Sunday, March 21, 2010
Private Universe Video 6
I just finished watching the sixth installment of Private Universe. This video was different in the sense it took place solely in a high school setting, whereas the others involved elementary settings in large part. The students in this video had to calculate the speed of a cat jumping in the tenth frame of still shots. The class was broken up into various groups and allowed to work together to come up with answers and then defend their conclusions in a presentation. As the assignment progressed, one element I found especially appealing was the students' ability to learn from each other, not solely relying on a teacher. This occurred relatively early in the video (approx. 20 minutes in) when one of the groups presenting showed the class a unique way of approaching the problem (constructing lines on a transparency). Students continued to work towards a solution. The end of this video was nice to see because it brought some closure to the 6 part series, as a graduation and interview segment allowed students to reflect on their participation and highlight some of its most valuable components (ability to analyze problems, group thinking, the importance of invested teachers).
Monday, March 15, 2010
NLVM Function Machine
My virtual manipulative this week is in Number Operations Grades 9-12. It is the Functon Machine and focuses largely on pattern recognition. The manipulative has a few numbers (1 through 4) that are entered into the function machine. The machine spits out an answer and the exercise it geared to recognize a pattern formed in the input inserted into the machine. The exercise closes by having the user make educated guesses on what the next values of outpit would be based on the attern recognized in the first 4 input values (1 through 4).
Video 5 Project Universe
Although this is not the topic of the post, I do want to point out it was nice to see Jersey City highlighted in this video. The lesson taught in the Jersey City high school focused on Pascal's triangle and incoporated recognition of patterns. As we did see in prior videos and parts of this one, pattern recognition is one of the fundamental components of algebraic thinking.
Sunday, February 28, 2010
Week 4 Lesson Preparation--'What Happens to the Area?'
The lesson I focused on this week for Color Tiles can be found under the Grade 6 component and is entitled “What Happens to the Area?” The objective is to introduce or expand a student’s knowledge of area. The NJ Core Content area is 4.2.6D 1. “Select and use appropriate units to measure angles, area, surface area, and volume.”
Students at the outset are instructed to create a 3 X 4 rectangle using any color combination of square pieces. The discussion focuses on the length and width of the creation to introduce how length multiplied by width equals the area.
Students can then be paired or be allowed to work individually to create their own geometric constructions using the introductory exercise as a guide. Students are asked to begin with their own design and then double, triple, and quadruple the length and width of their initial design. For example, if someone began with a design of two squares next to each other (length of two and a width of one), they would have to extend this to a length of four across and width of two. This activity is extended to both tripling and quadrupling the initial construction to see if doing so affects the total area in the same ratio.
As students perform this activity, they are asked if doubling the length and width doubles the total area. The same is asked of tripling and quadrupling. As the activity is extended out to the several constructions, they will hopefully realize a pattern develop and discussion can ensue to generalize the findings.
Students at the outset are instructed to create a 3 X 4 rectangle using any color combination of square pieces. The discussion focuses on the length and width of the creation to introduce how length multiplied by width equals the area.
Students can then be paired or be allowed to work individually to create their own geometric constructions using the introductory exercise as a guide. Students are asked to begin with their own design and then double, triple, and quadruple the length and width of their initial design. For example, if someone began with a design of two squares next to each other (length of two and a width of one), they would have to extend this to a length of four across and width of two. This activity is extended to both tripling and quadrupling the initial construction to see if doing so affects the total area in the same ratio.
As students perform this activity, they are asked if doubling the length and width doubles the total area. The same is asked of tripling and quadrupling. As the activity is extended out to the several constructions, they will hopefully realize a pattern develop and discussion can ensue to generalize the findings.
NLVM Fractions Comparing
The virtual manipulative I chose for this week is listed under Grades 6-8 Number and Operations. For students who have a difficult time understanding common denominators and comparing fractions without a common denominator, this is a wonderful tool. The second component to this manipulative gives students a sense of where the particular fraction falls on a number line when compared with another (for example comparing 1/2 to 5/11). Some students may have initial difficulty understanding which is greater without use of a common denominator, but the number line serves as another way of visually seeing where the respective fractions fall.
Saturday, February 27, 2010
Private Universe Video 4 Commentary
I enjoyed watching this video for several reasons. The first part of the video focused on the Tower of Hanoi project we learned about a few weeks ago. The video reiterated an important problem solving method (finding a pattern in a smaller problem) and then using this knowledge to solve the original question in hand. The second part of the video was teaching mathematics to high school students who had a teacher leave because of behavioral problems. The new classroom teacher taught in a way to make students learn together as a class. The students were working on a 'line of best fit' in a scatter plot. Several students went to the white board and provided detailed explanations as to why they came to their respective conclusion. Other students then commented and together the class came to an answer. The teacher took a different approach to learning in allowing the students to learn together, rather than just standing in front of a projector and performing problems on a transparency. I do think she did a wonderful job and would love to see more of this in classrooms because students have a tendency to simply lay back in class while the teacher does the work. Learning sometimes gets sacrificed. The only problem I have heard with the method employed in Part 2 of this video is students who do not like being called upon to answer for fear of being wrong in front of others.
Monday, February 22, 2010
Lesson Plan Week 3 Pattern Blocks
NJCCS
4.2.2 A Geometric Properties Grade 2
4. Recognize, describe, extend and create designs and patterns with geometric objects of different shapes and colors.
Entry Skills:
For successful adaptation of this lesson, students should be familiar with the properties of and be able to identify a trapezoid and a square.
Strategies Utilized for Achieving Objectives
• Direct Instruction
• Modeling
• Guided Practice
• Independent Practice
• Cooperative Learning
Materials: paper, pen/pencil, dry erase marker, board, pattern blocks comprised of the following geometric shapes (square and trapezoid)
Introduction:
Students will be provided a bag of pattern blocks. Each student will be instructed to pull out a red trapezoid and an orange square. Students will be asked to put congruent pieces together (a square and a square, a trapezoid and a trapezoid) to resemble a table and see how many seats can be obtained using these geometric constructions (with each open side considered an open seat).
Procedure:
Students will now be instructed to pair up with another student or work independently if they choose on the following activity. The teacher will instruct students to pull out several square and trapezoid pieces. Using the introductory example to illustrate how various shapes can be used to resemble a table, students will be asked to make as many constructions as possible to seat 25 total people (with each open side resembling a seat. Pieces do not necessarily have to be placed together, so 5 square pieces and a trapezoid piece would suffice). Students will also be instructed to write down their figure combinations on paper for a later class discussion. Approximately 15 minutes will be allowed for this exercise as the teacher walks around the room monitoring each group or individual student.
Follow Up Discussion:
A group discussion will occur following the 15 minute exercise. Students will be asked to verbalize their solutions as well as how they came to these conclusions. Solutions will be written displayed to the class as they were drawn by the respective groups.
Assessment:
Assessment and understanding will be based on participation in the activity and class discussion. The class discussion will focus in part on the thought process utilized by the students in this exercise and how conclusions were reached.
Problem Solving Strategies:
Some students will opt to create a table detailing the number of pieces used along with the number of open faces/seats. Other may opt to draw the their respective constructions for a more visual look.
Future Implications:
This lesson can be used as a lead in for future lessons on multiples and divisors, recognizing 5 tables with 5 seats each give the total 25 seats being searched for. Remainders can also be introduced if a student comes up with a seating construction showing 26 open seats (2 trapezoids, 4 squares), showing a remainder of 1.
4.2.2 A Geometric Properties Grade 2
4. Recognize, describe, extend and create designs and patterns with geometric objects of different shapes and colors.
Entry Skills:
For successful adaptation of this lesson, students should be familiar with the properties of and be able to identify a trapezoid and a square.
Strategies Utilized for Achieving Objectives
• Direct Instruction
• Modeling
• Guided Practice
• Independent Practice
• Cooperative Learning
Materials: paper, pen/pencil, dry erase marker, board, pattern blocks comprised of the following geometric shapes (square and trapezoid)
Introduction:
Students will be provided a bag of pattern blocks. Each student will be instructed to pull out a red trapezoid and an orange square. Students will be asked to put congruent pieces together (a square and a square, a trapezoid and a trapezoid) to resemble a table and see how many seats can be obtained using these geometric constructions (with each open side considered an open seat).
Procedure:
Students will now be instructed to pair up with another student or work independently if they choose on the following activity. The teacher will instruct students to pull out several square and trapezoid pieces. Using the introductory example to illustrate how various shapes can be used to resemble a table, students will be asked to make as many constructions as possible to seat 25 total people (with each open side resembling a seat. Pieces do not necessarily have to be placed together, so 5 square pieces and a trapezoid piece would suffice). Students will also be instructed to write down their figure combinations on paper for a later class discussion. Approximately 15 minutes will be allowed for this exercise as the teacher walks around the room monitoring each group or individual student.
Follow Up Discussion:
A group discussion will occur following the 15 minute exercise. Students will be asked to verbalize their solutions as well as how they came to these conclusions. Solutions will be written displayed to the class as they were drawn by the respective groups.
Assessment:
Assessment and understanding will be based on participation in the activity and class discussion. The class discussion will focus in part on the thought process utilized by the students in this exercise and how conclusions were reached.
Problem Solving Strategies:
Some students will opt to create a table detailing the number of pieces used along with the number of open faces/seats. Other may opt to draw the their respective constructions for a more visual look.
Future Implications:
This lesson can be used as a lead in for future lessons on multiples and divisors, recognizing 5 tables with 5 seats each give the total 25 seats being searched for. Remainders can also be introduced if a student comes up with a seating construction showing 26 open seats (2 trapezoids, 4 squares), showing a remainder of 1.
Subscribe to:
Posts (Atom)