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?
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Grade Level:
1st Grade