Fractions

Fractions

I cannot think of a better way to learn about fractions than with baking. You get a hands on approach and a treat when you are finished! You can any throw in a side lesson on temperatures if you want!

Monster cookies! 

3 eggs

1 1/2 cup packed brown sugar

1 cup white sugar

1 tsp vanilla extract

1 tsp corn syrup

2 tsp baking soda

1/2 cup butter

1 1/2 cup peanut butter

4 1/2 cup rolled oats

1 cup semisweet chocolate chips

1 cup baking m&ms

1. Preheat oven to 350 degrees (How many degrees Celsius?)

2. In large bowl, beat the eggs.

3. Add all remained ingredients, stirring after each addition.

4. Use a scoop or spoon to place rounded cookie dough on cookie sheet.

5. Bake for 12 to 15 minutes.

Yield 6 to 7 dozen (How many cookies is that?)

What if you get 6 dozen remainder 7...6 7/12 dozen, unless you are using a baker's dozen.

My family can easily go through that many cookies in a short time...but what if you didn't need that many cookies? Cut the recipe in half....lots of new fractions. What if you wanted more? Double the recipe.

People use fractions everyday.  I use them all the time while I bake or cook. With having 5 boys to feed, I often have to double a recipe or make it slightly larger by having the recipe and adding that half back to the whole. I have to do this in my head fast or else something will burn!

My kids use fractions before they know what a fraction is. That is my side of the room, that is my half of the couch. One lesson was splitting the last cookie. One of my son's got to split it, and I let the other one pick the half. My first son did not know that his brother would be picking which half was whose. He was not pleased with his 1/8 of a cookie!

Fun Fraction Video! 

Integers

I have to say one of the toughest things for me for this unit is spelling the word integer...I want to add an 'r' after the first e....maybe I will get it right one day.

 Integer: The sets of whole numbers including zero and their negatives. 

Adding integers: You find the first integer on the number, if it is positive you move your finger to the right the value of the second number. 6 + 4...you find 6 on the number line and move to the right 4 places to find 10.

If the second number is negative you move to the left. 

Subtracting integers: You find the first integer on the number line, if it is positive, you move your finger to the left the value of the second number. 6 - 4...you find the 6 on the number line and move to the left 4 places to find 2. 

If the second number is negative you move to the right.

Multiplication: When multiplying  two positive integers, the result will be positive. When multiplying two negative integers, the result will also be positive. When multiplying a negative and positive integers, the result will be negative.

Division: If you divide two positive integers, the result will be positive. When dividing two negative integers, the result will also be positive. When dividing a negative and positive integers, the result will be negative.

Examples of numbers that are not integers:

• fractions
• decimals 
• percents

Integers uses: The use of integers seems endless to me. You use integers everyday. Reading your alarm clock in the morning, how many cups of coffee you drink, the speed limit posted on your work to work. I cannot think of a job that would not put integers to use in some fashion. You look at the temperature to choose how to dress. Integers keep score for sporting events.

Integer Rap

Mind map of Integers

Prime Number and Factorization

Prime Numbers and Factorization

This was one of my favorite units. I always enjoyed this subject as a student in elementary when it was introduced and as an older student. Again, I am enjoying it as an adult. How do I share my enjoyment and interest in the subject with students? One way is to have fun with the unit and answer why we need to know what prime numbers are and why we would use factorization in a real life problem. 

I found a fun video about prime numbers to introduce the subject to students.

The video gives the definition of a prime number as the only factors are 1 and me. Factors that divide evenly. It rhymes, and it is an easy way for a student to remember what a prime number is.

I also found a fun game for prime numbers and factorization. It is a jeopardy game and could be a very fun review.

I also found a website called Study Jams that has fun games. Prime Numbers    Prime Factorization

My children love to go to the school website and play some of the games on them. Some teachers have a few games and some teachers have numerous games and update them as they come up to new topics. This makes me think about what I would have on my website. I would want relevant games and topics not just something that I slap up there generically at the beginning of the year.

I even found numerous websites that offer prime factorization calculators. I can see how this would be beneficial for checking work, but I think it could open up the possibility of cheating. I do not think I would add one of these calculators to my class website.

What is the importance of prime factorization and how could you use it in real life?

I believe that if students understand why they are learning something, how they can apply it in real life and what value it holds, they are more receptive and willing to learn. Sometimes knowing the answer to the simple question why?, students turn from extrinsic motivation to intrinsic.  

Prime factorization helps solve numerous types of problems. It helps solve problems about multiples and factors. The GCF is helpful if you need to divide things up into groups, for example. 

Prime factorization helps with numerous things in real life. How is your computer and the documents on it kept safe? Data encryption..prime factorization helps provide solutions to protect data! Cryptography is code breaking! Prime factorization is necessary in that career!

Cooperative Learning

Cooperative Learning

     What is cooperative learning? Simply: students working together to accomplish a goal.

There are many types of cooperative learning: think:pair:share, jigsaw and group investigations to name a few. Cooperative learning provides students with active learning time which provides more meaning for the students. Cooperative learning does take more time in the classroom and more preparation time for the teacher. Cooperative learning does take more time than lecture but that does not mean it is wasted classroom time. Teachers need to let go of the need for lecture and let students acquire knowledge in new and exciting ways.

Benefits of cooperative learning:

• Can reduce peer competition and isolation
• Can help learning disabled students work in a better setting for them
• Higher thinking skills
• Self esteem
• Satisfaction
• Self management

More benefits of cooperative learning.

Here is a video that shows the benefits of cooperative learning:

     Math has always been thought of working individually. I remember my math education being review previous homework, lecture, start new homework. There was not much change, and I am disappointed to not remember cooperative learning. Math is a great subject for cooperative learning. Students are able to get support from peers, ask questions among peers, discuss ideas and learn from one another. Math problems often have more than one way to  the solution. In a small group setting a student may show how she/he got to the solution. That solution could be the same way the teacher had shown during lecture, so it may not help all students in the group. But then another student shows a DIFFERENT method and a different logic to the solution....now things are happening in the group. Different learning styles and preferences are being demonstrated. This is when 'Aha' moments happen for students. 

     Math is not just silent work! It needs discussion too (other than classroom lecture). I do know that classroom lecture is time efficient and has a place in the classroom. I just do not think it should dominate the math classroom anymore. Teachers have to spend more time planning/implementing/monitoring students during a cooperative setting, but it is worth it in the end. People often forgot that students need to learn to learn. The expression "all I need to know I learned in kindergarten" could not be more true.....it is a whole year of learning how to learn. The rules and expectations set in kindergarten will follow you to adulthood. When watching cooperative learning in my mentor's classroom, it got more successful as the school year progressed. It is a first grade classroom and the students had to learn how to work in a cooperative group with their peers. My mentor explained that it sometimes takes up to a whole quarter for some groups to be a successful group. 

Here is a video on tips for cooperative learning:

     I feel that cooperative learning has a benefit for all students. It is very versatile and helps all types of learners. I feel that the advantages of cooperative learning outweigh the disadvantages. Cooperative learning takes a lot of planning, but there are a lot of good resources on the web to find good cooperative lesson plans that will save a lot of time. Cooperative learning takes more time in the classroom, but who can complain about active learning time?
     

The Mathematical Miseducation of American's Youth
By Michael Battista

     Michael Battista wrote an article about the miseducation of math that America's youth are receiving. It is a very torrid article about what is happening in math classrooms in America and the reluctance to chance, in fact, they want to go back to the way it was! Battista says that Americans suffer from "talkshow/tabloid" way of thinking. Americans are willing to base their arguments on information from ill informed or sensationalized media. We live in a time where people in the media are not always held to the highest standards and a lot of 'news' is sensationalized. In short, we live in an age of irresponsible journalism. The internet has exposed the world to unimaginable amounts of resources and information. With this mass wealth of knowledge and information, how do people discern what is credible and what is not? Unfortunately, we live in a world where people do not take the time to back up their thoughts or arguments with facts or sometimes even logical. We live in a world where one's own opinion is the most important. Michael Battista discusses some of these ideas in his article "The Mathematical Mideducation of America's Youth".
     There is an emergence that wants mathematical education to go back to the basics. They claim that reform mathematics has been a failure, meanwhile, never admitting that traditional ways were none too successful. Battista compares this argument with the likes of medical care. You would not seek medical care from a doctor who is using outdated skills, so why would you want your children educated with outdated educational practices?
     Traditions mathematical education involves memorization and using procedure that have little or no meaning to the student....it is all very forgettable. Traditional mathematics does not use any of the latest scientific research findings. Battista states,"The mathematic ignorance of our citizenry seriously handicaps our nation in a competitive and increasingly global marketplace." We live in a shrinking world. We live in a world where parts of super computers are built on different continents and then put together on an entirely different continent and then the OS is installed on a different continent. One machine more well traveled than the average math student. My point is that the world is shrinking and the local market is not down the street anymore. We are competing in a world of billions now, not just against the kids down the street. We need to ensure that our students are receiving the very best mathematical education to compete in the ever competitive job market. America needs mathematicians, engineers for our future. Not only do our youth deserve a good mathematical education, they deserve it.
     Battista points out that people are very willing to admit that they are not good at math, but they would not be as willing to admit that about reading. Why is math the lesser of the two important subjects in the eyes of many? Many students are only taught a very surface level of mathematics. It is very forgettable. After reading the article, it made me think that math classrooms are like factories. They expect the same results done in the same manner. But not all students think the same way!! Jean Piaget showed that students need to construct their own knowledge. How do they do this? By working, thinking, bouncing ideas off other students, being frustrated and being successful. Students need to understand procedures and equations, not just how to use them. No two students think a like, but they are taught in the same manner. When students are offered various ways of learning, different methods and allowed to put their hands not only their heads into, they really start to learn. Students need to learn, not memorize.

Read the article here: Battista article