Lisathorne's Blog

Mean: the average if a set of numbers.  First you add all of the numbers and then you divide them by how many numbers there are.

6 + 5 + 4 + 5= 20       20/4 = 5

taken from: www.coolmath.com

Median:  the middle number of a group.  First you place the numbers in order from smallest to largest and then the middle number is the median.

5, 2, 6, 4, 8

2, 4, 5, 6, 8   the median = 5

taken from: www.coolmath.com

Mode:  In a list of numbers, the mode is the one that occurs most often.

5, 6, 7, 7, 8     The mode is 7.

taken from: www.coolmath.com

Histogram:  a graphical display of tabulated frequencies.

taken from www.wikipedia.com

Survey: a gathering of a sample of data or opinions considered to be representative of a whole.

Taken from: www.kidsyahoo.com

4.  It is not a random sample because a random sample would give everyone in the city an equal chance of being included, but a telephone survey only include people with telephones.  In this day and age, you would also have to take into consideration people with cell phones who do not have land lines.

5.  If it was chosen at random the people with unlisted numbers would be excluded because there is no access to their numbers.

6. You would need to get a random sample of people with listed numbers, unlisted numbers and cell phone numbers.

1.  The envelope with “research study” on them.

2.  The nvelopes with money.

3. The psychologistsmay have thought that having “research study” on them may be tempting to take for someone who is nosey!

4. I would assme they were counted as though they were not read because it does not say otherwise.

5. The pattern that I see   is that there is not a significant difference between the area of the city that these envelopes were left.

6. It would all depend on what peoples motivations are.  What would be more tempting to one person may not be as tempting to the next.  For example, one person may be really motivated by money while someone else may simply be motivated by curiousity and choose the research envelope to be nosey!

Binomial Event- this is where outcomes can be broken down into two probabilities.  For example when you roll dice, the probability of rolling a four would be 1/6 and the probability of rolling something else would be 5/6.   ( Taken from http://cnx.org)

Tree Diagram-a tree diagram is a visual that can be drawn to show the possible outcomes of an event. 

(taken from wikipedia.org)

Outcomes-  a possible result of a probability experiment is called an outcome.

(taken from www.icoachmath.com)

Probability- this tells us how likely it is or an event to occur.  For example, when you flip a coin there is a 50% (1/2) chance that tails will come up.

(taken from www.coolmath.com)

Pascal’s Triangle- A triangle created by the French mathematician named Blaise Pacal.  This triangle is built on various patterns.

(taken from www.coolmath.com)

2.  The sum of the numbers doubles each row down – 2,4,8,16,32,64,128,256

3.  0    1    2     3      4    5

      1     5    10  10   5     1

4.  .08    8%

5.   .26    26%

6.  10

7.  10 x (.4 x .4. x .6  x .6 x .6)  = .35  35%

8.  10

9.  .35  35%

10.  5 ways

11.  5 x (.4 x .4 x .4 x.4 x .6)  = .08  8%

12.  (.4 x .4 x .4 x .4 x.4) = .01   1%

A problem I could pose with a class could be:

There are 6 girls in the class that are best friends,  what is the probability that all six girls get the swine flu?  What is the probability that 4 of the girls willget the swine flu?

I think that I could introduce this concept to my second grade students on a very basic level by looking for the patterns.  I found a website www.mathforum.org  that could help do this.

Face- the flat surface of a three-dimensional figure

Taken from www.coolmath4kids.com

Edge- the place where two faces meet (the lines outlines in yellow)

Taken from www.coolmath4kids.com

Polygon- A closed plane figure connected bythree or more line segments.

Taken from www.freedictionary.com and www.coolmath4kids.com

Prism- a polyhedron that is formed with two parallel polygons that are connected at the edges with rectangles.

Taken from www.coolmath.com

Here are my answers to Set 2 pg.271

1.  6-6-6

2. 8-8-4

3. 6-3-3-3-3

4. 12-4-6

5. 5-6-8  – no it would not

6. 5-5-10

    Yes, because 108*+108*+ 144* = 360*

7. Points A,D,E,B

8.  There ended up being a gap in the pattern

9. If a particular set of polygons surround a point, it does not mean that you can definately make a mosaic from it.  This is shown when you add 5-5-10 it comes to 108*+108*+144*= 360* but when you try to put it together into a  mosaic, there ends up being a gap.

Here are questions that can be asked using mathematical mosaics with 2nd graders:

1.  What polygon makes up this mosaic?  Assuming that they answer this question correctly, I would pick a point on this mosaic and ask them how many equilateral triangles surround that point. 

2.  Looking at this mosaic, what shapes are used? Can you determine a pattern?  Explain what shapes share a common point.

3.  I would give students square and triangles and encourage them to create their own mosaic.

Below are some great geometry links that I found!  Check them out and maybe you will find them to be useful too!!!

www.bcps.org/offices/lis/curric/elem/elemgeo.html

The first link that I located was an excellent link for helping to teach different geometry concepts to students.  You can choose the elementary grade level that you are looking for and then it is broken up by topic/activity.  Some of the activities that are included are a polygon playground, pattern blocks to slide, flip and turn, 2D shapes and Symmetry Around the World.

edweb.tusd.k12.az.us/ekowalcz/…/elementary_web_sites.htm –

When you go to this website you can click on geometry and measurement.  If you choose togo to Area Explorer students can practice finding square units.  The Banana Hunt allows students to practice the degrees of angles.  In Shape Cave they can learn about different shapes.

http://www.proteacher.com/100021.shtml

This site has various activities that teachers can use to teach geometry concepts.  One example of an activity would be a perimeter activity using graham crackers, brownies and pretzels.  It gets the students involved in the real world application of area and perimeter.

http://www.coolmath4kids.com

Students can do a number of different activities on this website to help them practice their geometry skills.  For example, they can learn more about geometric shapes using tessellations.

Function Machine:  This is an illustration used to help demonstrate how a function works.

Taken from: www.coolmath.com

Arithmetic Sequence:  a sequence fun by adding the same number to the preceding term.

Example:  8 ,20, 32, 44, 56

Taken from: Mathematics: A Human Endeavor

Geometric Sequence:  a number sequence in which each successive term may be found by multiplying the same number.

Example:  1, 5, 25, 125, 625

Taken from: Mathematics: A Human Endeavor

Ordered Pair:  Coordinates on the Cartesian Plane are a set of numbers called “an ordered pair” that are in the form x, y.

Taken from: www.coolmath.com

Exponent:  An exponent is when a little numer is to the right and a bit above a number.  It’s also called a “power.”

Taken from: www.coolmath.com

I really enjoyed this activity because I really enjoy working with patterns.   The first figure in the problem shows the 1st number in the triangular sequence which is 1 plus the second number in a triangular sequence which is 3.  It also shows 2 squared.  The second figure shows the 2nd number in the triangular sequence which is 3 plus the 3 rd number in the sequence which is 6.  It also shows 3 squared.  The third figure shows the3rd number in the triangular sequence which is 6 plus the 4th number in the sequence which is 10.  This figure also shows 4 squared.  The fourth figure shows the 4th number in the triangular sequence which is 10 plus the 5th number in the sequence which is 15.  It also shows 5 squared.  This activity showed the relationshipbetween the traingular numbers and squared numbers.

I had a difficult time thinking of ways that I use squared numbers daily.  The one way that I came up with was when you are making something or building something and parts of it need to be equal on all sides, you would use the square root or a number squared.  For example, I was watching HGTVand someone on the show was making a perfect square out of tiles on their floor. They could find the sqare root of the whatever the measurements are to create that perfect square with the tiles.

To introduce multiplication with my students we would make arrays and glue them on giant paper so that the students could see the patterns that were being created.