A Go Figure Debut for a Mathematician Who Is New!

Secondary Math Solutions

Julie has taught high school math for 22 years, having taught everything from Pre-Algebra concepts to Honor Pre-Calculus. The past four years she has been teaching Algebra 1 to 9th graders. Most of her students would be considered on-level or below-level. (This sounds like my remedial math college students.) She loves the challenge of figuring out a way to teach them so they can understand the concept, practice it in class, and feel successful while not getting frustrated and giving up.

Currently, her TPT store (Secondary Math Solutions) contains over 200 resources and many are Algebra 1 products she has created and used in her own classroom. A large number of the concepts are broken down into scaffolded steps or prior knowledge skills. There are also pages and activities that go over and over the same concept because that is what her students need. Julie’s products do not contain "difficult numbers" because she doesn’t want her students getting bogged down with trying to remember how to add fractions, when all she really wants them to be able to do is solve an equation or find the slope of a line. She tends to make notes and practice sheets that are very focused on a specific skill or skills (sometimes prerequisite) that need to be developed so that her students can be successful. Her TPT math products reflect this.

Julie endeavors to make her math classes as interactive and hands-on as possible. Her "4 Types of Slope Activity" allows the student to create their own diagram which helps them to remember the four types of slope. Educators recognize that the student will have a greater chance of recalling what they create rather than what they are told. This is a great activity that can be glued into an interactive notebook when finished.

Speaking of interactive notebooks, Julie uses foldables as well. Her "Writing Equations of Lines Foldable" reviews all the ways the student might be asked to write the equation of a line. They fill it in themselves after they have been taught all of the material. This allows them to gauge what they do and do not remember. After it is filled in correctly, the students can go back and use it as a study tool before a quiz or test.

If you are a math teacher, I hope you will check out Julie’s store and consider her focused resources created just for the high school math student!

Is Zero Even or Odd?

Is the number zero even or odd?  This was a question asked on the Forum page of Teachers Pay Teachers by an elementary teacher. She stated that Wikipedia had a long page about the parity of zero and that some of the explanation went a little over her head, but basically the gist was that zero is even because it has the properties of an even number. She further stated that before reading this definition, she probably would have said that zero was neither even nor odd.

Here was my reply. Zero is classified as an even number. An integer n is called *even* if there exists an integer m such that n = 2m,  and *odd* if 2m + 1. From this, it is clear that 0 = (2)(0) is even. The reason for this definition is so that we have the property that every integer is either even or odd.

In a simpler format, an even number is a number that is exactly divisible by 2. That means when you divide by two the remainder is zero. You may want your students to review the multiplication facts for 2 and/or other numbers to look for patterns.

2 x 0 =               3 x 0 =

2 x 1 =               3 x 1 =

2 x 2 =               3 x 2 =

2 x 3 =               3 x 3 =

There is always a pattern of the products. Let the students discover these patterns - Even x Even = Even, Even x Odd = Even and vice versa and Odd x Odd = Odd. Since ALL math is based on patterns, seeing patterns in math helps students to understand and remember. Now ask yourself, "Does zero fit this pattern?"

The students can also divide several numbers by 2 (including 0), allowing them to see a second way to conclude that a number is even. (The remainder of the evens is 0, and the remainder of the odds is 1).  Again, "Does zero fit this pattern?"

To demonstrate odds and evens, I like using my hands and fingers since they are always with me. Let's begin with the number two.  I start by having the students make two fists that touch each other. I then have them put one finger up on one hand and one finger up on the other hand. Then the fingers are to make pairs and touch each other. If there are no fingers left over (without a partner), then the number is even.  (see sequence below)

Let's try the same procedure using the number three. Again, begin with the two fists. (see sequence below) Alternating the hands, have the students put up one finger on one hand and one finger up on the other hand; then another finger up on the second hand.  Now have the students make pairs of fingers. Oops!  One of the fingers doesn't have a partner, (one is left over); so, the number three is odd. (I like to say, "Odd man out.")   

So, does this work for zero?  If we start with two fists, and put up no fingers then there are no fingers left over.  The fists are the same, making zero even. (see illustration below)

So the next time you are working on odd and even numbers, make it a "hands-on" activity.