NLVM-Factor Tree for 6-8 grade Algebra

Factor tree is a very useful lesson in algebra in any level. by practicing this lesson a student can easily get knowledge about possible factors of a number. Students can able to find out which one is not a possible factor. Student can easily know to compare the factors of two different numbers and then can easily find out GCF(Greater Common Factor)- the only common facors of two numbers. Student can also easily understand LCM(least Common Multiple)- the common multiple of two different numbers. Knowing GCF, and LCM is very important in the lesson of algebra in any level. Student can easily practice with different numbers in this lesson in order to get knowledge about FACTOR TREE.

NLVM-Number and Opperations/Fraction Comparing

This Manipulative lesson could help studens to learn about fraction, the size of fraction and the comparision of fractions. In this lesson a student can easily find a common group in a fraction. a student can easily practice of changing the numanator or denomantor and then easily compare the fractions. by practicing this a student can able to understand better about a fraction and its common group.

Private Universe Video-1: Analysis

This video showed that If you give an oppourtunity to a student to solve a problem they woud come out with some strategies to solve the problem. The video also proved that instead of giving a student a guided teaching the free thinking process would be more creative and challenging. This specipic strategy would be good in certain situation where a student can able to apply his own idea to solve that problem but teacher should be careful about choosing the problem. The reason is that few problem need some discussion prir to solve the problem. By practicing of giving student freedom of thinking to solve a problem is very good strategy to make the young kids confident where they would learn to take challange in future. Once a student able to come up with own idea to solve a problem it would be better understanable than following a guided instruction from a book or a teacher.

private universe video-2: Are You Convinced?

This videop showed the same struggle to solve a problem by a teacher or a student. In this video the teachers went throw the same problem in order to find the solution, the pattern. Even though both teachers and students had the same thinking process when they tried to solve the problem but they they used different stategies such as drawing the tower, patterns. I realized that some teachers had also same difficulty to justify their answer or verbalize their method. As student advances in grades it becomes more familiar for them to listen and respond the teacher individually. At the end the students wereable to see the problem in the tower concept and able to see a pattern with in their two partners. All students shared how they solve problem by discussing their strategies. In conclution the student established that coming up with a pattern would be the best strategies to to solve a problem with 4,5, and 10 towers.

Private Universe Video-3:Inventing Notations

This Video Shows that students got oppourtunites to share their ideas between the groups. I think this is one of the best way to learn from each other. When one group seemed to get frustated in short amount of time because of the difficulties then other group came out with different strategies to solve the problem. This whole process made the group of students engaged, energized. By allowing all students to discuss about the problem the students were able to see the problem and they tried to get the correct answers and also tried to satisfy every single person. The positive thing that the students got the idea is that without helping each one no problem couldn't be solved. This was a very good understanding that a good solution is possible by satisfying every single person who was involve in the process of solving the problem. Otherwise who wouldn't satisfy he wouldmight have the right answer. This was very unique way to solve a problem. The important observation is that little kids showed their attitude towards solving a problem.They also show their interest and sincerity by coming back to work as soon as lunch was finished. It is very challanging in today's class room lesson where student are taught a very formative way where flexibility doesn't exists. But this video shows how flexibility works out where students came out with different ideas and then came out with an unique solutions. Later a student came out a solution by using binary code whichone was very impressed. He was asked how he got the idea. He told that it just pupped out in his headThis shows students work in a group with flexibilty they could come out with an idea like mathematician.

Lesson Plan(Capturing the Flags):Cuisenaire Rods

I found this lesson is interesting for fifth to sixth grade. This lesson plan is taken from the CD. Capturing the Flag is interesting because in order to do this activity students need to the rods and their relationship between each other. In addition student need to know the numerical value of each rod. Student also need to know time table in order to calculate the values of rods to cover the flag. Students can easily learn about the fractions by placing the different rods in the flag. Finally student able to learn the strategic thinking because in order to finish the game they need to know how to start, where to start, and how to avoid the ending turn in order to win or loos the game. This lesson could be reversable if first round winner would be the last one who finished covering the flag the next round will be opposite is that the winner would be who didn't have to finish covering the flag.

lesson plan(making triangle): using cuisenaire rods

My lesson plan is to make triangle by using cuisenaire rods that is taken from the CD.In this lesson the students will find out to make different triangle by using differents rods. Students need to specify how to connect the edges of the rods. the special technique is that the two rods can be pushed down or lie down but can not be overlapped. Students need to find out any three rods is aable to construct a trangle? what is the reason for possible answre? student need to make a list of the combinations of rods that make triangle and other combination that don't make triangle. students need to explore of the properties of triangle like the lengths of two sides of a triangle are greater than the third side. students will ask to findout equuilateral triangle(all sides are equal), isosceles triangle(two sides are equal), scalene triangle(no sides are equal). finally student will ask to find any pattern is present in this process there.

NLVM-Geoboard for 6-8 grade to illustrate area, perimeter

I found this manipulative practice is a fun way of learning to illustrate different kind of polygon and measuring their area and perimeter. student can findout one polygon in different size and can measure its area and perimeter and also able to findout the possible maximum area and perimeter. student also can able to findout the relationship between the area of triangle and rectangle. student shouldn't limit their talents they can able to illustrate different kind of open and closed polygon. This lesson will help student to explore their geometric knowledge of polygon by themselves very fun way.

Area of Rectangle and Square.

Mohammed Uddin
Grde-4
Mathematics


NJCCCS: 4.2E1
OBJECTIVE:
SWBAT understanding the area of rectangle and square.

Pre- Discussion and Activity:
# Discuss about rectangle and squae and the area.
# Explain how to use geoboard and rubberband to make rectangle/square
# Explain how to draw model of rectangle and square on geo dot paper
# Mention the student about the distance between two pegs is one square unit.
# Measuring Area: Space to be measured in the center of a geoboard for an object two ways:
WAY-1: we can draw a model of rectangle or a square on geodot paper and count on squares.
Way-2: we can use the formulla of area= length*weidth

Materials:Geo Boards, Rubber bands, Geo dot Papers. Pencils.

Assesments:
- what is the area of square and rectangle and there is any differenc

Homework-
- Draw different sizes Rectangles and Square and find areas by using geo boards

Lesson Plan/Geometry(Polygons and its different shapes)

Mohammed Uddin
Grade-5
Mathematics

Objective:
SWBAT understanding the polygon and its different shapes, name it, learning angles and parallel lines.

Activity and Discussions:
# Before go to details operative activities explain students about polygon, its shape(closed/open), the lists of polygon(like different kind of triangle, rectangle, pentagon, hexagon etc.)
#Explain different angles, parallel lines.

# Expalin how to use Geoboard with rubberbands .

#Let Student create different Triangles-
Right angle, acute angle, obtuse angle

Different types of Quadilaterals-
Rectangle, Square, rumbas, Trapezoid

Other Polygons-
Pentagon, Hexagon so on.

Materials:
Geo Boards, Rubber Bands, Geodot Papers, Pencils

Assesments:
- Ask Questions about different angles, shape, and parallel line.
- In Which description the shapes are congurent?
- In Which shape two pairs parallel lines but not right angle?
- In Which shape has two pairs parallel line and right angle?
- In Which shape has only one pair parallel lines?
Homework:
- Draw different shape of polygons with their name on.

Savings Calculator and Loan Calculator

Whether in a particular curriculum Contains material on Finances, there are few topics more critical in a real life for a student to grow with savings and borrowing money. Without this two issues today's modern life is not worthy.
The savings calculator easily calculate an amount of savings in a different time frame with different interest rate. On the other hand loan calculator can easily calculate a loan with an interest rate in different time frame. By knowing these tools a student can easily figure it the relationship between savings and borrowing habit. A student can easily figure it out in order to earn something how much money need to be saved in what time and how much need to save in order to repay a loan also. These tools is very practical rather than regular classroom curriculum.

Pie Chart

The Pie Chart manipulative offers a convinient way to generate a representation of parts in relationship to a whole group. We can use Pie Chart to illustrate links between fractional and percentage representations of a group of given information. The Pie Chart is very useful and visiable graph to show the fractions and prencent.

Box Plot/ Histogram

Box plots and Histograms are both used to summarize data graphically. This two methods are very useful to find mean, median, maximum, average, percentage of number of given data. A box Plot(Box and Whisker Plot) shows the minimum data value, the lower quartile, the upper quartile, and the maximum data value of a number line. A box is created between the the lower and upper quartile and the median is marked inside the box.
A Histogram divides the range of values in a data set into intervals. Over each interval is placed a block or rectangle whose area represents of the data valuee in the intervals.

Week-6:Reaction to Private Universe Workshop-Problems and Possibilities

The 6th video demonastrated a problem that was asked to solve it as a part of Rutgers long Term study. The main idea for the whole purpose was that to introduce a calculus problem to a group of senior high school student who never got a chance to do that kind of problem and also to justify a calculus problem can be solved by everyone eventhough they never had calculus. The problem was a picture of a cat with 24 pictures of different movements. The problem was called ' Cat Walk' where the picture had a background so distance can be determined and the students were provided times. The groups were asked to find out the speed of the cat in the 10th and 20th frame. the students were devided in several groups and worked with in groups by sharing the individuals assesment. On the other hand the Researcher were allowing studens discoveries and cllaborations. The video demonastrated how students need oppourtunities to build personal representations by using science and mathematical skills. The students tried to find accelaration of cats speed in the 10th and 20th frame and putting infomations in a graph and able to draw picture of cat's walking eventhough each group came out with different data because each group follow different scientific method for measurement. the groups also able to put that information in a real life experiences. They expanded the distance from 10 times to 50times from the cat's walking distance and tried to follow the cat's speed when they walked like a cat with the distance. This such practice helped to visualize the cat's accelarartion lively. Then they able to findout the motion of the cat and where it was certainpoints and relate to the graph. This practice took couple of days in a two week camp that shows how a mathematical problem solving ability grown. In my opinion this such practice would never possible in a real life classroom setup but it shows that how it could be different and interesting to show others an ideaa of solving a math problem.

Virtual Manipulatives-fifteen Pizza

The goal of this pizza is to arrange the fifteen numbered tiles to make a particular pattern. The basic goal of this technique was to understand patterns, relations and functions. the student has so much to think about the possible pattern and arrangement. They can come out too many ways with too many shapes by using fifteen tiles in different patterns. They need to use their math skills to arrange yhese tiles in a specific shape. I liked this lesson for middle school students because they can use their algebric knowledge and geometric knowledge as well to rearrange all tiles for a particular shape.

WEEk-5 Reaction To Private Universe Workshop-Building On Useful Ideas

I think this is an interesting video about the about the ability of a student in different grade level where they were asked by their teacher to use their individual skills, knowledge and creativity. The important think was that in this video the student were asked to do the activity without any formal instruction or any formal answer. For that reason all individuals able to use their own thinking to solve the problem and able to see their own problem whichone was stated by Mr. Arthur Powell "own a problem" by an individual. It is very important to get skills in any situation to see that problem well, it makes easy to solve the problem. In this video all the teachers in different grade level gave students oppourtunity to think about the problem and come out a solution where they were able to justify their answers. For example Melissa Sharp- a first year teacher in Englewood School District was asking her student all the possible questions to justify the answers because she believes that by practicing this student would be more understandable with a solid foundation for their future grade. The effectiveness of the method was seen in the high school students when they were asked to solve a problem where they used pascel theoram to solve a problem which one they learned before grade. finally it is very simple to say that if you would allow students time and oppourtunity they will able to see problem and solve the problem as well, and they could able to use this skills in any time they need to use it.

week-4 Reaction to Private Universe Workshop 4-Thinking Like a Mathematician

The important message about this video is that let kids think, be patient, try to simplipy the problems, and look for a pattern that work to justify the problems. The another important toos is that let kids work in a couple of groups and then sharing their groups thought between the groups and finally try to come out a common solution where every individual is satisfied. The role of the teachers were very crucial. Every individual teacher gave students enough chances for critical thinking and tried to navigate their all thoughts in a common direction instead of being helpful by giving the clue. The Problem solving math is kind of realistic math where kids can feel interest eventhough it seems hard.the whole process in the video for different criteria were very active learning where kids involved themselves, questioned, stressed out to findout the common pattern and justify the findings and continue worked until get aperfect answer.One thing I foundout that pretty differnt then todays most of the classroom activities where kids just follow the procedure given by their teacher to solve a problem in a very limited time . In todays classroom activities do n't really allow kids and teachers enough time and envirinment to use the strategy that used for problem solving mathematics in this video.
Finally I would like to saythe teacher and kids need the oppourtunity and the environment where school will allow both parties to create a huge numbers of active learner where kids would love to think and apply all toughs strategise like a real mathematician.

Algebra Tiles-Visualize multiflying and factoring algebric expressions.

This method is very simple to understand about factors of a multiplications, grouping of one equal to how many things, finding the unknown variables by visualizing tiles in different scenerio. I believe this method of using tiles to learn algebric expression for the youngers would be very helpful. visualizing a problem solving seems very effective than any other method because by putting the tiles in in different combination in different shape like different size of rectangles in a systemic order like one group of variables in horizental mood and other group of variables in vertical mood help to find out the multiplication of two different factors, for example (2x+y)(3x+2y). On the other hand combination of one variable and different numbers in a rectangle shape can easily show the the value of the variable(the unknown number), i.e. x=? can easily findout from x+2 and 2x+8 combinations of tiles by putting in a rectangle shape. this tiles method also help to know about grouping. Like (2m+8) is how many groups of ( m+4) can be easily vsiable by putting rectangle shape tiles in a rectangle shape worksheet. The interesting thing about this method is that kids can use their creativity of making different shape tiles with different colors tiles for different numbers, and variables.