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Showing posts with label Math. Show all posts
Showing posts with label Math. Show all posts

Friday, December 3, 2010

Math Homework and Practice

While working with many different children as well as my tutoring student, I realized the importance of completing one's homework. The children need to practice the skills done during the week so they will be prepared for the test. Homework not only allows the children to practice, it gives them an opportunity to clear up any confusion. We assigned math homework about every other day in order for the students to get plenty of practice.



Teaching Math



I spent many days working with the students on math. I was allowed to teach many different things. Here are some pictures of me teaching Math. I worked on multiplying fractions for several days.

Math Student that I tutored

Student: Tanner
He is a fifth grader, and is ten years old. Tanner told me that math was not his favorite subject and that he was not interested in doing it. That information threw me off in my questioning and so I asked some of the other questions that may interest him. He likes video games, and wants to be a forensic scientist. After he informed me of that, I did mention that math was a huge part of that profession and that he needed to become aware before he entered that field. When he is not in school or working on homework he plays on Facebook and the game Farmville. He likes doing math but it is not his favorite subject. His favorite television shows are the shows such as Criminal Minds and the CSIs. When I asked him what else he likes to do, he told me that he likes to watch TV and likes to play with friends and family.
Math Concept: Multiplication
The concept that Tanner struggled with the most was his multiplication tables. I began working with him at the beginning of the semester. He was struggling with the concept of multiplying. I began by quizzing him, by randomly walking up to him and asking him a problem. I also work on the different methods of figuring them out, such as partial product, estimation, place values, and the box method (not sure of the technical name). We worked together almost everyday. His understanding has grown, I feel because he memorized his multiplication tables to some degree. However, as we moved on to division, I noticed that Tanner was still having trouble. While I watched him work I realized that he new the steps to division, but he still makes mistakes doing the multiplication. I would let him finish the problem, and would then ask him to check his work. As he did the multiplication he did was right but he say that the answer was not the same as the division problem. Therefore we would go back and check his work on the division problem. He saw how his one simple mistake got the problem wrong.
Conclusions and Recommendations:
After working with Tanner for the past few weeks, I realized that he is a very eager to learn student. He understands the mechanics of the problems, but still makes mistakes when working with his multiplication. I would recommend that Tanner continue to practice and memorize his multiplication facts. I would also remind him that it is not a race, and to take his time while he worked and think about the problems that he is working on.
I also told Tanner that he must do his homework, although I think there were only two times out of the first two quarters that he had not completed it, I reminded him of how important it was. I also reminded him of his favorite game, Farmville. I told him that he did not have the big farm in the beginning, I told him that he had to work hard to get the stuff he had, and that it took time. I reminded him that multiplication is the same way. One must work hard and constantly to keep up, because more things are beginning to be added, and are becoming more complicated.
Other Areas:
I also worked with Tanner on fractions. He understood the mechanics but it took him a long time to figure out the problems. I assured him that he would be quicker at the problems as soon as he got the hang of it. I would sit there and he would always look up for reassurance, and questioning as if I would give him the answer. I would never give him the answer directly. I would always ask him how his teacher and I had worked with the students on how to check your work. He would look down and check his work and smile every time he got it right.

Morning Meetings with Math

Every morning the teacher and I would come up with math problems to put on the board for students to work on as part of their morning work. It was fun watching the children come up with differing answers.





Saturday, November 27, 2010

Working with Fractions

As we progressed through this semester, we worked with fractions. I have to say this was one of the most interesting topics we have covered so far. I realized that the students learned differently than the way I did, and I found myself re-learning along with them. Here are some of the students working with number lines to solve fraction problems and estimation.





Also we worked with fraction strips, that the children created. This not only allows them to work with fractions visually, but gives them a hands on manipulative.



1. Subject/Content Area: Mathematics/Fractions
2. Alabama Course of Study Correlation: Grade 5:
3.) Solve word problems that involve decimals, fractions, or money
• Converting Fractions and mixed numbers to decimals and percents
3. Concept or Skill: Constructing Fraction Slips in order to find equivalences and the greater numbers.
4. Behavioral Objectives: The Student will be able to
• Build his/her own fraction slips including 1, 2, 3, 4, 6, 8, 9, 10, 12 as fractions.
• Use the fractions slips to find equivalences.
• Determine greater numbers represented by fractions.

5. Evaluation: Walk around the room to see if the students are creating their own fraction slips based on teacher instruction. Can they follow the teacher’s lead and make strips according to teacher instruction? Are any of the students needing help constructing their slips? Ask the students to find equivalences using their fraction slips after the teacher asks for and equivalence. In the closure, students will be able to determine the larger fraction by using their fraction slips and the number line on the board.
6. Materials:
• SmartBoard
• Number line, drawn on board
• Construction Paper, cut into strips in 8 different colors
• Marker


7. Teaching and Learning Procedures:
A. Motivation: Ask the students if they think that money can be represented as a fraction and if so how? Relate to students by explaining that a dime is 1/10 of a dollar, a quarter is ¼ of a dollar, and so on.
B. Instructional Procedure:
C. 1)
• Distribute the cut construction paper that has been previously cut into strips, and counted out.
• Choose the first color (red) and have the students write the number 1 on the strip. This will represent the whole number.
• Then have the students chose the next color (blue).
• The teacher will demonstrate how to fold this strip in half to the students.
• Students will respond by folding their paper in half. The students will then write ½ on each side of the strip.
• Teacher will hold up the next color (yellow) and fold this strip in three equal folds.
• Students will follow the teacher’s lead and fold their strip in three equal folds.
• The teacher will number each of the folds 1/3 and have students write 1/3 in the equal thirds spaces
• Take the green strip. Fold it into four equal quarters, and have students’ copy.
• Students will fold their paper equally and number each fold ¼.
• The teacher will then take the purple strip and fold this strip into six equal sections and ask students to copy.
• At different times during these procedure the teacher may need to stop and help individual students prepare their strips.
• Students will write 1/6 into each of the equal sections of the strip.
• The teacher will then choose the next color (white). The teacher will fold this strip into equal sections of eight.
• Students will copy this procedure, and number the equal portions with 1/8.
• Teacher will choose the next color (brown) and have students watch as it is folded into ten different sections.
• Students will copy this procedure and fold their strips accordingly, then label each portion 1/10.
• Finally the teacher will choose the color (orange) and fold it into 12 different yet equal portions.
• The students will copy and then label each equal portion 1/12.
2) Once the strips have been formed the teacher will write the number line on the board.
<0-------------------------------------1>
• Teacher will ask students to look at their strips. Teacher will state that no matter what the fraction is ½ to 50,000/100,000 that those fractions will be in this section of the number line.
• Teacher will then ask students to look at their fraction strips and tell me another fraction that is equal to ½.
• Students will respond 3/6 of 6/12.
• Teacher will then ask for another fraction that is equivalent to 8/12.
• Students will respond ¾.
• Teacher will continue to work with the handcrafted manipulatives comparing the fractions in front of the children.

3) Teacher will write a fraction on the number line (3/4).
• Teacher will then ask students if 9/12 is greater than, less than, or equal to ¾.
• Students will use their manipulative to determine that the number given is greater than the number on the board.
• Teacher will then write the fraction ½ on the number line.
• The teacher will ask students to come up with two other fractions that are less than ½.
• Students will respond ¼ , 1/12, 2/8, and so on.
• Teacher will then ask students where they think those numbers should go on the number line.
• Teacher will instruct them to look at the fraction strips and determine where they fit on the number line.
• Teacher will spend five minutes working with placement of fractions on the number line.
Sample Questions to use throughout the lesson:
Is ½ equal to 3/6?
Is 8/12 greater than 3/4?
Who can tell me another number that is equivalent to 1/2?
What is greater on the number line, 1/3 or 2/8?
How are 8/8, 12/12, 3/3, 4/4 alike and how are they different?
Does 10/10 mean that it is greater than 1?

D. Closure: Allow each student to discuss their fraction slips and have them try to stump each other.. Ask if anyone had problems with their fraction strips? Some students may need help reconstructing strips. Discuss, as a class different ways that fractions and money are similar. Share any problems that were brought up during the lesson.
E. Supplemental Activities: As a supplemental activity, I will have the students build other fraction strips to add to their collection, such as a 1/5th strip, 1/7th strip, and a 1/11th strip.
F. Early Finishers: There will be no early finishers, this will be done as a whole group, and early finishers will be asked to work on further strips.
Enrichment: Students will be asked to place fractions on the number line and find the right placement of each. Furthermore, students can begin converting fractions into decimals.
Remediation: Students needing remediation will be asked to come to small group and bring their fraction strips. The teacher will work with them using the manipulatives, folding the strips and showing equivalences.

My Favorite Math lesson this Semester

I would have to say that my favorite math lesson this semester had to be the one in which I was able to teach number puzzles to the students.

1. Subject/Content Area: Mathematics/Multiplication
2. Alabama Course of Study Correlation: Grade 5: 2.) Solve problems involving basic operations on whole numbers, including addition and subtraction of seven-digit numbers, multiplication with two-digit multipliers, and division with two-digit divisors. c) Demonstrating computational fluency with addition, subtraction, multiplication, and division of whole numbers
3. Concept or Skill: Understanding Number Puzzles and Finding Common Factors
4. Behavioral Objectives: The Student will be able to
• Find all the factors of a number.
• Find all the ways to multiply whole numbers for a given product.
• Use properties of even, odd, prime, square numbers and the relationships of numbers to solve problems.
5. Evaluation: Walk around the room to see if the students can find the factors of the numbers given. Can they find all of the factors? Are any of the students missing any of the factors? Observe students while they are working in pairs, creating their own puzzles that each have created. In the closure, students will solve puzzles and factors from numbers and puzzles created by the teacher on the SmartBoard and those created by each other.
6. Materials:
• SmartBoard
• Smart Document Camera or Elmo
• Paper
• Pencils

7. Teaching and Learning Procedures:
A. Motivation: Ask the students if they like solving puzzles. Discuss how there are many different types of puzzles, and that today we are going to be working on Number Puzzles. Ask the students if they can remember all of the prime numbers.
B. Instructional Procedure:
C. 1) Review factors of numbers by writing numbers on the board and asking for volunteers to come up to the SmartBoard and find all of the factors based on previously learned material.
2) Spend about five to ten minutes reviewing factors, prime, even, odd, and squared numbers. The teacher will inform students of the importance of the lesson, and how numbers can be represented different ways. Furthermore, the numbers in the problems can help in everyday life, when dealing with percentages, bills, and interest. Also, there may be a point when some students encounter problems where the student may need to solve in order to get the most logical answer. Teacher may need to review squared numbers and how they are created (multiplying a number by itself, ex 6x6, 3x3, 5x5).
3) Teacher will write a Number Puzzle on the Board, involving factors; such as:
• This is a square number
• This number is less than 100
• This number is even
• This number is a multiple of 4
Solution: 4, 16, 36, and 64
4) Create another example on the board and ask students to solve, ex.
• This number is a prime number
• This number is less than 20
• This number is odd
Solution: 1, 3, 5, 7, 11, 13, 17, 19.
5) Ask the students to pair up, use their neighbor across the table, and ask them to try and create their own puzzle. Give each student about ten minutes to come up with his or her own puzzle, similar to the examples, and have them ask their neighbor to solve. If there are questions the partner should ask his or her neighbor to explain the answer, with feedback from the teacher if necessary.

Sample Questions to use throughout the lesson:
Is that number prime?
Is that number odd?
Is that a factor of (?) number?
Can you find another number that is a factor of (?) number?
Can you explain to your neighbor if there are any other factors in the problem?

D. Closure: Allow each student to discuss their problems that they have created. Ask if anyone had problems with their puzzle? Discuss, as a class different ways there may be to solve individual’s puzzles. Share any problems that were brought up during the partner session.
As a way to motivate the students I would see if they think any of the students from the other classes could answer their riddles, or stump the other classes.
E. Supplemental Activities: As a supplemental activity I will write numbers on the SmartBoard and ask the students to find all of the factors for those particular numbers, and see if there are any other problems that they can come up with to stump the teacher.
F. Early Finishers: These students will be asked to come up with new problems that can be assigned for homework or study guides for the rest of the class.
Enrichment: Students will be asked to solve harder problems that will be found in a center, or an area designed for a math workshop, where students can proceed with extra activities.
Remediation: Students needing remediation will be asked to come to small group and we will solve the problems together, or as a group; asking and answering questions as we go, thus allowing the student to gain a firm grasp on the number puzzle concepts.

Reflection:
I really enjoyed this lesson with the kids. They seemed a little confused in the beginning, and I did struggle in the beginning. The teacher had to step in a couple of times and assist me in explanations. Once I caught on to his line of thinking however, I was able to continue with my lesson with fewer helpful tips from him. Furthermore, the only other part that I will change next time, is that I will have more examples in mind and written on paper. Two of the examples I came up with , off the top of my head, were a little to advanced for the kids, but they did not want to move on to a newer problem, they wanted to finish what we had started. After the lesson was over and the children were working in groups to come up with their own problems, they really enjoyed it. I saw how they enjoyed trying to stump the teacher and their classmates. Finally, when the lesson was almost done, I chose one groups’ work, and had the class try and solve it. There were two problems here; one, the children that did the problem tried to solve it, and two I wish I had more time to pick more students to work their problems on the board as well.

My Philosophy For Teaching Math

As I look back on my own learning experience, I remember how I struggled with math. I found that answering questions written on the paper were very frustrating to figure out. I constantly came home complaining of homework and classwork relating to math. The reason I hated it, one and only one way to find the answer. My philosophy for teaching math is simple; to find many varying ways to teach a concept, with as many hands-on experiences as possible. I believe that math can be taught by different approaches and ideas to reach all learners.

Tuesday, October 5, 2010

Arrays


My first experience in the classroom that involved a hands-on activity was the activity on arrays. The students were learning and reviewing multiplication facts, and the Mr. Civitelli thought that the students would learn the material better if they had a hands-on experience. therefore, Mr. Civitelli got out the masking tape and painters tape, and divided the class into groups. The groups were given a multiplication fact, such as 5x5, on a card. The students were then instructed to make an array on the floor. Here is an example that one group of students worked on.