Great Word Problems

http://algebra-word-problems.blogspot.com

Hello everyone, I'm sure you are all busy with finals right now but I found I great link that I think will help you if you are a math education major. It certainly helped me. Its a link that gives a bunch of different algebra word problems and the answers.  It even has different levels of algebra depending on what type of lesson you might be planning.  I love word problems because they teach students a lot about how to use and apply different formulas to everyday life, but it also teaches them critical thinking skills as well because they must first come up with a plan to solve the problem.  This link that I found is really great because it will be a huge help to me in my future lesson plans.  Not only does it have word problems but it has word problem videos and contains links to other fun brain games to challenge students while keeping them interested and engaged.  The problems on this site are great because they are challenging but on level.  They often have more than one step and require a great deal of critical thinking but require a mathematical background that is on level and appropriate.  I also like that the problems do get more difficult as they go on and require the students to perhaps draw a picture in order to plan out how to solve the problem.  This is an amazing site and if you get a chance you should definitely look at it because I believe it will help you plan lessons and allow your future students more opportunities for critical thinking.

Final Project Area of Triangles Lesson

My lesson plan is about teaching students how to calculate the area of a triangle.  I believe that I could complete the lesson within two days but we may need a third day to really understand all of the concepts.  The first day consists of reviewing how to find the area of a rectangle. I would start by putting a few examples on the smart board and asking for student participation.  They should already have an understanding of how to calculate the area of a rectangle but if they have forgotten anything it is always important to have a quick review. We start with calculating length multiplied by width, which hopefully the students themselves will be able to explain.  I will show students that this is the same as saying base times the height.  It will now be easier to explain to the students how to get the formula for area of a triangle.  I will start the explanation by drawing another rectangle on the smart board and drawing a diagonal line across the center. if By drawing this diagonal line across the rectangle the students will be able to see that we would get two triangles.  I will ask the students to use their critical thinking skills to see if they can tell me what area of one of the triangles is given the area of the whole rectangle. Hopefully through this visualization the students will be able to tell me that to find the area of one of those triangles we would simply divide the number we have for the rectangle by two. This now gives us the formula one half times base times height.  At first it is easier to work with only right triangles because they are easier to draw and measure.  When using right triangles the students can draw two equal triangles and make a rectangle, which also helps them better understand the formula we just came up with.  After allowing the students to explore these concepts and formulas using graph paper, pencils, rulers and protractors, we will discuss acute and obtuse triangles.  The students must first understand the difference between these two triangles and how to draw them.  After practicing drawing these two new types of triangles, I will explain to the students that the same formula we used for finding the area of a right triangle also works for finding the area of an obtuse or acute triangle.  The only difficult part about this of course is finding the height of the triangle.  I will of course have to explain that the height or altitude of a triangle is the line segment from one vertex (or angle) of a triangle to the opposite side so that the line segment is perpendicular (or forms right angle) to the side.  The students will work in groups to draw and label the sides and heights of different triangles.  Using The Geometer Sketchpad the students will have to create three examples of each different type of triangle (right, obtuse and acute).  The students will then record the data (lengths of sides and altitude) that they themselves have created on the computer and use that data to calculate the area of each triangle.  In this activity the geometer’s sketchpad is extremely useful because it will allow the students to explore many different types of triangles as well as better understand the relationship between base and altitude and the opposite vertex.  On top of all this, it gives the students accurate measurements of angles and sides so that they can have more accurate data and more accurately calculate the areas of their created triangles.  The final assignment of the lesson will to be to calculate the area of different shapes that I give them using their new information about triangles.  I will give the students a few different shapes such as octagons and stars, which they will have to break up into different size and shaped triangles in order to find their areas.  The students will use the geometer’s sketchpad to draw the triangles inside the given shapes. They will then label the measurements for each side and calculate the area of each small triangle that they have created.  Adding the areas of the triangles together they will be able to calculate the area of each of the given shapes.  They will have to submit their work and drawings online as well as show how they calculated each area on paper so I can feel confident that they have understood the lesson.

 The following is the link to my lesson plans:

 https://docs.google.com/spreadsheet/ccc?key=0AoktAYMszf1ndENsSDF0YzVBUFdnSVFwUU16M250Mmc

Edutopia Video

I love the most recent edutopia video! it seemed like the students were having a lot of fun, and they were learning so much! not only in the classroom but in their athletic activities; however in the sports they were competing in such as cheer leading, they are learning not only about their health but about velocity and other aspects of sports that work into different ares of study such as science and mathematics.

Interactivity #5

The teacher I interviewed is an Algebra I and Algebra II teacher in Newton Public Schools.  When asked about the use of technology in the classroom the teacher did not seem extremely thrilled about the idea, but admits that the smart board has been a nice addition to the classroom because it is very useful when proving and working out problems on the board.  The teacher also admitted that NETS-S and NETS-T standards are a new concept because though the school does encourage the use of technology in the classroom, the NETS standards are not stressed.  He agrees that the first standard is important in mathematics because using graphic visuals to visualize a function can be very beneficial and help the students to better understand the curves and slopes of functions.  If the students can visualize these functions at a young age, they will have an easier time with more advanced levels of mathematics such as calculus when they will need to find the areas under these curves.  On the other hand, he like most math teachers feels that if the students use calculators too often they will become dependant on the calculators and not be able to the math on their own.

He also agrees that the other standards are important because they deal with analyzing data and being able to effectively collect that data, graph the data, and then analyze what the data tells us and report results.  Graphing is an important tool in a mathematical classroom, and he agrees is something that he could incorporate more into the lesson.  I tell him that there are a lot of different technological tools that make graphing easy, and remind him that graphing using these technological tools will allow the students to make more accurate graphs and be able to much more accurately analyze the data they are working with.  Practice using these tools will also help students in the future if they take any statistic or data analysis classes.   These skills are extremely important in today’s society and will make these students better citizens in the future, which is of course one of the main points of education.

Something important that I believe came from our conversation is that these technological tools are not always a crutch to students, but they can be used as important educational tools on which the students can build and gain a better understanding of mathematics.

You can view the changed to my Lesson Plan in Google Docs at 

https://docs.google.com/spreadsheet/ccc?key=0AoktAYMszf1ndFRqVnRBamV4aXVXOFJwLUxlbHFzalE

Interactivity #4

 

https://docs.google.com/spreadsheet/ccc?key=0AoktAYMszf1ndFRqVnRBamV4aXVXOFJwLUxlbHFzalE

I chose this lesson plan because is well written and clearly laid out.  It also satisfies some of the important NJ standards.  I saw that the teacher used technology but she was not taking advantage of all the technology available.  I felt I would be able to incorporate different technologies that would help the students better understand the lesson and aid them with homework.  I did feel that the curriculum goals and the teacher strategies were very well aligned.  She had clear goals and strategies for explaining the lesson and assessing student understanding.  Unfortunately as I mentioned before, she did not take advantage of the technologies available.  The only material she listed was an overhead projector which is a great tool to use every once in a while, but students have a tendency to loose interest if the teacher is only putting different slides on the projector instead of using different interactive technologies.  The technologies that I listed, such as the in class math game, I feel are essential to achieving the curriculum goals because it gets students involved during the class.   The other technologies such as cramster and youtube are also extremely important because they can help the students during their homework by giving them examples and step-by-step instruction. Through seeing additional examples on these sites the students may be able to better understand the steps and formulas needed to solve the given homework problems.  Also though using these additional resources the students will have a better understanding of the lesson and be able to apply their knowledge to future tests.

#3 Useful Classroom Technologies

I thought this was a great group activity because we had to work together and be sure to read each other’s technology choices so we did not repeat them.  I liked reading my group members ideas because they were often things I had either never though of or had forgotten about, many of which we have used in many of our math classes already.  This activity definitely makes you realize how important and how helpful technology is in a math classroom.  At first it seemed like a lot of work to find 10 different technologies used in the math classroom, but once I started researching the topic there were so many, it was almost hard to narrow it down to what I thought were the ten most effective teaching technologies. 

As we learn in our other classes, two important aspects of teaching are teaching literacy and assessing understanding.  Many of the technologies on or list are visual aid because in math is so important to connect terms and formulas to graphs to gain literacy and understanding.  A few of the technologies are also tools for assessment such as “Math Teacher Tools” which helps teachers create worksheets which can then be graded, “Math Pad Plus” which allows the students to do the worksheets online, or my personal favorite “Dream Box Learning” which assesses the student’s progress, identifies the area which the student is struggling in, and provides further practice and instruction.  “Dream Box Learning” has games and animations that make learning fun for the students and assessment easy for the teacher.

#2 Calculators: A Helpful Tool

Calculators are an important technological tool in a math class because they aid in calculations as well as allow the student to better visualize the equation through graphs; however, the picture illistrates how important it is to still know and understand how to do the calculations by hand.