Week 3: Virtual Manipulative: Fraction - Adding
For this week's Virtual Manipulative I used the Fraction Adding manipulative. This manipulative shows what it means to find a common denominator and combine. Students have to find the common denominator and then add the fractions. Students are able to see what the fractions look like. Being able to see it visually gives them a better understanding of fractions. I like how it lets you add the parts and see what the answer looks like. Also that it tells you when the answer is wrong. The students who have trouble finding common denominator could use the figure to find the common denominator. To find the answer students can drag the representation of each fraction to be added into the blank box on the right. Others could just type in the common denominator and answer.
Week 3: Private Universe Project
For this week’s Private Universe Project I watched Workshop 3: Inventing Notations. When solving math problems we all use different techniques. I think it all has to do with the type of learners we are. I am more of a visual learner that is why when I solved the pizza question in class I made a list. I do not think anyone in our class made a picture but then again we are adults so I do not think any of us would have made pictures. Do you think you would have drawn pictures if this problem was given to you in elementary school?
Students need to be given the freedom to solve a problem how they see fit. Some students will surprise us with the methods they use. It is interesting to see what children can do. They invent their own notations and their own ways of communicating to each other. The fact that they can come up with their own way of solving problems is great but that they can also explain it to their classmates and teachers is even better.
Week 3: Lesson Plan (Pattern Blocks)
Cover The Caterpillar
NJCC Standards:
4.3.2 A. Patterns
Recognize, describe, extend, and create patterns.
4.4.2 A. Data Analysis
Collect, generate, record, and organize data in response to questions, claims, or curiosity.
4.5 B. Communication
Use communication to organize and clarify their mathematical thinking.
Overview:
Children will find combinations of blue and green Pattern Blocks that can be used to cover four yellow hexagons.
Objectives:
With this lesson students will be able to:
· Use patterns to solve a problem
· Work with equivalence in a geometric context
Materials:
· Pattern Blocks, at least 6 yellow, 20 blue and 40 green per pair
· Caterpillar outlines
· Crayons
Teaching:
Introduction:
1. Students will be asked to find a way to cover their yellow Pattern Block using exactly 4 blocks.
2. Students will go over the only combination that works: 2 blue blocks and 2 green blocks.
3. Students will be asked to cover the hexagon using exactly 5 blocks.
4. Students will go over the only solution: 1 blue block and 4 green blocks.
Activity:
1. Students will be asked to pick a partner.
2. Students will be asked to answer the following question: How many different ways can you use only blue and green Pattern Blocks to cover the caterpillar?
3. Students will put 4 yellow blocks together to make their caterpillar.
4. Students will use only blue and green Pattern Blocks to cover their caterpillar.
5. Students will record their solution by coloring the caterpillar outline.
6. Students will keep track of the number of blue and green blocks used and also the total number of blocks used.
7. Students will find as many solutions as possible.
8. Students will look for patterns in their work.
Follow Up Discussion:
1. Students will be asked discuss how they worked on the activity.
2. Students as a class will create a class chart with their findings.
3. Students will be asked some of the following question to prompt class discussion:
a. How many different combinations of blue and green blocks did you find that will cover the caterpillar?
b. What is the greatest number of blocks that anyone used? What it the least?
c. What strategies did you use for solving this problem?
d. Did you notice any patterns that helped you find solutions? If so, describe them.
Grade Level:
2nd Grade
Sunday, February 21, 2010
Sunday, February 7, 2010
Week 2
Week 2: Virtual Manipulatives – Peg Puzzle & Towers of Hanoi
For this week’s virtual manipulative I asked my Dad to doing it. I first started my giving him the directions. I explained that he could not move backwards or jump over more than one. I explained that the goal is to switch the pegs on the left with the pegs on the right by moving one at a time. He started off with two pegs; he got that one right away. When it came to do four pegs it took him a little longer; he got it after three tries. As he was trying to do the four pegs he told me he did not like doing these kinds of activities. He said that there must be a pattern but that he could not see it. I asked him to go back to the two pegs and then the four pegs and see if he could find the pattern. He still could not find the pattern. When it came to the six pegs he tried four times and could not finish. So I solved it as he watched. I told him to try to find the pattern. I did it slowly so that he would be able to clearly see what I was doing. After the second time I did it he noticed that the empty spot was always between pegs of the same color. Once he noticed this I told asked him to try the six pegs again. He did it twice and could not finish so I helped him with the first three steps and after that he was on his own. We did that twice and on the third time he finished the puzzle. He noticed that all the reds were moved to the right first then the blues to the left and then back to the reds. The eight pegs we did together.
The Towers of Hanoi were much harder for him to complete. I explained that he could only move one disk at a time and that a larger disk could not be stacked on top of a smaller disk. I explained that the goal of the Towers of Hanoi is to move a stack of disks from one peg to another in as few moves as possible. He completed two disks without a problem. When he completed the three disks he completed the stack in the middle peg and the computer accepted the stack in the middle peg; I was surprised when this happened. The stack of four took a little longer then the stack three for him to finish. I guided him through the stack of four. He stopped at the stack of four. I went back and tried to get the stack of four to end up in the middle peg. After a few tries I figured it could end up in the middle peg but it would take more moves and that would defeat the purpose of the game.
Week 2: Private Universe Project
For this week’s Private Universe Project journal I watched Workshop 2: Are you convinced? I always ask my students why the answer is the answer. Most of the time they answer “Because it is.” I try to get them thinking about the problem. When I am working on word problems I try to find out why the answer makes sense. I cannot always explain it to other people but to me it makes sense. It is important to know why an answer is the answer. These students were put to the challenge of finding an answer and then try to explain why it is the answer. It is interesting to see how they each explain why they know the answer is right. The students and the one group of teachers noticed the same pattern; added two towers for each one from the previous pattern. The teachers and students found similar patterns but explained them differently. Students should always be challenged to explain why the answer is correct. Get them thinking beyond the problem given. Like we did in class not only did we have to solve the peg puzzle but also explain how we did it. Mathematics is full of Whys.
Week 2: Lesson Plan (Pattern Blocks)
How Many Seats?
NJCC Standards:
4.3.2 A. Patterns
Recognize, describe, extend, and create patterns.
Overview:
Children use Pattern Blocks to model a problem involving the number of tables needed to seat a given number of guests.
Objectives:
With this lesson students will be able to:
· solve an open-ended problem
· explore concepts of multiplication, division and remainders
· explore patterns that allow them to count more efficiently
Materials:
· Pattern Blocks, 13 squares and 13 trapezoids per pair
· Pattern Block triangle paper
Introduction:
1. Students will be shown a square and a trapezoid on the chalkboard.
2. Students will be asked to pretend that each of the blocks is a table: The orange square seats four people and the red trapezoid seats five.
3. Students will be asked to come up and draw a picture that shows how many people could be seated if two square tables were used.
4. Students will be asked to do the same thing for two trapezoids. (Making sure drawings show that if the long sides of the trapezoids are put together, the answer is 6 seats; if short sides are put together, the answer is 8 seats.)
Activity:
1. Students will be asked to pick a partner.
2. Students will be asked to imagine they are in charge of arranging the tables for a special school lunch party. How could they set up the tables so there are enough seats for everyone?
3. Students will use 2 kinds of Pattern Blocks- orange squares and red trapezoids- as tables.
4. Students are to arrange the 2 kinds of tables to seat 23 students, themselves, their teacher and the principal.
5. Students will be asked to come up with different arrangements that work.
6. Students will record each solution on triangle paper and will be ready to tell the class which they think works best and why.
Follow Up Discussion:
1. Students will be asked to come to the chalkboard and show one of their solutions, and explain how it works.
2. Students will be asked some of the following question to prompt class discussion:
a. How did you count the number of seats?
b. Did you notice any patterns when you were counting?
c. Why did you think one of your solutions was the best?
d. Which solutions have the exact number of seats that are needed? Which have extra seats?
.
Grade Level:
1st Grade
For this week’s virtual manipulative I asked my Dad to doing it. I first started my giving him the directions. I explained that he could not move backwards or jump over more than one. I explained that the goal is to switch the pegs on the left with the pegs on the right by moving one at a time. He started off with two pegs; he got that one right away. When it came to do four pegs it took him a little longer; he got it after three tries. As he was trying to do the four pegs he told me he did not like doing these kinds of activities. He said that there must be a pattern but that he could not see it. I asked him to go back to the two pegs and then the four pegs and see if he could find the pattern. He still could not find the pattern. When it came to the six pegs he tried four times and could not finish. So I solved it as he watched. I told him to try to find the pattern. I did it slowly so that he would be able to clearly see what I was doing. After the second time I did it he noticed that the empty spot was always between pegs of the same color. Once he noticed this I told asked him to try the six pegs again. He did it twice and could not finish so I helped him with the first three steps and after that he was on his own. We did that twice and on the third time he finished the puzzle. He noticed that all the reds were moved to the right first then the blues to the left and then back to the reds. The eight pegs we did together.
The Towers of Hanoi were much harder for him to complete. I explained that he could only move one disk at a time and that a larger disk could not be stacked on top of a smaller disk. I explained that the goal of the Towers of Hanoi is to move a stack of disks from one peg to another in as few moves as possible. He completed two disks without a problem. When he completed the three disks he completed the stack in the middle peg and the computer accepted the stack in the middle peg; I was surprised when this happened. The stack of four took a little longer then the stack three for him to finish. I guided him through the stack of four. He stopped at the stack of four. I went back and tried to get the stack of four to end up in the middle peg. After a few tries I figured it could end up in the middle peg but it would take more moves and that would defeat the purpose of the game.
Week 2: Private Universe Project
For this week’s Private Universe Project journal I watched Workshop 2: Are you convinced? I always ask my students why the answer is the answer. Most of the time they answer “Because it is.” I try to get them thinking about the problem. When I am working on word problems I try to find out why the answer makes sense. I cannot always explain it to other people but to me it makes sense. It is important to know why an answer is the answer. These students were put to the challenge of finding an answer and then try to explain why it is the answer. It is interesting to see how they each explain why they know the answer is right. The students and the one group of teachers noticed the same pattern; added two towers for each one from the previous pattern. The teachers and students found similar patterns but explained them differently. Students should always be challenged to explain why the answer is correct. Get them thinking beyond the problem given. Like we did in class not only did we have to solve the peg puzzle but also explain how we did it. Mathematics is full of Whys.
Week 2: Lesson Plan (Pattern Blocks)
How Many Seats?
NJCC Standards:
4.3.2 A. Patterns
Recognize, describe, extend, and create patterns.
Overview:
Children use Pattern Blocks to model a problem involving the number of tables needed to seat a given number of guests.
Objectives:
With this lesson students will be able to:
· solve an open-ended problem
· explore concepts of multiplication, division and remainders
· explore patterns that allow them to count more efficiently
Materials:
· Pattern Blocks, 13 squares and 13 trapezoids per pair
· Pattern Block triangle paper
Introduction:
1. Students will be shown a square and a trapezoid on the chalkboard.
2. Students will be asked to pretend that each of the blocks is a table: The orange square seats four people and the red trapezoid seats five.
3. Students will be asked to come up and draw a picture that shows how many people could be seated if two square tables were used.
4. Students will be asked to do the same thing for two trapezoids. (Making sure drawings show that if the long sides of the trapezoids are put together, the answer is 6 seats; if short sides are put together, the answer is 8 seats.)
Activity:
1. Students will be asked to pick a partner.
2. Students will be asked to imagine they are in charge of arranging the tables for a special school lunch party. How could they set up the tables so there are enough seats for everyone?
3. Students will use 2 kinds of Pattern Blocks- orange squares and red trapezoids- as tables.
4. Students are to arrange the 2 kinds of tables to seat 23 students, themselves, their teacher and the principal.
5. Students will be asked to come up with different arrangements that work.
6. Students will record each solution on triangle paper and will be ready to tell the class which they think works best and why.
Follow Up Discussion:
1. Students will be asked to come to the chalkboard and show one of their solutions, and explain how it works.
2. Students will be asked some of the following question to prompt class discussion:
a. How did you count the number of seats?
b. Did you notice any patterns when you were counting?
c. Why did you think one of your solutions was the best?
d. Which solutions have the exact number of seats that are needed? Which have extra seats?
.
Grade Level:
1st Grade
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