Lesson: Product and Quotient Rule (Blog Post #4)

The product rule and the quotient rule are helpful in regards to differentiating a function. However, they can be tricky if the student doesn't understand the rules. Even then, understanding isn't enough. One must apply it and be able to do various problems while keeping in mind the foundational aspects of the two rules. After all, practice makes perfect. 

Regardless of whether or not you are a fledgling or a pro at the product and quotient rule, it doesn't hurt to do a little review. 

*Important Note:
While the two parts of the product rule can be switched around due to it being addition, the quotient rule does not allow for switching to occur as it involves subtraction.

For example, nine minus five is different than five minus nine. For convenience sake, keep them both in order at all times.

Extra Credit Blog 3.5 Matt Kwong

1.) http://www.mathplayground.com/

Mathplayground is a free popular learning math site. It has lots of math games, logic games, word problems and math videos which are fun and challenging. Teachers or students can use this website for getting the correct math concepts or having some fun with those games. Also, teachers may use it during class.

Skills:

Basic reading and computer skills

Different math skills according to different games they play. For example, basic algebra, linear equations and angles and velocity.

I think this website would be appropriate for students from early childhood to grade school, or even high school. It provides concept that students need in their math class and they can also play those games as a revision.

I would recommend this website to students who are not interest in reading a long text book but want to know more about some math concept.

2.) http://www.math.com/

Math.com is a website that students can get lots of math knowledge from it. There are subjects like basic math, algebra, statistics, calculus, etc. Math.com also provides practices, calculators and games.

Skills:

Basic reading and computer skills

Math knowledge depends on what practice or subject students are looking for.

I believe this website is appropriate from kindergarten to high school, college kids may not interest in it but it helps. The website has different techniques for each math subject. This gives a chance for students from different level to use this website.

I would recommend this website to all students and teachers. It can be a useful tool for them. Teacher can add things to their teacher resources from the website. Students can do review from the website or play some games to exercise their brain.

3.) http://www.mathsisfun.com/

Mathisfun.com is fun website to learn math. Just as its name, it is fun! The website is colorful and the texts are easy to read. It gives tools for student to use so that students can learn easily. The website has different math topics, such as index, date, measurement, and most important it has games.

Skills:

Basic reading and computer skills

Basic math concepts (students can learn more from the website.)

This site is appropriate from Kindergarten to High school. It is a good site to get general explanations for some math words because it has a dictionary in it. Also, students can look up math formulas which help their homework or study.

This website can use as a review section for students. When students are trying to finish their homework or study for test, student can use this as an extra resource.

4.) http://www.coolmath.com/

Coolmath.com is a attractive, colorful and interesting math website to visit. Students can play lots of math games in this site. Learning and playing at the same time is always better to have a lecture. Just as it says in its front page, bored with math? Confused by math? Hate math? Coolmath can fix it.

Skills:

Basic reading and computer skills

Basic math skills, students can learn more from this site.

This site is for ages 13 to 100. But I think kids under 13 can still use this site under parents or adults help.

I would recommend this site to all students that enjoy playing more than learning. This site can do both things at the same time. So, why don't take a visit to coolmath.com? This site can be a extra resources and an extension of school.

Extra Cred 3.5-Tammy

Tammy Bah

25 November 2014

Applied Calculus

Blog #3.5

Part A: #1

Website: http://www.coolmath.com/

Brief summary:

Coolmath.com is a fun, colorful, free and easily accessible website that allows kids to learn a wide range of math games dealing with topics such as algebra, geometry, pre calculus, and calculus as some examples. The site started in 1997. Coolmath.com also has other websites that teachers, parents, and those who are into finance and benefit from. The interesting thing about this particular website is that the participants are able to have an interaction with the games. This means that, the website users are able to communicate directly with the machine; I think this is a pretty cool feature of Coolmath.com. The website even has a section titled, Totally Stressed Out. Coolmath.com also has bright colors that help distinguish what is associated with what topic.

Skills Required:

• ·      To know basic math techniques
• ·      To know how to use a computer/have a computer
• ·      To read words and understand what they mean in the mathematical concepts
• ·      Understand how to use a computer as well as sentences dealing with math

Appropriate for Age?  This website is for ages 13 to 100. For the 12 and under crowd, they might need more help or adult supervision. But just like anything in life, repetition is needed.

When/how this source is best used? Since the concept is that math is cool and fun, this should be used at anytime whether it be at class or at home before dinner. I think that it is best used when the student knows how to use the Internet and is comfortable enough to use the computer on his or her own.

Recommendations: I would recommend this to students who need extra practice or just genuinely like to do math problems.

Part A: #2

Website: http://www.mathisfun.com/

Brief Summary:

Mathisfun.com is a website that is supposed to be fun and enjoyable to learn math for those who use the website. This is intended to be for students to use as a tool to learn more about math in a fun way and a way that is easier for them because they do not have to worry about the pressures of a classroom. The website also has little blurbs on the topic in ways that are helpful for the average person. The website is also great because you can choose which grade, whether is be second grade or fourth grade. Topics included are counting, fractions, and bar graphs, however this is all based on what grade one choose.

Skills Required:

·      To know basic math techniques

·      To know how to use a computer/have a computer

·      To read words and understand what they mean in the mathematical concepts

Appropriate for Age? I believe this site is age appropriate from Kindergarten to Year 12 of high school. What is good about this site is that you can choose which age group you are seeking. Although, children who are too young to use a computer will need help from a teacher, parent, sibling, etc. Other than that, the site is very appropriate and clear about age ranges. Additionally, the site could be used by college freshmen who might need a refresher on topics learned in their last year of high school.

When/how this source is best used? I believe this source is best used for teachers in schools and parents at home to help their children get the extra help they need, if there are concepts that need tuning up.

Recommendations: I would recommend this site for working parents who do not have the time to teach their children after they get off of work. It is something that the kids can use in the kitchen while parents are cooking dinner and they can ask parents for help, if needed. I would also recommend this to teachers who would like to use computers in class as a “starter exercise” or “warm up”

Part A: #3

Website: http://www.wolframalpha.com/

Brief Summary: WolframAlpha is a website that I use frequently, being an econ major and taking many econ and math courses. It is a commercial website that was founded in 2009. The main purpose of this website is an answer machine of sort! Basically, it’s like Google but for math, you can type in many questions and computations and then you receive an answer. However, there are limitations to the kind of questions you can ask. This is free and you can also get it as an app on a smartphone as well or your one computer. As of 2012, there has been Wolfram Alpha Pro, which means that with a monthly subscription fee, one can get a lot of other things that aren’t in the regular one like audio and images.

Skills Required:

No skills required! However, one must know how to type in their question correctly with the correct symbols or else you will get an error or a wrong answer, which would suck.

Appropriate for Age?  I believe that this site/app is appropriate for ages 13 (8^th grade) and up. This website can literally be used by anyone because there are so many features not only in math but physics, stat, chem and engineering.

When/how this source is best used? This is best used to make sure you did a problem right or how a graph looks like in comparison to your graph.

Recommendations:

I would recommend this to anyone and I can sincerely say that because I use it!

Part A: #4

Website: http://www.funbrain.com/

Brief Summary: Funbrain is a website that is known as the Internets #1 educational site for kids in kindergarten to 8^th grade dealing with games in grammar, science, spelling, and history. It was founded in 1992, one year before I born. It is also a part of Pearson Education, which is a big publishing division in academia. This is a non-interactive game, which means that it provides some safety to the kids out there on the Internet. The type of games and difficulty level varies based on topic (math, reading) and the students’ level of comfort with the type of question.

Skills Required: There are no major required skills, as most kids will be using their knowledge form school, however one must know how to use a computer and how to use a mouse.

Appropriate for Age?  This website is great for the age group that it is intended for, I think it would be nice for kids to take turns and do them, maybe to create a slight competition among friends. FRIENDLY!!

When/how this source is best used? Many teachers and plenty of students to help on learning more techniques for math use this! I think its great for home as well or aftercare at schools with those kids of programs.

Recommendations: because of its credentials, I must say that I recommend Funbrain to children and their families, as math is a very hard concept if not done frequently.

Extra Credit Blog 3.5 Technology Anthology - Wasim Ashshowwaf

Extra Credit Blog 3.5 - Technology Anthology

Khan Academy

·      Summary of recourse

o   Khan Academy provides a variety of lessons covering different math topics. It has interactive and video materials that are very useful for learning math. The interactive part tests your knowledge and then provides you with answers and the opportunity to practice. The video part takes you step by step to learn math. It usually has a person explaining problems on a black board drawing. I like how easy to follow the videos are.   

·      Skilled required

o   As there are a variety of lessons on different topics such as algebra and callus, there are no specific skills. The student can basically select the lever she/he is at and then start from there.

·      Appropriate for age setting?

o   As I mentioned, Khan Academy a large varies of lessons serving different level. This means there’s not age/level restriction

·      When/how this source is best used?

o   A student can use Khan Academy to prepare for class in advance. So to watch some videos in the summer for example. Another case is when a student needs help in understanding a certain concept as she/he prepares for an exam or want to solve a problem. I think the best way to use it is to maybe start doing the interactive problems to identify which I aspect in approaching a problem needs to be worked on. The watching the video, if necessary again and again to understand a certain concept or a problem.

Mathisfun.com

·      Summary of recourse

o   Math is fun, is a website that covers different math topics such as Algebra Geometry, and financial math. It also has a math dictionary and some interactive and fun stuff like puzzles and games.

·      Skilled required

o   The website does not need any skills since it cover basic topic such as kindergarten math and never the less more advance martial that takes about probability and statics or financial math. So it’s appropriate for most age setting.

·      When/how this source is best used?

o   I think it’s a great tool to look up genial explanations of math concepts and also definitions. It’s also helpful to look up formulas such as the ones on financial math, which includes compound interest.

Wolfram Alpha

·      Summary of recourse

o   WolframAlpha.com is great website and also mobile app tool that solves problems and provide instant answers, which includes graphing, finding the derivative and providing steps for it. I have used it many times and found it very useful.  It also helped me understand the component of a function. For example, I used it once to identify the elements and transformation of a trig function. I like how the website gives you different aspects and information about a certain function or a problem. It’s also useful for those who don’t have a graphing calculator.

·      Skilled required

o   Wolfarm Alpha doesn’t need any specific skill other than imputing the problems in the box in the website or app. And the problems could be as easy as algebra or as advance as calc. 

·      Appropriate for age setting?

o   I would say this website tool is appropriate for most ages, however, mostly toward age 12 I think. That’s because this is when they would be interested get use to using website or mobile Apps.

·      When/how this source is best used?

o   I think it’s a good idea to use this tool to verify or understand the component of a certain function though it’s graph and the details it provides about it. So for example, after or before solving a certain problem. It also can be useful to learn about and draw connection between the elements in a function and how they look in the graph. For example, in a trig function to identify the number of cycles and the amplitude. 

Video Calculus iPad App

·      Summary of recourse

o   This App provides a large collection of pre-calculus and calculus videos. The person, who made the videos, teaches math in real life, as I believe. I watched a few of his videos and they are easy to follow and digest. The person in the video usually explains the lessons in a fun way, and gives clear examples. The down sides to this app are that, as far as I know, it’s only available on the Apple iPad, and it needs a paid subscription.

·      Skilled required

o   Because this App is focused on calculus, the skills needed to use it, is basic knowledge of pre-calc. Keep in mind that the videos starts with video explaining what a function is, and then goes more in details calculus.

·      Appropriate for age setting?

o   This App is appropriate for college student especially as they start to take their calculus courses. I would also think it’s useful for high school juniors and seniors who take calculus.

·      When/how this source is best used?

o   I think the best way to use the recourse is to start with the level at. I would also check the syllabus for my class and see what topics are covered so I can match them the videos. I think it’s a good idea to watch the whole video and take notes. And sometimes to watch it over and over, and pause if needed to think about a concept for example.

Christine Mazzocchi- Blog Post 3.5

1) Brainpop (www.brainpop.com/math)

Brainpop is a website and an app available for students to use. The purpose of this resource is to provide a fun and interactive way to review math skills. Brain pop tests the knowledge of students ranging from algebra to geometry, to probability. Students have the ability to choose a topic of their choice and then get to watch a video which explains the topic and then students have the opportunity to take a quiz to test their knowledge. There are also some activities and worksheets to accompany the video. 

Skills students need are to:

-Read and interpret printed text

-Be able to use an app or click bubbles on the internet

-Read and interpret mathematical symbols

-Understand basic and intermediate math skills (algebra, geometry,  measurement, probability, data analysis, ratios, percents, etc.) 

This resource would be appropriate for students who are in third to eighth grade. The website and app are very easy to navigate because of the clear labels of all of the subjects. The videos may not fit every student’s learning style, but it is a different approach to hear the basis of a topic from someone other than their classroom teacher. 

In my opinion, this website can be used by teachers in their classrooms because they can incorporate the videos into their lesson plans. Students might find this different way of teaching to be intriguing and actually pay attention. The interactive quizzes at the end of videos will be fun for the students to complete as a whole class. At home, children might need to be supervised to keep them on track in the math section, because BrainPop does have other subjects besides math. 

2) AplusMath (www.aplusmath.com)

AplusMath is a website which has interactive math resources for teachers, students, and parents. This website has worksheets, games, flashcards, and homework help available. Students have the option to choose a topic of their choice and then choose the activity that will benefit them the most. Students, teachers, and parents are able to print out the worksheets, as well as the option to view answer keys to check their progress. Such games include MATHO(math and bingo combined) and solving the hidden picture by solving math problems. 

Skills students need are to:

-Read and interpret printed text

-Be able to have access to the internet 

-Read and interpret mathematical symbols

-Understand the following math concepts (addition, subtraction, fractions, geometry, algebra, multiplication, division)

This resource would be appropriate for students in grades one to eight. This website provides many different techniques for each math topic provided. This means that students with different learning abilities will find this website helpful because they could choose what technique helps them better understand the material. 

In my opinion, this website can be used as a tool to help both students and teachers. At home, students can use this website to add to their learning of a particular topic. The website has all of the topics listed at the top, so it is easy for younger students to navigate. This also means that teachers can use this in their classrooms. Children can use this website in a computer lab while the teacher facilitates to the class what they should be doing. 

3) Math Playground (www.mathplayground.com)

Math Playground is an online website which will “give your brain a workout.” This website provides a fun approach to math, which most find difficult and challenging. Students will be able to use this website if they wanted to watch videos which can help clarify a topic or try out games in the arcade which would serve as an aid in their understanding of a particular topic. Students have the option to try out games such as Grand Slam Math, Hungry Puppies, and Dirt Bike Proportions. 

Skills students need are to:

-Read and interpret printed text

-Have access to the internet

-Read and interpret mathematical symbols

-Understand basic math skills including addition, subtraction, percents,   decimals, multiplication, division, and algebra

This resource would be appropriate for students in grades one to six. This website uses a very hands-on approach because it provides and interaction between the computer game and the student. Some games might be considered childish for older students, but the math concept is still conveyed. 

In my opinion, this website should be used by students at home for extra practice in a particular unit of math. This website slightly focuses on games, rather than learning math skills. Especially for younger children, parents should monitor what their children are doing and keeping them on task. 

4) Math Is Fun (www.mathisfun.com)

Math Is Fun is a website, which as it is described in the name, makes math fun! This website is primarily useful for students but, can be used by teachers to become inspired by some of the lessons. After choosing a topic, students will be able to click on links which will bring them to a quick summary of the topic and some basic definitions that they should be aware of to better understand the topic. After students get a little refresher, they can access worksheets and activities which cover topics such as area, symmetry, and time. 

Skills students need are to:

- Read and interpret printed text

- Able to have internet access

- Read and interpret mathematical symbols

- Understand these math skills: numbers, algebra, geometry, measurements, money, puzzles, and data

This resource would be appropriate for those from kindergarten until seventh grade. The children in younger grades might need some direction to veer them away from the sections for older students. Parents can help their children choose which links they should be clicking on and help them when necessary. 

In my opinion, this website should be used at home, when students are trying to reinforce what they learned in class. Students should pay attention in class to what the teacher’s lesson plan is and use this website as an extra resource, not as an alternative.