Review of PUMAS February 4, 2012

Wow! This sie is full of real life activities showing the relationship between science and math into our world today in a fun and helpful way. Each activity also provides the teacher with the benchmark and objective so it can be linked to state standard. Key words are provided at the beginning so the teacher can do a clarifying of vocabulary before beginning the activity. They can be used as introductions to a unit, practice with the unit, homework or enrichment. The activities offer a large range of topic and They could be used with the class as a cooperative group activity for summary and evaluation purposes. ( my district is big on group work, all classrooms have to be arranged in 3-5 groups setting.

I liked the Algebra Magic Games the best. I would use these as an introduction to the Algebra Unit as an “ice breaker”. Many students are apprehensive in their ability to do math, imagine what turmoil  using letters will cause. These activities ask students background knowledge that should be easily  recalled, lowering the anxiety. It shows them how the number’s can represent a letter  in an algebraic expression and has them solve the equation. This also relates real life to algebra. I especially liked game #2 when the answer provides you with your age (15) and the number of sibling you have (3) in one number 153.

Vocabulary February 2, 2012

Inverse refers to the relationship to the opposite  of a number. It can mean to reverse something, turn it upside down. Or it can mean the opposite.

When adding, add the opposite:

a+ -a = o     3 + -3= 0

Used in matrix.

When multiplying, find the reciprocal

a * 1/a = 1

for whole numbers

1. Convert to fraction: 3= 3/1

2. To inverse turn upside down   1/3 known as reciprocal.

So the inverse of 3/1=1/3   so 3/1 * 1/3=1           (a/1=1/a)

Used in dividing rational numbers and in a Matrix

Everyday Math Stories January 28, 2012

Everyday Math Stories

Last week, while having lunch with the Home Ec teachers that worked in my district, one of them brought out a curtain design problem. She had a 4×4 sample of a curtain design she had seen in a store and wanted to make. It had a pleat and you were to fold the inside pleated corner back, button it open, thus reveling a contracting fabric in the center under pleat. See diagram #1. Her sample was all out of muslin so you had to use your visual imagination. Basically she was asking us if her design would work.

In her sample she had sewed 2 different fabrics together and pleated one side. Although this got the design across, it would not create the two fabric effect she desired.

1^st we explained the lining fabric was just that, lining and would only show from the outside.

2^nd We explained, she needed to know exact width of finished curtain.

3^rd Decide how deep her pleats would be.

4^th Measure the entire width of pleated area and add 1¼” for seam allowance. This is width of contrasting panels

5^th Calculate the # of pleats she would install.  This tells number of contrasting panels to cut.

6^th Measure the finished length. Subtract out casing (she is add it separately). Add bottom hem allowance. This is length to cut all panels.

7^th For width of the top fabric panels, measure the distant from the edge to the first pleat, and add 1¼” for side seams. This is the width of the  top panels. Cut # needed. (1 pleat 2= 2 panels. 2 pleats = 3 panels, 3 pleats-4 panels)

9^th Pin and sew panels together. One top, 1 contrasting fabric, top fabric, etc. see diagram 2

10^th With right sides together, sew to lining to panels. Clip,turn and press.

11^th Form pleats. Press, Stitch in place.

12^th Add casing.

 were to fold the inside pleated corner back, button it open, thus reveling a contracting fabric in the center under ,. See diagram 1. Her sample was all out of muslin so you had to use your visual imagination. Basically she was asking us if her design would work.In her sample she had sewed 2 different fabrics together and pleated one side. Although this got the design across, it would not create the two fabric effect she desired.1st we explained the lining fabric was just that, lining and would only show from the outside.2nd We explained, she needed to know exact width of finished curtain.3rd Decide how deep her pleats would be.4th Measure the entire width of pleated area and add 1¼” for seam allowance. This is width of contrasting  Calculate the # of pleats she would install.  This tells number of contrasting panels to cut.6th Measure the finished length. Subtract out casing (she is add it separately). Add bottom hem allowance. This is length to cut all panels.7th For width of the top fabric panels, measure the distant from the edge to the first pleat, and add 1¼” for side seams. This is the width of the  top panels. Cut # needed. (1 pleat 2= 2 panels. 2 pleats = 3 panels, 3 pleats- 4 panels)9th Pin and sew panels together. One top, 1 contrasting fabric, top fabric, etc. see diagram 210th With right sides together sew to lining to panels. Clip,turn and press.11th Form pleats. Press, Stitch in place.12thAdd casing.

Diagram 1    Diagram 2

Diagram 1

Diagram 2

Mathography

Mathography 1

 

The first thing I remember about Math is that as far back to second grade you were regrouped f with the other second grade classroom. I was always in the lower of two or the middle of three these groups. We had a workbook for math and we were allowed to write in it, no other book did you dare write in. There was also a lot of repetition, we had a drill at the beginning of every class, we’d graded each others, you got to write your problem on the board, and we always had homework. In third grade, I remember we were adding and subtracting multiple digit numbers and the teacher was telling us we were smarter them kids in public school, because when they carried a number or borrowed they would scratch though the original number and write the new number above for subtraction.  For adding they would record the amount carried over above the new column. We were not allowed to do this, we just had to remember. Perhaps this was her way of teaching mental math.

The first concept I remember learning in math was the counting song “one, two buckle my shoe, three four, close the door”. At school, I remember in second grade, we had to memorize the times table on the back of our copybook. My mother would quiz me at night when going to bed and in the morning at breakfast. It must have been important! In seventh grade I remember spending about 2 months making Christmas wreaths out of tissue paper. The teacher called it applied geometry, my father was furious, complaining it was a waste of time, I would have to agree. In ninth grade, at the end of the year, I remember the whole class tried to convince teacher to begin teaching us algebra, she refused, even though most of us were signed up for algebra 1 the next year. I guess this is what I disliked the most, it seemed I was always held back from what I thought I could. Then in algebra 2, I was lost in work problems. I would go to my algebra 1 teacher, who was the best math teacher I had, to get help. Part of my problem was I couldn’t get the connection from method to applied situations. I was good at solving problems but no connection to life had ever been made.  Problem 2, the class was a zoo, and the teacher didn’t teach, we just went over homework. To me my algebra I teacher, Mrs. Ruben, was the best teacher because she explained thing s very clearly. She also didn’t have a problem the students helping students, but she was always there to help us. I was learning something new and challenging and fun.

I didn’t like school early on, but math was my favorite subject because I did get good grades in math and I do enjoy working with numbers and solving things.  Reflecting back and comparing math with today’s elementary schools, it seems they are more advanced. When I got to 8^th grade, Home Economics became my favor subject. However there is math in Home Ec., in measuring, unit pricing, counting nutrients, time management, budgeting, sewing, crafts and decorating. I am always doing something with math in these areas.

Math Recourses January 23, 2012

             

                                                       Math Resources

 Code T= teacher site      S= student site

Http://Ezschool.com

S & T site

This website provides printable worksheets for middle school students in the form of  computation, multiply choice, matching and word problems. Topics include  algebra expressions and equations, exponents, fractions, geometry,  graphing, integers, ratios, square root, statistics and also SAT and PSAT preparation questions.

In addition to worksheets, students can work within sight on video tutorials with game like assessments at end that use manipulatives (e.i measuring angle provided a protractor that you click and drag onto angle for measuring).

Teachers could use this within the classroom if they have access to computers. It could be used during a resource time or study hall for independent tutorial  remedial work.Teacher could send this site home for parents to work with students there. great sight

Also there is a game section with games for over 30 topics. I like the Alien multiplication game.

Http://Internet.nsca/PD/BLM/tableofcontents.htm

T site

 This is a great is for creating worksheets or test as it offers blank printable templates for multiplication table algebra tiles, base ten blocks, cubes, calendars, clocks, decimals, isometric dot paper, fraction circles, grid paper, thermometers,dominoes and much more.

http://nces.ed.gov/nceskids/createagraph/default.aspx?ID=884a33823f5e4fc1ad286d2a2f70a5ec

http://www.mathplayground.com/piechart.html

http://www.shodor.org/interactivate/activities/PieChart/

T site

The above three sites are for teaching the different kinds of graphs using a smart board or eno board within your class.  I t provides the graph and a fun way to learn.

http://www.shodor.org/interactivate/activities/

Http://www.apangealearning.com

S site

Offers interactive self pace learning for 7th or 8th. If students get the answer wrong or don’t understand they can access a show me button for help. Student earns points thought learning and win real prizes like mp3 players or candy bars. Depending on their points earned they can save up points for the bigger prizes. So it is teaching decision makes skills also. Teacher must sign up and enter students as users. I have never created a class but have worked with 8th grade students using this, they were

truly engaged in the learning. It can be used as a warm-up activity ( as in this case as home room and 1st period was the same, and helps teacher transition for one class to next without wasting class teaching time. Or for the students that always finish early, since you work at own pace.

• http://atlantamathtrail.wikispaces.com/
• http://riverbendmath.org/modules/Math_Trail/
• http://www.pmspf.org/new/images/mtb.pdf

These are sites that provide interactive real life situations that require math skills to solve problem. They require various  types of math concepts to solve. Good for small group actvity.  I like Atlantamath trail because it has a city environment. The other 2 are parks, nature theme.

http://thinkzone.wlonk.com

S&T site

Great site for explaining and defining types of numbers. Gives definitions, number lines, vinn diagrams, graph. Also offers a poster of such for purchase. Has games and homework practices, aranged by grades.

http://www.mathopenref.com/coordtrianglearea.html

Great site for working with triangle. Interactive, you take triangle to size and it developes the formula.

http://www.eric.ed.gov/PDFS/ED323097.pdf

Activities for getting girls involved in math

Name	Pumas Activity	Description/Link
Lisa	Cross Section and Slope Square Root of 2: Irrational, Yes! Impractical, No! How Now, Pythagoras? Algebra Magic- Create Your Own Number Puzzles	·         fun way to help students develop estimation and spatial visualization skills https://pumas.gsfc.nasa.gov/examples/index.php?id=36 ·         standard sizes of paper (the “A” series), have a very close relationship to √2 https://pumas.gsfc.nasa.gov/examples/index.php?id=78 ·         uses Pythagorean theorem to square corners of cabinets https://pumas.gsfc.nasa.gov/examples/index.php?id=47 ·         two number/magic puzzles that can be demystified and explained by using algebra https://pumas.gsfc.nasa.gov/examples/index.php?id=2
Lindsey, Jody. Brian, Michael	All Fives Domino Game	score points by adding to the domino trains, so the ends of all the trains add up to be a multiple of five https://pumas.gsfc.nasa.gov/examples/index.php?id=116
Nichol	Dream Job	addresses many components of number sense- requires students to add, multiply, estimate, understand place value and the magnitude of numbers, as well as organize data https://pumas.gsfc.nasa.gov/examples/index.php?id=40
Kimberley, Susan	Algebra Magic Puzzles	two number/magic puzzles that can be demystified and explained by using algebra https://pumas.gsfc.nasa.gov/examples/index.php?id=2
Donna	The Fall of the Ruler	teaches how an ordinary ruler can measure (human reaction) time https://pumas.gsfc.nasa.gov/examples/index.php?id=84
Brian
Chris	What is Wind Chill	Learn what causes wind chill and how it is determined https://pumas.gsfc.nasa.gov/files/10_31_01_2.pdf
Keith	The Mathematical Implications of Lying	explores how statistics can be interpreted in different ways to yield different conclusions https://pumas.gsfc.nasa.gov/examples/index.php?id=85
Pat	Dollar$ or Cent$?	describes using two coupons from the paper to teach comparing and converting decimals and fractions to eliminate the confusion between the $ and the¢ in daily life https://pumas.gsfc.nasa.gov/examples/index.php?id=38

Link: Function Machine – http://nlvm.usu.edu/en/nav/frames_asid_191_g_3_t_1.html?from=grade_g_3.html
(Note: you may be prompted

http://www.learner.org/vod/vod_window.html?pid=1544

Website  with videos for more on patterns and functions

Here is an interactive site to color Pascal’s Triangle in different ways to change the patterns.

http://www.shodor.org/interactivate/activities/ColoringMultiples/?version=1.6.0_13&browser=MSIE&vendor=Sun_Microsystems_Inc.

Here is the link to an animation showing how the triangle is formed.

http://en.wikipedia.org/wiki/File:PascalTriangleAnimated2.gif

Resources: ESCOT PoW Applets http://mathforum.com/escotpow/puzzles/

Illuminations http://illuminations.nctm.org

National Library of Virtual Manipulatives http://matti.usu.edu/nlvm/nav/

From Donna- Function machine with cooking examples

found a cool idea on how to use the function machine at: www.uen.org/Lessonplan/preview?LPid=18863

Math Vocabulary

Graphic organizer to use with math vocabulary

Frayer Diagram

1. Integers- all whole numbers and their opposites.

Integers- any of the natural numbers, the negatives of these number or zero.

Merriam Webster The Free Dctionary\

2. Number sense  Ones awareness and understanding about what Numbers are,   the relationships, the magnitude, the related effect of operating on numbers, including the use of mental math and estimation.

Number sense In mathematics education, number sense can refer to “an intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations.”^[

There are also some differences in how number sense is defined in the field of mathematical cognition. For example, Gersten and Chard say number sense “refers to a child’s fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world and make comparisons.”

http://en.wikipedia.org/wiki/Number_sens…

Posted 1 year ago

3. algebraic Numbers variables that represent rational numbers.

The sub set of the real algebraic numbers: the real roots of polynomials, Real algebraic numbers may be rational or irrational.

Http://thinkzone.wlonk.com/Numbers/NumberSets.htm.

An algebraic number is any real number that is a solution of some single-variable polynomial equation whose coefficient s are all integer s.

http://whatis.techtarget.com/definition/0,,sid9_gci283964,00.html

4. Real numbers all numbers, rational or irrational.

Real numbers are all the numbers on the continuous number line with no gaps. Every decimal expansion is a real number. Real numbers may be rational or irrational, and algebraic or non-algebraic (transcendental). pi = 3.14159… and e = 2.71828… are transcendental. A transcendental  numbers can be defined by an infinite series.

Http://thinkzone.wlonk.com/Numbers/NumberSets.htm

 5. Whole numbers counting numbers and their factions, 6/1 including 0.

Whole numbers counting numbers, positive integers. can be refered to as natural numbers
http://thinkzone.wlonk.com/Numbers/NumberSets.htm

6. Rational Numbers Any number that can be expressed as a/b with b not equal to 0.

Rational numbers are the ratios of integers, also called fractions, such as 1/2 =0.5 and 1/3 = 0.333… Rational decimal expansions end or repeat.

http://thinkzone.wlonk.com/Numbers/NumberSets.htm

 7. Irrational Numbers- any number that cannot be expressed as a/b. In decimals never ending.

8. Commutative properties –

For adding

The order in which you add a series of numbers doesn’t change the sum. Simple  for any numbers a and b,  a + b = b + a.

For multiplying

The order in which you multiply a series of numbers doesn’t change the product.

Simply for any numbers a and b ab = ba,

9. Addends-  numbers being added.

10. Inverse refers to the relationship to the opposite  of a number. It can mean to reverse something, turn it upside down. Or it can mean the opposite.

When adding, add the opposite:

a+ -a = o     3 + -3= 0

Used in matrix.

When multiplying, find the reciprocal

a * 1/a = 1

for whole numbers

1. Convert to fraction: 3= 3/1

2. To inverse turn upside down   1/3 known as reciprocal.

sS the inverse of 3/1=1/3   so 3/1 * 1/3=1           (a/1=1/a)

Used in dividing rational numbers and in a Matrix

 

 

Introduction to Kim January 19, 2012

Hi! I’m Kim Marsey and I live in Southern Pa. I have been a Family and Consumer Science Teacher for 33 years. Last year due to the district’s debt and budget cuts, they eliminated my program along with tech ed, computers, and music. They did approve a sabbatical instead of unemployment, so here I am trying to be a math teacher. I have never taken a class online, never blogged, never even Facebook, so this is all new and trying. I did get my husband to connect a keyboard to the laptop ( our newest computer) so hopefully that frustration of slow & old won’t be a problem.

My two goals for taking this class are to gain a better understanding  of Algebra. And gain some creative methods for teaching math to my middle school students. I don’t feel that just passing a test makes you a math teacher.