Focus on Math

Helping children become mathematicians!

Math Camp (gr 6-8) 2011 August 31, 2011

What a great group of participants we had at yesterday’s gr 6-8 math camp! I was delighted with all of the group sharing that we were able to facilitate — there is always so much that teachers can learn from each other.

The workshop yesterday focused on several things: mental math, integers, fractions, and algebra. These areas, I believe, are important for students to master if they are to be successful in subsequent levels of mathematics.

Mental math is a skill which is only developed if practiced, and we discussed some particularly useful strategies that might be incorporated into regular practice sessions. First, mental math begins with basic facts! From there we can have students practice thins such as these:

  • adding multiples of tens (MOT’s) (20 + 50)
  • subtracting single digits from MOT’s (50 – 8 )
  • adding single digits to non-MOT’s (39 + 6)
  • adding to get 100 or – from 100
  • adding any two-digit #’s (47 + 39)
  • doubling numbers
  • halving numbers
  • multiplying by 10, 100
  • dividing by 10, 100
  • multiplying by 20 (by doubling and then multiplying by 10)
  • multiplying by breaking up numbers (using “nice” numbers)

Response boards are a great way to do immediate full-class assessment during mental math practice.

Our focus on integers was in using “chips” to have students learn about positive and negative numbers in a very visual way. It is helpful for students if they understand the power of zero in adding and subtracting integers, and zeros can be visualized by an equal quantity of positive and negative chips. Using the chips to solve addition, subtraction, multiplication, and division problems involving integers allows students to build a conceptual understanding of integers which goes far beyond memorized rules.

For fractions, we discussed the need for students to develop number sense regarding them. Using benchmarks to estimate fractions is one way to help facilitate this. We talked about making pocket charts for both the teacher and the students to use in practicing this. (Pocket chart directions.)

As for algebra, once again, visualization was the key to helping students make sense of this generally abstract area. By having students display and manipulate equations in a concrete way on a “balance scale”, they have the opportunity to learn what are acceptable or “legal” moves in solving algebraic equations. (Balance scale.) A hands-on, visual approach to algebra allows every student to be successful in this area!

One of the teachers at the workshop is going to email me a rubric that she used in her math classes last year, and I will up-date this post with that rubric once I have received it. (later) Here is the link for the rubric. When we discussed this, the “traffic light” part was really important. Remember that students can self-assess their understanding and record it as red (“I am totally stuck.), yellow (“I am able to work some on the problem but not I am not really sure about it.), or green (“I understand this well enough that I could teach someone else.)

In the meantime, I hope you will think about how you might better teach these areas of mathematics that are critical for students in these grades.

Mathematically yours,


Math Camp: K-1 (2011) August 27, 2011

Thank you to all the wonderful participants in yesterday’s Math Camp session! Judging by the sense of excitement that was in the room by the end of the workshop, I know you were taking away with you some great ideas for the new school year.

Remember that much of what you do in Kindergarten and Grade 1 needs to centre around number relationships (primarily these: whole-part-part*; anchoring numbers of 5 and 10; one and two more/one and two less; and visual-spatial relationships.) It is as children have numerous opportunities to explore these relationships that they begin to develop number sense.

* Do note that I prefer the term “whole-part-part” to the more common “part-part-whole”. The emphasis in this number relationship is the pulling apart of a number, not the pushing together of two parts to make a larger whole. Primary teachers may make a connection to a similar distinction in reading, namely the difference between decoding and encoding words. They denote two very different processes. Traditionally in math the emphasis has been placed on “encoding” numbers, or adding them together, with little or no emphasis given to to “decoding” numbers or pulling them apart. Children need repeated practice in pulling numbers apart in different ways. We want them to notice that in different circumstances, different parts are more beneficial.

As promised in the workshop, I am posting links for the blackline masters that we referred to during the workshop. I hope up you make good use of them! (Click on any item below to download the file.)

dominoes (large) template
small dot cards template
large dot cards – 1       NOTE: these large, demonstration-sized dot cards appear to go off the page.
large dot cards – 2       That is normal. There are only two large cards fully on each page.
large dot cards – 3       Ignore the stuff on the sides! The two that matter are there!
student ten frames
teacher ten frames
blank 5 frames
blank 10 frames
folding whole-part-part cards

As always, let me know if I can be of more specific help.

Mathematically yours,