Glossary

Glossary:  Module 7

        All informal definitions are based on

my own experience and knowledge

Term: Mean

       Informal Definition:

The mean is the average of several numbers.

Formal Definition:

The mean is the average of the numbers: a calculated

“central” value of a set of numbers.

Definition from: mathisfun.com

Example of Mean:

Example from: quia.com

Term: Mode

         Informal Definition:

The mode is the number that occurs the most.

Formal Definition:

The mode is the number that is repeated more often than

any other.

Definition from: purplemath.com

Example of Mode:

 
Example from: room17math.wikispaces.com

Term: Median

         Informal Definition:

The median is the middle number in a set of numbers.

Formal Definition:

The median is the middle number (in a sorted list of numbers).

Half the numbers in the list are less, and half the numbers

are greater.

Definition from: mathisfun.com

Example of Median:

  
Example from: blogs.oregonstate.edu

Term: Range

         Informal Definition:

The range is the difference between the highest

score to the lowest score.

Formal Definition:

The range is the difference between the largest and 

smallest values.

Definition from: purplemath.com

Example of Range

 Example from: easycalculation.com

Term: Frequency Distribution

      Informal Definition

A frequency distribution is a way to organize

and display to identify relationships among

that data.

Formal Definition

A table that lists a set of scores and their frequency

(how many times each one occurs).

Definition frommathisfun.com

Example of Frequency Distribution:

 

 Example from: math.tutorvista.com

Glossary

Glossary:  Module 6

        All informal definitions are based on

my own experience and knowledge

Term: Probability

         Informal Definition:

Probability is a number that tells the likelihood that an

event will happen.

Formal Definition:

Probability is the chance that something will happen.

Definition from: mathisfun.com  

Example of Probability:

 Example from: exchange.smarttech.com

Term: Outcome

         Informal Definition:

Outcome is the final product.

Formal Definition:

Outcome is the result of a single trial of an experiment.

Definition from: math goodies.com

Example of Outcome:

Example from: onlinecraps.net

Term: Independent Event

         Informal Definition:

Independent events are consecutive events that do not

depend on what happened previously.

Formal Definition:

Independent events are events in which the outcome of one

event does not affect the outcome of the other event.

Definition From:  coachmath.com

Example of Independent Event:

Example from: rchsbowman.wordpress.com

Term: Tree Diagram 

     Informal Definition:

 A tree diagram is a visual aid that shows all feasible

outcomes. 

Formal Definition:

A tree diagram is a graphic organizer that shows all the

possible outcomes of an event.

 Definition from: icoachmath.com

Example of Tree Diagram

Example from: math.youngzones.org

Term: Pascal’s Triangle

         Informal Definition:

Pascal’s Triangle is a triangle of numbers where every

number is the sum of the two numbers above it.

Formal Definition:

Pascal’s Triangle is the arrangement of the binomial

coefficients in a pattern.

Definition from: icoachmath.com  

Example of Pascal’s Triangle 

 

Example from: shodor.org 

Glossary

Glossary:  Module 5

        All informal definitions are based on

my own experience and knowledge

Term: Reflection Symmetry

         Informal Definition:

One half of the picture looks exactly like the other half

Formal Definition:

A figure that contains a line along which a mirror can be

placed to reflect either half of the figure so it reproduces

the other half.

Definition from:  Mathematics: A Human Endeavor, 3rd Edition

Example of Reflection Symmetry:

Example from: http://www.1stwebdesigner.com

Term: Rotational Symmetry

        Informal Definition:

An object is moved around a middle point so it appears again

Formal Definition:

A figure that can be rotated through an angle of less than 360′

so that it coincides with its original position.

Definition from:  Mathematics: A Human Endeavor, 3rd Edition

Example of Rotational Symmetry:

Example from: http://doyle.webnode.com

Term: Regular Polyhedron

       Informal Definition:

A solid that has same shape and size on each of its faces

Formal Definition:

A solid having faces in the shape of a regular polygon.

All of its faces, edges, and corners are identical.

Definition from: Mathematics: A Human Endeavor, 3rd Edition

Examples of Regular Polyhedrons:

Example from: http://www.math.rutgers.edu

Term: Pyramid

        Informal Definition:

Has a polygon base and triangle sides

Formal Definition:

A pyramid is a polyhedron with a polygonal base

and triangles for its faces.

Definition from: Icoachmath.com

Example of a Pyramid:

Example from: http://www.wiki.superdupergames.org

Term: Prism

        Informal Definition:

Has two same polygon bases and same size rectangle sides

Formal Definition:

A solid with two congruent parallel faces, where any cross

section parallel to those faces is congruent to them.

Definition from: http://www.mathopenref.com

Example of a Prism:

Example from: http://home.comcast.net

Mathematical Mosaics

In your home, down a street, or even in ordinary objects, mosaics make their mark on our daily lives.  A mathematical mosaic is a group of shapes (with sides of equal length and measurement) arranged together to form a repetitious pattern in which they share sides at each corner point.  Each corner point contains the same neighbors throughout the pattern. (Mathematics: A Human Endeavor, 3rd Edition)

For example, everyday I walk over this.

At first glance it looks like ordinary tile.  However, if you look closer it is mathematical mosaic composed of rectangles and squares.  To make this arrangement you need four rectangles and one square.  The four rectangles create the point all having interior right angles.  The equation for the angles would be 90°+90°+90°+90° = 360°.   The rectangles have rotational symmetry creating a square in the pattern.

Everyday I cuddle up to this seemingly innocent lap quilt.

But in reality it is a mathematical mosaic.  The pattern is composed of eight isosceles triangles. The triangles have one right angle and two forty-five degree angles. The eight triangles around the point each have an interior angle of 45.  Thus the equation would be 45°+45°+45°+45°+45°+45°+45°+45°= 360°

Incorporating activities like finding mathematical mosaics in everyday life into your lessons give the student not only an understanding of how mosaics influence our world but also a real world application of math.  It helps the student understand that math can be applied to our everyday environment and lives not just in the classroom.

Here are some questions you might consider using in a lesson on mathematical mosaics.

How do you know if a mosaic is really a mathematical mosaic?

If you were given triangles and squares how many different math mosaics could you create in a 6×6 square?

If you have a mathematical mosaic made up of octagons and dodecagons, what other polygons could you use to complete the mosaic?  Give reasons why you chose each polygon.

Do you think the number of sides of a polygon has any correlation between the corresponding interior angles of that polygon?  Can you prove your answer?

Glossary

Glossary:  Module 3

       all informal definitions are based on

my own experience and knowledge

Term: Arithmetic Sequence

       Informal Definition:

A sequence made by adding or subtracting

the same number each time

Formal Definition:

An arithmetic sequence goes from one term to the next

by always adding (or subtracting) the same value

Definition from: http://www.purplemath.com/modules/series3.htm

Example of Arithmetic Sequence:

Example from:  http://www.virtualnerd.com

Term: Geometric Sequence

       Informal Definition:

A sequence made by multiplying or dividing by the

same number each time

Formal Definition:

A geometric sequence goes from one term to the next

by always multiplying (or dividing) by the same value

Definition from:  http://www.purplemath.com/modules/series3.htm

Example of Geometric Sequence:

Example from: http://www.virtualnerd.com

Term: Common Difference

        Informal Definition:

The number you add or subtract to get to the next

number in an arithmetic sequence

Formal Definition:

The number added (or subtracted) at each stage of an

arithmetic sequence

Definition from: http://www.purplemath.com/modules/series3.htm

Example of Common Difference:

Example from: http://www.virtualnerd.com

Term: Common Ratio

       Informal Definition:  The number you multiply or divide each

term by to get to the next term in a geometric sequence

Formal Definition:  The number multiplied (or divided) at each

stage of a geometric sequence

Definition from:  http://www.purplemath.com/modules/series3.htm

Example of Common Ratio:

Example from: http://www.mathplanet.com

Term: Function

       Informal Definition:

A special kind of relationship between numbers

Formal Definition:

A special relationship between values. Each of its input

values gives back exactly one output value.

Definition from: http://www.Mathisfun.com

Example of Function:

Example from: http://www.virtualnerd.com

Web Resources

Web Resources To Help Teach Functions to Elementary School Students……

As you know the web is a fabulous resource for both the teacher and the student.  The amount of material you can find can be overwhelming.  I have found a few sites that might be useful in your never-ending quest for great material to help you be the best teacher.

The focus for these sites were ones that could help teach functions

1. http://jmathpage.com/middleschoolmath/middleschoolmath.html;

This is a great site if your teaching any grade K-8.  The resources on this site are endless. The author has a wide variety of fun ideas and games for both teacher and student.  This would be also be a great resource if a student needs some extra practice with a concept at home.

2. http://www.mathplayground.com/functionmachine.html

I like the idea of introducing function tables as a type of machine. Math Playground has a function machine that students of various skill levels can explore input/ output concepts.  This site also has a short video section called, “How to Do Almost Anything in Math.”  This is a great resource for struggling students or students that might need more challenge.

 3. http://www.mathsisfun.com/sets/function.html:

Math is Fun is a great website that explains math concepts in a straight forward easy to understand manner.  It is colorful and has lots of visuals illustrating concepts.

4. . http://nces.ed.gov/nceskids/createagraph:

There are several things I like about The Kids Zone website.  The first being that it has a great online graph maker that lets you graph coordinates.  The “Grab Bag” and “Chances” sections are what I really like about this website.  These aren’t your usual math quizzes and games.  They have famous mathematician fun facts and quotes. They also have finding math in art.  This site connects math to real people and places.

Glossary

Glossary:  Module 3

*all informal definitions are based on
 my own experience and knowledge

Term: Deductive Reasoning

       Informal Definition:  drawing a conclusion based on

observations or statements

A good example of deductive reasoning is watching how

a detective works. He collects clues and then draws a conclusion

based on the clues he collects.

Formal Definition:

To arrive at a conclusion using facts, definitions, rules, or properties

Definition from:     http://www.icoachmath.com

Example of Deductive Reasoning:

 

Example from:  http://www.thatquiz.org

Term: Inductive Reasoning

       Informal Definition: 

Coming to a conclusion based on general conclusions

You take specific information and draw general

conclusions

Formal Definition:

Mathematical induction is a method generally used to prove

or establish that a given statement is true for all natural numbers

Definition from:  http://www.icoachmath.com

Example of Inductive Reasoning:

Example from:  http://www.thatquiz.org

Term: Operation

       Informal Definition:

An activity that works to change numbers

Formal Definition:

a mathematical process applied to solve a problem

Definition from:  http://www.icoachmath.com

Examples of Operation:

              

Examples from:   http://www.kathimitchell.com  

and  http://blog.biguniverse.com

Marbles in Matchbox

Marbles in Matchbox

In this deductive reasoning exercise there are three matchboxes.  The first matchbox contains TWO RED marbles.  The second contains TWO WHITE marbles.  The third matchbox contains ONE RED and ONE WHITE.  Here is the catch: all the labels on the matchboxes are wrong. You are permitted to peak inside one matchbox far enough to see ONE marble.  THE CHALLENGE IS TO EXPLAIN HOW YOU CAN FIGURE OUT FROM THE GIVEN INFORMATION WHAT IS IN THE MATCHBOX.                                                        

10.  If I opened the box labeled “2 red” and saw a red marble I would know that the other marble could only be white.  The directions stated that the label on each box had been switched. 11.  However, if I opened the box and saw a white one the other marble could either be red or white. I would need to have more information to know for sure.

12.  If I opened the box labeled “2 white” and saw a white marble I could conclude that the other marble was red.  The box was incorrectly labeled “2 white” so the other marble must be red. 13.  If I opened the same box and found a red marble I would know that the other marble could be either red or white.

14. If I opened the box labeled “1 red, 1 white” and saw a red marble I would have to conclude that the other marble was red because the box was incorrectly labeled.  If I saw a white marble I would know that the other marble was white because the label of “1 red, 1 white” is not correct.

16. I think after all the processing we have done so far the best box to look in would be the one labeled “1 red, 1 white”. Based on the color of marble you see you would know the other marble had to be the same color.

ARE YOU STILL HANGING IN?????

17. If I see a red marble when I opened the box “1 red, 1 white” I could conclude that the other marble was red.  Remember the boxes have been mislabeled. 18. I would know that the marbles in the box labeled “2 white”  was really 1 red, 1 white.  19. And finally by elimination I would know that the box labeled “2 red” was really  2 white marbles.

Glossary

         Term: Line

 Informal Definition:

A one-dimensional object that goes on infinitely in either direction

This definition was created from my own experiences.

Formal Definition:

A line is a straight one-dimensional figure having no thickness

and  extending infinitely in both directions

This definition came from Wolfram Math World.

Example of line:

Image taken from:  http://mathworld.wolfram.com/Line.html

Term: Angle

 Informal Definition;

The area between two lines that intersect

This definition was created from my own experiences.

Formal Definition:

A shape, formed by two lines or rays diverging from a common

vertex.

This definition was taken from Math Open Reference.

Example:

Image taken from:   http://mathworld.wolfram.com/Line.html

Term: Shape:

 Informal Definition

An enclosed space

This definition was taken from one of my fifth grade students.

Formal Definition:

The quality of a distinct object or body in having an external surface

or outline of specific form or figure

This definition was acquired from the online dictionary.

 Example:

Image taken from:  http://www.tsooj.net/examples/imagemapper

A Bit About Me.

The aim of this blog is to discover and explore ideas about learning, teaching, and understanding math.  (For me, it usually happens in that order.) What an adventure!  My journey to the classroom was circuitous; I taught fifth grade in the public school system, took some time off to homeschool my two sons, who are now in college, and now I hope to return to the classroom.  A great math teacher should provide motivation, engage the students, and present explanations for the material.  I am hoping that through this course I can enhance my current mathematical practices to make learning more meaningful.  I am also looking for ways to boost the student’s mathematical confidence.   As the saying goes, “Life is an adventure, teaching even more so.”  I think teaching math might be the greatest adventure of them all.

Thanks for visiting my blog,