Wrapping it up

Well, the semester of Math for Elementary Teachers is wrapping up this week! You would think after all the math classes I have taken, I wouldn't have anything else to learn. But, your wrong. I can not believe all the great skills, information, and techniques I learned this year. Out of all the different things I learned this year, the one thing that always came back to me was all the new techniques that are out there today that I never learned when I was in grade school. The new "ways" seem so much more engaging and easier to understand. Its great that they have come up with so many different ways to figure out one problem, because what works for some...doesn't always work for others. I do believe it is important to not forget about the older techniques as we are teaching the new ones though. There were many different times in grade school when I couldn't understand a problem and my dad helped me understand it with techniques that he learned when he was in school! So, remember as great as the new techniques seem, the old ones can be just as great!

Another important part of this class was learning about how important it is to keep your students engaged. I found this great video on youtube of a teacher showing different techniques he uses in a high school math classroom to keep his students engaged throughout the lesson. I believe the techniques used in this video can be used with any age group.

Here is another useful video on keeping your students engaged in a first grade math classroom. I think that using hand gestures, repeating, working with partners, etc. are a great way to keep your students engaged and following the rules. This video shows exactly that....

So, lets make a pact as teachers, parents, mentors, etc that we will work to keep our students or children engaged in learning so that it can be an exciting experience for both them and yourself.

To end this blog, here is a great website that lists different tips/techniques to keep children engaged in a classroom. Remember, not only can teachers use these techniques in the classroom but parents can also use these techniques at home.

http://www.edutopia.org/classroom-student-participation-tips

Fractions - why are they important?!

Whenever the unit of fractions comes up, I always go into a little panic. I understand the concept of fractions but I always get confused when it comes to adding, subtracting, multiplying, and dividing fractions. There are so many different steps to each problem that it confuses me. Multiplying and dividing fractions is always the most confusing to me, but once I learned the different properties it all became a lot easier to me.

Here is a great example of some of the basic properties for multiplication of rational numbers:

Here is a website about why equivalent fractions are important and the steps to working them out. It goes over the theorem, adding, subtracting, multiplying, dividing, and formulas.

http://www.cccoe.k12.ca.us/edsvcs/commoncore/summit/HWu/importance_of_equivalent_fractions.pdf

Now, we think...why is it important to learn about multiplying and dividing fractions? I'll give you a great example.

My husband and I have this great rhubarb plant in our back yard and it keeps growing and growing. I found a great recipe for a rhubarb cake that I wanted to make for my husband but I only needed to make half a recipe considering it was just my husband and I eating it. I had to cut the whole recipe in HALF! Now, before this chapter...I would not have known how to do this. Here is the recipe: (the part in parentheses is the 1/2 version)

1/4 cup butter, softened (1/8 cup)
1 1/2 cups brown sugar packed (3/4 cup)
1 egg (1/2 egg)
1 teaspoon pure vanilla extract (1/2 teaspoon)
1 1/2 cups flour (3/4 cup)
1 teaspoon baking powder (1/2 teaspoon)
1/8 teaspoon salt (1/4 teaspoon)
1 cup dairy sour cream (1/2 cup)
4 cups fresh rhubarb cut into 1/2 inch pieces (2 cups)

1/3 cup granulated sugar (1/6 cup)
1/2 teaspoon freshly grated nutmeg (1/4 teaspoon)

Preheat oven to 375 degrees
Line a greased 8 x 5 (I used 4 x 4) pan with parchment paper.
Beat butter and brown sugar in a bowl until creamy. Beat in egg and vanilla.
In another bowl, mix flour, baking powder, and salt. Stir into creamed mixture alternately with sour cream. Stir in rhubarb. Pour mix into pan.

Mix sugar with nutmeg. Sprinkle over batter. Bake 40 minutes (took about 30). Cool in pan for 30 minutes, remove from pan to a cooling rack. Refrigerate leftovers.

Now, you see if I didn't know how to divide fractions I would have had to eat this whole cake! (not that it would be a bad thing) But, this made it a lot more reasonable for a household of 2. I hope you enjoy the recipe, let me know what you think!

GCF and LCM

This week when looking through the book and starting my homework, I was at the same daze I always am when it comes to finding the greatest common factor and least common multiple. I always seem to get the two confused with each other! After reading through the book more and doing some of the examples I definitely understand the information a lot better. A few of the things that helped me (and that can hopefully help you) were to have the definitions in front of me, examples to look back at, and the steps to refer to.

Greatest Common Factor - the greatest natural number that is a factor of both numbers. (Also known as the greatest common divisor, GCD)

Example: Finding the GCF of 24 and 30.
                 A= the set of factors of 24= {1,2,3,4,6,8,12,24}
                 B= the set of factors of 30= {1,2,3,5,6,10,15,30}
                 The set of common factors of 24 and 30 = {1,2,3,6}
                 ANSWER: 6 is the GCF of 24 and 30.

Least Common Multiple - the smallest natural number that is a multiple of both the natural numbers.

Example: Finding the LCM of 6 and 8.
                C= the set of multiples of 6= {0,6,12,24,30,36,42,48....}
                D= the set of multiples of 8= {0,8,16,24,32,40,48,56,64....}
                The set of multiples of 6 and 8 = {0,24,48..}
                ANSWER: 24 is the LCM of 6 and 8.

I found a great website that gives you step by step instructions on finding the GCF and LCM. It gives great examples and understanding. I hope this website is as useful to you as it was to me!

http://www.purplemath.com/modules/lcm_gcf.htm

After going through these definitions and examples finding the GCF and LCM was like riding a bike... I will remember how to do it now and years down the road. I hope this information helps you as much as it helped me!