters on)
  • blank 10-frame
  • blank double-10-frame (two blank 10-frames on one card)
  • set of filled in 10-frames (1-9, multiple 10’s)
  • bead bracelet (10 beads in two colours, 5 of each) to be worn draped over the fingers so the beads can be manipulated. Two bracelet may be worn to use for numbers in the teens.
  • large flattened paper plate or cut out paper circle for making dot plate configurations with bingo chips
  • mini bags of small coloured wooden sticks or other small materials for patterning
  • teeny-tiny Hundreds Tens and Ones (HTO’s) — miniature place value pieces cut out of large plastic canvas (found in crafting stores)
  • place value cards — overlapping cards that show, for example, 425 can be pulled apart to reveal 400, 20 and 5 (click on image above to print)

Intermediate Tools:

  • booklet of mini 100 charts to be coloured in to show multiples (x2, x3, x4, etc.)
  • metre tape (purchased or created by taping photocopied paper lengths together)
  • fraction-bar card (a card with a fraction bar in the middle — students use numeral cards to place as the numerator and denominator)
  • fraction percent circles (two different coloured circles partitioned off in hundredths each cut along one radius and then placed together so they “spin” over each other to show different percent values)

As you can see, there are many things that can be used as “tools” in the teaching of mathematics. Creating a toolkit with students is a wonderful way to make lessons engaging.

Mathematically yours,


Math Toolkits for Students (part 1) May 17, 2011

When I worked with a group of teachers last week, one of them asked about math toolkits for students. I have talked a lot about this idea in my district, and even did a workshop on the topic a couple of years ago. It has come up again as a topic of interest in a number of teacher groups, and I thought it would be a good idea to post some ideas about toolkits here.

I first heard about the idea of creating a toolkit about 15 years ago when I went to a workshop offered by Kim Sutton. I loved the idea then, and still do. In fact, as I work with children all day at Charlie Lake School each Wednesday, I have a toolkit in each desk for students to use during the day. When I had my own classroom, each student individually had his or her own toolkit. The way I have my one-day-a-week room now is that a toolkit must be shared with all the children who happen to sit at that desk during the day (I teach 8 groups of students during the day ranging from grade 1 to grade 5). I confess I do not like the shared tookit quite as well as each student being responsible for his/her own toolkit, but it is still working out pretty well.

I have used some of Kim Sutton’s ideas for the toolkits, and added other ideas of my own, all with the purpose of helping children “do mathematics”.

So this post does not become unwieldy, I will talk about some general components of a toolkit, and separately post some specific ideas for primary and intermediate toolkits.

The Toolkit Container:
I have always used a large, Ziploc-brand freezer bag. I prefer the “squeeze to close” kind, without the little white slider, as I found that those sliders come off too easily with consistent use. We call them “large plastic bags” only on the very first day when they are passed out. After that they are always referred to as “toolkits”. I liked that the bags were basically flat, and I always have had students store them right in their desks. For me, this is part of the “power” of the toolkits: they are easily accessible for students to use, whether in an activity directed by me, or by their own choice as they work to solve problems.

Although plastic bags are my personal preference, some of the teachers in my district have used other things. One teacher would go out at the beginning of the school year when school supplies are on sale and purchase large, plastic cases for her students. These became the math toolkits and they were stored at the side in the students’ cubby-holes. A variety of containers would work — they just need to fit the kinds of things you are going to put into the toolkits.

Building the Toolkit: My personal philosophy about toolkits is that I do not give them to students packed with tools. I remember hearing about a mechanics program in which all of the would-be mechanics were given empty toolkits, and as they went through the program and learned how to use a particular tool, then the tool became part of each student’s toolbox. At the end of the program the toolboxes were full, but the students knew how to use all of the tools inside. That is my thinking for the math toolkits. On the day I give the bags and introduce the toolkits, I also give out the first tool and we use it together in class. Thereafter each time a new tool is introduced, we work with it as a class and then it goes into the toolkits.

I’ll begin to talk about the contents in my next post.

Mathematically yours,