# Focus on Math

## Helping children become mathematicians!

### Simplifying Radicals — Play the Game!October 29, 2012

Filed under: General Math,Middle School/Secondary School Math — Focus on Math @ 3:31 pm
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After reading about the game that Richard DeMerchant created for practicing the skill of approximating square roots, Katie Wagner (a friend and colleague) adapted the idea and created a game for practicing the skill of simplifying radicals! I think this is another winner, and hope that you will try this in your secondary classroom as it fits into your curriculum.

Thanks for sharing this, Katie. Link to Katie’s game here.

Mathematically yours,
Carollee

### Approximating the Square Root of Numbers — Play the Game!October 13, 2012

For those teachers who are looking for a way to have their students practice approximating square roots in an interesting manner, Richard De Merchant (a friend and colleague) has created a game for just such a purpose.

He explains how to play the game and adds some other helpful tips on his blog Math in the Middle (click here for the link to this particular post).

If this is something your students need practice with, then I heartily recommend that you check out this game ðŸ™‚

Mathematically yours,
Carollee

### Algebra and the New York TImes (or other newspapers…)October 1, 2012

Filed under: General Math,Middle School/Secondary School Math — Focus on Math @ 9:37 am
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Making connections is one of the processes listed in the Western Canadian Protocol documents, the BC curriculum documents (IRP’s), and the National Council of Teachers of Mathematics (NCTM) documents. It is critical that students make connections between the different strands of mathematics (e.g., number, algebra, geometry, data) as well as make connections to mathematics in the real world.

High school and middle school math teachers are often looking for ways that they can help students connect math to real-life situations. In this blog post Patrick Honner provides some ideas for making such connections. He suggests things like mathematically modeling mortgages, redoing recipes, looking at Olympic records, examining population growth, and solving for stocks. The ideas are clearly not new, but maybe the article can remind you of a project you have done before or inspire you to take on a new one.

How are you making math “real” for your students?
Mathematically yours,
Carollee

### Free On-Line Graphing CalculatorJune 21, 2012

Â 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

### A Small Change but a Big ResultMay 13, 2011

Yesterday a teacher in our district, Kevin, shared with me a wonderful story about math in his classroom. Kevin and I go back a ways — I was the Faculty Associate when he completed his Professional Development Program (student teaching) through SFU, and he had also taken the “how to teach math” course from me. He was hired in my district, and he has spent most of his career teaching at a rural K-12 school where for the past number of years he has taught the gr 8-12 math courses.

Kevin told me of his frustration, as well as his students’ frustration, in the math classes over the last years. He would present a lesson, have the students begin working on the problem set in the text book, and then have the students do the remainder of the assigned problems for homework. However, invariably the students had difficulty with the homework problems and would become increasingly frustrated with trying to solve those problems. The next day Kevin often felt he needed to get on with the new lesson, but clearly time was needed with these homework questions which, being later in the practice group, were often the more difficult problems in the set.

Kevin remembered the emphasis I had put in the “how-to-teach-math class” on the power of students solving problems, and he decided to change up the class time with his students to see if he could incorporate more problem solving in his class.Â  So, instead of this:

• teach a concept
• do the first, easier problems in the practice set in class, students working together
• send home the later, harder problems in the practice set, students working alone,

Kevin changed his time with students to look like this:

• do the later, harder problems from yesterday’s lesson in class, students working together
• teach a new concept
• send home the first, easier problems as homework, students working alone.

Kevin found this to make a profound difference for his students. Where many of them had felt unsuccessful in math, never being able to complete the homework on their own, they were now able to do so. This began to build their confidence. When they worked onÂ  the harder problems together in school, most students found the knew most of what to do. Sometimes they were forgetting only a small step. Kevin realized when the students had tried the problems at home, if they could not arrive at the answer at the back of the text, most would erase all of their work, believing they were completely off track. Working together in class students had the opportunity to make connections to previous lessons, to communicate their thinking, to reason about the logic of what they were doing, to justify their answers. By engaging in these processes day after day, the students began to build a set of problems solving skills and strategies than empowered their mathematics thinking.

The three “chunks” of the lesson really did not change, but in changing the order in which they happened (which in turn changed which problems were addressed through the mathematical processes**) Kevin facilitated a change in student understanding and success. Way to go, Kevin!

I hope you will look at how math is going in your classroom and see if you need to turn it “upside down”!
Mathematically yours,
Carollee

P.S. The NCTM lists the process standards as these: connections, communication, problem solving, reasoning and proof, and representation. More information about these can be found at this link:
http://www.nctm.org/standards/content.aspx?id=322
In BC, and for the members of the WNCP in Canada, the mathematical processes are defined as these: communication, connections, mental math and estimation, problem solving, reasoning, technology, and visualization. More information about these can be found in the “front matter” of the BC IRP curricular documents found at this link:
http://www.bced.gov.bc.ca/irp/subject.php?lang=en&subject=Mathematics

### Get “Illuminated”!

I was talking to some math teachers yesterday, and one of the things I mentioned to them was a great site run by the NCTM (National Council of Teachers of Mathematics) called Illuminations. The site is a treasure trove of lesson plans and activities for grades K-12. Many of the lessons have interactive applets embedded in them and, as such, are suitable for using with a white board.

Searching for particular lessons is easy. You can create a specific search by choosing a grade band, math strand, and then adding specific terms (for example, gr 3-4, geometry, with the words “right angles” typed in) or choose to cast a wider net and use broader criteria in your search. There are some really wonderful ideas there, and I encourage you to bookmark the page and try some of the ideas presented.

Remember as you look at lessons and/or activities that they are grouped in four grade bands: K-2, 3-5, 6-8, and 9-12. You will need to be aware of the curricular requirements of your province or state and check the lessons and/or activities against your curriculum. It is, of course, never a problem to “stretch” students beyond the given curriculum, but for assessment purposes, it is important to assess against the standard set by the grade level curriculum.