Tuesday, 21 October 2014

Happy Deepavali...



Saturday, 18 October 2014


Money can give you bread 

But not hunger

Money can give you a bed

But not  sleep.

Money can give you medicine

But not health.

Money can give you comfort

But not peace.

Money can give you power

But not respect.

Money can give you a degree

But not Knowledge.

Money can give you security

But not freedom.

It is character and character

Alone that can give

You everything.

with love


Fear of death

Makes one forget

The joys of life.

Be cheerful

You  are the childern

Of immortal bliss.

Death is only for the body

It is not for you.

yours loving


Monday, 6 October 2014

Some nice puzzles

Here are some rather nice wooden puzzles found by Noel-Ann on recent trips.  I'm not commenting on solutions here!

Two Marbles

Two marbles - start position

Noel-Ann found this one in Texas.  The object is to get the two marbles into the holes simultaneously, like this:

Marbles puzzle solved

A Secret Box

The other puzzles were brought back from a market in the Dordogne. This, amazingly, is a secret box which can be opened by performing a series of operations.

Secret Box

A packing problem

This one starts off as a rather nice box with a red slab on top.

A packing puzzle box

When one slides the lid open one finds that it is packed full with more wooden blocks.  How can one add the red block and close the lid?

Inside the box

Another Packing Problem

This one has four pieces each composed of two overlapping slabs. Can one fit them into the tray?

Another packing problem

Sunday, 5 October 2014

Important Tips for Studying Mathematics

Go To Class Regularly:
Remember that math is cumulative. If you don’t go to class you will miss important material that will be used in later sections and important announcements.
Get to Class On Time.
Sometime important announcements are only given during the first few minutes of a class.
LISTEN During Class.
In order to get something out of the class you need to listen while in class. Often this can be difficult to do but it is very important. Sometimes important ideas will not be written down on the board, but instead just spoken by the teacher.

Watch for things the teacher emphasizes, even if just in words. This often means the teacher thinks it’s important. The more important that  teacher thinks a topic is, the more likely that it will show up on the exam!
Take Good Notes.
Try to write down everything that teacher puts on board. It may seem easy when watching the teacher, but it often is not so easy when it comes time for you to do it. A good set of notes will help remind you how to do these problems. For some teacher writing down everything may be difficult. In these cases you should try to write down as much as possible.

Note as well that this seems to contradict the previous tip. It is often hard to both listen and take a good set of notes. This is something that one often only gains with practice. You need to be able to listen while you are writing down the important parts of the lecture.
Ask Questions.
If you don’t understand something then ask your teacher. Chances are you are not the only one who doesn’t understand.
Listen When Others Ask Questions.
When other students ask questions make sure you listen to both the question and the answer. It may be that the student asking the question thought of something that you didn’t think of.
Review Notes After Class.
After each class you should review your notes. Note the topics that you found confusing and formulate questions that you can ask your teacher or tutor to help you understand the topic.
Make a Set of Index Cards.
Make a set of index cards with important formulas and concepts on them. You can carry these around with you to look over when you’ve got a few spare minutes. Use them to help you memorize the important formulas and concepts.
Note Due Dates. Write down the due dates for homework and dates for exams someplace you’ll see them so you don’t forget about them.
Budget Adequate Time For Studying/Homework. It often takes more time studying mathematics to learn the subject than you may require in other classes.

Do Homework After Each Class.
At the end of each class budget some time to look over the homework from that days lecture and attempt to do it Doing this will allow you time to really work at understanding the concepts covered that day. Do not wait until the last minute to do the homework as this often results in an incomplete homework set and an incomplete understanding of the concept.
Do Homework Without Notes and Book.
After the first few homework problems, put your notes and book up and try to do the remaining problems without referring to your notes and/or book. In most cases you will not have these during your exams so get used to doing problems without them.
Do More Homework.
Do not limit yourself to just the homework that your instructor assigns. The more problems that you work the better off you’ll be.
Practice, Practice, Practice.
Practice as much as possible. The only way to really learn how to do problems is work lots of them. The more you work, the better prepared you will be come exam time.
You will not just instantly get every topic that is covered in a math class. There will be some topics that you will have to work at before you completely understand. The only way to really grasp some topics is to go home and think about it and work some problems. You will often find that after a little work a topic that initially baffled you will all of a sudden make sense.
Keep Old Homework and Exams.
Do not throw away homework and exams once you get them back. The homework is a good source of study material for exams and both the homework and exams is a good source of study material for comprehensive final exams (if you’ve got one).
Don’t Forget Your Textbook.
If you get stuck on a topic that was discussed in class do not forget that you do have a textbook. Often the text book will contain examples not worked in class and/or a different approach to a problem.
Seek Help If You Need It.
If you are having trouble with your maths class you have many options open to you and you should take advantage of them. You can go to your tescher’s office hours, go to the tutoring room or hire a tutor to get help.

yours loving


Maths History-Notation

Notation, language, and rigor
Most of the mathematical notation in use today was not invented until the 16th century. Before that, mathematics
was written out in words, a painstaking process that limited mathematical

In the 18th century, Euler was responsible for many of the notations in use today. Modern notation makes
mathematics much easier for the professional, but beginners often find it daunting. It is extremely compressed: a few symbols contain a great deal of information. Like musical notation, modern mathematical notation has a strict
syntax and encodes information that would be difficult to write in any other way.

Mathematical language can also be hard for beginners. Words such as or and only have more
precise meanings than in everyday speech. Additionally, words such as open and field have been given specialized mathematical meanings. Mathematical jargon includes technical terms such as homeomorphism and integrable. But there is a reason for special notation and technical jargon: mathematics requires more precision than everyday speech. Mathematicians refer to this precision of language and logic as "rigor".

Rigor is fundamentally a matter of mathematical proof. Mathematicians want their
theorems to follow from axioms by means of systematic reasoning. This is to
avoid mistaken "theorems", based on fallible intuitions, of which many
instances have occurred in the history of the subject.The level of rigor
expected in mathematics has varied over time: the Greeks expected detailed
arguments, but at the time of Isaac Newton the methods employed were less rigorous. Problems inherent in the
definitions used by Newton would lead to a resurgence of careful analysis and formal proof in the 19th century. Today, mathematicians continue to argue among themselves about computer-assisted proofs. Since large
computations are hard to verify, such proofs may not be sufficiently rigorous. Axioms in traditional
thought were "self-evident truths", but that conception is problematic. At a formal level, an axiom is just a string of symbols, which has an intrinsic meaning only in the context of all derivable formulas of
an axiomatic system. It was the goal of Hilbert's program to put all of mathematics on a
firm axiomatic basis, but according to Gödel's incompleteness theorem every
(sufficiently powerful) axiomatic system has undecidable formulas; and so a
final axiomatization of mathematics is impossible.
Nonetheless mathematics is often imagined to be (as far as its formal content)
nothing but set theory in some axiomatization, in the sense that every mathematical
statement or proof could be cast into formulas within set theory.

with Love

Saturday, 4 October 2014

Ten Helpful Resources for Middle School and High School Math Teachers

By Request -

Recently, on the Free Technology for Teachers Facebook page someone asked for suggestions for math resources for grades 7-12. That covers a broad range of topics in math, but I've done my best to cobble together a list of resources that I think will help middle school and high school math teachers and their students. I have not included the obvious option of Khan Academy.

Get the Math is a super website designed to provide teachers and students with Algebra-based mathematics challenges. Get the Math tries to put the challenges in the context of the  "real world" scenarios of fashion design, video game design, basketball, restaurant management, movie special effects, and music production. Get the Math features short videos of professionals explaining and showing how mathematics is used in their professions. After watching the videos students try to complete a series of challenges based upon the work done in the professions of fashion design, video game design, and music production. For example, after watching the Math in Fashion video students have to design a shirt to match a specific price point

A couple of months ago Curriki released a series of six PBL geometry projects that could make geometry interesting and fun for high school students.Curriki's new geometry course features six PBL projects. Each of the projects is aligned to Common Core Standards. The course is not a self-directed course for students. The course is designed to be taught by mathematics teachers who want to incorporate PBL. The projects in the course can be used in sequence or used as stand-alone units. All materials needed for leading the projects are included available on the Curriki site. You will have to create an account and sign-in in order to access the materials. Curriki accounts are free.

Opus is a service that aims to help middle school mathematics teachers discover sample math problems aligned to Common Core standards. To find problems on Opus search by entering a topic and selecting a grade. You can also find problems by clicking the "browse the Core directly" link on the Opus homepage. Either way when you find a problem you can save it to your free Opus account where you can then generate a Word doc or Google Document of all of your saved problems. You can also create an answer sheet in your Opus account.

MathDisk is a service that teachers can use to develop interactive mathematics worksheets. Through MathDisk's "Math Builder" tool you can design mathematics models that your students can use online. The models and worksheets you develop online can also be downloaded to use offline if you also install the MiBook software on your desktop or on your Android device. If you don't have time to create new materials, the MathDisk gallery has pages of models and worksheets that you can choose from. Everything in the gallery, like everything you create through MathDisk, can be downloaded and or embedded into your own website or blog.

TenMarks is a service that offers an online mathematics program designed to supplement your in-classroom mathematics instruction. All of the problems in TenMarks' bank of more than 20,000 are aligned to Common Core standards. Within TenMarks teachers create class rosters and accounts for their students. After creating rosters teachers can assign practice problems to students. Teachers can assign problems based on the Common Core Standards that their students are trying to reach.

If you use GeoGebra in your classroom, you should bookmark GeoGebraTube. GeoGebraTube is a community site for teachers who teach with GeoGebra to share and find a wide range free resources. On GeoGebraTube visitors will find user-created tutorials, lessons, and worksheets. Visitors can search for resources by age group, language, and material type. All materials are freely available for noncommercial re-use.

Math Open Reference is a free online reference for geometry teachers and students. Math Open Reference features animated and interactive drawings to demonstrate geometry terms and concepts. The table of contents on Math Open Reference is divided into four basic categories; plane geometry, coordinate geometry, solid geometry, and function explorer tools. Click on any subject in the first three categories to find definitions, examples, and interactive drawings. In the function explorer category users can select linear functions, quadratic functions, or cubic functions to explore how changes in variables affect the graphed output.

Dan Meyer has a site called 101 Questions on which he is sharing images and videos as prompts for developing math questions. Each image and video has a 140 character field in which you can enter your question. Questions are compiled and can be Tweeted. Take a look at the top 10 to get a feel for what you will find on 101 Questions. I've embedded one of the videos from 101 Questions below. I won't pretend to be able to explain the larger purpose of the site as well as Dan does, so I'll just encourage you to go read his blog post about it. And if you need more background on who Dan Meyer is, watch his TED Talk Math Class Needs a Makeover.

Incredible Shrinking Dollar from Dan Meyer on Vimeo.

ULearniversity is a free site featuring arithmetic and algebra lessons. On ULearniversity you can watch tutorial videos and practice the concepts taught in the videos. ULearniversity provides instant feedback on your practice problems. As a registered ULearniversity user you can track your progress.

Math Shorts is the latest addition to Planet Nutshell's line-up of  animated educational videos. Math Shorts will eventually have twenty videos in the series. Right now the series contains eight animated videos for elementary school and middle school students. Each of the videos has a Common Core standard aligned to it. All of the videos have supporting materials from PBS Learning Media attached to them. The first video in the series is embedded below.

Suggestions welcome: I have never taught math and I'm open to suggestions for resources that should be added to this list. If you have a suggestion please feel free to email me at richardbyrne (at) freetech4teachers (dot) com. 

Thanks  with