Focus on Math

Helping children become mathematicians!

Free On-Line Graphing CalculatorJune 21, 2012

For those doing secondary mathematics, this free on-line graphing calculator may be of interest. For those who have iPads, there are free graphing calculator apps available, but it is nice to have one available on a home or laptop computer as well. Besides being helpful for completing homework assignments, the graphing calculator is a great learning tool as well. For example, by comparing the graphs of particular equations [such as those for x^2, x^2 + 3 and (x + 3)^2] one can gain an understanding of how a graph is translated on the Cartesian plane.

Mathematically yours,
Carollee

NCTM Sessioin: Packing a Powerful Punch with PatternsApril 23, 2012

I am excited to be heading off to Philadelphia later today for the National Council of Teachers of Mathematics (NCTM) national conference. I am also delighted to have the privilege once again of presenting a session at the conference.

My presentation this year is “Packing a Powerful Punch With Patterns: Foundations of Algebraic Thinking”. Elementary teachers are often involved with patterning with students, but don’t always have a clear vision of where the patterning leads in the algebra strand of mathematics. My session in Philadelphia will explore this. We will look at types of patterns, and then go more deeply into growing patterns as we examine how to translate the pictorial view of the pattern to an algebraic function or rule.

If you are at the conference I hope you will join me Thursday at 1:00 pm (Session #195, room 204A of the convention centre). It will be hands on and lots of fun!

Mathematically yours,
Carollee

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