Marvin the Paranoid Biological Android
The String Theory Rabbit Hole
It was while thinking about Roger Penrose and some of his interesting patterns, polynomial reflective properties, inter-dimensional frequencies and parallel Universe existence in a six dimension cylinder construct in groups of ten that it struck me that Super-string theory was a complete waste of time other than opening of a window into pan-dimensional parallel Universes.
It became crystal clear to me while dwelling on it a bit too much that we have been thinking about multi-dimensional constructs in completely the wrong way.
All of the science and math theory ends up contradicting the other and no sooner does a proof come along than another branch of science makes a total mockery of it.
A calculation proof in the reverse should also apply and if it does not you are simply barking up the wrong tree kind of thinking seems to cloud our knowledge aspirations.
This works well in the same domain, but the minute we try and rationalize Quantum realms with pure mathematics we run into problems. Big problems....
A math formula in reverse to check the proof and thinking is sound is great but when you try and make celestial mechanics work with choice components and pieces and leave out others, you will have a few issues.
Quantum mechanics in this instance is the proverbial spanner in the works.
The conventional thinking is that Quantum mechanics should be a mirror of celestial mechanics but it clearly does not mirror such in any way.
I have been looking into what led us to believe that it is or should be.
If you think about it, expecting solar systems and galaxies to behave the same way as atoms and their components do is a trifle over-simplistic.
The thing that does not follow logic for me there is we all know the charge and electrical properties of protons and neutrons etc. factor in but for planets and suns suddenly its not relevant?
Why they then break with this thinking and just take gravity into account and ignore the electrical and magnetic properties of celestial bodies is baffling to my sole surviving synapse.
Nobody worries about gravity in calculations involving protons and neutrons. They do worry about the electrical charge properties though.
Why is the electrical and magnetic properties of a planet ignored when working out its movements? What is the relationship between gravity, electrical charge and magnetic flux?
Academia at large should have paid more attention to Nicola and what some of his electric motors were doing with the magnetic field side of the equation.
Even today this stuff is mostly overlooked and ignored.
One can look at a simple triangle and postulate and determine all sorts of proofs mathematically about it in 2D and 3D and tie it all up very neatly in a bow and everything is wonderful with trigonometry and our thinking about basic shapes et al.
We can even expand the math theory into ten dimensions with no problem.
When you start introducing frequency and multi-dimensional constructs with theoretical math and start introducing gravitons and electro-gravitic theory into the trigonometric picture, things start to fall apart very quickly.
The conclusion I have come to looking and attempting to understand all of this is that our fundamental understanding of the structure of matter, the macrouniverse-cosmology and the macrouniverse-Quantum view with the microscopic views is based on the theory we supposedly understand them intimately and that they follow the same laws and principles.
Clearly, we do not understand this well enough and there are clearly different laws that bind each domain.
My conclusion is that our expectation that one set of laws apply to everything in the micro and Quantum Realm as well as the cosmological realm is where the train hurtles off the track in a spectacular fashion.
If you examine gravity and space time for example without taking gravity into the equation Einstein's theory of relativity pops out and all that math makes perfect sense.
In the reverse if you apply string theory math to quantum mechanics and discount gravity string theory neatly morphs into quantum theory.
The problem is string theory offers no evidence from measured data, experiments or observations to support it in any way.
Mathematics only evidence has in fact driven many a physicist completely insane and in truth to get deep into this stuff you need to be a little insane yourself.
I dream math equations and that is centered around polynomials and the math of reflections in particular which builds up to Penrose Patterns in a sort of super-trigonometric fashion.
I cannot explain why I do it, I just do. It has eye popping possibilities in the field of chemistry.
There is something rather fundamental and beautiful about the symmetry of polynomials that I feel is the key to unlocking the door that is standing between us and understanding how it all works.
I sometimes wake up from this polynomial dreamscape feeling I perceived the entire Universe with breathtaking simplicity.
Dragging the clarity back from the dreamscape into our real-world reality has proven most elusive though.
Sometimes it does happen but with things not related at all to what I am trying to puzzle out.
This was how I fell into Chess and AI actually.
I often play entire tournaments spanning hundreds of hours in a single dream session and kind of lie there in a semi-REM state while doing it.
Not awake and not asleep.
I once did this for three days and spent the next three days executing proper sleep to recover from it.
That kind of sleep is very exhausting indeed!
However, the pattern I came up with doing this got me to winning my first few Chess tournaments.
This also happened at the same time I left ePlus and went to Accelstor in 2018.
It was probably my most creative period ever.
Obliquely enough I have found the current turmoil in political matters has led me to dreamscapes that focus on my Quantum correlations I have been attempting to understand as an amateur dabbling in a new field for these past 22 years.
It seems a distraction of X is leading me to solve problem Y so to speak.
I awoke the other morning after a similar semi-REM session all night around the correlation of relativity, Quantum realms and Roger Penrose merged with string theory but I was focused on freedom of speech and other political expression challenges of the current era we find ourselves in as I lay there pondering it all and drifted into polynomial math-sleep.
This led me to understand, in my tiny mind at any rate, that the whole string theory thing is a giant rabbit hole and a thorough waste of time.
A Segway to insanity in fact.
Each avenue and realm has its own laws that do not flow into everything else.
The macroverse-Universes and the micro-Quantum Universes do not operate on the same laws and why we think they do is where we have been going wrong.
We need to focus on what gravity is and what electro-magnetics really are and understand they are the missing forces we have been searching for to explain a good few things in physics and math.
We have been trying to run in the Olympics and we cannot even crawl yet.
A classic case of ambition and hope clouding reality via assumption.
Making assumptions seems to cost us a lot of time in fact. Especially when almost every time they prove wrong.
I was mulling over some of Feynman's lectures on Tensor Calculus in curved spacetime when thinking of the Universe as a large torus the other day and realized that the geometry of each event and the interval between events completely determines the geometry everywhere.
In curved space, the dot product of two 4-vectors Aμ and Bμ is:
Aμ Bμ = Aμ Bμ = gμσ Aμ Bσ = gμσ Aσ Bμ =
+ gtt At Bt + gtx At Bx + gty At By + gtz At Bz
+gxt Ax Bt +gxx Ax Bx +gxy Ax By +gxz Ax Bz
+gyt Ay Bt +gyx Ay Bx +gyy Ay By +gyz Ay Bz
+gzt Az Bt + gzx Az Bx +gzy Az By +gzz Az Bz
If dsµ is the separation 4-vector between two nearby events, the invariant interval ds2 between those points is:
dsµ = (cdt, dx, dy, dz)
ds2 = dsμ dsμ = dsμ dsμ = gμσ dsμ dsσ
Here, ds2 is an invariant scalar - it measures the separation between nearby events, and has the same value in any coordinate system.
In Feynman’s sign convention, ds2 equals c2dτ2 where τ is proper time, the time measured by an ideal clock moving between these nearby events.
In 4-D curved spacetime, we only sum repeated free indices if one is covariant and the other is contra-variant.
The difference between the two is demonstrated by the covariant and contra-variant position 4-vectors (in Feynman’s sign convention).
xα = (ct, –x, –y, –z) is contra-variant
xα = (ct, x, y, z) is covariant
The metric in flat spacetime, in Feynman’s sign convention, is:
In polar coordinates, the metric near a black hole in Feynman’s sign convention is:
Here, the gθθ and gϕϕ components are the normal polar coordinate factors, which are unaffected by gravity.
Gravity dilates time and stretches space through the factor Ω=1–2GM/c2r, where G is Newton’s gravitational constant, M is the black hole’s mass, and r is the distance from its center.
Note that odd things happens when Ω=0 at r=2GM/c2, the location of the black hole’s event horizon.
One interesting effect is that the event horizon is timeless — the passage of time has no effect whatsoever on the event horizon, because gtt is zero at that radius.
In the most common modern notation, the metric gμσ has a minus sign on the time component and plus signs on the three spatial components, the opposite of Feynman’s convention.
The Lorentz transformation tensor is:
Here, β = v/c and γ = 1/√(1–β2).
Some typical index operations are:
Lowering an Index: xµ = gµσ xσ
Raising an Index: xµ = gµσ xσ
Lorentz Transform: Xσ = Λβσ xβ
Like other square matrices, the metric tensor for most geometries can be diagonalized, meaning all non-diagonal components can be made zero with suitable transformations.
The invariant interval is then reduced to 4 terms, and the inverse metric is simply gαα = 1/gαα.
Diagonalizing the metric tensor can mix the coordinates in surprising ways.
For example, the time coordinate t and radial distance coordinate r might be replaced by the coordinates u=ct+r and w=ct–r, leaving nothing that represents pure time.
Since the tensor calculus of general relativity works in any coordinate system, such mixing is mathematically valid; it can simplify our calculations even when it defies our intuition.
When one becomes comfortable with tensor notation, it is possible to drop the indices altogether, as we do in vector algebra. We can then write equation (3) as:
X = Λ x
Ramanujan did this simplification quite a lot with much of his work and it is interesting reading books on his proofs on much in math he was not aware already existed.
Actually I think one of the greatest setbacks in human history was the premature death of Ramanujan at the age of 32, some 100 years ago.
NASA uses a shocking amount of his math in various projects these days.
The biggest contribution old one beer (Einstein) made to mankind was not:
It was in fact:
G = 8π T
Here, G represents the geometry of spacetime, and T represents all forms of energy, including mass and momentum.
G is now called the Einstein tensor, and T is called the mass-energy-stress tensor.
Both are symmetric, rank 2 tensors.
We say equations, the plural, because G=8πT represents 16 component equations: 4 describe the conservation of energy and momentum; 6 relate energy density to spacetime curvature; and the remaining 6 are redundant. John Archibald Wheeler said the meaning of G = 8πT is:
“The geometry of spacetime tells mass and energy how to move, while mass and energy tell space how to curve.”
I have been thinking about this quite a bit these past weeks and I am calling BS on it.
The reason why is in the case of a binary star, the theory says they should curve spacetime the same amount each, but we do not see this.
The first aspect of Einstein’s theory of Relativity I will deal with is that space is curved around a massive object.
Therefore, a body in curved space is moving in the direction of that curve.
It feels no force.
But as pointed out by many, there is a fatal flaw described above by Mathis, who elsewhere writes: “The first logical critique I made of curved space was in my article on tides. I showed that tidal theory relied completely on Newtonian forces at a distance [and not on curved Einsteinian space]. This theory is wholly dependent on Newtonian force at a distance . . . An orbiter traveling in curved space would not logically be expected to feel the same tidal forces as an orbiter traveling in a Newtonian orbit . . . “. . .
Once you introduce a second body, say the Moon, it is also warping the space around it [as does the Earth]. The warp around the moon is convex, like the warp around the Earth.
The problem is that the tidal influence is going both ways.
The Moon is supposed to be causing tides on the Earth at the same time that the Earth is causing tides on the Moon.
So is the space between the Earth and the Moon convex or concave? It must be one or the other.
Space cannot curve two different ways at the same time? Maybe it does....
Nor can it be a vector addition of the curvatures.
If two bodies flatten out the curves of the other, they also must flatten out the tidal effects.
The curvature according to Einstein is both mathematical and physical.
If the curve is flattened, the tide is gone.
In General Relativity, the space is the field.
They are the same thing.
Unless Einstein meant to propose that we have an infinite number of gravitational fields interpenetrating each other with no collisions or effects, his postulate [that two bodies such as the Earth and Moon warp space to cause tides on both bodies] is a non-starter.
And if this is the case, there is really no way to assign any or all of these fields to space.
As one can clearly see, the Earth and Moon cannot both curve space to create tides on both bodies at the same time in the same direction.
This, in terms of general relativity, is impossible and illogical.
I want to drive home the point Mathis makes.
To do this, let us examine the orbits of identical twin stars.
These are binary stars that have the same mass. According to Cecelia Payne-Gaposchkin, “Identical twins [binary stars] span the entire main sequence . . . almost all have perfectly circular orbits.”
The concept that bodies orbit one another in warped / curved space must also be explicable here, but it is in fact contradicted here.
Each of the identical twin binary stars are warping / curving space identically around them.
At the midpoint between their orbits, this warping / curving will be cancelled out because they have the same mass.
Neither of these partners should be revolving around the other in the warped / curved space of the other.
Equal and opposite curves cannot reach from one partner to that of the other. So why are they orbiting each other in non-warped / curved space in almost perfectly circular orbits?
There is no curved space enveloping both binaries to allow this to happen.
The stars cannot orbit in their own self-same individual warp / curves.
A single star in space does not and cannot be in such an orbit, according to Einstein, because its own warped / curved space leads nowhere.
Based on this concept of Einstein’s, identical twin-stars should not be orbiting one another.
The theory breaks down based on its own premises and on the basis of these observations conclusively negate it.
Einsteinians can’t have it both ways.
More evidence the whole of reality as we know it is just an elaborate hologram.
They can’t have two equal and opposite warp / curves affect the orbits of these stars, and at the same time to have these self-same stars orbiting one another as if both were in the warped / curved space.
Brian Greene describes Einstein’s field equations as the choreography of the cosmic ballet of the universe.
It is a duet in which both parties lead one another.
Now if old One Beer, Roger Penrose and his pal Immanuel Velikovsky had spent a bit more time looking at Nicola Tesla and Brown's work on Gravity, electric fields and magnetism.......
If we go back to One Beer's famous calculation I think the M (mass) part needs some work to include Gravity, Electrical charge and magnetic flux as just M is far too simple of a generalization to make Universal reality sense.....
But us amoebas don't know much, now do we?? My brother Ian excluded....😂


The National Centre for Excellence in the Teaching of Mathematics is a major initiative funded by the Department for Children, Schools and Families (formerly the DfES) to enhance professional development for mathematics teachers, established in response to the recommendations of ACME (Advisory Committee on Mathematics Education) and those made in Professor Adrian Smith's report 'Making Mathematics Count'. Working with the wider mathematics community, they facilitate, enhance and provide strategic direction and leadership for all aspects of continuing professional development in mathematics.
The aim of Adults Learning Mathematics is to promote the learning of mathematics by adults through an international forum which brings together those engaged and interested in research and developments in the learning and teaching id adult mathematics (here understood to include numeracy). The group comprises both researchers and adult education practitioners; it organises and annual conference, and produces a regular newsletter an international web-based journal.
The Advisory Committee on Mathematics Education is an independent committee, which acts as a single voice for the mathematical community, seeking to improve the quality of education in schools and colleges. It advises Government on issues such as the curriculum, assessment and the supply and training of mathematics teachers.
The Association of Mathematics Education Teachers is specifically for those teaching on both primary and secondary initial teacher education courses in the UK. It holds an annual day conference and produces a journal called Mathematics Education Research.
The Association of Teachers of Mathematics exists to bring about improvements in the teaching of mathematics and its applications, and to provide a means of communication among students and teachers of mathematics. It supports the teaching and learning of mathematics by encouraging the joy of mathematics, developing the understanding of how people learn mathematics, sharing and evaluating teaching and learning strategies and promoting new ideas and possibilities. It produces two journals, 'Mathematics Teaching' and 'Micromath' as well as holding an annual conference and day courses.
Links to discussion papers, case study examples, research articles and ideas for practice in mathematics.
The British Society for Research into Learning Mathematics is a major forum for sharing research in mathematics education in the United Kingdom. It provides a supportive environment for both new and experienced researchers to develop their ideas. Members' interests include the teaching and learning of mathematics, mathematics assessment, mathematics curriculum development and mathematics teacher education and professional development across the full range from pre-school to further and higher education. They organise three day-conferences each year and produce publications including occasional monographs and an annual collection of reviewed research papers.
An article ‘Starting as a Researcher in Mathematics Education’ is available online.
The British Society for the History of Mathematics principal aims are to promote research into the history of mathematics at all levels and to further the use of the history of mathematics in education. Its web site includes a comprehensive gazetteer of places in the UK with information about where mathematicians were born, lived, worked, died, or are buried or commemorated. There is also a useful links page to web sites containing material relevant to the study of history of mathematics and information about sources of further information in this area.
The Conference of Heads of Departments of Mathematics is the body that represents UK departments of Mathematics and Statistics by co-ordinating senior members of these departments. It is committed to advancing educational opportunities in the Mathematical Sciences, and to ensuring the academic well-being of the disciplines of Mathematics, Statistics and Operational Research, as they are taught and developed within Higher Education.
The Edinburgh Mathematical Society was founded in 1883 for “the mutual improvement of its members in the Mathematical Sciences, pure and applied” and is firmly established as the principal mathematical society for the university community in Scotland. Its membership is drawn from all the Scottish universities and other educational institutions as well as from mathematicians in industry and commerce both at home and overseas. It provides a range of support and information particularly for those working in Scotland.
The Further Mathematics Network is a new DfES-funded initiative to establish 40-50 regional Further Mathematics Centres across England. The primary functions of these Centres are to set up and provide teaching and tutoring of Further Mathematics AS/A-level to students in schools and colleges that couldn't otherwise offer it and to support students and teachers in schools and colleges that do teach Further Mathematics. Each Centre will also have a role in promoting Mathematics in general by organising initiatives to help attract more students into post-16 Mathematics, and a responsibility to support the CPD (Continued Professional Development) of teachers, to help them teach Further Mathematics in their own schools and colleges.
The Institute of Mathematics and its Applications is a professional and learned society for qualified and practising mathematicians. The IMA Education Services Area (ESA) is active in promoting mathematics education at secondary and tertiary levels. The society produces a range of journals including Teaching Mathematics and its Applications for secondary and tertiary mathematics teachers.
The Joint Mathematical Council of the United Kingdom serves as a forum for discussion between societies and works to promote the advancement of mathematics and the improvement of the teaching of mathematics at all levels from primary to higher education. One of its activities is to organise The British Congress of Mathematics Education which aims to provide a unified view of mathematics education, provide a forum for discussion of relevant issues and to help in preparation for the International Congress of Mathematics Education.
The London Mathematical Society was established for the promotion and extension of mathematical knowledge. The Society has an Education Committee, which supports a wide range of activities within mathematics education.
The Mathematical Association is a major professional association for those involved in mathematics education. Its membership includes teachers from primary and secondary schools, further and higher education, advisors, inspectors, practising mathematicians and students. It was formed in 1871 and works to improve mathematical education. The MA publishes a range of journals, books and reports. It also supports a number of meetings, conferences and professional development opportunities.
Mathematics in Education and Industry is an independent UK curriculum development body, covering the age range 11 to 19 and beyond. MEIís major activities include:
- Responsibility for specifications at GCSE, AS and A level (serviced by OCR);
- Provision of textbooks covering year 7 up to Further Mathematics;
- Continuing professional development of mathematics teachers;
- Provision of extensive on-line learning facilities;
- Contributing to national discussions about the mathematics curriculum an education.
The membership of MEI consists almost entirely of working teachers.
The National Association for Numeracy and Mathematics in Colleges is an association of further education, tertiary and sixth form colleges formed in 1993 with the aim of assisting colleges nationally in developing quality in all aspects of their work in mathematics and numeracy.
The National Association of Mathematics Advisors is for advisors, inspectors and consultants in school mathematics education. It aims to ensure that inspection, advice and support, individually and collectively, make an effective contribution to mathematics education and holds an annual conference as well as having a regular newsletter.
The NRICH project aims to enhance the mathematics experiences of school age students by giving them the opportunity to explore and engage with mathematics activities. It also aims to research and develop the use of technology and to contribute to national and international debate about the teaching and learning of mathematics. The web site is a rich source of challenging ideas offering a resource both for teachers to use and for direct pupil use. Other parts of the project provide discussion boards and email lists both for teachers and pupils as well as events and training.
The Operational Research Society aims to encourage awareness, learning, practice and research in OR - the discipline of applying advanced analytical methods to help make better decisions. The Society has an 'OR in Schools' task force which hopes to raise awareness of OR in those studying mathematics and to provide materials to support decision mathematics modules.
This site is primarily for those who prepare students to take A level mathematics and contains starting points for a range of A level topics.
The Royal Society is the UK's independent national academy and represents the British scientific community within Britain and in relations with individuals and groups of scientists throughout the world. The main focus of the education work of the Society is the science and mathematics education of 11-19 year olds through a variety of projects.
The Royal Statistical Society aims to develop, foster and disseminate statistical knowledge, methodology and good practice for the benefit of all society. It has an Education Strategy Group and is concerned with supporting and promoting statistical education.
The School Mathematics Project is an educational charity aiming to improve the teaching of mathematics. It has funded a variety of activities but its main contribution gas been in the production over 40 years of high quality teaching and assessment materials in secondary schools, devised and trialled by teachers.
The United Kingdom Mathematics Trust exists to advance the education of children and young people in mathematics. They organise national mathematics competitions and other mathematics enrichment activities for 11-18 year old UK school pupils. These range from popular Ďmassí maths Challenges to team competitions, forums for teachers and the selection and training of the UK team for the International Mathematical Olympiad. The site includes some sample maths challenge questions to try online and information about teacher meetings.


We apologize for repeat, but as we figure out our new program we had the wrong link for families in this previous post. In order for it to send out again to all we made a duplicate. :)
This year as we will be posting videos that reinforce the concepts we are teaching in class for the week. This will allow you and your child to watch together and have conversations about what they are learning. It also is a great opportunity for you to see and hear the ways in which you could support your third grader at home with their math.
Our first math unit is multiplication and division. We will be teaching this unit through at least the first week of October. The focus is on students developing a solid understanding through models and strategies. This unit lays the foundation for our future units in multiplication and division.
The following videos are concepts we have learned so far. When there is a pause in the video, that is the opportunity for the viewers to stop and talk to solve the problem before hitting play again. Please click on the following links:


Tail risk is a form of portfolio risk that arises when the possibility that an investment will move more than three standard deviations from the mean is greater than what is shown by a normal distribution. Tail risks include events that have a small probability of occurring and occur at the ends of a normal . Tail risk is the additional risk of an asset or portfolio of assets moving more than standard deviations from its current price, above the risk of a normal distribution. Prudent asset managers are typically cautious with tail risk involving losses which could damage or ruin portfolios, and not the beneficial tail risk of outsized gains . Viele übersetzte Beispielsätze mit tail risk – Deutsch-Englisch Wörterbuch und Suchmaschine für Millionen von Deutsch-Übersetzungen.
Nach der Finanzkrise und der Pleite von Lehman Brothers wurden so genannten Tail Risks – das hohe Risiko, das unvorhersehbare Ereignisse mit sich bringt – von Investoren in ein ganz anderes Licht gerückt. Nicht antizipierbare Risiken haben in der Portfoliokonstruktion einen immer höheren . Broadly speaking, a tail risk is an event with a small probability of happening, says Bob Conroy, professor of finance at the University of Virginia Darden School of Business. Definition of tail risk.
Tails are the end portions of distribution curves represented by bell-shaped graphs that show the statistical probability of a measured event. The tails on the left and right of the bell shape represent the least likely outcomes. In investment terms bell curves can be used to plot investment outcomes.
Tails” refer to the end portions of distribution curves, the bell-shaped diagrams that show statistical probabilities for a variety of outcomes.
In the case of investing, bell curves plot the likelihood of achieving different investment returns over a specified period. As shown in Figure in a normal . Masazumi Hattori, Andreas Schrimpf und Vladyslav Sushko. Die unkonventionellen Massnahmen, die in den vergangenen Jahren von verschiedenen Zentralbanken ergriffen wurden, haben nach allgemeiner Einschätzung . It is a measure of volatility and in turn, risk.
For math- oriented readers, standard deviation is the square root of the variance. Englisch-Deutsch-Übersetzung für tail risk im Online-Wörterbuch dict. Tail – Risk im Englisch-Deutsch-Wörterbuch dict. So “left tail risk ” was getting tossed around a lot at the investor conference you attended yesterday.
Reinhold Hafner is CIO of AllianzGI Global Solutions and CEO of its centre of competence for investment and risk advisory, risklab. There has been talk about “ black swans” and tail risks for a number of years. What do these terms mean? In the financial services industry, a black swan describes a very . TAIL Cambria Tail Risk ETF.
The Cambria Tail Risk ETF seeks to mitigate significant downside market risk. The Fund intends to invest in a portfolio of out of the money put options purchased on the U.
There are a number of ways that investors can limit tail risk —including using derivatives or simply choosing sectors that are less. Lowered volatility and high market valuations make it an inexpensive time to implement this strategy, giving investors a hedge with limited time decay. Tail risk it is the risk of an asset or portfolio of assets moving more than three standard deviations from its current price.
Technically, tail risks arise when the possibility that an investment will move more than three standard deviations from the mean is greater than what is shown by a normal distribution (see the chart below).


How far are Kilometers to Centimeters? This is a question many will have asked at one time or another when they are considering the distance between two points on a map. Although most will have come across the conversion’s kilometres to miles, ‘ many may not be aware of it. This article intends to explain what exactly is involved with this simple conversion. It also aims to highlight the main reasons why it is important to convert between these measurements.
First of all, why is measuring distance so important? Most people will have to choose a conversion to measure the distance between two points on a map. Using a different base unit such as meters to Kilometers and centimetres to centimetres, the accuracy of the measurement is improved. By making this small change, the measurement can be more accurate and more precise. For example, if you were to measure your house from one meter to another, then using the metric system, you would get one meter exactly, regardless of how many houses you measured. However, if you were to measure the house from one centimetre to two centimetres, you would receive a measurement of one centimetre, regardless of how many houses you measured.
There are also some important practical reasons you may want to convert units of distance: many athletes and those who train in distance trains to improve their speed and run faster. So if you were to convert between kilometres to centimetres, you would be closer to being able to train at a faster pace and increasing your speed. Those who run or cycle on long-distance courses often need to measure their stride length relative to other runners. This way, they can calculate their average speed relative to other course records.
The only problems with using the metric system for Kilometers to Centimeters is accuracy. This is because the units are not mutually exclusive. They are often used in pairs. If you were to measure the distance from two kilometres to two hundred meters, you could say that the distance was two kilometres and the distance of two hundred meters was considered three kilometres. You, therefore, would get a range that would change as you go further away from the original base unit, rather than being a fixed distance like the centimetre.
Another problem with using the centimetres and the kilometres is that it is very difficult to determine exactly how many kilometres have been covered when you use this method. Even if you convert a distance of one kilometre to a distance of one centimetre, this conversion will not give you a precise estimate of how many kilometres you have covered. This is because the rounding of numbers to the nearest whole number tends to make the distances smaller than they are. Also, some people, especially marathoners, who strive to beat their records, may round their distances to smaller values to cover as many kilometres as possible in the shortest time possible. These practices can give a much more accurate figure, but they can also throw off the conversion accuracy.
In general, if you want to convert between kilometres to centimetres and from centimetres to miles, then you need to use a reliable formula that rounds the result to the nearest whole number. For instance, you can use the formula below: Distance = (meters of Miles * 24) * 3.4 centimetres. Use this formula to convert between kilometres to cm and from centimetres to miles.


Awarded to identified gifted students grades K- 12, who are currently participating in a gifted program and who want to enrich their learning experience during the summer months. The maximum summer scholarship award is $400. Students may use these scholarships to attend programs with an academic, fine arts, or performing arts focus.
A $2,500 scholarship awarded to a graduating GT high school senior who has demonstrated outstanding academic achievement, possesses a strong sense of purpose and clearly defined goals, and has a long-term plan for achieving these goals.
A $2500 scholarship awarded to a graduating GT high school senior who has demonstrated outstanding leadership.
Attend the Summer Mathematics Institute (SMI), a 3-week residential program with an intense focus on mathematics. Sponsored by the Texas Academy of Mathematics and Science at the University of North Texas.


I am always asked about the scale of my models, and how to convert them to other popular, standard modeling scales. Well, Donald, at "passingloop.com" posted this tidbit of information that might be helpful to those of you who want to convert my 1/66 scale mansions (Bates, Liberty Square, New Orleans Square and Phantom Manor) to HO, O and N scale for train set ups.
The Bates House is in 1/66 scale so to convert it to your scale divide the scale number by the scale you want to model to get a percentage enlargement or reduction value.
For example, to go to HO (1/87) scale :
66/87 = 0.7586 which is approximately 75% reduction. So when you are ready to print, check your printer options where you can type in a percentage of reduction or scaling. Punch in 75 and you will have an approximate HO scale drawing ready to print and cut.
So, if you want to go to say O (1/48) scale:
66/48 = 1.375 which is approximately 137% enlargement.
For N scale: 66/160 = 0.412 which is around 40% reduction.
So, in summary, the Plan Conversion Formula Factor is:
(Scale of drawing plan / Scale you want to model) X 100
Reduce plan by the above factor if less than 100 or Enlarge if more than 100."
Thanks again, "passingloop.com"!


Are the building blocks for math skills… literal building blocks?
This is Sandra Tsing Loh with the Loh Down on Science.
Luis builds a tower. Kim builds a town. Rosie crashes in, and it all falls down! Building blocks are great for preschoolers playing pretend, but do they REALLY teach kids anything?
Jeffrey Trawick-Smith and colleagues at Eastern Connecticut State University think yes. In particular, blocks might help with… MATH! Blocks deal with size, shape, and number. So, Trawick-Smith predicted that block play might help children express — and even DEVELOP — math skills.
To investigate, the researchers videotaped a preschool classroom. They rated HOW children played with blocks. Were their builds complex? Were they playing with others? How long did they play? Children took a math test before and after the year-long study. It focused on concepts like measurement and geometry.
Results? Children who made MORE COMPLEX buildings made MORE PROGRESS in math. TEAMWORK during block play was also linked to bigger improvements. However, the researchers can’t assume cause-and-effect. Still, the result suggests building blocks can be learning TOOLS, not just TOYS.
It all stacks up!
Trawick-Smith, J., Swaminathan, S., Baton, B., Danieluk, C., Marsh, S., & Szarwacki, M. (2017). Block play and mathematics learning in preschool: the effects of building complexity, peer and teacher interactions in the block area, and replica play materials. Journal of Early Childhood Research, 15(4), 433-448.


This series takes an in-depth look at some of the world's most prolific serial killers and interviews those who were closest to them before learning about their secret, dark lives.
Runtime: 60 minutes
Twisted - Twistor theory - Netflix
Twistor theory was proposed by Roger Penrose in 1967 as a possible path to quantum gravity and has evolved into a branch of theoretical and mathematical physics. Penrose proposed that twistor space should be the basic arena for physics from which space-time itself should emerge. It leads to a powerful set of mathematical tools that have applications to differential and integral geometry, nonlinear differential equations and representation theory and in physics to relativity and quantum field theory, in particular to scattering amplitudes.
Twisted - Notes - Netflix
Twisted - References - Netflix


CRC Concise Encyclopedia of Mathematics: Print Location: Ref QA5 .W45 2003. This encyclopedia provides definitions, formulas and derivations, figures, tables, and resources for further research. A version is available online.
CRC Standard Mathematical Tables and Formulae (31st Edition): Print Location: Ref QA47 .M315 2003. This book covers topics like analysis of numbers, algebra, discrete math, geometry, continuous mathematics, special functions, probability and statistics, scientific computing, and financial analysis.
Facts on File Calculus Handbook: Print Location: Ref QA303.2 M36 2003. This book is intended for use by middle school, high school and college students taking single-variable calculus.
Facts on File Geometry Handbook: Print Location: Ref QA445.2 G67 2003. This book provides a basic introduction to geometry.
Mathworld: This website, best described as a mathematics encyclopedia, provides information on a variety of subjects: algebra, applied math, calculus, discrete math, the foundations of math, geometry, math history and terminology, number theory, probability and statistics, recreational math, and topology.
Oxford Reference Online: This resource provides quality, up-to-date information from a series of well-respected books, including books on mathematics.


- How do you write a floating point number?
- How do you convert a floating point number into a decimal?
- What is a floating point number example?
- What is a floating number in Python?
- How do you represent 1 in a floating point?
- How do you convert a floating point number to binary?
- How many floating point numbers are there?
- How do you convert a number to hexadecimal?
- How do you calculate floating point numbers?
- Why is it called floating point?
- What is a floating point number in programming?
- What is a floating point in computing?
- How do I convert IEEE 754 to double precision?
- What is a floating point number in C++?
How do you write a floating point number?
Decimal floating-point numbers usually take the form of scientific notation with an explicit point always between the 1st and 2nd digits.
The exponent is either written explicitly including the base, or an e is used to separate it from the significand..
How do you convert a floating point number into a decimal?
The rules for converting a floating point number into decimal are simply to reverse of the decimal to floating point conversion:If the original number is in hex, convert it to binary.Separate into the sign, exponent, and mantissa fields.Extract the mantissa from the mantissa field, and restore the leading one.More items…
What is a floating point number example?
Floating point numbers are used to represent noninteger fractional numbers and are used in most engineering and technical calculations, for example, 3.256, 2.1, and 0.0036. … The most significant bit indicates sign of the number, where 0 indicates positive and 1 indicates negative.
What is a floating number in Python?
float (floating point real values) − Also called floats, they represent real numbers and are written with a decimal point dividing the integer and fractional parts. Floats may also be in scientific notation, with E or e indicating the power of 10 (2.5e2 = 2.5 x 102 = 250).
How do you represent 1 in a floating point?
The sign of a binary floating-point number is represented by a single bit. A 1 bit indicates a negative number, and a 0 bit indicates a positive number.
How do you convert a floating point number to binary?
For converting a floating point number from decimal format to binary involves a step-by-step process. First, the integer part of the number is converted to binary. Next, the mantissa part is converted to binary by multiplying the exponent by 2 until we get a 23-bit mantissa in the binary format.
How many floating point numbers are there?
For any given value of the exponent, there are 2 24 = 16777216 possible numbers that can be represented. However, the exponent decides how big that number will be. With a single bit reserved for sign of the exponent, 7 bits are available. This gives an exponent range of -126 to 127.
How do you convert a number to hexadecimal?
Steps:Divide the decimal number by 16. Treat the division as an integer division.Write down the remainder (in hexadecimal).Divide the result again by 16. Treat the division as an integer division.Repeat step 2 and 3 until result is 0.The hex value is the digit sequence of the remainders from the last to first.
How do you calculate floating point numbers?
Converting to Floating pointSet the sign bit – if the number is positive, set the sign bit to 0. … Divide your number into two sections – the whole number part and the fraction part.Convert to binary – convert the two numbers into binary then join them together with a binary point.More items…
Why is it called floating point?
The term floating point is derived from the fact that there is no fixed number of digits before and after the decimal point; that is, the decimal point can float. … FPUs are also called math coprocessors and numeric coprocessors.
What is a floating point number in programming?
As the name implies, floating point numbers are numbers that contain floating decimal points. For example, the numbers 5.5, 0.001, and -2,345.6789 are floating point numbers. Numbers that do not have decimal places are called integers. Computers recognize real numbers that contain fractions as floating point numbers.
What is a floating point in computing?
The term floating point refers to the fact that a number’s radix point (decimal point, or, more commonly in computers, binary point) can “float”; that is, it can be placed anywhere relative to the significant digits of the number.
How do I convert IEEE 754 to double precision?
The first step is to look at the sign of the number. Because 0.085 is positive, the sign bit =0. … Write 0.085 in base-2 scientific notation. … Find the exponent. … Write the fraction in binary form. … Now put the binary strings in the correct order –
What is a floating point number in C++?
Floating-Point Numbers Real numbers are numbers that have a fractional part. … C++ uses the decimal point to distinguish between floating-point numbers and integers, so a number such as 5.0 is a floating-point number while 5 is an integer. Floating-point numbers must contain a decimal point.


Learning about the mechanics of a slot game can help you win more often. Learn about the Random number generator, Scatter symbols, and the Return to player feature. You can even unlock jackpots and unlimited progressive multipliers. You can also try your luck at playing games with free spins or bonus features. But remember to choose your favorite game before you start playing.
The game mechanics of slot machines are very important to the success of the machine. Slot games are among the lowest-cognitive-load games in the industry, but they can still provide a high level of entertainment. Game designers should consider neuromarketing when designing a slot game. The knowledge gained in neuromarketing will help them design addictive slot games.
A slot machine’s payline determines how much the player can win. Some machines have as many as hundreds of paylines. Players with a low budget should play games with fewer paylines.
Random number generator
The Random number generator is a critical component of a slot machine and is essential for fair gaming. It generates random numbers, which cannot be predicted by humans, and correlates these numbers with the symbols on the slot reels. These random numbers allow players to bet on the outcomes of a game based on probability rather than luck. The randomness of these numbers helps keep games fair and ensures that every player can win.
A random number generator is a computer program that generates random numbers. These numbers are determined by a mathematical algorithm. A random number generator starts with a number with millions of digits after the decimal, and uses different mathematical operations to determine its value. The random numbers are then displayed on the slot machine reels.
Return to player
Return To Player is a term used in the casino industry to refer to the return of the money that the player has wagered on a particular slot game. This percentage is calculated on a per-spin basis, and is not based on the total number of games that the player has played. The Return To Player is determined over tens of thousands of spins, which makes this metric irrelevant for any single gaming session.
RTP is an important statistic to consider when choosing a game. It helps you understand how much you are likely to win or lose. Knowing the RTP will help you plan your bankroll and betting strategy accordingly. In a sense, the RTP can be viewed as a mathematical advantage for online casinos, since the higher the Return To Player, the more likely you are to win.
Scatter symbols are symbols that appear on the reels of a slot game and can open special features. These features can include free spins, bonus rounds, and interactive mini-games. These bonuses are attractive to gamers, who will often visit a slot that features more scatter symbols. Aside from that, they can also increase the winning potential of the game.
Scatter symbols can appear on all or some of the reels in a slot game. However, they cannot replace wild symbols or stacked wilds. In addition, they must be present in at least three spots to trigger the bonus round. In this round, you can multiply your winnings, as long as you hit at least three scatter symbols. This is crucial for maximizing your winning potential.
The payback percentage of a slot machine is not the same for every slot machine. While some machines may return as much as ninety percent, others can only pay out eighty-nine cents on average. As a result, the payback percentage of a slot machine is not indicative of how much money you can win or lose.
Payback percentages vary greatly from casino to casino, but the average in Las Vegas is around 92%. Video poker machines, on the other hand, can have payback percentages ranging from 95% to 99%. In order to maximize your chances of winning, consider switching over to video poker instead of playing slots.


A 4-bit Binary Adder is actually quite interesting when you get down to how it really works. Before the carry look ahead adder was created a ripple adder would be used to make simple binary calculations. However, this was inefficeint in that a ripple adder relies on a completed summation in order to continue, this in effect would take much longer to compute and in a fast paced world made very little sense.
Fast forward, a few very intelligent people devised a way to make an adder that would look ahead at previous carries and would be able to preform calculations where all of the results could be summed and a correct answer would be outputted all at the same time.
In this lab we were asked to not only add two 4bit binary values but to also subtract, increment and decrement a number using the 4bit adder circuit. I found it to be very simple and was able to complete it within about 30 minutes. It was a cool lab and I definitely recommend to others to try it for themselves.


An Introduction to Algebraic Topology , By Joseph J. Rotman
Obtenir le lien
Series: Graduate Texts in Mathematics (Book 119)
Hardcover: 460 pages
Publisher: Springer (July 1, 1998)
A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.


Editor's Note: You just can't make this crap up. Institutionalizing mental illness . . . teaching this crap to "educators."
From page 6 of this PDF:
Deconstructing Racism in Mathematics Instruction
White supremacy culture infiltrates math classrooms in everyday teacher actions. Coupled with the beliefs that underlie these actions, they perpetuate educational harm on Black, Latinx, and multilingual students, denying them full access to the world of mathematics.The table below identifies the ways in which white supremacy shows up in math classrooms.
Dismantling white supremacy in math classrooms
We see white supremacy culture show up in the mathematics classroom even as we carry out our professional responsibilities outlined in the California Standards for the Teaching Profession (CSTP). Using CSTPas a framework, we see white supremacy culture in the mathematics classroom can show up when:
• The focus is on getting the “right” answer.
• Independent practice is valued over teamwork or collaboration.
• “Real-world math” is valued over math in the real world.
• Students are tracked (into courses/pathways and within the classroom).
• Participation structures reinforce dominant ways of being.


Tips: Can you win with a successful trading system?The answer is possibly no.
Here is an example.Jerry’s strategy: win twice in each three trades with same stop loss and take profit of 1%. Jerry trade 3 times a day. So his average gain is 1.01×1.01×0.99-1.00=0.98% per day. And 34% per month, 3367% per year.
Tom thinks Jerry’s strategy is good. He asks Jerry to make the lots ten times as large to Jerry. Therefore the trades’ stop loss and take profit are 10%. Tom’s gain is 1.1×1.1×0.9-1.0=8.9% per day. 1190% per month. And 21 trillion times of deposit per year.
Bob thinks Jerry’s strategy is good. He asks Jerry to make the lots 100 times as large to Jerry. Therefore the trades’ stop loss and take profit are 100%. Bob’s gain is 2x2x0-1.0=-100% per day. He has to deposit some more money every day to continue.
In the story, who will be the richest in the end of the year?
The answer is Jerry. To Tom, even if he bears 3 continuous losses, the total losses will be 27% of his balance. He will think the strategy is rubbish and stop to use it. Meanwhile, Jerry can bear at least 11 continuous losses and the total losses will be 10% of his balance.


Daily Quiz is the basic part of Himachal GK. It is helpful to increase your knowledge. It is a series of Himachal Gk MCQs.
1. What is the number that does not come in roam counting?
2. Chandra Bahadur Dangi was the smallest man in the world who weighed only 15 kg. How tall was he?
(A) 1 feet 10 inch
(B) 2 feet 10 inch
(C) 3 feet 10 inch
(D) 4 feet 10 inch
3. When did Google start G-mail?
(A) 1 April 2005
(B) 1 April 2006
(C) 1 April 2004
(D) 1 April 2007
4. How much did the titanic ship cost?
(A) 30 crores 17 lakhs
(B) 35 crores 70 lakhs
(C) 35 crores 50 lakhs
(D) 36 crores 40 lakhs
5. Which animal cannot walk upside down?
6. Which is the country that has never been enslaved to anyone?
(B) Sri Lanka
7. How much did it cost to make the titanic film?
(A) 2 billion
(B) 5 billion
(C) 7 billion
(D) 10 billion
8. Which number that is divisible by all numbers from 1 to 10?
9. In which country monkey work as waiters?
10. How many kilograms of jalebi is the world record in a hotel in Mumbai?
(A) 18 kg
(B) 20 kg
(C) 15 kg
(D) 25 kg
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P a g e | 40 MATHEMATICS (6 Credits Required) Math Sequence 9 th 10 th 11 th 12th Modern Geometry Modern Algebra 2 Pre-Calc Calculus Algebra Modern Geometry Modern Algebra 2 Pre-Calc Algebra Geometry Algebra 2 Algebra 3 Pre-Algebra Algebra Geometry Algebra 2 ALGEBRA (NCAA) Course Length: 1 Year Credits: 2 Elective/Required: Required Option Grade Level: 9 This is a course extending basic mathematical concepts to the use of variables. Solving problems with an unknown will also be presented. Students who enroll in this class should have a sound math background. It provides the fundamentals of a standard algebra course: simplifying variable expressions, solving equations, graphing linear and quadratic functions, and problem solving. ALGEBRA 2 (NCAA) Course Length: 1 Year Credits: 2 Elective/Required: Required Option Prerequisite: Passing grade in Algebra or Algebra 1B, and Geometry Grade Level: 11, 12 An elective course for students interested in increasing their proficiency in mathematics. Since algebra is the basic foundation for many careers, students will find this course expands on topics covered in Algebra 1. Graphing calculators will be used throughout the year. Students are encouraged but not required to purchase a TI-83 Plus graphing calculator. ALGEBRA 3 (NCAA) Course Length: 1 Year Credits: 2 Elective/Required: Required Option Prerequisite: Passing grade in Algebra 2 or Modern Algebra 2 both semesters Grade Level: 12 Algebra 3 is an elective course. It is a continuation of many of the same topics included in Algebra 1 and Algebra 2, but at a more complex level. Topics include linear functions and inequalities, quadratics, conics, polynomials and rational functions, exponential and logarithmic functions, linear systems, matrices and determinants. Additional topics may include trigonometry, sequences, series, permutations, combinations and probability. Students are encouraged to purchase a TI-83 or TI-84 calculator to use during this course.


Day 10 was some mostly list/stream processing, but with some finicky rules about counting them. The core of the problem was to find the signals, a pair of the register value and the cycle during which it had that value.
Running the script
Parsing the input was standard attoparsec.
data Operation = Noop | Addx Int deriving (Show, Eq) operationsP = operationP `sepBy` endOfLine operationP = noopP <|> addxP noopP = Noop <$ "noop" addxP = Addx <$> ("addx " *> signed decimal)
Applying the operations was a two-step process. First, I converted each operation into the one or two cycles it took and the change in register value after that cycle. Second, I combined those changes (with
zip) into a trace of the register value and the cycle during which it held.
type Signal = (Int, Int) -- during cycle, register apply :: [Operation] -> [Signal] apply = zip [1..] . scanl' (+) 1 . concatMap applyOp applyOp :: Operation -> [Int] applyOp Noop =  applyOp (Addx d) = [0, d]
That took some care, and comparison to the examples, to check there were no off-by-one errors.
This was a bit of arithmetic to find the correct cycles of interest (in a
filter), then a list comprehension to do the multiplications.
part1 :: [Signal] -> Int part1 = calculateSixSignals . extractSignals extractSignals :: [Signal] -> [Signal] extractSignals = filter (\(t, _n) -> (t + 20) `mod` 40 == 0) calculateSixSignals :: [Signal] -> Int calculateSixSignals signals = sum [ (t * n) | (t, n) <- signals , t <= 220 ]
There was another source of off-by-one errors here. While the time counts up from 1, the display column starts at 0. That gets handled in
columnOf, extracting the column of the CRT's ray during each cycle. Given that,
isLit returns if the pixel is within the sprite, and
showPixel converts a pixel value into the displayed representation.
All that's left is to chunk the pixels into rows and combine them.
part2 :: [Signal] -> String part2 regVals = unlines display where pixels = map (showPixel . isLit) regVals display = chunksOf 40 pixels isLit :: Signal -> Bool isLit (n, x) = abs (x - c) <= 1 where c = colummOf n colummOf :: Int -> Int colummOf n = (n - 1) `mod` 40 showPixel :: Bool -> Char -- showPixel True = '#' -- showPixel False = '.' showPixel True = '█' showPixel False = ' '


Choosing What a Mode in Math
How it works, the way that it attracts, the entire game logic from start to complete. In June you will observe some key adjustments to the games you already know and hopefully a couple new titles. Much like with movies, the perfect board game usually provides a good way to escape your everyday grind for precisely the total amount of time you’re able to afford to invest in it.
The background image is a lovely art design, the tiles are clear and simple to read, and the total design is completely solid. The table indicates the results. It is not likely that you will select a blue marble.
Ok, I Think I Understand What a Mode in Math, Now Tell Me About What a Mode in Math!
Just click the section you want, and it’ll take you to a more comprehensive page. In the event the data aren’t in a list, I advise you to establish a tally chart to assist you count the numbers. https://www.iam.kit.edu/wet/4567.php In-app purchase necessary for full access.
The range must also be 8. In other words, it’s the number that is repeated most, i.e. the number with the maximum frequency. Simply locate the middle number that’s the Median.
Things You Should Know About What a Mode in Math
A set of values could possibly be put into the idea of a value system. It’s equal to the sum of all of the values in the group of information divided by the complete number of values. It is when you add each of the numerical values and divide by the complete number you have.
The area below the curve is equivalent to 1. The mode is the sole measure of average that may be used with nominal data. Probability is a means of describing the likelihood an event will occur.
In order to get the median of a set of numbers, first you need to order the series from least to greatest. http://paper-now.org/ A sample collects data from part of the populace. To locate the mean you’ve got to add together all the data.
Median calculation is utilized in several branches of mathematics but it’s primarily utilised in probability and statistics. Finding the mean, also called averaging numbers, is a very helpful point to understand how to do, especially whenever you desire a precise estimate or an extremely accurate generalization.
The child would have to say that the assortment of results is larger, but the mean average is quite similar. The mean is what you receive if you share everything equally, the mode has become the most frequent price, and the median is the value in the center of a set of information. It is the value that can replace every existing item, and have the same result.
Lies You’ve Been Told About What a Mode in Math
The very first step is to ensure that your numbers are in order from least to greatest, which they’re in this dilemma. HTML math is strong enough to describe the scope of math expressions it is possible to create in common word processing packages, along with being suitable for rendering to speech. This example illustrates the issue.
You’re extremely intelligent and you’re an outstanding speaker. Just make sure you keep your mind sharp and your work organized, and you’re going to be in a position to tackle SAT statistics problems right away. Again you will locate the effective use of technology involves a whole lot of critical thinking.
Few folks argue that everybody should have the ability to read and write, but there’s the fuzzy notion that mathematical competence is optional. This realization might not be super obvious at firsta lot of folks aren’t really conscious of the labor which goes into making the things they play. In reality, the idea of counting dates farther back.
The sole thing you control is the sum of return you need and the time you’re well prepared to wait. Selecting a candidate has lots of consequences, and selecting the incorrect person may give rise to a company numerous difficulties. By exactly the same token, lots of folks make the error of buying too few shares.
What a Mode in Math and What a Mode in Math – The Perfect Combination
Unlike the other worldwide objects, Math isn’t a constructor. It is the most frequent value in a set of data. It is simply the specific value that occurs most frequently.
1 EXECUTE intent can target several devices, with numerous commands. Also, it’d be great to provide a formula autobuildup option in Word as it’s simpler to find out what you’re typing whenever you don’t need to wade through myriad control words. Hit MORE to scroll by means of this submenu.
All uses of a particular identifier must refer to the specific same object. A double bar graph can be employed to compare two sets of information, usually about the exact same topic. Mode 6 data might not always be clear, and it might be reported in undefined units.
The One Thing to Do for What a Mode in Math
This way, even the brightest math student doesn’t end up winning every single time you play. The notion of math literacy is a significant one. Thus the answer is (E) none of the above mentioned.
When you’re studying math equations, formulas and algorithms then it is probable you will repeat mistakes and will truly feel a need of a fast assistance. You may choose to talk about the answers as a piece of a class discussion. An excellent instance of this is figuring out what the normal score for all of the students who took a test in a course.


This compilation of printable two-digit and single-digit subtraction worksheets is designed to help students of Grade 2 to grasp the basic concepts of regrouping and no regrouping. Blast Off is a mental maths game for 5 to 8 year olds which can help you to know your two digit numbers and help with addition and subtraction skills. Showing top 8 worksheets in the category - Softschools. Each worksheet includes 20 double-digit addition problems, a number line, and a second page with the answers. Add three two-digit numbers. Administration; 2019-2020 Academic Calendar; Badger School District Literacy Plan; Badger School Technology Plan; District Revenue and Expenditures Budget. If you don't remember how to do it, please visit these. Represent data on number lines, grids and line plots. DA: 93 PA: 85. than 2, it is necessary to take 1 ten from the 4 tens and add it to the 2. To discover just about all images in 46 Super Single Digit Subtraction Worksheets pictures gallery you need to adhere to that url. We have worksheets from preschool, kindergarten, First grade to sixth graders. Contraction Worksheets Teaching Contractions Printable worksheets for teaching students about contractions A contraction is two words joined together with an apostrophe Long Division – 3 Digits By 1 Digit – Without Remainders Math Worksheets on Graph Paper. And then the really tricky one: two thousand, three hundred, seventy eight. Green slime blobs with subtraction problems drip down from the top of the screen toward a laser cannon at the bottom. You can count this as an activity worksheet. *This post contains affiliate links. Please try again later. Look for and express regularity in repeated reasoning. Practice ye subtraction facts while havin' a blast! Muddy's Marsh. Single Digit for Addition and Subtraction Mixed Problems Worksheets These single digit addition and subtraction worksheets are configured for 2 numbers in a vertical problem format. Two digit subtraction worksheets are an excellent introduction to advanced equations. Adding 2-digit numbers without. Below are six versions of our grade 2 math worksheet on subtracting a 2-digit number from a 2-digit number with borrowing. Ace Maths Solutions Unit Two - Developing Understanding in Mathematics (word) 1. If the answer is correct then they get a chance to untie the balloon with the same number written. 6: Demonstrate fluency for addition and subtraction within 10. Each place has a value of 10 times the place to its right. 2-digit Subtraction. Educational Games Our Classrooms Contact Us Academic Calendar Subtraction (Math): Value of the Underlined Digit:. Learn exactly what happened in this chapter, scene, or section of Scientific Notation and what it means. Math Worksheets > Grade 2 > Addition > Adding two 3-digit numbers in columns - no carrying. Just pick a worksheet, print and you're ready to go. On this worksheet, students will add both two- and three-digit numbers. After solving all 20 subtraction math problems on the quiz, check your answers. 10 Less Subtraction – 2 Digit 1 digit number to a 2 digit number with regrouping – Six Worksheets. 2 Fluently add and subtract within 20 using mental strategies,. 3 digit subtraction worksheets with regrouping. Muddy lives in the marsh in Murb. Choose from 500 different sets of addition 2 digit subtraction flashcards on Quizlet. Math Worksheets on Graph Paper Addition No Regrouping Addition Regrouping Subtraction - No Regrouping Subtraction Regrouping 3 Digit Addition With Regrouping - Carrying - 6 Worksheets Worksheet 1 - Download Worksheet 2 - Download Worksheet 3 - Download Worksheet 4 -. Educational Games Our Classrooms Contact Us Academic Calendar Subtraction (Math): Value of the Underlined Digit:. Click Test below and then bookmark the page using your Internet browser (Windows: Ctrl-D, Apple: Cmd-D). Subtraction Games - Fishing Subtraction Game. 109 days until Last Day of School! (Includes holidays and weekends). These place value worksheets are appropriate for Kindergarten, 1st Grade, and 2nd Grade. Welcome to The 6-Digit Plus 6-Digit Addition with NO Regrouping (A) Math Worksheet from the Addition Worksheets Page at Math-Drills. This p0st section brings along 85 photograph of Grade, some of them are including Free Printable Second Grade Worksheets Insightsonline Org. Subtraction Math Learning 2 Digit Subtraction with Regrouping. com/ Math websites- http://www. Math Worksheets. 3-Digit Plus/Minus 3-Digit Addition and Subtraction with SOME Regrouping (637 views this week) 2-Digit Plus/Minus 2-Digit Addition and Subtraction with SOME Regrouping (431 views this week) Multiplying and Dividing Facts to 144 (358 views this week) 50 Adding and Subtracting Questions with Facts From 1 to 10 (346 views this week) 100 Horizontal Multiplication/Division Questions (Facts 1 to 12. Take advantage of the amazing lists of 5th grade math vocabulary words we have created to help your students! With our fourth grade math terms, your students will have an upper hand that cannot be taken from them with the additional knowledge they will gain!. 1 Use technology hardware and software responsibly. Practice with this 7th Grade Exponents / Powers Crocodile math game. In our decimal number system, the value of a digit depends on its place, or position, in the number. Learn to add and subtract upto 3-digit numbers and a bit about multiplication and division. Printable drill worksheets, a scoot game, a magic digits game, task cards, graph paper math, and word problems. With the numbers right underneath, children easily make the association between the visual cues and the act of addition. Get Started. Math: Ordering Numbers 1-100 http://www. This is perfect for daily skill review or homework. khanacademy. A And An Worksheets Chapter #1. Students are to supply the missing addends to complete the equation. org/math/cc-fourth-grade-math/cc-4th-add-sub-topic/cc-4th-subtracting/v/basic-regrouping-or-borrowing-when. Subtraction Step-by-Step with Regrouping http://www. Preview of "Monkey Math School Sunshine" by THUP Games. Click on the hyperlink to download the pdf and print out the pages for use in your classes. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Students. to our suprise they all needed additional help in Subtraction. Studies show that lots of math practice leads to better math grades. Practice one, two, and three-digit adding. Softschools Subtraction, 1000 About Addition Subtraction Ideas Place Value Addition, 1st Grade Math Worksheets And Grade Math, Addition And Subtraction And Strategies Scholastic Parents, Softschools Info Free Math Worksheets Free Phonics Worksheets Math And, 25 Best About Psia Math Math Mental Maths And Number Sense, 3 Digit Subtraction With Regrouping Practice Education Math Math Subtraction. 3 Digit Subtraction Activities 3 digit subtraction with regrouping worksheets thoughtco, here are 3 digit subtraction worksheets requiring regrouping subtraction with Read More Three digit addition (no regrouping). This Subtraction Worksheet may be printed, downloaded or saved and used in your classroom, home school, or other educational environment to help someone learn math. UNIT SOLUTIONSSolutions Unit Two: DevelopingUnderstanding in Mathematics From the module:Teaching and Learning Mathematics in Diverse Classrooms South African Institute for Distance Education 2. If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it. Add or subtract 2-digit numbers arranged in column and horizontal format. Labeled with. Be the first player to reach the finish line by recognizing correct and incorrect answers. Two Digit Subtraction With and Without Regrouping Worksheets Two Digit Subtraction With Regrouping, Two Digit Subtraction Without Regrouping Common Core State Standards: 2. com Crunch some numbers -- and some mountains -- with this two-digit subtraction with borrowing game that helps third graders scale subtraction. 1 Use technology hardware and software responsibly. Be ready to share your problem with the class (do not solve it we will solve it in class, so make it great!) Have fun learning!!! Example of a subtraction equation: 87 - 19-----. Each place has a value of 10 times the place to its right. SuperKids Math Worksheet Creator Have you ever wondered where to find math drill worksheets?. It may be configured for 1, 2, and 3 digits on the right, and up to 4 digits on the left of the decimal. 8 Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. In this math game, kids will subtract two-digit numbers. Drag 'N' Drop Math is an online workshop in which students can easily complete multi-digit addition, subtraction (with regrouping), multiplication, and div. 3 Digit Subtraction Worksheets-2. Just pick a worksheet, print and you're ready to go. In this math worksheet, your child can practice adding 2-digit numbers. Math Games Click on the website links to play Two Digit Addition Soccer : You can select four different difficulty levels of subtraction problems in this game. The early learning materials are numbers, counting, and measurement worksheets. com/social_studies/13_colonies_map/. You may select up to 25 problems per worksheet. Some of the worksheets below are Addition Flash Cards – 1 Digit Addition, Super Teacher Worksheets – 1 Digit Addition, addition and subtraction triangle flashcards –Use the attached triangular flashcards to practice both addition and subtraction facts, Addition Flashcards: Set of 12s, Addition Flash Cards Doubles –1 Digit and 2 Digits Addition, Free Addition Flash Cards 0-12 –1 Digit. Players: 4. Easier to grade, more in-depth and best of all 100% FREE! Kindergarten, 1st Grade, 2nd Grade, 3rd Grade, 4th Grade, 5th Grade and more!. This activity will teach students how to line up addition problems and solve them. Math Worksheets > Grade 2 > Subtraction > Subtract 2-digit numbers , no regrouping. softschools. SoftSchools (2-digit with regrouping) SoftSchools (3-digit with regrouping) Wack an Answer (2-digit addition) Subtraction Fruit Splat (within 10; 1 and 2-digit; multiplies of 10;regrouping) SoftSchools (2-digit with regrouping) SoftSchools (3-digit with regrouping) Alien Addition Minus Mission: Fact Families. Hard multiplication 2 digit problems standards met two digit also free three digit addition worksheets choose from several variations easy to challenging Division. 2 digit addition and subtraction with regrouping word problems worksheets; 2 digit addition and subtraction worksheet generator; 2 digit addition and subtraction worksheets 2nd grade; 2 digit addition and subtraction worksheets without regrouping; 2 digit addition with regrouping worksheets 2nd grade pdf; 2 digit addition with regrouping. Practice math problems are a great way for kids to get extra math practice. Why Logical Reasoning Number Series? In this section you can learn and practice Logical Reasoning Questions based on "Number Series" and improve your skills in order to face the interview, competitive examination and various entrance test (CAT, GATE, GRE, MAT, Bank Exam, Railway Exam etc. edu/ Math games by topic http://www. These two worksheets have multiplication problems with digits 1 through 12. Perfect for acing essays, tests, and quizzes, as well as for writing lesson plans. Multiplication Fact Fluency Worksheets New Subtraction Worksheets from math fluency worksheets , source:lesdereglees. These 2nd grade subtraction worksheets are all about subtracting 1, 10 or 100 to a range of 2 and 3 digit numbers. 4-Digit Subtraction. In our decimal number system, the value of a digit depends on its place, or position, in the number. elapsed time word problems worksheets softschools in english provides free math games grammar 3 digit subtraction 5 online addition to 10 2 soft schools quizzes. Social Studies Constitution Day: 12 Colonies: http://www. Math Worksheets and Printable PDF Handouts. This compilation of printable two-digit and single-digit subtraction worksheets is designed to help students of Grade 2 to grasp the basic concepts of regrouping and no regrouping. To discover just about all images in 46 Super Single Digit Subtraction Worksheets pictures gallery you need to adhere to that url. When they get the answer correct, a silly animated character dances and jumps around. Using these sheets will help your child to: subtract 1, 10 or 100 to a 2 or 3 digit number; solve missing number problems. In this math worksheet, your child can practice adding 2-digit numbers. com/literacy. softschools. Then these worksheets turn into winter animal coloring pages. com/math/grade-2/regrouping-tens-and-ones http://www. Addition and Subtraction Worksheets with Decimals Vertical Format. Intro to subtraction with 2-digit numbers. Students also. What We're Learning This Week; Using models to make two digit numbers, reading and writing two digit numbers, and identifying odd and even numbers. Improve your math knowledge with free questions in "Subtract numbers up to three digits - word problems" and thousands of other math skills. Problems involve the addition, subtraction and / or comparison of 1 digit decimal numbers. Play Math Car Racing online, here. Grades: Grade 1, Grade 2, Grade 3. Below are three versions of our grade 4 math worksheet with word problems involving addition and subtraction. 57 Add and subtract within 1000…. This is the disclaimer text. Blast Off is a mental maths game for 5 to 8 year olds which can help you to know your two digit numbers and help with addition and subtraction skills. Page 1 of 6 Let's just dive right in and do one!. Coding Activities; Brain Pop Jr. Multiplication Fact Fluency Worksheets New Subtraction Worksheets from math fluency worksheets , source:lesdereglees. Printable subtraction worksheets with single and multi-digit problems. As you scroll down, you will see many worksheets for subtract multiples of tens, subtract a 1-digit number from a 2-digit number, subtract 2 - digit numbers, ways to make a number - up to 2 digits, word problems, input/output tables, subtraction sentence, subtraction equations, use addition. Our School" About Our School; Mission. ) 1 2 3 4 5 6 7 8 9 1011 1213 1415 1617 1819 20. Students also. Using these sheets will help your child to: subtract 1, 10 or 100 to a 2 or 3 digit number; solve missing number problems. Counting the red squares interactive mad maths Counting to 10 (fingers) Interactive Counting Objects (up to 10) What comes next (to 20 in sequence) What comes before (within 20, in sequence) What comes next (within 100, in sequence). Some of the worksheets below are Addition Flash Cards - 1 Digit Addition, Super Teacher Worksheets - 1 Digit Addition, addition and subtraction triangle flashcards -Use the attached triangular flashcards to practice both addition and subtraction facts, Addition Flashcards: Set of 12s, Addition Flash Cards Doubles -1 Digit and 2 Digits Addition, Free Addition Flash Cards 0-12 -1 Digit. 3 Digit Subtraction Worksheets-2. 1 tower is taller and 1 is shorter. Easy Addition and Subtraction Worksheet 1. 5 Fluently add and subtract within 100…. 1 or 2 Digit Subtraction Integers Worksheets. More Subtraction. than 2, it is necessary to take 1 ten from the 4 tens and add it to the 2. You are here: Home → Worksheets → Grade 2 addition Grade 2 addition worksheets. In other cases, the two-digit number, also known as the addend, is on the bottom row of the problem. fun christmas math worksheets. Time Worksheets. Sqworl makes it easy to organize and share multiple links with just one url. Welcome to The 6-Digit Plus 6-Digit Addition with NO Regrouping (A) Math Worksheet from the Addition Worksheets Page at Math-Drills. 1 Place Value to 999 (T02) Know the value of a given digit in whole numbers to 999 MA. One of the problems many students have is carefully reading the number words. Strategies for adding and subtracting within 100. Give your young mathematicians an addition and subtraction skills boost with this practice worksheet that includes both vertical and horizontal equations. Reply Delete. This regrouping sort pack will allow first and second grade students to practice quickly recognizing the need to regroup in 2-digit and 3-digit addition problems. htm Choose from three pages of multiplication games http://www. Students were also introduced to the standard algorithm as a shortcut to using the base-ten pieces and their recording sheets. To get subtraction worksheets for different skill level, change the default values. Our library of first grade subtraction worksheets and printables offers your students an opportunity to strengthen and challenge their math skills with interactive, engaging activities. Even though we took off a few days for spring break, when I mentioned a game they came running. Tthere may be two or three addends or subtrahends with up to 4 digits in any given problem, though generally the computations are kept relatively simple. Practice ye subtraction facts while havin' a blast! Muddy's Marsh. 6-Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. 8 Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900. Incorporate the addition and subtraction fact family worksheets comprising sorting the number sets, find the missing members in the triangles, circles, number bonds and bar models; writing the four addition and subtraction facts in the house models, dominoes, picture models and more. softschools. Students are to supply the missing addends to complete the equation. Addition Worksheets. Subtracting a Number From a 2-digit Number Online Quiz - Following quiz provides Multiple Choice Questions (MCQs) related to Subtracting a Number From a 2-digit Number. Mad Minute Worksheets - showing all 8 printables. If you don't remember how to do it, please visit these. Addition and Subtraction Worksheets with Decimals Vertical Format. I also projected the first two pages on my promethean board while introducing double digit addition and subtraction. com/language_arts/phonics/games/oi_oy_sounds. Ace Maths Solutions Unit Two - Developing Understanding in Mathematics (word) 1. Give your young mathematicians an addition and subtraction skills boost with this practice worksheet that includes both vertical and horizontal equations. 358 - 125 2. Set students up with solo work, or let them get together in small groups, and the following activities will help them blossom into masters of two digit subtraction. This is to avoid more than three of the same letter in a row. Page 2 Unit 8: Addition, Subtraction, and the Number System Grade 2: Unit 8 Subtraction Students subtract from 100 using a variety of strategies. 1 tower is taller and 1 is shorter. This worksheet contains two separate pages, each of which includes a mix of 3 addition/subtraction word problems. Mad Minute Worksheets - showing all 8 printables. Mad Minute Math - Addition http://www. This selection of 2-digit subtraction worksheets will help kids further hone their skills in subtraction with a stronger grasp on the concepts of regrouping and no regrouping. Bones & Muscles -- Bill Nye. Skip to content. Worksheet # 2 Name: http://math. That graphic (Single Digit Subtraction Worksheets 41 Doc Basic Subtraction Worksheets to 20 Free Printables) over will be labelled having:submitted through Kelly Jenkins with 2018-01-22 15:17:08. The first two pages of this Powerpoint may be printed on cardstock and placed in page protectors for use with dry Erase markers in centers or for small group instruction. Like last year, you will have access to the online version of the book. Live links to learning sites for kids recommended by a retired second grade teacher. 1 or 2 Digit Subtraction Integers Worksheets. Addition and Subtraction Fact Family Worksheets. ) 1 2 3 4 5 6 7 8 9 1011 1213 1415 1617 1819 20. Practice, Practice, Practice! Students need daily practice with addition and subtraction with regrouping to master this concept. Print out Fraction Strips, Fraction circles, and fraction worksheets. 0 Summit 2013 MT Learning Goals by Measurement Topic (MT) Students will be able to. Our graded 2 digit graded subtraction sheets are below the generator. In second grade, children practice addition a lot. DA: 3 PA: 54 MOZ Rank: 68. Some of the worksheets below are Addition Memory Match Game worksheets, Subtraction Memory Match Game worksheets, Math Card Games – just print and play worksheets, How to improve your memory using a memory palace worksheets, memory – A Five-Day Unit Lesson Plan for High School Psychology Teachers, Addition Worksheet, making math more fun – printable math games collection. 2 digit addition and subtraction with regrouping word problems worksheets; 2 digit addition and subtraction worksheet generator; 2 digit addition and subtraction worksheets 2nd grade; 2 digit addition and subtraction worksheets without regrouping; 2 digit addition with regrouping worksheets 2nd grade pdf; 2 digit addition with regrouping. Worksheets: Subtract a 2-digit number from a 2-digit number in columns, no borrowing. Objective ‐ multiplication facts fluency, demonstrated by recall in 2 seconds or less, AND the ability to simply fractions fluently. Subtraction of 4 by 4 place numbers math game online Learn how to subtract four digit by four digit numbers in this interactive online math game for 3rd grade. regrouping worksheets | regrouping addition worksheets | regrouping subtraction worksheets | regrouping worksheets | regrouping math worksheets | regrouping wor. https://www.


The first level, known as primary 1 to primary 3, covers the first three years of primary education and is focused on providing children with a strong foundation in basic subjects like math, language, and science.
The second level, known as primary 4 to primary 6, covers the next three years of primary education and builds on the skills and knowledge learned in the first level. During this stage, students begin to study more advanced subjects like history, geography, and computer science.
The third level, known as junior secondary school, covers the final two years of primary education and is focused on preparing students for the transition to secondary school.
Overall, the primary school curriculum in Nigeria is designed to provide students with a well-rounded education that lays the groundwork for future academic success.
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Standardized test-score results released in August show that the Douglas County School District outperformed the state in all but one test category, but the district saw drops in several categories since last year.
Under the Colorado Measures of …
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Douglas County School District compared to the state
Mean scale score for fifth grade ELA: DCSD — 750; state — 745
Algebra 1 scores that met expectations: DCSD — 45.5 percent; state — 31 percent
Eighth-grade math scores that met expectations: DCSD — 17.3 percent; state —19.6 percent
Third-grade math participation rate: DCSD — 92.7 percent; state — 96.7 percent
Seventh-grade math scores that met or exceeded expectations: DCSD — 32.2 percent; state — 25.8 percent
Fifth-grade science scores that met expectations: DCSD — 40 percent; state — 30.6 percent
SAT mean score: DCSD — 1,086.9; state — 947
Source: Colorado Department of Education
Under the Colorado Measures of Academic Success standards, students take science, math, social studies and English language arts tests at the end of each school year. Test results tell how students are performing and growing compared to their peers across the district and state, according to the Colorado Department of Education.
Douglas County School District's results paint a picture of student achievement and growth, said Assistant Superintendent Ted Knight. He pointed out that every traditional high school in the district scored above the state average on the PSAT and SAT. Rock Canyon High School, SkyView Academy and Stem School Highlands Ranch were in the state's top 20 schools for SAT scores.
“Overall, we are proud of our results,” Knight said, “and we always know that there is work to do.”
DCSD tends to have a high opt-out rate compared to the state and other school districts when it comes to testing, interim Superintendent Erin Kane said in a letter to parents posted on the district's website.At the elementary level, 86 percent of DCSD students took the test. In charter schools, 88 percent of students tested. At the middle school level, 63 percent of students tested. And across all high schools, just 44 percent of students participated.
The district saw growth in some test areas. Third-, fifth-, sixth- and seventh-grade ELA saw a rise in the “met or exceeded expectations” category from the 2015-16 school year. It saw dips in middle- and high-school math. Fifth-grade math had a 0.5 percentage point drop in the “met or exceeded expectations” category, Integrated Math 1 had a 9.4 percentage point drop and Algebra 1 had an 8.2 percentage point drop.
Douglas County students outperformed the state in the “met or exceeded expectations” categories in ELA, science, social studies and math — all grades except eighth, in which many students opt to take the Algebra 1 test instead, according to the district.
School board member David Ray noted that assessment results are only one snapshot of how well the district's students are performing.
“Unfortunately, there is a tendency to use these results as a way to recognize `high performing' schools as opposed to considering the many variables that contribute to a student's success,” Ray said in an email. “These variables go beyond quality instruction and include parent involvement, positive school cultures, skilled leadership and clearly defined academic expectations.”
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Having students practice their skills on worksheets allows them to answer test-like questions without worrying about receiving a grade. Start them off with simple worksheets that focus on basic short division.
This product includes division with 2 to 10 with tables and coloring keys. Student will enjoy to do homework with coloring worksheet and divisions with fun.
Maths easy way Teaching-times-tables-and-multiplications View the worksheets What would your students like to do for counting money their piggy bank has? How will they count them? They would most likely coins into groups of two, three, or possibly five coins, and then add the groups. If students put the coins into groups of 3 and formed 10 groups of coins, it might not take too long to add 3 ten times for a total of 30 coins. They might even skip-count by 3. But, if there were 300 coins, skip-counting by 3, or adding 3 one hundred times would take quite a long time. The easiest way to find the total number of items in equal groups is to use multiplication. Multiplication allows you to do repeated addition quickly and efficiently. You can write a multiplication sentence to show 100 groups of 3 pennies. The numbers you multiply are called factors. The answer is the product. Here included tables from 11 up to twenty with numbers and words. Students first read all these times tables and try to solve questions given in worksheets. They can make a mini times tables book. Just they have to do is to print all these papers contain times tables with numbers and words. Arrange them properly from the table 11 to 20. Make one folder. They can make a nice cover for your times table book. Visit some more Maths practice at:


The pressure is real: kids are expected to master certain skills at certain ages in our culture, and math is one subject that makes many homeschoolers feel anxious. We research curriculum after curriculum, we push our kids to do more and know more at younger ages, and we stress over falling "behind."
But if we can take a step back, and be willing to look beyond grade-levels, we can find the bigger picture. What do we really want for our kids with regards to math?
I think the real long-term goal for many of us is to have children (and later, teens and adults) who aren't just proficient in math, but also enjoy it. To not just know their times tables or how to solve a quadratic equation, but to also find the delight in understanding how math works in the world around them.
Delight in math?!? Yes, that really can be one of the goals! And if we open ourselves to that possibility, many of the typical math learning methods fall woefully short. Drill-and-kill, textbooks, math problems ad nauseam with no connection to real math in our lives, testing to see who is "behind" and obsessing over specific math skills - these methods prevent the delight in math from germinating.
It's All About the Environment
So, how do we foster both proficiency and delight in math? It comes down to the environment we are creating. In the early years of our homeschool, I learned firsthand what doesn't work well: If we require our kids to stop playing to do their math work, they will hate math. If we force our kids to do a certain number of math problems every day, they will dread math. If we test our kids and tell them they are behind in math, they will feel like failures.
What if, instead, we show our kids that the purpose of learning math isn't to be able to complete problems on a worksheet, but to be able to manage and understand the world around them? We can do this by:
finding ways to connect math to our everyday lives
playing lots of games together, not for the math, but for the fun, and the math practice happens along the way
reading books that involve math on our own, and then sharing interesting concepts with our family over dinner
finding ways to connect math with our kids' own individual interests
A Math-Rich Environment
Math doesn't have to be about textbooks and worksheets! We can make learning math a natural part of our everyday lives, showing our kids that math is relevant and interesting. We can set-up our home environment to encourage math exploration by having math manipulatives, rulers, tangrams and pattern blocks, tape measures, graph paper, and even simple calculators.
If we look around, math really is everywhere in our lives, from baking to shopping to arranging furniture to road trips to gardening to laundry and everywhere in-between.
Math is there in Legos, chores, daily routines, playdates with friends, the music we listen to, the weather outside, how long it takes to drive to the library, on and on, if only we are willing to look for it.
Real life math lessons can be taught in many simple ways, such as:
saving money as a family for an upcoming activity or vacation, with real money being placed in a jar in a prominent location
noticing when a person at the market has to pull out their phone to do simple arithmetic, and later discussing it with our kids
paying attention to the weather outside, with an outdoor thermometer and the use of weather websites
letting the kids help with measuring ingredients when baking or cooking
making sure we'll have enough cookies for our guests
figuring out how much gas money we'll need to drive to grandma's house
measuring distances and lengths that come up in our reading or explorations of other subjects
counting and sorting rocks, seashells, beans, etc.
weighing produce at the grocery store
giving our kids cash to spend for their back-to-school supplies, and letting them go through the check-out line on their own (for young kids, make sure to help with figuring out the taxes or just give them an extra dollar or two before they go to pay to cover the taxes)
Let's give our kids what so many of us missed out on in our own math educations. By being willing to think about math and math education in a new way, we can create a new paradigm that aims at both delight and proficiency in math!
What has been your experience with
math and math education?
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I believe in growth mindset - the idea that you can get better at things by working at them. It can be a hard thing to live at times - we all seem to have certain places where we have blinders about our ability to improve (or our students' ability to improve!)
With that in mind, I have been working on my mental math abilities. I've been playing a game where I keep track of changing numbers by adding and subtracting. The numbers are pretty small - usually less than 10, though not always, but the running total can grow fairly large.
I am sure that it's good for my brain to play this game, that I'm improving my ability to do mental math.
Here's what I wonder, though: does it matter if I get the right answer? I have discovered at times that as I keep track of the running total, I have made computational errors - not particularly surprising, since it isn't something I'm particularly stellar at. My sense is that it's the activity of trying the math rather than getting the right answer that's important, especially since I doubt that I'm reinforcing bad math by occasionally adding numbers incorrectly. However, I can believe it would be a problem to form neural pathways to bad computation. I don't know of any studies that have looked at this, so I'm not sure we know the answer.