More than you might think.
In particular, people are gaining new insights about each of the three subjects through statistical models that analyze data to make predictions.
That was the message conveyed at a recent presentation by Dimitris Bertsimas, an MIT Sloan School of Management professor who teaches a course called “The Analytical Edge.”
Bertsimas, who spoke last week as part of a colloquium at the MIT Sloan School, described equations that help predict wine quality and baseball wins. For example, wine quality can be predicted through an equation that factors in winter rainfall, average growing season temperature and harvest rainfall. Bertsimas also explained that companies can analyze data from their employees’ healthcare transactions to better predict healthcare costs.
Of course, even good statistical models can’t anticipate everything. Bertsimas explained that last year, his baseball model predicted that the Boston Red Sox baseball team would win 90 games in the regular season — and they in fact won 89. This year, he predicted the Red Sox would win 101 games in the regular 162-game baseball season. But, one-quarter of the way through the season, the Red Sox had won only half their games so far.
“They are behind [the predicted record], I admit,” Bertsimas said.


Fourier Life is a system of cellular automata which spontaneously forms self-replicating structures. The picture above has the first system I found and shows 16 iterations of the system (each square with dots in it is a small portion of the cellular automata grid). Note that after 12 iterations, the original structure has replicated itself, although now each copy is rotated from the original. At each iteration (or generation), a filled cell either survives or dies and an empty cell can either remain empty or have a cell born into it. In the example above, the fate of each cell depends on how many neighbors (filled cells) it has surrounding it (up to 8).
If you click on the Run button (under the grid of cells at the top of the page) with System A and Rule 1 selected, you can see these structures appear out of a random field of cells, begin dividing in two, and then take over the entire cellular automata world.


These best math trivia questions and answers help everyone learn without the struggle. Whether you are a math novice or an algebra expert, you’ll enjoy this quiz!
The mathy puns throughout the quiz make you laugh too – because math is fun!
How to Play Math Trivia
Test your knowledge!
- Split into two teams and ask the math trivia questions to an individual from each team. (The person who answers first gets the point.)
- Or just quiz a friend and see how many they can get right.
- Use the table of contents to find the math quiz that works for your level and interest.
Now, who will be named the math champion? Let’s find out!
Pro Tip: If you’re playing with kids and need a prize for the winner, check out our free kids coupons!
Easy Math Trivia for Kids
Young kids love these easy math trivia quiz questions!
1. What is the sum of 5 and 3?
2. How many sides does a triangle have?
3. What is the product of 10 and 2?
4. How many corners and sides does a square have?
5. What is half of 12?
6. What is the difference of 6 and 2?
7. What is the shape of a stop sign?
8. If you have 2 dimes and 3 nickels, how much money do you have?
9. What is the time when the big hand is on 12 and the little hand is on 6?
10. What is an even number?
Any number that ends in 0, 2, 4, 6, 8.
11. What is the smallest odd number?
13. How many quarters are there in 2 dollars?
14. What is 20 divided by 4?
15. What is the shape of a soccer ball?
16. How many sides does a hexagon have?
17. What is the product of any number multiplied by 0?
18. What is the sum of any number added to zero?
The number stays the same.
19. What is the next number after 89?
20. What is the number before 67?
21. Name the next number in this pattern: 11, 13, 15, __
22. If you have 28 candles and take away 10, how many do you have left?
23. If a shape has two long sides and two shorts sides, what shape is it?
24. How many days are there in two weeks?
25. What time is it if it is half past 8?
Related: Best Kids Trivia Quiz
Medium Math Facts Quiz
Older kids, teens, and adults will enjoy this harder set of math trivia questions.
26. What is the metric system based on?
Units of 10
27. What is the smallest prime number?
28. What is the largest two-digit prime number?
29. What is the approximate value of pi (π)?
30. What is the only number that can’t be negative or positive?
31. What is the first odd number?
32. What is a prime number?
A number that is only divisible by 1 and itself.
33. What is the only even prime number?
34. What is the smallest two-digit prime number?
35. What is the smallest odd prime number?
36. What is the first cube number with 4 digits?
Hint: A cube number is any number which has been multiplied by itself, twice. (2X2X2)
37. What is the smallest composite number?
Hint: A composite number is a number that is divisible by smaller positive numbers apart from 1 and itself.
38. What is the first perfect number?
Hint: A perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself.
6 (6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6.)
39. What is the first abundant number?
Hint: An Abundant number is a positive integer for which the sum of its proper divisors is greater than the number.
12 (Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16.)
40. What is the sum of the first three square numbers (not including 0 as the first)?
Hint: A square number is an integer (whole number) multiplied times itself.
14 (1×1=1, 2×2=4, 3×3=9)
It is also a prime number!
42. What comes after a trillion?
43. What is the largest one-digit prime number?
44. What number less than 50 is a number whose digits product is twice the sum of its digits?
45. What is the square root of 64?
46. What is the first square number with an odd root?
47. How can you quickly tell if a number is divisible by 9?
The sum of the digits will equal 9 or be a multiple of 9.
48. 32, 40, 48, 54 are all multiples of what number?
49. What number is the square of 10 and is known as the “perfect square”?
50. What number is neither prime nor composite?
Math Shapes Trivia Picture Quiz
Next, decide what shapes are in the images.
Related: Harry Potter Picture Quiz
Basic Geometry Trivia Facts
Test your geometry knowledge with these great fun facts!
60. What is a triangle with sides of equal length called?
61. What is a type of rectangle with all sides equal in length?
62. 1/2 x base x height is the formula for finding the area of what?
63. What shape has 5 sides?
64. What is the formula for finding the volume of a cube?
length x width x height
65. What is the sum of the angles of a square?
66. What does this symbol (∞) stand for?
Infinity- It represents a quantity that is endless.
67. A right triangle has one angle that measures what?
68. What is the formula for finding the area of a rectangle?
length x width
69. How do you find the perimeter of a rectangle?
The perimeter equals twice the length plus twice the width or P=2L + 2W.
70. What type of parallelogram has all sides equal in length?
71. How many faces does a cube have?
72. The formula A=πr2 finds the area for what shape?
73. What type of triangle has two sides of equal length and two equal angles?
An isosceles triangle
C = 2πr
75. What does the sum of the angles in a triangle equal?
76. A right prism is a 3D shape where the base and sides meet at what type of angles?
77. The sum of what is (n-2) x 180°, where n is the number of sides?
The interior angles of a polygon
78. What theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides?
The Pythagorean Theorem
79. The Babylonians used what base number system? We still use it today for measuring time and angles.
Base-60 number system
80. Ancient Egyptians used geometry extensively in their architecture and construction, including the building of what famous monuments?
81. What is the distance around a circle called?
82. What is the term for two lines that never intersect and are always the same distance apart?
83. If one angle of a triangle is a right angle, what is the term for the other two angles?
84. What is the name of the point where two sides of a polygon meet?
Vertex (or corner)
Middle School Math Facts Trivia
If you get stuck, use the word bank below to help you with this math trivia quiz!
85. What term refers to how many times a number is multiplied by itself?
86. What is the term for the smallest number that is a multiple of two or more numbers?
Lowest common multiple (LCM)
87. What is the term for a number that represents part of a whole?
88. What is the top number of a fraction called?
89. What is the bottom number of a fraction called?
90. What is a comparison of two quantities and can be written using a colon or as a fraction?
91. What term used in statistics is the average of a data set?
92. What term used in statistics is for the value in the middle of a data set?
93. What term used in statistics is the number in a set of numbers that appears the most often?
94. What is the term for a number’s distance from zero on a number line?
95. What is the name for this?
x = (-b ±√(b^2 – 4ac)) / 2a
96. What is the name for a statement that two expressions are not equal or that one is greater than or less than the other?
97. A coordinate system uses an x-axis and what other axis to locate points on a plane?
98. What is the point (0,0) called on a coordinate system?
99. True or False: Rational numbers are numbers that can be expressed as fractions or decimals.
100. True or False: Real numbers include only rational numbers.
False- Real numbers include both rational and irrational numbers.
101. True or False: Integers are whole numbers, including positive and negative numbers, as well as zero.
102. What unit of measure is used in the U.S. customary measurement system?
103. What is this property called? a(b + c) = ab + ac
A. Commutative Property?
B. Associative Property
C. Distributive Property
D. Property of Zero
Answer: C: Distributive Property
104. What operation is first in the order of operations?
B. Multiplication & Division
D. Addition and Subtraction
Answer: C- Parentheses
Related: Best Trivia For Teens
Interesting and Funny Math Facts Trivia
105. What number, considered unlucky in many cultures, is considered lucky by Italians?
106. What 3-digit number is considered lucky in many cultures?
107. What number is considered unlucky in Japan because it sounds similar to the word for death?
108. In Hinduism, what number is considered sacred and appreas in many religious traditions and practices?
109. What appears in many natural phenomena, such as the arrangement of leaves on a stem or the spirals on a seashell and is where each number is the sum of the two preceding numbers?
The Fibonacci sequence
110. True or False: The ancient Chinese believed that even numbers were feminine and odd numbers were masculine.
111. What did the ancient Greeks believe that the universe was made up of which they believed were indivisible and had a mathematical structure?
112. In Chinese culture, when this number comes before a lucky number, the result is considered unlucky. What is this number?
113. The ancient Egyptians expected that fractions should always have what digit in the numerator?
114. The ancient Babylonians were the first to us a positional number system. What does this mean?
The value of a digit depends on its position in the number.
115. Using complex mathematical formulas and tables, the ancient Babylonians were able to calculate the position of what?
116. What civilization developed a sophisticated calendar system that was based on complex mathematical calculations and observations of the stars and planets?
117. The word “mathematics” comes from what Greek word which means “that which is learned.”
118. What mathematical theorem is named after the actor Kevin Bacon?
The “Bacon Number”
Answer: A- Equal sign
120. What is the name of the ratio found in nature and that has been used in art and architecture for centuries?
A. Archimedes’ Constant
B. The Golden Ratio
C. Duplicate Ratio
D. Euler’s Number
Answer: B- The Golden Ratio
Related: Fun Art Trivia Questions
121. Where do the first written records of trigonometry come from?
D. Ancient Babylonians
Answer: D- Ancient Babylonians
122. What number is known as the “Hardy-Ramanujan number” after a famous exchange between mathematicians G.H. Hardy and Srinivasa Ramanujan?
Answer: A- 1729
123. What term for a number equal to 1 followed by 100 zeroes was coined by a nine-year-old boy named Milton Sirotta in 1938?
Answer: C- Googol
124. Where was the concept of zero first developed?
A. Ancient India
Answer: D- Mesopotamia
125. How many perfect shapes did the Greeks believe there were?
Answer: B- Five: tetrahedron, cube, octahedron, dodecahedron, and icosahedron
Related: Modern & Classic Book Trivia
Fun True or False Math Trivia Questions
127. True or False: The Pythagorean theorem has been proven using over 200 different methods.
False- It has been proven using over 300 different methods.
128. True or False: The word “algebra” comes from the Arabic word “al-jabr,” which means “reunion of broken parts.”
129. True or False: The ancient Greeks used a geometrical method called “squaring the circle” to try to construct a rectangle with the same area as a given circle.
False- They used this method when trying to construct a square with the same area as a given circle.
130. True or False: The word “geometry” comes from the Greek words “geo” meaning Earth, and “metron” meaning meter.
False- “Metron” means measurement
131. True or False: The concept of negative numbers was not widely accepted until the 19th century.
False- It was the 18th century.
132. True or False: The concept of infinity has been debated by mathematicians for centuries.
133. True or False: Googolplexian is the largest number with a name in English.
134. True or False: The number 111,111,111 x 111,111,111 equals 12,345,678,987,654,321.
135. True or False: The Riemann hypothesis is one of the most famous unsolved problems in mathematics.
136. True or False: The Cauchy-Schwarz inequality is a fundamental concept in geometry.
False- It is a fundamental concept in linear algebra.
137. True or False: In Japan, the number 7 is unlucky since the pronunciation sounds like the same word for pain.
False- It is the number 9.
138. True or False: The ancient Chinese used a decimal system that included symbols for negative numbers and zero.
139. True or False: The ancient Greeks believed that the universe was governed by mathematical laws and principles.
140. When someone runs a 10 kilometer race (or 10k), it’s 3.1 miles.
False. It’s 6.2 miles.
Hard Math Facts Trivia Quiz
Next, if you are advanced, you’ll love these expert level math trivia questions.
141. What is the sum of all natural numbers (1+2+3+4+…)?
142. How many prime numbers are there?
143. The square root of -1 is an imaginary number and is represented by what symbol?
The symbol “i”
144. The number e is the base of the natural logarithm and is approximately what?
145. How many sides does an enneadecagon have?
146. What is the name of the symbol used in division?
147. What conjecture suggests that there are an infinite number of prime pairs that differ by 2?
The twin prime conjecture
148. What conjecture was one of the most famous unsolved problem in topology until it was proven in 2003?
The Poincaré conjecture
149. What conjecture suggests that every even number greater than 2 can be expressed as the sum of two prime numbers?
The Goldbach conjecture
150. What conjecture suggests that no matter what positive integer you start with, its sequence of iterations will eventually reach 1?
The Collatz conjecture
151. What equations describe the motion of fluids and are widely used in engineering and physics?
The Navier-Stokes equations
152. What is the number 0.999…(repeating) equal to?
153. True or False: There are more real numbers than there are natural numbers.
154. What is the shape of a football?
A prolate spheroid
Related: Fun Football Trivia Quiz
Roman Numerals Quiz Questions
And finally, how well do you know your roman numerals? Let’s find out!
156. What is the Roman numeral for the number 10?
157. What is the Roman numeral for the number 50?
158. What does the Roman numeral XXVIII stand for?
159. What does the Roman numeral IX stand for?
160. What number does the Roman numeral M represent?
161. What is the Roman numeral XLVII written as a standard number?
162. The Roman numeral C = 100. So what does the Roman numeral XC stand for?
163. What does the Roman numeral D stand for?
164. How would you write the number 900 in Roman numerals?
165. How would you write the number 1600 in Roman numerals?
166. How would you write the Roman numeral for the number 3?
167. Translate the Roman numeral CXLIII to a standard number.
168. What does LXXX stand for?
169. What does MCM stand for?
170. True or False: You cannot repeat a Roman numeral over three times.
171. True or False: When you place a smaller Roman numeral in front of a larger Roman numeral, this indicates addition.
False: It indicates subtraction.
172. Which is the correct Roman numeral representation of the number 40. XXXX or XL?
173. Write the number 26 in Roman numerals.
174. Write the number 70 in Roman numerals.
175. Write the number 1700 in Roman numerals.
Don’t miss all of our fun trivia for kids and adults! Check out:


Books In Progress
We are currently working on Textbook Companions for the following books
- Probability And Statistics For Engineers And Scientists, S. M. Ross, 3rd edition, Elsevier, New Delhi, 2005.
- Linear and nonlinear programming, D. Luenberger, 2nd edition, Kluwer Academic Publisher, New York, 1984.
- Nonlinear programming, D. Bertsekas, 2nd edition, Athena Scientific, 1999.
- Optimization Techniques, A. K. Malik, S. K. Yadav, S. R. Yadav, 1st edition, I.k. Internationlal Publishing House Pvt. Ltd, 2012.
Suggested List of Books that can be taken up for TBC project
- Engineering Optimization Methods and Applications, Reklaitis, G.V., Ravindran, A. and Ragsdell, K. M., 2nd edition, John Wiley,New york 1983.
- Probability, Random Variables and Stochastic Processes, Athanasios Papoulis, S. Unnikrishna Pillai, 4th edition, McGraw Hill Education (India), 2002
- Optimisation Techniques , Rao S.S. , 2nd edition, Wiley Eastern, 1985


Global Optimization Toolbox
The global search and multistart solvers use gradient-based methods to return local and global minima. Both solvers start a local solver (in Optimization Toolbox) from multiple starting points and store local and global solutions found during the search process.
The global search solver:
The multistart solver uses either uniformly distributed start points within predefined bounds or user-defined start points to find multiple local minima, including a single global minimum if one exists. The multistart solver runs the local solver from all starting points and can be run in serial or in parallel (using Parallel Computing Toolbox™). The multistart solver also provides flexibility in choosing different local nonlinear solvers. The available local solvers include unconstrained nonlinear, constrained nonlinear, nonlinear least-squares, and nonlinear least-squares curve fitting.
Using Global Search for Optimization Problems
Find local and global minima of the


Introduction One of the most subjective decisions made when using ordination techniques is the number of components to retain for interpretation. Generally, the researcher subjectively decides, but more objective methods are described below. Based on a literature review of the use of factor analysis and principal components analysis (Franklin et al. 1995, J. Veg. Sci. 6:99-106), more objective methods are necessary. The parallel analysis (PA) must match the number of samples (n) and number of variables (p) in your real data set (i.e. that data collected from the field). Further, the PA must match the type of analysis (e.g. factor analysis or principle component analysis), and must correspond to the type of matrix being decomposed (i.e. correlation of covariance). By setting criteria for the interpretation of ordination results, a researcher can objectively decrease the number of axes for interpretation and number of variables of interest , thus facilitating interpretation. Decomposing a correlation matrix: The program LONGMAN.SAS given below is the easiest program for interpreting the number of components to retain when decomposing a correlation matrix. Simply change the N and P values (on the first line after explanation text only) to match your field data set and run the program. The values derived from the analysis are the 95th percentile eigenvalues for each component based on the regression equations of Longman et al. 1989 (Multi. Behav. Res. 24:59-69). The regression equations are based on a Monte Carlo analysis. Eigenvalues from the analysis of the field data that are greater than the PA eigenvalues (comparing each axis separately - PA eigenvalue for axis one versus real eigenvalue for axis one, PA eigenvalue for axis two versus real eigenvalue for axis two, etc.) are significant at the 0.05 level, and should be retained for interpretation. The analysis should be rerun using the appropriate number of components. Decomposing of covariance matrix: The program COVRPARA.SAS given below will produce a pseudorandom matrix based on the means and standard deviations of the real data. Here, each variable in the analysis contributes to the distributions and variance of the pseudorandom matrix. Insert the standard deviations and means where appropriate and add or subtract variables as necessary. In this analysis, the program performs the Monte Carlo analysis, the number of which can be set as K (99 or 999 are recommended). Change appropriately the X1-X?? for number of variables, and the J size for the number of samples. Make sure the analysis used (e.g. factor analysis with rotations) on the collected data is the same as on the randomized data set created in this program. The results derived are the maximum eigenvalues from all the K analyses. Eigenvalues retained for interpretation should be greater than these eigenvalues. The analysis should be rerun using the appropriate number of components. Determining Significant loadings: When decomposing a correlation matrix, use the program LOADINGS.SAS. When decomposing a covariance matrix, use the program COVRPARA.SAS (see above). This program creates a random data set with the same n and p size as the collected data set and should be subjected to the same analysis (e.g. factor analysis with rotations). This step follows the determination of the number of components to retain, and this number (?) should be set in the PROC FACTOR statement as N=?. Set the number of samples (yyy), variables (www), and randomizations (zzz) in all areas and run. The results give you the maximum loadings from all the data sets analyzed. To determine the 95th percentile, multiply the number of the components by the number of variables (3 * 16 = 48), then multiply that number by 0.05 (48 * 0.05 = 3 with rounding). Thus, the third highest loading from the maximums shown gives the 95th percentile cutoff, and only loadings greater than this value should be interpreted. This program is written for a factor analysis. The univariate procedures need to be modified for any other types of analyses, so that the univariate analysis is performed on the appropriate variable.
TITLE 'PROGRAM TO DECOMPOSE A CORRELATION MATRIX - THE LONGMAN METHOD'; OPTIONS LS=73 NOCENTER; DATA LONGMAN; * THIS PROGRAM PRODUCES ESTIMATES OF THE 95TH PERCENTILE EIGENVALUES FROM A PARALLEL ANALYSIS, USING THE WORK OF LONGMAN ET AL. (1989). CHANGE THE VALUES OF N AND P TO THOSE OF YOUR DATA MATRIX. THIS PROGRAM SHOULD ONLY BE USED WHEN DECOMPOSING A CORRELATION MATRIX; N=36; P=13; * N = SAMPLE SIZE, P = NO. OF VARIABLES. ; LN = LOG (N); LP = LOG(P); LEIG1 = 0.0316*LN +0.7611*LP -0.0979 *(LN*LP) -0.3138; LAM1 =EXP (LEIG1); LEIG2 = 0.1162*LN +0.8613*LP -0.1122 *(LN*LP) -0.9281; LAM2 =EXP (LEIG2); LEIG3 = 0.1835*LN +0.9436*LP -0.1237 *(LN*LP) -1.4173; LAM3 =EXP (LEIG3); LEIG4 = 0.2578*LN +1.0636*LP -0.1388 *(LN*LP) -1.9976; LAM4 =EXP (LEIG4); LEIG5 = 0.3171*LN +1.1370*LP -0.1494 *(LN*LP) -2.4200; LAM5 =EXP (LEIG5); LEIG6 = 0.3809*LN +1.2213*LP -0.1619 *(LN*LP) -2.8644; LAM6 =EXP (LEIG6); LEIG7 = 0.4492*LN +1.3111*LP -0.1751 *(LN*LP) -3.3392; LAM7 =EXP (LEIG7); LEIG8 = 0.5309*LN +1.4265*LP -0.1925 *(LN*LP) -3.8950; LAM8 =EXP (LEIG8); LEIG9 = 0.5734*LN +1.4818*LP -0.1986 *(LN*LP) -4.2420; LAM9 =EXP (LEIG9); LEIG10= 0.6460*LN +1.5802*LP -0.2134 *(LN*LP) -4.7384; LAM10=EXP(LEIG10); PROC PRINT; VAR N P LAM1-LAM10; RUN;
TITLE ' PARALLEL ANALYSIS DECOMPOSING A COVARIANCE MATRIX'; *NOTE: THIS USES MEANS AND STANDARD DEVIATIONS FROM FIELD DATA; DATA ONE; OPTIONS LS=73; DO K = 1 TO 100;*SET NUMBER OF PERMUTATIONS; DO J = 1 TO 30; * GIVE NUMBER OF SAMPLES IN DATA SET; *** THE FOLLOWING FUNCTIONS CREATE PSEUDORANDOM DATA SETS USING THE MEANS AND STANDARD DEVIATIONS FROM THE REAL DATA; x1 = normal(0)*24 + 21.43; x2 = normal(0)*0.5 + 0.345; x3 = normal(0)*1.8 + 0.3; x4 = normal(0)*18 + 7.93; x5 = normal(0)*2.5 + 1.16; x6 = normal(0)*10 + 6.1; x7 = normal(0)*0.3 + 0.03; x8 = normal(0)*0.6+ 0.287; x9 = normal(0)*40 + 40.97; x10 = normal(0)*0.2 + 0.043; output; end; end; RUN; DATA TWO; SET ONE; PROC FACTOR COV METHOD=PRINCIPAL N=6 OUTSTAT=RESULTS;VAR X1-X28;BY K; DATA FINAL; SET RESULTS; IF _TYPE_ = 'EIGENVAL'; OPTIONS LS=73; PROC UNIVARIATE NOPRINT; VAR X1-X10; OUTPUT OUT=EIGEN MAX=MAXE1-MAXE10; PROC PRINT; RUN; DATA FINAL2; SET RESULTS; IF _TYPE_ = 'PATTERN' AND _NAME_ = 'FACTOR1'; OPTIONS LS=73; PROC UNIVARIATE NOPRINT; VAR X1-X10; OUTPUT OUT=PATTERN MAX=MAXP1-MAXP10; PROC PRINT; RUN;
TITLE 'THIS PROGRAM WILL GENERATE SIGNIFICANT LOADINGS'; * THIS PROGRAM SHOULD ONLY BE USED WHEN DECOMPOSING A CORRELATION MATRIX; OPTIONS LS=73; DATA ONE; * GENERALIZED PARALLEL FACTOR ANALYSIS PROCEDURE: 1. NUMBER OF VARIABLES IS SET WITH THE WWW INDEX VALUE, 2. NUMBER OF OBSERVATIONS IS SET WITH THE YYY INDEX FOR J IN THE FIRST DO STATEMENT AND IN THE VAR STATEMENT, 3. NUMBER OF ANALYSES IS SET WITH THE ZZZ INDEX, 4. LASTLY, PERFORM THE SAME FACTOR ANALYSIS ON THE SIMULATED DATQA MATRIX THAT YOU PERFORMED ON THE ACTUAL DATA MATRIX.; ******WARNING - THIS PROGRAM GENERATES A BIG LISTING****** ; ARRAY X (I) X1-X16; * SET THE NUMBER OF VARIABLES (WWW); DO K = 1 TO 50; * SET THE NUMBER OF ANALYSES (ZZZ); DO J = 1 TO 133; * SET THE SAMPLE SIZE (YYY); DO OVER X; X = NORMAL (0); END; OUTPUT; END; END; RUN; DATA TWO; SET ONE; * SET THE NUMBER OF FACTORS WITH THE N = PARAMETER; PROC FACTOR COV METHOD=PRINCIPAL N=3 OUTSTAT=RESULTS; VAR X1-X16; BY K; RUN; DATA FINAL; SET RESULTS; IF _TYPE_ = 'EIGENVAL'; OPTIONS LS=73; PROC UNIVARIATE NOPRINT; VAR X1-X16; OUTPUT OUT=EIGEN MAX=MAXE1-MAXE10; PROC PRINT; RUN; DATA FINAL2; SET RESULTS; IF _TYPE_ = 'PATTERN' AND _NAME_ = 'FACTOR1'; OPTIONS LS=73; PROC UNIVARIATE NOPRINT; VAR X1-X16; OUTPUT OUT=PATTERN MAX=MAXP1-MAXP16; PROC PRINT; RUN;
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©1996, Southern Illinois University at Carbondale.
Last revised: 10 Sept, 2003 by DJG.


That’s all well and good in practice, but how does it work in theory?
Things are looking up! If you’re a linear equation with a positive slope, that is… OK, no math jokes for me. For the first time in 12 years, I’m tackling an issue that’s been bothering me. What does it take to succeed in math education? A perfectly rational question… It’s taken daily practice, determination, and patience to find an answer, and I’m only getting started.
Resources in order of the SPECTRUM Acrostic
Science…or math? “Wait,” I ask myself as I sit down to write my science and STEM education blog, “I don’t understand. This adventure is about… math?” Yes, math. “Except, isn’t this about adventures from a science teacher cultivating student-centered classrooms in STEM? Yes, and today we’re talking math. Math. Besides, “Mpectrum” doesn’t quite work, so let’s just roll with this.
Math, other than being the obvious character playing the “M” in STEM, is the language that science speaks. It’s the ball of sports – imagine trying to play football or basketball without the ball. One simply cannot do science without math. Science teachers use math to teach the math-y parts of science, like density or light years or population growth. Yet, at least in my experience, I don’t see a lot of science teachers who are certified to teach math or vice versa. Does this seem right to you?
This is a question I do not know the answer to. Knowing how involved teaching science is, I don’t automatically expect science teachers to get certified in math. Maybe they shouldn’t be. They are different professional disciplines, after all, supported by different administration and professional development conferences. They use different types of curriculum and are held to different knowledge and skills standards. As a member of several science education organizations, I can barely keep up with my own kind. Still, my heart aches as I hear math teachers complaining their students refuse to work on gravity “because it is science.” My man Einstein would, of course, disagree. I do hope there are science teachers like me who want to do more math/science integration and vice versa. More than any other combinations of subjects, I believe science and math need to be firmly integrated into teacher and student education. The trouble is, I have no idea where to start.
Once, through my alma mater at the University of Montana, we worked with the math education preservice teachers to build an integrated unit. Helpful exercise, sure, but it went unpracticed in the classroom and therefore quickly forgotten. Thanks to the direct integration of Common Core State Standards for Math through the Next Generation Science Standards, curriculum programs can better embed the needed math needed for each grade level in science. Yet that’s only for states that have adopted NGSS, right? Even with the uprising STEM education has established throughout the US, I’m concerned about the competency level a typical teacher needs to achieve to seamlessly combine subjects through a single unit, let alone with a whole school year.
The last couple months I’ve been working in several middle school math classes, humbled by 8th-grade linear equations and quadratic functions, rushed to recall distributive properties in 7th-grade algebra, yet relieved that two-step equations came back like riding a bike. It’s been awhile since I’ve completed these subjects as a student, let alone tackled as a teacher if not directly tied to scientific content. Do all teachers feel like this? I caught a break today and was able to work with students to calculate the composite area with each panel of various international flags as though they were ordering the material for manufacturing the exterior of the United Nations. Areas of rectangles, triangles, and circles…
Fortunately, STEM is a great place to start. Thanks to a gaining presence for STEM education and career awareness in recent years, I get encouragement from this push for interdisciplinary studies. Groups like the Maryland STEM Festival, National Environmental Education Foundation (NEEF), and professional development with programs like NAGT are doing a lot with effective integration.
Yet, I recently discovered with my very own eyes a disconnect between science and math middle school education. I speculate that we are widely varied in our competency levels for not just math and science integration, but STEM integration as a whole.
What does a quality program for learning how to teach science and math look like? I recently came across a 7th class where science and math are combined. “Sometimes it’s double science, sometimes it’s double math, other days it’s separate. It just depends on what we are studying,” students explained when I asked them what their week looks like.
These magnet 7th grade students were conducting a collaborative investigation where they used shared data to answer questions on digestion including “What is the effect of being a vegetarian on calcium intake? Vitamin A?” “What is the effect of the average of weekly fast food on the average American’s fat intake?” and my personal favorite, “How does the time of day affect calcium intake in middle school? Carbohydrate intake?” They used Google sheets filled with anonymous data from their peers, Google slides to create presentations based on their data interpretation, and other multimedia to demonstrate their claim.
Closer to my answer, I met with their teacher and asked him what his goals were and how he thinks this type of approach can grow in the future. Mr. Greg Young, an administrator, and National Board Certified science teacher at Roberto Clemente Middle School in Germantown, Maryland, is in his first year of implementing the new science/math combined course for the campus. Because his background is in middle school education, with certifications in both secondary math and middle school science, he’s always approached science, math and engineering teaching with a combined focus. Before I forget, here is a Competency based curriculum, reflecting on practices in other countries than USA, just placing here for future notes.
“This is what I should be doing. [Since] we teach in such an isolated world, we are quick to forget that there is a world of millions of people trying to do the same thing we are. I know I’m hitting the right swings.”
Soon, Mr. Young will begin an astronomy unit that will study the frequencies of radio telescopes and look at data from radio towers to prove the shape of the Milky Way Galaxy. Students will respond to a Request for Proposals to the National Radio Astronomical Association with to acquire time and data collection capacity on the giant telescopes. They will use multivariable quadratic equations and graphs to investigate measurable elements and molecules such as hydrogen, glucose, chlorophyll and water. It’s all part of the science of looking for life, “and we are looking at elements that are searchable through the universe. In all my prior teaching, I could imply a connection between subjects for students, but this is the first time I’m able to make a direct connection with them.I feel like I am at the beginning of a big wave.”
His students studying health in the example above were using overlapping skills for finding explanations in science and solutions in engineering. According to the NGSS Science & Engineering Practice “Using Mathematics and Computational Thinking,” they were using computers to work with large data sets and use mathematical representations (mean, mode, and median) to support or refute their claim. According to NGSS’ Appendix J, “During the middle school and high school years, students develop a number of powerful quantitative tools, from rates and proportional relationships to basic algebra and functions, to basic statistics and probability.” I like to make fun of science when I teach engineering. Context is everything, especially graphing and units. I always teach science with an engineering lens.”
Creating everything from scratch, Mr. Young is meeting all county benchmarks and students are completing their Quarterly Assessments for math and Common Tasks for science on schedule. He’s found lots of connections between the subjects, starting with bacterial and exponential growth and experiential design. When students are collecting their own data, and presenting it, they are engaged in inquiry – it doesn’t matter if they are in math or science. Students must explain standard deviation, p-value, and the overall value of their data in their statistical analyses. “Two plus two does not equal four. Two apples and two oranges do not equal four apples. Units are important,” Mr. Young reminds his students that numbers mean nothing without context and units of measurement.
After primarily teaching science for 20 years, Mr. Young seems excited about the potential from this combined approach pilot. “I’ve always approached teaching from an integrated perspective, but have never had the opportunity to do both. I was always told that I should remain with one Professional Learning Community, either science or math. But not both,” said Mr. Young. “It wasn’t until last year, while at a training, that we just happened to have a conversation with the math chair, magnet center coordinator, and assistant principal that allowed us to begin this project.”
What about regular science and math programs on the same campus? While true integration has its merits, it might be more feasible to work with science and math teachers to create integrated units through the school year. What does your school do? What do you prefer? I want to hear from you.
I spoke with Mr. Ben Stano, a middle school math and science teacher, currently teaching 6th-grade science. On how to effectively integrate concepts and skills? “A good example of successful math integration in 6th grade science is using computer simulation with bar graphs with models of watersheds. It’s an easy interpretation from evapotranspiration to infiltration, and using simulations means they could easily check their own work. Arithmetic was not well represented, and I think it should be better represented.” When students reach for a calculator to finish their science assignment, “they are applying concepts without quite realizing it.”
Integration does provide a certain flexibility and an approach that is likely teaching the teacher just as much as the students. “This is a drop in the bucket of what it could be if it’s done right. If you just give teachers a chance to naturally integrate and not segregate, there are lots of connections. We’ve spent so much time separating disciplines, now kids think that everything is different.”
When asked how he recommended for campuses to adopt this approach, he remarked, “it’s a structural philosophy that requires more than just teachers to get on board. It requires the support from the whole administration. I’m loyal to this campus, and it’s been loyal to me. I’ve never found a principal who was willing to try this before.”
As for communicating the results from his research? “If I could communicate what we’re doing here, through a presentation of the data we’ve collected and gains among the students, then perhaps we could get district-wide encouragement to get more teachers involved. But we have to start with one school first.”
Both the US Department of Education and the National Science Foundation have Math Science Partnerships. Doesn’t this mean that there is funding available for more integration?
How would Mr. Young recommend young professionals proceed through this challenge? “Don’t quit. Don’t stop trying. I’m a bit of a stick in the mud, and I’m loyal to a fault. I will make it work here, this is the school where I started and will probably retire from 25 years from now. If I can convince my department chairs that this works out, show evidence of connections and successes, then maybe I can get another teacher to do it with me. Maybe I can start to build something.”
As for me, I’m still stumbling along, teaching my various math and science middle school classes and helping out elsewhere when I can. I see students struggle, I cringe when I see math curriculum in standard measurements and science in metric. I regret not getting involved with this predicament 12 years ago when I got started in this field, but I like so many others got a degree and teaching certificate in science, not math. I’m just as guilty.
I’ve learned this. Provide context. No one can make sense of their world, or what you’re trying to teach them – be it music, math, history, English, PE, Spanish, or media – if they don’t have context. When we just threw the definition of density = mass/volume in front of those poor 6th graders in fall without coordinating the scope and sequence with the math teachers, we really did those kids a disservice. Perhaps with a bit more context, students can model this approach for us. This also goes for consistent units of measure, as Mr. Stano confirms, “This needs to be more cohesive. We could teach density AFTER students see the match concept, and we can put more thought into the science from a conceptual perspective. The logic that you’re asking to apply should match with the logic you are teaching them.”
Since I have no idea where to start, I did some basic searches and included them here, both elementary and secondary. As always I’m including science/math/music by Herbie Hancock because this reference spans so many great topics. Somehow I found this blog, make what you will but it’s got some interesting headlines. And this newsletter has some great links to STEM organizations.
There’s so much more I wanted to cover in this adventure. Graphing, argumentation, assessment, solving problems (single and multi-step), and more. I realize now this is not an adventure, but an ongoing process in a journey unlike any other. I’ll be back, but for now I must move forward.
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A horizontal bar graph is a graph with horizontally running rectangular bars. It’s a type of data visualization. These bars are proportional in length to the values they represent. The title of the bar chart specifies which data is being displayed. The horizontal axis shows a value, while the vertical axis represents the categories being compared. This type of graph depicts categorical data in a visual manner. This information is bundled together.
Months of the year, age ranges, shoe sizes, and animal species are all examples. To make a horizontal bar graph, start by deciding on a scale that is acceptable for the data values. Then, on the vertical axis, label the data categories, and on the horizontal axis, label the values. After that, each data category’s bands should be drawn.
A line graph is a form of a graph that shows data that changes over time. Straight lines are used to link many points in a line graph. A line chart is another name for it. A line graph is made up of two axes: the ‘x-axis and the ‘y’ axis.
- The x-axis refers to the horizontal axis.
- The y-axis refers to the vertical axis.
Plotting a Line Graph
- Draw the x- and y-axes on graph paper. Make careful to write the title above the table so that the graph’s objective is evident.
- For example, if one of the components is time, it is shown on the x-axis, which is the horizontal axis. The y-axis, or vertical axis, would then be plotted with the other factor. Both axes should be labeled according to their respective factors. The x-axis can be labeled as time or day, for example.
- Then, on the graph, highlight the exact values using the previously provided data. You may form a clear conclusion about the trend after connecting the points.
Reading a Line Graph
- Take a look at the two axes and try to figure out what they represent.
- Then have a look at the graph and the values of the points on the graph’s lines.
- By following the lines, you can determine whether there is a rise or fall. Also, see if there are any repeating patterns or lines that cross each other.
- It’s also likely that you’ll see new patterns that can help you forecast the trend.
Line Graph Advantages
The advantages of using line graphs are as follows.
- It’s useful for displaying changes and trends over time.
- Small changes that are difficult to measure in other graphs can also be shown.
- Because they are straightforward, easy to understand, and efficient, line graphs are popular and successful charts.
- Anomalies within and across data sets can be usefully highlighted.
- As a comparison, more than one line can be plotted on the same axis.
Line Graph Disadvantages
- Too many lines plotted over the graph make it cluttered and difficult to read.
- It’s difficult to plot a wide range of data on a line graph.
- They are only suitable for displaying data with numerical values and total numbers, such as monthly rainfall totals.
- The data in a line graph may appear wrong if consistent scales on the axis are not applied.
- Line graphs are sometimes problematic when plotting fractions or decimal quantities.
Reading a Horizontal Bar Graph
- The data that the horizontal bar graph shows is described in the title.
- On the vertical axis, the data categories are depicted. The colors indicate the data categories in this case.
- The values corresponding to each data value are represented on the horizontal axis. The data values here are the number of pupils who favor each of the colors on the vertical axis.
- On the horizontal axis, the scale displays the value of one unit.


Hello, fellow CFA charters or actuaries. Ronda's mom's comment in UFC 190 Vlog Epi 3 really bugs me. She said. "Even if someone has a one in a million chance per second of beating you, if you let it go 60 seconds where you could have done it in ten, you give them six times the chance, that's just stupid" Now there are three possibility in each second, Ronda wins, Ronda loses or proceed to the next second. Therefore this is basically a Trinomial Option Pricing Model, right? She implied that the probability of an opponent winning in a 60 second is six times greater than an opponent winning in 10 seconds, that must mean the probability is additive, which is erroneous. A simpler example, say Bethe has 1 in 1000 chance of winning per second, if it's additive, than that means after 1000 seconds, the Bethe has a 100% chance of winning. Which is not true. If you do a two step trinomial model starting from the 10th second of round 1, which we denote as t_0, and for the sake of easier of calculation, let Ronda chance of winning per second be 3/10, Bethe winning = 1/10 and proceeding to the next second be 6/10. probability at t_1, or 1 second after t_0, is 3/10 for Ronda (R), 6/10 going into next second (N) and 1/10 for Bethe (B). Or mathematically, P(R)_1 = 0.3, P(N)_1 = 0.7 and P(B)_1 = 0.1 At t_2, which means they have to go through the previous second, which had a 0.6 probability, therefore P(R)_2 = 0.3 * 0.6 = 0.18, P(N)_2 = 0.6^2 = 0.36 and P(B)_2 = 0.1 * 0.6 = 0.06 etc At each second, the probability of Ronda beating Bethe is always the same, At the 60th second, or t_50, Bethe's chance is 0.1 * 0.6^49 = 1.34714 E-12, the cumulative chance from t_1 to t_50 and to the of the match is 0.25 via a KO, TKO or submission for Bethe. 0.25 is not 50 times bigger than 0.1. I mean she's got a PhD and an expert in SAS apparently, how can she make up statistically incorrect statement?


Dr. Ahmet Ay
Ahmet Ay, Associate Professor of Biology and Mathematics at Colgate University, has been selected as the R. Gaurth Hansen Alumnus Awardee for 2016. Dr. Ay worked with Dr. David Arnosti (Department of Biochemistry & Molecular Biology) and Dr. Chichica Chiu (Department of Mathematics) at Michigan State University. He received his Ph.D in Mathematics and Quantitative Biology in 2009 studying the mathematical modeling of gene regulation in early Drosophila melanogaster embryos.
At Colgate University, Dr. Ay has developed an interdisciplinary undergraduate curriculum in systems biology with support from the Howard Hughes Medical Institute. His current research interests lie in applying mathematical modeling and computer programming to understand gene regulatory networks at multiple levels. (1) He develops statistical learning techniques to construct and analyze large-scale gene regulatory networks from genomic datasets. (2) He studies small-scale gene regulatory networks such as zebrafish segmentation clock using mathematical modeling and biological experimentation. (3) He also uses mathematical modeling to analyze the similarities and differences between conserved alternatively designed gene regulatory sub-networks.
Dr. Ay's research has appeared in more than 20 articles in Molecular Systems Biology (Nature Press), Development, eLife, and other leading journals.


How To Solve Differential Equations With X And Y. Equations inequalities simultaneous equations system of inequalities polynomials rationales complex numbers polar/cartesian functions arithmetic & comp. In the last step, we simply integrate both the sides with respect to x and get a constant term c to get the solution.
Rewrite the linear differential equation in pfaffian form. In the last step, we simply integrate both the sides with respect to x and get a constant term c to get the solution. This is what it means to separate it.
Example 3 Convert The Following System To Matrix.
It is easy to reduce the equation into linear form as below. Differential equations in the form y' + p(t) y = g(t). Here we will look at solving a special class of differential equations called first order linear differential equations.
This Is What It Means To Separate It.
In order for a differential equation to be called an exact differential equation, it must be given in the form m(x,y)+n(x,y)(dy/dx)=0. This integrating factor is such that multiplying the above equation by it. (y d x + x d y) (1 − x 2 y 2) + x d x = 0 is there any way i can get this into the form of a separable, bernoulli, exact, or any other form of.
F = ∫ Q × I.
Remember from the introduction to this section that these are ordinary differential equations (odes). Type 1 type 2 by homogeneous differential equations a. Solving differential equations means finding a relation between y and x alone through.
These Equations Are Evaluated For Different Values Of The Parameter Μ.for Faster Integration,.
We have, d y d x = x x 2 + 1. Rewrite the linear differential equation in pfaffian form. In this section we solve linear first order differential equations, i.e.
Y 2 = − X 2 + C.
Now only terms involving y are on the left, and terms involving x are on the right. These kinds of homogenous differential equations can be solved by putting \(x = vy,\) after that, follow the same five steps which we applied for case \(1.\) linear differential. They are first order when there is only dy dx, not d 2 y dx 2.


The Möbius paradox has been a mystery to mathematicians for 46 years. Finally, the problem has been resolved.
Two mathematicians published a conjecture in 1977 that proposed the minimum size of a paper strip required to make an embedded strip. They offered an aspect ratio of 1.73 (or 3) but were unable to verify it.
A mathematician from Brown University successfully proved the conjecture about 50 years later, as evidenced in a preprint uploaded on the arXiv server.
The Möbius strip is a well-known mathematical object. The Möbius strip, discovered in 1858 by two German mathematicians, August Ferdinand Möbius and Johann Benedict Listing, is a mind-bending form that’s actually quite simple to produce. Take a piece of paper, twist it, and tape the ends together.
However, the shape’s simplicity reveals its mathematical complexity. The Halpern-Weaver Conjecture, put forth in 1977 by mathematicians Charles Sidney Weaver and Benjamin Rigler Halpern, speculated on the smallest size of that strip of paper required to create a Möbius strip.
Isn’t it simple? No, not really. There were a few rules added to this conjecture, the most important of which was that the paper strip had to be “embedded” rather than “immersed.” This means that the item could never intersect itself. In other words, there may be no overlaps in the embedded paper, Möbius.
While Weaver and Halpern postulated a length, they were unable to verify it definitively, which is where Brown University mathematician Richard Evan Schwartz comes in. Schwartz answers the nearly 50-year-old enigma in a work published on the preprint service arXiv, finally proving the lowest size indicated by the original Halpern-Weaver conjecture—an aspect ratio of 1.73, or 3.
“These Möbius bands have these straight lines on them.” “They’re referred to as ‘ruled surfaces,'” Schwartz said to Scientific American. “Whenever you have paper in space, even if it’s in some complicated position, still, at every point, there’s a straight line through it.”
Schwartz told Scientific American that he attempted numerous solutions for years before arriving at a geometric solution by dividing the problem down into more manageable bits. To ultimately arrive at the proper solution, Schwartz corrected a previous error in his calculations in which he had incorrectly determined that slicing a Möbius strip at a specific angle would result in a parallelogram—it was actually a trapezium.
“Oh, it’s not the parallelogram.” Schwartz told Scientific American, “It’s a trapezoid. The corrected calculation gave me the number that was the conjecture.” “I was astounded… I hardly slept for the following three days, simply writing this stuff up.”
The Möbius strip is shrouded in even more mystery. This conjecture, for example, only demonstrates the smallest size of a Möbius paper with one twist, not three or more. It’s astonishing that such a simple shape can still be so confusing, more than 160 years after its discovery.
The German mathematicians Johann Benedict Listing and August Ferdinand Möbius independently discovered the Möbius strip as a mathematical entity in 1858. However, it has been recognised for a long time, both as a physical object and in artistic portrayals; it can be found in various Roman mosaics from the third century CE, in particular. Many of them simply feature coiled ribbons as borders. These ribbons are Möbius strips when the number of coils is odd, but they are topologically equal to untwisted rings when the number of coils is even. As a result, whether the ribbon resembles a Möbius strip may be fortuitous rather than intentional. In at least one instance, a ribbon with distinct colours on either side was drawn with an odd number of coils, prompting the artist to undertake a crude patch where the colours did not match. Another mosaic from Sentinum (above) shows the zodiac as a band with a single twist that the god Aion is carrying. There is no convincing evidence that the one-sidedness of this visual depiction of celestial time was deliberate; it might simply have been chosen to make all of the zodiac signs appear on the viewable side of the strip. Some additional ancient images of the ourobouros or figure-eight-shaped ornaments are said to depict Möbius strips, but it’s unclear whether they were meant to depict flat strips of any kind.
Independent of their mathematical heritage, machinists have long known that forming Möbius strips on mechanical belts reduces wear by half since the entire surface of the belt is used rather than just the inner surface of an untwisted belt. Furthermore, a belt of this type may be less prone to curling from side to side. This approach was originally described in writing in 1871, shortly after the first mathematical papers on the Möbius strip. Much earlier, a 1206 work by Ismail al-Jazari illustrates a chain pump with a Möbius strip layout for its driving chain. In Paris, seamstresses used this surface in another way (at an unknown time) by instructing beginners on how to sew a Möbius strip as a collar onto a garment.


We are offering a set of smart maths and statistics calculators which are both integrated directly in our search results and also can be accessed via this index. The list is not yet complete but will steadily extended. For the moment the following calculator are available for usage:
Online P-Value Calculator
Helps to obtain a p-value immediately from a Chi2 and NDF. The p-value will also be automatically translated into a significance in units of sigma.
P-Value from Chi2 and NDF
Translates any p-value into a significance in units of sigma.
Significance from P-Value
Poisson Distribution Calculator
Allows you to obtain a probability from any poission distribution.
Probability from Poisson Distribution
More smart tools will follow soon!


Financial options have an intrinsic and a time value. The intrinsic value for a call option is simply the spot (S) minus the strike price (X). The time value of the call option can be derived using the Black-Scholes formula. The resulting price of the option minus the intrinsic value of the option results in the time value of the option.
The following graph illustrates the intrinsic value (red line), the price of the option (grey line) and the time value of the option (dark grey area).
Using the following code you can replicate the figure:
In every finance class, one of the first topics students are confronted with is the efficient frontier. Even though the intuition behind the efficient frontier might be easy to grasp, I show you that it can also be very easy to derive the efficient frontier – even using multiple assets.
Using the following code you can replicate the image:
stocks <- c("TSLA","AAPL", "FB")
x<- dailyReturn(TSLA) y <- dailyReturn(AAPL) z <- dailyReturn(FB)
g <- as.data.frame(cbind(x,y,z)) a <-as.data.frame(cov(g[2000:2620,]))
Writing a financial paper is often associated with an OLS regression model. One major issue can be heteroskedasticity: the variance of the error terms vary. I show you how you can detect heteroskedasticity and how to implement robust standard errors in R.
Step 1: Implement a regression model in R
model1 <- lm(dist ~ speed, data=cars) # initial model using car data
Step 2: Detect heteroskedasticity using the Breush Pagan Test. When the p-value is below the 10% we can reject the null hypothesis that the variance of the residuals is constant.


Tutoring programs for students
We know that learning continues outside the classroom and that students and parents need access to resources.
The Ontario government and its partners offer tutoring services for students to help them succeed.
Homework Help is free, real-time math tutoring by certified Ontario teachers available to students in Grades 7 to 10 in all English-language school boards. Students have access to live, interactive online math help funded by the Ministry of Education. This program is password protected and not available to the general public.
TVOKids Homework Zone
Homework Zone is a TVO segment that invites students to call or email questions to a teacher who provides answers, solutions and tips on air. The focus of the segment is on literacy, math and science, and an archive of the videos is made available online for students, parents and educators.
SOS Devoirs, which is operated by TFO, provides tutoring services and educational resources such as dictionaries and multimedia learning objects to French-language students from Grades 1 to 12. Students can get help in any subject matter from specialized teachers via chat, by phone and by e-mail. SOS Devoirs' tutoring services are available Monday to Thursday, from 3:30 p.m. to 9 p.m., during the school year.
Tutors in the Classroom
The Tutors in the Classroom initiative assists school boards in hiring post-secondary students enrolled in Ontario colleges and universities to work as tutors in JK to Grade 6 classrooms. The tutors support the work of classroom teachers by working directly with students to reinforce previously taught literacy and numeracy concepts and skills.
Ontario Focused Intervention Partnership Tutoring
OFIP Tutoring supports school boards in initiating or extending programs that help students in Grades JK to 6 to strengthen their literacy and numeracy skills beyond the regular school day. This includes programs such as before and after-school tutoring, homework clubs and cultural programs that focus on literacy and numeracy skill development. Partnerships with existing community-based programs that provide tutoring for students are encouraged.
Most often when you ask students about their favourite school subjects, math isn’t something you’ll typically hear. Why is that? Math is used in almost everything we do, yet it is one of the most feared and struggled with subjects in school. Extra help is often recommended for struggling students but finding a qualified yet affordable mentor is not so easy. Math tutoring has an infinite list of benefits but in today’s expensive world, it is not an option for most.
Fortunately, Homework Help provides FREE online math resources available 24/7 and FREE 1:1 live tutoring with an Ontario Certified Teacher 5 days a week: Sunday-Thursdays 5:30pm-9:30pm ET.
Homework Help is funded by the Ontario Government and administered by TVO’sIndependent Learning Centre. The program offers FREE online tutoring to Grade 7 to 10 students in 60 English public school boards in Ontario. In addition, the website has a collection of over 250 videos, tutorials and pre-recorded presentations available to students online at any time. Students can access all of this and more by creating a free account. Students can register at homeworkhelp.ilc.org using their Ontario Education Number and their date of birth.
This online math haven allows students to get help after school hours, when teachers or parents are unavailable to help. It also acts as a great resource for teachers, as they can incorporate the lessons available online and helpful tools into their classroom. We sat down with Isha Seth, the Client Relations & Outreach Officer for Homework Help and chatted about this fantastic educational resource.
How does Homework Help encourage collaboration?
We encourage each tutoring session to be approached as a collaboration – with the tutor providing leading questions and the student working through various strategies and approaches to the topic. Not only can students engage with a tutor, they can watch other student’s and learn from their strategies, approaches and successes. At any time a student observer can tag a session to their own digital locker for future learning.
What are success stories you have had from your project?
We’ve received some great success stories from students, parents and teachers! We have received testimonials from our students crediting Homework Help with the increase in their marks, confidence and for their improved understanding. One user had asked over 150 questions in our Ask A Tutor chat and reported a 30% jump in their marks over the school year. We’ve also received feedback from parents who express gratitude for the extra help we provide their children. For parents, it’s difficult to remember some of the math concepts their children are exploring now since many of them learned the same material ages ago. Imagine the amount of stress having to teach your child something you don’t remember! Homework Help provides comfort to parents by providing the math help their children need. All of our tutors are Ontario Certified Teachers, so they are familiar with the curriculum and the employ differentiated instruction to help every student reach their math potential.
How do you encourage problem solving conversations on the site?
Every homework question is an opportunity for a math conversation! Tutors encourage students to explore a question in a format that makes sense to them. The student and tutor are able to converse through the chat or try different approaches on the whiteboard sharing ideas and experiences that culminate in a rich learning experience for each student.
Reading is an important factor in mathematics instruction. How does your site improve literacy of students while solving math problems?
Our tutors don’t shy away from using numerical terminology and stretching our students’ understanding of mathematical terms and the context being described in their questions. Our Glossary is accessible from within the chat, enabling students to look up terms they are unfamiliar with and take ownership of their own understanding. Often the majority of a session will be spent interpreting and working with the wording of a question, and then the math begins!
How do you train your tutors?
All of our Homework Help tutors are Ontario Certified Teachers. Every tutor is trained to use the chatroom to engage and empower students to tackle their math homework. Practices used in the classroom are brought into the chat room to ensure the consistency of instruction.
What are other sites or services do you offer?
Homework Help is administered by TVO’s Independent Learning Center (ILC). The ILC offers a wide variety of online distance education courses , GED testing programs and also offers Ask A Teacher, another free online chat for grade 11 and 12 students for math, english and science! All of these great services can be found on www.ilc.org.


Dear 100 Hour Board,
How much cheese have you eaten in your life? Answers to be as scientifically accurate as possible, please.
-I'm serious. This is a serious question. Seriously.
Dear Totally Serious,
First, let's consider time as a continuous medium, and measure cheese in terms of time it's taken me to ingest it. But let's also reorder the times in which I've been ingesting cheese in the following manner: divide the total time I've existed (which, if you believe in the Church of Jesus Christ of Latter Day Saint's theology, is the same amount of time as the universe) into thirds recursively, collecting the third points and saying those are the only points at which I have eaten cheese.
Note I have just created a bijection with the Cantor set. Thus, I have been eating cheese for an uncountably infinite number of points, yet the total collection of time over which I've been eating cheese is of measure zero.
So there you go: infinite cheese, but the amount of cheese is zero.


If you need to calculate the area of an odd-shaped room, simply follow these steps:
If you plan to paint the trim a different colour, calculate these areas separately. Simply multiply the length by width of each trim then add your totals together.
A skirting board area is its height multiplied by its length (which is generally the same as the perimeter of the room).
Estimating time brings in a new set of variables. In 1 hour, you're likely to cover about 7 square metres of an ordinary surface, or about 5 square metres of bare wood or plaster.
You'll probably be able to paint that 4m x 5m room with one coat in 5–6 hours. If you apply 2 coats, you must allow time for the first coat to dry. Allow 4 hours for water-based paint and overnight for oil-based paint (check the paint can label). You can safely estimate 2–3 days to paint a room and clean up afterwards.


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These Printable Number Flashcards are perfect for kids of all ages! These number flashcards go from 1-100 and can be used as flashcards, a matching game, or as the classic game of Go Fish!
Printable Number Flashcards
These printable number flashcards are so colorful, bright and fun for kids of all ages! A few weeks ago I was on the hunt for some flashcards that I could use to help my son get more familiar with all his numbers, including numbers past 20. In my search I couldn’t find any flashcards that went all the way up to 100 without being double sided. I wanted to find flashcards that I could use in more ways that just one. Learning is more fun when you make a game out of it and we wanted to be able to play a matching game or the classic game of “GO Fish” but you can’t do that when the cards are double sided. 🙂
So after searching and not finding what I was looking for we decided we needed to just take care of it ourselves. I absolutely love how these number flashcards turned out and I am excited to share them with you!
This post contains affiliate links.
How can I protect my printable number flashcards?
We decided to laminate our number flashcards so that we could continue to use them without them getting damaged. You will want to print out your number flashcards and then cut them out using scissors or a paper trimmer. Follow your laminator instructions to complete the cards. We cut our cards out first and placed them an inch or so away from each other to ensure the cards would be fully covered with the laminator sheets. Don’t have a laminator at home? Just take them to a local store that has a laminating service.
Three ways to use Number Flashcards
- Just like regular flashcards – Once you laminate your cards you can punch a hole into the top corner of each card and put them on a ring for easy review. You can put all your cards on one ring or separate them into amounts that work best for you! You can even put even numbers and odd numbers on different rings, add them by 5’s or by 10’s, add numbers as you need them. It’s flexible with the needs of your own child.
- Classic Go-Fish Game – one of the first games my kids learn how to play is Go-Fish! It’s great for number recognition while also learning to sit still. NOTE* In order to play GO-FISH you will need to prepare TWO sets of flashcards. While it’s a bit of work in the beginning you will be able to use them over and over again!
- Matching – another game that is great for number recognition but also for memorization. Even little ones that don’t know any of their numbers yet can still play as each pair of cards also has a matching clipart.


A friend of mine recently proposed the following problem on twitter: Given f y z =108 – (815 – 1500/z)/y, x0 = 4, x1 = 4.25 and xN+1 = f xN xN-1 then what is x80? Note: This might not be as easy as it looks — Mårten Rånge (@marten_range) October 19, 2013 I didn’t…Read More Round-offs in floating-point arithmetic
For those that attended my last evening presentation about F# at Ronua Roadshow in Timisoara (but not only), here is the demo I’ve shown, and one that I planned to show but didn’t due to lack of time. The purpose of these demos was to shown simple Windows Forms applications written in F#. Mandelbrot Fractal…Read More Resources for the F# Presentation at Ronua Roadshow
In this post I want to show how you can implement common list operations: union, intersection, difference and concatenation. Concatenation is the simplest of them all, because type List already has a function call append that does everything for you.
let concat left right =
List.append left right
The union of two lists is a list containing all the distinct elements from…Read More F# Operations on List
The Game of Life is a cellular automaton devised by the John Horton Conway in 1970. It is the best-known example of a cellular automaton. It consists of a collection of cells which, based on a few mathematical rules, can live, die or multiply. Depending on the initial conditions, the cells form various patterns throughout…Read More Game of Life in F#


|Submited By: D. G. Shands on 01/15/2007|
I love the fact that this calculator puts the equations in the form they are learning in school. You actually get to see the equation, not just the answer. AND it shows the dividing "bridge" in division, not the dash with dots over/under it.
I think it helps my son see the equations in a form that is meaningful because it s how his teacher does it & how it is on his homework. He s 6 & thinks it is fun to just sit around & practice with equations, testing himself before he hits equal for the answer. Glad I bought it.


I have been taking a MOOC called How to Learn Math. The course is for teachers, homeschoolers, parents, and anyone else involved in teaching children math. I'm taking it because I have a son who delights in math, and as a homeschooler I want to be sure I'm never the one to take that joy away from him. What I love about these courses is their flexibility. You can engage at whatever level you have time for or interest in. What you get out of it depends entirely on what you put into it.
The first session was quite interesting. There was a lot of discussion about the math anxiety so prevalent in our society and the negative messages we pick up (and pass on) about math. It really made me think about my own education in math, and how it has affected my attitudes towards math. Lockhart's essay A Mathematician's Lament has been incredibly thought-provoking for me since Alice (our PEI resident homeschool math expert) first introduced me to it back in May, and I'm so glad the course included it. I think I can safely say that though I don't agree with everything in it, it has completely changed my perspective on math.
Here's a copy of one of my assignments for the course: a concept map.
I was rather fortunate that my childhood experience in math did not leave me with a fear of math. Other than the fact that all the drill was frustratingly boring in the elementary years (pages and pages of long division, ugh!), I did well and got good grades. Then high school came, and algebra and geometry were introduced. I loved these. (for all the wrong reasons, according to Lockhart. I think maybe he could have been more open to allowing us non-creative logical/analytical type thinkers to enjoy math in our own way. Not that I don't wish that I had more training in problem solving and creative mathematical thinking as he describes it.) Though I did well with math as a child, there was no joy in it, no exploration and discovery, no creative problem solving. It was all a matter of being a "good student" and following directions well.
And yes, I did think I was smart because I could "do" math. I remember telling Stephen about an incident where my younger sister, who did not enjoy algebra the way I did, exclaimed in frustration "But why?" I replied, "It doesn't matter why. It's like a puzzle...just go through the steps and you'll get the right answer." Stephen was shocked by my reply..."You mean you did it all without understanding it?" And yes, I guess I did. He described how he could visualize a problem, which was a totally foreign concept to me (I am so not visual. I don't even understand being a visual thinker. The closest I come is the way I can usually tell how a recipe is going to taste when I read a recipe.). So maybe I'm not as smart as I thought...
Lockhart's music analogy really spoke to me. When I was a young child, we had an organ in the house. My mother taught me the bare basics of reading music, and from then on I was on my own. I played with the organ all the time. I learned to play hymns quite fluently, though I always thought the ones without sharps or flats were the easiest to play. I can remember figuring out that I could play anything I wanted without using black keys by simply moving my hands up or down the organ from where the written notes indicated I should play. I worked out a whole system where I counted the sharps or flats and figured out how many notes up or down I had to play to get into the key of C. Of course, I knew nothing at all about keys...I just knew that if I did this I could play without using black keys. I can still remember the moment when my "cheating" was discovered. I think my guilt that I wasn't playing it "right" the way it was written colours my memory of the experience. More likely the girl who found me out was simply surprised that I was confidently playing in a key other than what was on the page in front of me. At one point, my parents decided to give me organ lessons. They took me every week, then watched as my interest in playing dropped to near zero. Wisely, they stopped the lessons before permanent damage was done. Later, as a young teenager, I bought my own piano. I played and played, and gradually got better at it. I met someone who could play by ear, decided to learn how to do that, and did. Perhaps I would have learned more if I had had lessons. I could have learned to use the right fingers on the right keys. I could have gained some fluency if I had practiced some scales. But as it was, every minute of playing the piano was purely for the enjoyment of it.
So what's my takeaway for math? Because of my "unschooled" experience with music, I believe that unschooling in math could have its advantages and disadvantages. The biggest advantage (and this is huge!) is that, given the right resources and challenges, the joy of discovery and learning is never quenched. The disadvantage is that without disciplined application at the right time, children may not gain the fluency and facility that would enable them to continue to discover and enjoy at a higher level. On the other hand (as Lockhart expressed so well in his essay), the "drill and kill" method so common today is much worse. Even when it is "successful" and children do well according to the tests they take (as I did), they may never explore the wonder of the order and patterns that God built into His creation and gave us the ability to appreciate and enjoy. They may never experience the joy of successfully figuring out a challenging and complex problem. I did not, but now I am so looking forward to discovering all that is wonderful about math and to passing it on to my children.
I believe the approach expressed in Charlotte Mason's philosophy is the best. "Education is an atmosphere, a discipline, a life." It is also a "science of relations" (Lockhart spoke of that, too, when he referred to the importance of historical context in the study of math.). Unschooling emphasizes the atmosphere and life, Classical education emphasizes the discipline, but I think Charlotte Mason brings a needed balance to both.
How do I see this working in my home? SA's natural enjoyment of numbers and measurement is what first set me on the path of finding a better way of teaching math, one that would not take away his joy. First, I will try to provide an atmosphere in the home that fosters learning. This is a bit difficult for me when it comes to math, given my own experience and gifts (or lack thereof -but at least I'm still learning!). I have found that a book like Family Math can be a real help if everyday math situations are not your strong point. I want to provide a rich variety of resources and challenges that will continue to stimulate SA's interest. I also want to teach him the discipline of taking on a difficult challenge and persisting until it is solved. Of course, we are just starting out. I'm sure real life will give me a lot more insight than I have now! This course is looking promising, too.
So there it is...long and rambling and only a fraction of all I've been thinking about lately. How would you describe your math experiences as a child? How did they affect the way you feel about math today? If you're taking the course, has it given you any insight or sparked any thoughts so far?


Factors Affecting Insulation Batt Quantity
- Area to Be Insulated: Calculate the total square-foot area for accurate estimation.
- Desired R-value: Determine the recommended R-value based on your climate and energy efficiency goals.
- Insulation Batt Size: Batts come in various sizes; ensuring compatibility is vital.
Calculating Insulation Batts Needed
The formula to calculate the number of batts required:
Number of Insulation Batts=Total Area / Area Covered by One Batt
For example, for a 1000-square-foot area and 100-square-foot batts:
Number of Batts = 1000/100 = 10 batts
Estimating Based on R-Value
Consider the R-value to determine the thickness required for proper insulation:
- Higher R-Value: Higher R-values might need thicker insulation batts for adequate coverage.
- R-Value Per Inch: Different insulation types have varying R-values per inch, affecting the quantity required.
Recommended Insulation Batts
- Ceiling vs. Walls: Differentiate between ceiling and wall insulation, each requiring a distinct estimation.
- Professional Consultation: Seeking guidance from insulation experts ensures accurate calculations for your specific needs.
By understanding your space’s area, desired R-value, and insulation type, you’re better equipped to estimate the number of insulation batts required for adequate insulation.


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Beste online casino forum slot kostenlos spielen - Casinos ausLeave a Reply Cancel reply Your email address will not be published. In general, problems as listed below require a multi-step approach which involves first the analysis and understanding of the problem, then writing out the mathematical equations to be used and finally solving these equations. They were busy planning our next projects. Equiblibrium of particle Problem 3. September 20, - A negative value of the x-component means that the x- component is pointing in the direction of the minus x-axis. Also shown is an orthogonal coordinate system whose axes I labelled x and y. On the other hand, to determine the components of the resultant of several forces Equation 3. Three points of interest: The angle used as argument of the cosine function is always determined by going on an arc from the positive x-axis in counter-clockwise direction towards the force of which you want to determine the x-component. Two computer programs Using the concept of x-, y-, and z-components is also a great way to write computer programs which can tackle generalized problems. Equiblibrium of particle Problem 3. The computer programs can help you nicely with the last step.
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1. Ellipse Noun
A closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it.
The sums of the distances from the foci to any point on an ellipse is constant.
|See Answer||تمہاری شادی کو کتنے سال ہو گئے ہیں|
Circle ellipse in which the two axes are of equal length; a plane curve generated by one point moving at a constant distance from a fixed point.
Bill Broadsheet Broadside Circular Flier Flyer Handbill Throwaway an advertisement (usually printed on a page or in a leaflet) intended for wide distribution; "he mailed the circular to all subscribers".
Closed not open or affording passage or access; "the many closed streets made travel difficult".
Cone any cone-shaped artifact.
It Used of a nonhuman entity; "I don`t like you, that`s it".
Through (of a route or journey etc.) continuing without requiring stops or changes; "a through street".


The periodical publishes papers on modern topics of contemporary natural sciences: mathematics, mechanics, informatics, computing sciences, physics, materials engineering, nanotechnologies, teaching methodology and history of natural science, and related sciences.
Accepted for publication by Council of V.N. Karazin Kharkiv National University (minutes № 5, 28.04.2014)
All the articles are peer-reviewed and checked for plagiarism.
Ukrainian registration number №20344-10144Р from 12.08.2013
©V.N.Karazin Kharkiv National University, 2014


Boost Your Child’s Math Skills with Fun Math Games
Boost Your Child’s Math Skills with Fun Math Games: A Step-by-Step GuideAs a parent, you need the best for your kid. Furthermore, one of the primary abilities you can assist them with creating is their numerical abilities. Math is a crucial subject that establishes the groundwork for the overwhelming majority of different disciplines. It helps youngsters create decisive reasoning, critical thinking, and logical abilities.
However, can we just be honest? Math can be a complex subject for sure for kids. That is where fun numerical games come in. They can make learning math charming and draw in offspring, all equal. In this article, I will tell you how to help your kids develop their numerical abilities with fun number-related games.
The Significance of Math Abilities in a Youngster’s Turn of Events
Math is a fundamental subject that assists kids with creating numerous abilities they will require throughout their lives. Math abilities go past the homeroom and apply to regular day-to-day existence. For instance, math abilities assist youngsters with overseeing cash, measuring elements for cooking, and ascertaining time and distance.
Also, math abilities are significant for some callings, like designing, software engineering, and money. By assisting your kid with fostering their numerical skills, you are setting them up for a compelling future.
How Fun Number-related Games Can Upgrade Learning
Kids love messing around with. At the point when games are instructive, they can improve learning while at the same time making it agreeable. Fun number-related games can assist youngsters with mastering math ideas and abilities in a fun and locked-in manner.
Fun numerical games can likewise assist kids with creating significant fundamental abilities, for example, decisive reasoning and critical thinking. At the point when youngsters play math games, they figure out how to examine issues, recognize examples, and track down arrangements. These abilities are fundamental to progress in solving numerous everyday problems.
Advantages of Integrating Fun Number-related Games into Your Youngster’s Daily Schedule
Integrating fun number-related games into your youngster’s standard has many advantages. To start with, it assists kids with fostering an inspirational perspective on math. At the point when youngsters consider math to be fun and connecting, they are bound to appreciate learning it.
Second, fun numerical games can assist youngsters with building trust in their number-related capacities. When youngsters prevail at math games, they feel a sense of achievement, which can help boost their confidence.
Third, fun numerical games can assist youngsters with creating interactive abilities. Number-related games expect youngsters to cooperate, which can help them figure out how to convey reality and function collectively.
All Kinds of Fun Numerical Games Accessible at Various Age Gatherings
There are many kinds of fun numerical games accessible for various ages and gatherings. Here are a few models:
For preschoolers, math games ought to be essential and straightforward. Here are a few models.
Counting games: Counting games can assist preschoolers with figuring out how to count and perceive numbers.
Shape games: Shape games can assist preschoolers with figuring out how to distinguish and name shapes.
Design games: Design games can assist preschoolers with figuring out how to perceive and make designs.
For primary and younger students, math games can be more complicated. Here are a few models:
Math games: Math games can assist kids with learning expansion, deduction, augmentation, and division.
Table games: Table games, like Restraining Infrastructure and Chess, can assist kids with mastering systems and critical thinking abilities.
Web-based games: Numerous web-based numerical games can assist youngsters with mastering math abilities in tomfoolery and connecting ways.
Center and Secondary School
For center and secondary school understudies, math games can be more tested. Here are a few models:
Rationale puzzles: Rationale puzzles, for example, Sudoku and Crossword puzzles, can assist understudies with creating decisive reasoning abilities.
Math-based computer games: Math-based computer games, like Numerical Blaster and DragonBox, can assist understudies with learning math ideas in tomfoolery and connecting ways.
Math rivalries: Math contests, like Number-related Olympiad and MathCounts, can assist understudies with developing critical thinking and insightful abilities.
Methods for Presenting and Executing Fun Number-related Games Actually
Presenting and executing fun number-related games requires some preparation and readiness. Here are a few hints to assist you with getting everything rolling:
Pick age-fitting games: Ensure the numerical games you pick are reasonable for your kid’s age and ability level.
Make it fun: Ensure the games are charming and locked in. If youngsters aren’t having some good times, they won’t have any desire to play.
Integrate games into day-to-day schedules: Integrate math games into your kids’ daily programs, for example, before sleep or supper time.
Mess around with your kid: Messing around with your kid can help them acquire and foster significant interactive abilities.
Reward achievement: At the point when your youngster prevails in a numerical game, reward them with acclaim or a little award. This can assist with supporting their certainty and inspiration.
The most effective method to Make Learning Math Fun and Drawing in for Your Youngster
At last, here are a few extra tips on the most proficient method to make learning math fun and drawing in for your youngster:
You can use genuine models: Simple models, like estimating elements for cooking or working out distances, to help your kid see the reasonable uses of math.
Use innovation: Use innovation, for example, math-based applications and internet games, to make learning math more tomfoolery and intelligent.
Make it a game: Transform numerical statements into a game by timing your youngsters or provoking them to tackle issues quickly.
Show restraint: Learning math takes time and exertion. Please be careful with your youngsters and encourage them to continue.
All in all, fun number-related games are an excellent method of helping your youngster develop numerical abilities. They can make learning math pleasant and connecting while likewise assisting youngsters with creating significant fundamental skills. By following the means illustrated in this article, you can help your kid foster an uplifting outlook toward math and set them up for a fruitful future.


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March 4, 2021
The latest A-Levels and IGCSE exam results are out — and UAE students got ‘impressive’ scores, school heads reported on Thursday.
Students in Years 11, 12 and 13 received either final grades or modular results on Thursday across subjects like Arabic, English, biology, chemistry, physics, geography, mathematics and statistics. These results (A-Levels and AS-Levels) can be used for getting into universities in the future.
The UK government cancelled the usual GCSEs and A-level exams this year because of Covid-19 restrictions, so several international boards held modular exams in January for IGCSEs and international A-levels.
Two Brighton College Dubai pupils achieved a 100 per cent Grade 9 (A*). Simon Crane, headmaster of the school, said: “I am incredibly proud of the achievements of our first GCSE pupils who have exceeded their targets. Given the worldwide exam uncertainty, this year has been a demanding one and we do not underestimate the amount of effort that has been required from both pupils and teachers who have had to adapt to a fluid learning style.”
IGCSE is equivalent to the GCSE qualification for which students appear in the exams in Years 10 and 11, while an A-level is a qualification offered across different subjects to students in Years 12 and 13.
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An exciting offer for serving and returning secondary teachers who are moving into teaching mathematics, but do not have a previous mathematical qualification. It will enable staff to develop a deeper knowledge and understanding of all aspects of mathematics.
St Helens TSA has successfully run this programme since 2014-15 with a total of 62 delegates completing the training programme. This innovative Maths Subject Knowledge Enhancement (TSST) course is delivered in partnership with experienced staff from Rainford High School working to support the maths hub alongside extremely experienced staff from Liverpool Hope University.
Please see this flyer for more details: Mathematics_Teacher_Subject_Specialism_Flyer_STH_April 2018
All school based sessions will be delivered at Rainford High School.
If you are interested in attending please follow the link on the flyer to express and interest or register.
This programme is FREE of Charge.
Director of the St Helens Teaching School Alliance and NW Maths Hub 3
Director of School Improvement- Three Saints Academy Trust