Differentiation Tools

Year 3 mental arithmetic: Sets 5 and 6

2011-12-11T11:23:00.000-08:00

This week I have the following two sets of mental arithmetic questions published for 3 years. They concentrate on one-step problems, recalling addition and subtraction facts up to 20, adding and subtracting multiples of ten and know 5 and 4 times tables.

There are several ways that these questions can be used and how children to answer them. It is sometimes a good idea to use a numeral cards, so that children can keep up the answer. Number of fans a similar goal. Sometimes you might want to be called the answers, or to be written. The sheets of the question can be used for this purpose.

Y3 mental arithmetic set 5 and 6

Bad boys of physics

2011-12-07T22:44:00.000-08:00

In the July issue, about Lenny Susskind Scientific American runs a bad boy or Physics story (see also here). Here is the "nut graph":

Physicists want to understand the deepest levels of reality now largely working within a framework of Susskind. But a funny thing happened along the way. Susskind wonder or physicists reality can understand.

In the interview, Susskind explains that he was a bad boy as a youth, but "just so much better than anyone else, including the professor." In recent years he is the most prominent promoter of the string theory multiverse, and now claims that this pseudo-science convincing the area dominates (SciAm seems agree ...), with the situation like in the early days of QCD:

A large part of the physics community has left trying to explain our world so unique, as the only mathematically possible world. Right now the multiverse is the only game in town. Not everyone is working, but there is no coherent, sharp discussion against it.
In 1974 I had an interesting experience on how scientific consensus forms. People worked on the as yet untested theory of hadrons [subatomic particles such as protons and neutrons], that Quantum Chromodynamics or QCD is called. At a Conference of physics I asked, "you people, I would like to know your belief about the likelihood of QCD the correct theory of hadrons." I took a poll. Nobody gave it more than 5 percent. Then I asked: "what are you working on?" QCD, QCD, QCD. They worked all on QCD. The consensus was formed, but for some strange reason, people wanted their skeptical side. They wanted to be hard-nosed. There is an element of the same thing around the multiverse idea. A lot of physicists don't want to just fess up and say, "look, we do not know another alternative."

Susskind had a DISTINGUISHED career as a theorist for many years, and has managed to do very well with his multiverse campaign for quite a while now. There's a lot of coverage of this story on this blog, for some high points, see here, here, here and here.

In other news, the media full of stories about another physicist who has been a bad boy, David Flory. He began his career as a HEP theorist back in the late 1960s, as a student at the Yeshiva University, and collaborator with Susskind. Just as a large number of other people, he got his permanent academic job in 1969, and has since then at Fairleigh Dickinson University.

Year 5 Division problems: calculation of mentally

2011-12-03T15:38:00.000-08:00

Here is the second page that year 5 Division problems who looks using mental skills can be answered. The questions deal with a number of concepts relating to Department, including:

scrap

divisibility rule for 9

and factors.

Watch out for errors that in issues such as number 9 occur, where the number of whole lengths of wire is calculated and the rest is irrelevant.

This page, and other similar worksheets can be found in the year 5 category.

Division problems (2)

Year 4 mathematics worksheet: tenths of rectangles

2011-11-29T05:36:00.000-08:00

A good way of working with decimals is the use of shapes that are divided into ten equal parts. The form is a single whole and each part is a tenth, which can be written as 0.1.

This page has a selection of shapes and asks the child to write down the amount that is gray. When all parts of a shape are shady this counts as ten tenths, or entire one.

While the printed pages almost always display the decimal point located on the line most schools show like half way up the line: the main thing is that it appears clear.

This page can be found in our year 4 mathematics worksheets in Counting the number and category.

Tenths of rectangles (1)

Year 1 mathematics vocabulary

2011-11-25T15:07:00.000-08:00

If a child does not respond on a mathematical question can it be because they don't understand the words or instructions used. Another problem can occur when a mathematical term has a different meaning in everyday English, for example, ' table '.

In the category of mathematics year 1 there is an excellent list of the vocabulary children needed to understand and use in year 1. For example, the following list has the new words that they are in school in year 1 encounter have to do with the compute and solve problems.

Words to do with the compute and solve problems:

plus near double

How much more is. ..? how much less is. ..?

subtract min

half halve

equals sign

number sense

operation

There are similar lists for the calculation, measures, and position. These words may greater be printed so that they can be used as ' flashcards ' or displayed on the wall.

Go to the year 1 vocabulary lists.

Local Blogs

2011-11-21T11:18:00.000-08:00

There are now several excellent blogs somehow to mathematics is carried out by the local population, including a few new ones, so I thought that would be a good idea to mention here these related:

Andrew Gelman of Columbia Statistics Department runs the very active Statistical Modeling, causal inference and Social Science blog, which boasts a wealth of all kinds of different subjects, from technical ones about statistics, to social sciences applications.Emanuel Derman, who began his career as a HEP theorist, was one of the early migrants to the financial industry and now has here teaches at Columbia in the Financial Engineering program, a new blog at Reuters. His last book was the very interesting my life as a Quant, this autumn, he has a new coming out right models worn Badly. Cathy O'Neil, a mathematician who learned here for a while before you change career path, starting with a job at the hedge fund D.E. Shaw, has recently started with the beautiful Mathbabe blog. I think I mentioned this already, but one of my colleagues, Johan de Jong (Cathy's husband) also has a blog, the stacks Project Blog. If your metrics to evaluate blogs like "quality of information is" x "degree of abstraction and technical", are the best blog in the world.

If you have comments on these blogs, I encourage you to post them there rather than here. I would be interested in hearing about any other local mathematics/physics related blogs that I am not aware of.

Update: another local mathematics, physics-related blog has made its debut today, Davide Castelvecchi degrees of freedom. It is part of a network of new blogs today being launched by Scientific American, who is based in New York.

Toddlers and Math

2011-11-17T21:54:00.000-08:00

Learning mathematical concepts actually beginning with toddlers. After all, think about how excited a toddler is when they tell you they are going to be 2 years or 3 years old. They are so quick to parrot those numbers, although they are still not sure about conservation of number or number correspondence. However, it is a great time to promote number concepts and develop a joy of math in concrete methods. discover what these early number concepts are and how to use them to promote and develop the significance of those years toddler and beyond.

See also: math concepts learned in kindergarten.

Source of the Week: reflective symmetry

2011-11-13T14:48:00.000-08:00

There is quite a lot of work in the year 6 on symmetry and the subject often comes in the key stage 2 SATs.

This number includes important vocabulary and by the end of the year 6 children must know and be able to read, write and use the following quite tricky words:

Mirror, line of symmetry, line symmetry, symmetrical, reflect, reflection, translation, axis of symmetry, reflective symmetry.

They must also be able for symmetry with the help of a mirror and by folding testing.

Children are expected to outline the reflection of a simple form in a line of the mirror where no or only a part of the shape's edges parallel or perpendicular to the line of the mirror.

This might seem simple, but actually prove problematic to many children. A small mirror or tracing paper can be a great help with this.

Year 6 maths worksheet: reflective symmetry

Year 6 equivalent fractions

2011-11-09T16:18:00.000-08:00

Here is another page of equivalent fractions. A part of each pair of fractions is missing and the missing numerator or denominator should be entered. Remember, equivalent fractions are fractions that have the same total value.

One interesting way to check whether two groups equivalent is to perform a couple of multiplications; What is known as cross multiplication. To verify that a/b is equal to c/d just multiply a by d, and then (b) multiplying c. If the two answers are equal then the fractions equivalent. This is a really good way to check to see if the answers are correct.

Equivalent fractions (pg 2)

Year 5 mathematics: written multiplication

2011-11-04T23:53:00.000-07:00

Here we have a second page questions that an intermediate step in the progress in the development of an efficient, standard written method of multiplication. It assumes a good knowledge of tables before you start.

This method breaks the task in four parts. For example, when multiplying 538 by 4, the four parts are:

1. the multiplication of 500 by 4

2. the multiplication of 30 at 4

3. multiplying 8 by 4.

4. Add the four answers to reach the final answer.

While this is a good method I prefer to work in the reverse order of starting with the units, then the trans-European networks and finally the hundreds, although if the child understand what happens it makes little real difference.

Multiply a number by a 3 digit number 1 digit (2)

Year 1 mathematics resources

2011-10-31T10:41:00.000-07:00

All worksheets mathematics for year 1 must be found by clicking on the link for free math worksheets at the top of the page. The worksheets are organized into categories according to the directives of the primary framework for mathematics, although this is now revised.

The categories are:

Counting and number: watching small numbers in steps of one count and write numbers.

Some facts to know: count on and back in two and knowing addition facts to 5.

Calculation: including small numbers, and an introduction to add money

Understanding form: in this stage recognition of triangles, rectangles and squares, as well as the introduction of some 3D shapes

Measuring: using non-default measures and compare

Treatment data: mainly creating lists

Using and applying mathematics: number of stories and investigations.

While there is a significant amount of here is that it is next to nothing compared to the URBrainy site the best that I found online, with more than 1,700 colorful pages of mathematics for the year 1 is have, including full answers.

Go to our year 1 mathematics resources

Mathematics resources: Written addition

2011-10-27T05:52:00.000-07:00

One of the most popular parts of the site for parents is our free math worksheets: four rules pages on written addition.

Many parents think that the methods they learned at school (and for many this would in the 1990s) different from today. This is only partially true. Since the beginning of the numeracy strategy and later that the primary framework for mathematics has been the emphasis on the preparation of children so they understand the written methods that they use. There's a lot of preparatory work and methods, often called "the pursuit of the standard written method ' so that cannot be known to parents, but the end result is pretty much the same. It is this intermediate stages which some parents find puzzling.

The default method is written the layout the sum vertically, with numbers will be added under each other. The units are added first, then the trans-European networks and so on. We have several worksheets to illuminate this method completely.

Go to written methods of addition

Fast printing: chart, grids, and Dot paper

2011-10-23T22:10:00.000-07:00

Can't make it to your stationary shop? Some isometric paper needed? graph paper? grid paper? No worries, it's okay here. Four grids per page or per a grid page, you will find some quick PDF is printed here. dotted grids with or without numbers, everything to your homework needs is here, only thing needed is your printer and paper.

Building better Math teachers

2011-10-20T19:59:00.000-07:00

Many educational jurisdictions have school improvement programmes in place to improve the overall performance in mathematics., however, what does this look like?

A change in curriculum? A change in the developmental sequence of concepts learned? Hiring more qualified teachers? Larger blocks of time spent on teaching mathematics?Providing professional development to existing mathematics teacher?

A professor and Chairman of mathematics education in the Faculty of education, Dr. Brent Davis has a few answers, I am inclined to support. Davis claims "We can build a better math teacher." "But it's more about the fascinating Deconstructing concepts than about learning more advanced math or involved in solving problems with each other." Science daily.

Teachers who work with teachers in support of the evidence and research-based strategies takes time and money, but it seems that the benefits are there, but all too often that a teacher wants to learn in the way they were taught, however with the support, mentoring and ongoing professional development, it seems we may ' build better teachers. "

Maximize summer holiday

2011-10-17T06:20:00.000-07:00

Teachers often complain about the lag in learning when students come back from summer vacation. There really doesn't need to be a delay as learning during the summer in a fun and engaging way. Especially so with mathematics.

The Math Playground is interactive and offers practice in fractions, decimals, percent, angles, early algebra, trig, multiplication and much more. If children just spent 15 or so minutes 4 or 5 times per week, the results will surprise you and will most definitely keep happy teachers. Although worksheets fine for practice, they are not a lot of fun and holidays are taking a break and some fun! ?

Year 6 maths worksheet: Equivalent fractions

2011-10-14T05:35:00.000-07:00

Insight into equivalent fractions is the core of understand how fractions work. Much work needs to be done in previous years to show that fractions such as 1/2 and 2/4 have the same value. This is usually done by colors or shading parts of rectangles, circles.

Two fractions that are equal in value that we say are are equivalent.

2/5 is equal to 4/10 which is equivalent to 40/100.

If we start with a group and both the numerator (top number) as the denominator (bottom number) multiplied by the same number remains the break with the same value. The same goes with Division, but not add or subtract.

This makes multiplying fractions much easier than adding or subtracting from them.

Equivalent fractions (pg 1)

Strings 2011

2011-10-09T13:45:00.000-07:00

Strings 2011 began today in Uppsala, with presence quite a bit lower than in the past (259 registered participants, versus 500 or so on some of the past such conferences). One reason for this may be the cost of the Conference on high (discussed here), another possible that excellent video of the talks is available, so why bother travel to Uppsala?

The opening talk was by David Gross, who tried to address the question "where do we stand?" for string theory. He claimed that the field is "very healthy", "lively and exciting", "enormous progress in a variety of areas", with "huge progress" in N = 4 flat nr. At the same time, he acknowledged that it was "very disappointing" that string theory was 43 years old.

Strings XXXX conferences featured in the past, often a call for progress towards making predictions which could be tested on the LHC. With LHC data now, gross acknowledged that this has been a failure: there are no string theory LHC predictions. He put a positive spin on this by noting that the absence of any BSM signal on the LHC so far not a concern for string theory, since string theory cannot be tested on the LHC. As for the absence of any supersymmetry signal so far, he says that "I personally am not still concerned", while acknowledging that some people are becoming increasingly pessimistic. While no SUSY not a concern for string theory is, he feels that "it would be very nice for string theory as SUSY appeared". Presumably, he bets on SUSY at the LHC, but he gave no indication of when he would begin to worry (or the bets pay) as SUSY remains there are not.

The main area of progress he sees is the usual gauge-gravity duality that has dominated the field for years, along with progress in N = 4 SYM amplitudes. He sees the Verlinde "entropic Gravity" as an "exciting development I find immensely interesting". Apparently later this week to discuss Verlinde his latest ideas which supposedly an explanation of dark energy and dark matter.

Gross went on quickly the questions about string theory he first raised in a similar talk 26 years ago, which usually are unanswered, including the basic "what is string theory?". The supplementary questions raised by attempts to understand the emergence of space time in the background of a deSitter were a factor that inspired him to end up with the quote that:

The main product of the knowledge is ignorance.

To which he added "after 43 years of string theory, it would be nice to have some answers."

Surprisingly, not a word of gross on great ape or the multiverse. I assume that he is still an opponent, but perhaps feels that there is no point in beating a dying horse. Susskind is not there and oddly enough, the only multiverse-related conversations are from the two speakers brought to do public lectures (Brian Greene and Andrei Linde, hawking's health has kept him from a scheduled appearance of). So is the multiverse with a large proportion of the public profile of the Conference, but pretty well suppressed on the scientific sections. It is also pretty well suppressed "string phenomenology", or any attempt to use string theory to do integration. From 35 or so conversations I see only a few related to this, which is still the advertised primary objective of string theory.

I'm curious about the discussions of Witten, Gaiotto and Gukov, which I hope provides a gentle introduction to their intriguing recent long papers on the arXiv. As far as I find time to watch discussions this week and have comments about them, I will try and add updates to this post.

Update: after most of the discussions online look, is the most notable thing about Strings 2011 how little there is about string theory. One of the speakers, Chris Hull, began his speech with the comment:

During the lunch today was one of the organizers observe that my talk was unusual in one of the few actually talks about string theory. It would be interesting to speculate about what that could mean about the condition of the field, but it would be shameful to do here.

One of the main themes of the Conference so far has been the study of mathematically interesting supersymmetric QFTs in 3, 4, 5 and 6 dimensions, often obtained from a specific class of 6 d theories, which itself remain poorly understood (what is known about them was reviewed by Greg Moore). Witten gave an overview of his work relating Khovanov Homology and QFT, where a chain of different 6 d, 5 d, 4 d, 3D and 2d QFTs. Nati Seiberg reviewed the technology used for the construction of these theories over different backgrounds, noting that this was all about "rigid" SUSY theories and Supergravity, string theory create no appearance.

Update: the videos of the talks are all now. I took a look at the Verlinde spoken, and the ideas he sets still seems to me pretty much empty of all important content. In Jeff Harvey's summary of the Conference he notes that many people have noted that the Conference has not been a lot of string theory. About the landscape is his comment that "personally, I think it's probably not possible to do science in this way." He describes the situation of string theory unification as the Monty Python parrot "no, he is not dead, he rest." while some hope that a miracle will take place on the LHC or in the study of string vacua, revival of the Parrot to speak out.

That the summary main speaker at the Conference for a field the State of the main public motivation for the field as similar to that of the parrot in the Monty Python sketch would compare is pretty remarkable. In the sketch, the whole joke is the Parrot's seller reluctance, no matter what, admit that what he sold was a dead parrot. It is a good analogy, but surprisingly that Harvey would use.

Year 3 mental arithmetic Sets 3 and 4

2011-10-04T19:55:00.000-07:00

Two sets of mental arithmetic questions suitable for 2 years. These sets of 10 questions relate to the count and back in dozens, addition, subtraction, and place value.

I have been asked for more in the way of mental arithmetic questions on many occasions and as the weeks go by this must be in a really useful resource. I'm also trying to match the questions to the primary framework for mathematics Planning, so this could be particularly relevant for the first few weeks of the autumn term.

Year 3_Mental arithmetic (3 and 4)

Source of the Week: magic square with negative numbers

2011-09-30T02:30:00.000-07:00

With the year 6 SATs and another half term in mathematics to get by there never been a better time to some studies and puzzles. One of my favorite topics is the magic square, as it can be incredibly simple or extremely complex. This special magic square is quite challenging when it comes to adding positive and negative numbers, so it is a good check to see if children trust dealing with negative numbers

To convert the numbers in the squares is given on all three magic squares and on the first puzzle there is an indication that each row, column and diagonal adds up to-3.

One of the best strategies to use with this is to work out what the number should be and what the total for each row etc should be. It is also a good idea to cut out small squares with the numbers on around the Board so that they can be moved with ease.

Please note that there are several ways of solving this magical squares and only one way it appears on the page response.

Magic square negative numbers

Short Division of decimals (2)

2011-09-26T13:51:00.000-07:00

Here is another page of practice on the use of the short method of Division of decimals. All unnecessary write numbers with the short method is avoided. The numbers are distributed are just units and tenths that helps with getting the method correctly.

One of the best ways to smooth with this method is to talk through out loud. Eventually this leads to talk by, ' in your head '.

If we look at question 1 divided by 3 7.2, the verbal stages:

a. how many 3s in 7?

b. 2 times 3 is 6 so there 2 with a remainder of 1.

c. Insert the 2 on the line response, directly above the 7.

(d). Insert the decimal answer just above the line, so that it can be clearly seen.

e. the rest 1 is placed just before the 2 (usually smaller written).

f. how many 3s in 12?

g. 3 x 4 is 12 so the answer is 4.

h. place the 4 on the line response, directly above the 2 (tithes).

i. reply 2.4

This page can be found in our four lines, Division category.

Division of decimals (2)

$ 6.5 million for entropic gravity

2011-09-22T06:45:00.000-07:00

One of this year the Spinoza prize goes to Erik Verlinde. It comes with 2.5 million euros to the winner of research fund. Last autumn Verlinde received a 2 million euro ERC Advanced Grant for the funding of its research programme, so that's a total of 4.5 million euros, or about $ 6.5 million this past year.

Verlinde's current research focuses on the ideas about "emergent gravity" (see here and here). According to Wikipedia explains his work the observed value of the cosmological constant.

I have no idea how Verlinde will spend the money, but it seems that emerging Ernst research particularly well will be financed. 6.5 million dollars that I would estimate corresponds to approximately 100 post-doctoral years. In a few weeks will Verlinde reveal his latest work on strings 2011. Because that is one of the most expensive conferences around (see here), maybe he could chip in to fund. He must be able to finance one strings 20XX via at least 2,050 I would estimate.

Know Division facts: year 5 maths worksheet

2011-09-18T02:19:00.000-07:00

There is no doubt that most children find Division harder than multiplication, but there is little real reason for this to be so. Most Division questions can be turned on their head be made to look like multiplication. For Example:

30 ÷ 5 =?? can be considered as 5 times what number makes 30?

?? ÷ 6 = 7 can be considered as 6 times 7.

60 ÷?? = 10 can be considered as 10 60 times what number makes?

The key to success with Division is a really good knowledge of times tables.

This worksheet looks on this species Division question, all with simple numbers and no waste and is a good assessment sheet to see if Division is understood and tables known.

This can be found in our category year 5 know number facts.

Know Division facts (1)

How the Hippies stored physics

2011-09-13T13:29:00.000-07:00

An outline that I wrote of how David Kaiser of the Hippies stored physics is now available from the American scientist. A short summary is that I think it's a wonderful book, tell in well researched and entertaining a story that I've always wanted to know more about fashion. I am not convinced by the main argument of the title, that this group of people "Physics saved", rescuing a suffocating ideology "shut up and calculate" by the road to the importance of the theorem of Bell's tones and help start the field of quantum information theory. Maybe emulates the author just his subjects, known for their playful outlandishness.

There are quite a few interesting things I learned from the book that didn't make it in the review. An example is the story of the (of EST fame) Werner Erhard theoretical physics conferences in the late 1970s and early 1980s, organised in collaboration with Sydney Coleman and Roman Jackiw. One of the factors that these events put an end to was the advent of string theory: it was felt that no string theory Conference without attending the whites would be taken seriously, and then nothing wanted to Whiten with EST and its founder (although he had attended, with the likes of Feynman and Weinberg, the earliest Conference in the series back in 1977).

If you do find interesting this topic, I highly recommend the book.

For a different take on the same subject, one of the main participants, is Jack Sarfatti memoirs Stargate free available these days in a pre-publication version here.

I'm afraid that my own description of where the physicists described in the Kaiser would not book ended the field of quantum information theory, but the much larger quagmire of dubious claims about quantum physics which is still very influential. For example, this week at the AAAS meeting in San Diego there is a session on Quantum Retrocausation is, see this listing from the world of parapsychology.

Update: I must also mention that Chad Orzel the book discusses here and here.

Singapore Math the answer? Look again ... ...

2011-09-09T20:01:00.000-07:00

More than 2000 schools throughout the US have adopted the Singapore math method. Singapore is doing well with its methods, then again, Singapore is Singapore. And, although Singapore on the 2nd in fourth grade math and, researchers tend to support their strategies, working in the same way here? Perhaps not. Unfortunately, when tried, the scores have dipped lower than normal. In fact, the scores were very disappointing. One would think that a heavy focus on the ' back to basics ' approach to transitional period type students. If not Singapore, what works? In my opinion-balance! And I will stop there. However, it's worth checking out the challenges that faced a school while trying of Singapore.

6 times table space challenge

2011-09-05T02:11:00.000-07:00

Children need so many opportunities as possible to practice their knowledge of tables and teachers are always looking for something else to maintain interest. Hopefully this page will be useful, since there is a bright and fun way to show how well the 6 times table is known and it can also be used as a timed challenge.

Beginning at the start moving to the first box, and write the number 6 time shown on the left side, then on to the next box, and so on. There are 20 questions at all; Some children can be ' stuck ' on a question, encourage them to go and then return to the end. If they are stuck remind them, for example, that if they forget 6 x 6 is the only six more than 5 x 6 which they must be able to remember.

This page can be found in our section math worksheets, multiplication four lines, and hopefully I will be adding similar pages for other tables times did not last long.

6 x tables space challenge