Focus on Math

Helping children become mathematicians!

NCTM 2013 Denver PresentationApril 18, 2013

I am looking forward to a great hands-on session tomorrow as we are “Packing a Powerful Punch with Patterns” (presentation #500, located in the Hyatt Regency, Centennial Ballroom E beginning at 1:00). We will be focusing on how to help students make the transition from basic patterning skills to algebraic thinking, uncovering the deeper math that is embedded in patterning. Our vehicle will be growth patterns that we make out of pattern blocks. If you are here in Denver this week, I hope you are able to join us for the session.

The handouts given out in the session were a truncated version of the PowerPoint presentation, and as promised I am making the full version of the handout available here. If you use these in your classroom, I would love to hear from you about the lessons and even see some samples of student work, too.

Mathematically yours,
Carollee

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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.

Click here for the link to the on-line graphing calculator.

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

click here for conference handouts

Fraction Question for “Thirds”May 12, 2011

First, let me say what a wonderful year of collaboration it has been with the teachers from Alwin Holland Elementary School. Thank you, ladies, for your hard work in mathematics this year. We all came away having more informed than we were about mathematics education.

Part of our last day together was spent in two different classroom where I did demonstration lessons. In the grade one classroom I demonstrated the teaching of the +9 addition strategy (as learned in the basic facts addition blog) using 10-frames.

In the grade 2/3 split classroom, the teacher was interested in a fraction lesson that centered around problem solving.

I started the lesson by talking about a class which was made up of 1/2 boys. I asked the children if they thought the class had only two students in it, one of which was a boy. They all agreed that, no, the class was larger than two, and they offered suggestions of how many might be in the class, and then how many of them would be boys. At one point I asked if they thought 23 might work for the class number, and they knew that being an odd number, it did not work to divide the class in half. I then presented this question that I had written for the lesson:
Marcie grabbed some bingo chips from a bag on the table. After sorting her chips, she told her friend that 1/3 (one-third) of them were red. What might her chips have looked like? Find as many different solutions as you can. Each solution should use a different number of chips altogether.

The students had bags of bingo chips to share in their table groups, and they used the chips to find a variety of solutions. All of the children were able to come up with some solutions, and a few of them realized they could keep adding one more chip to each of their sets to find more answers.

When we shared our solutions I put the information on a T-chart with one side labeled “number of red chips” and the other “total number of chips”. Students gave their answers in random order, and after we had quite a list, I suggested we look for a pattern. I made a new T-chart with the same headings, but we listed our answers in order of number of red chips: 1, 2, 3.. No one had given an solution with 7 red chips, but it was easily figured out by looking at the pattern that presented itself. The students recognized the pattern in the second column was “skip counting by threes”. Then I proposed some big numbers of red chips such as 20, 100, 1000 and they could answer the total number of chips to be 60, 300, and 3000 respectively. Finally we looked for the “n-rule”: for n number of red chips, how many chips altogether. At first students guessed other large numbers (500, a million, etc.), but finally one boy said “It would be n + n + n.”
It was the first look at the n-rule for the students, but the teachers were motivated to go back to some other patterns and play with that idea with children. Anytime we help kids move to that point, we are laying the foundation for algebraic thinking.

All in all it was a fabulous day! Thanks again to the collaboration group from Alwin Holland School!

Mathematically yours,
Carollee