Year 3 mental arithmetic: Sets 1 and 2

I'm embarking on something new this week which will hopefully to a really useful source will grow as time goes by. It is the first in a series of mental arithmetic questions aimed at 3 years.

It consists of two sets of ten questions, followed by an answer sheet. Each set is a full A4 page so they can be used in different ways. If given orally, the teacher/parent page-only the answer print, like all questions are included on this and the kids can just write the answers or call them out. If the teacher/parent wants the child to read the questions can then they print the question sheets as well. This can also be displayed on a whiteboard.

The first series of questions focus on writing integers, count on and back in the trans-European networks, addition, subtraction, and place value.

Year 3 mental arithmetic (set to 1 and 2)

Summer Vacation

Summer holiays are great! We've been anticipating them for weeks now. summer provides us with a time to relax, a time to leave the stress behind and enjoy the great weather. However, the major concern for educators about summer vacation is that the potential gap in learning. Summer Vacation offers a great opportunity to learn without the gap to give summer! How is this done? Well, take the a subject that causes grief. For many students, this is all it takes to close the gap, or to ensure the gap no wider math., is 20 or so minutes 3 o 4 times per week do a little exercise and reviewed. The benefits are considerable.

Check out the following worksheets to ensure that you stay on top of these mathematical concepts this summer:

Year 5 line charts

With a nice hot summer for us, what better way to spend a mathematics lesson then watch line graphs of temperatures?

In year 5 children should build and interpret line graphs. The important aspect of a line chart is that each point on the line will have a value. The chart in this worksheet indicates the minimum and maximum temperatures every month for London. It would be very worthwhile to find other temperature charts for cities around the world and compare them.

Another great idea is to find data for countries in the southern hemisphere and compare the shape of the line graph to London.

Why not go to our page Handling data and probability for year 5?

Mathematics and physics, in the summer 2011

This week in Philadelphia the String-Math 2011 Conference is underway, scheduled as the first of a series, with String-Math 2012 next summer in Bonn. Slides of the talks are listed here. There was also supposed to video, but the saved video seems to be a kind of UPenn login required, and I haven't been able to get the streaming video to work. Public talk by Cumrun Vafa crosses the classic message that strings have come to the rescue of physics, unifying QM and gravity, and which:

Flexible geometry of strings seems to explain all known interactions (at least in principle)

The techinical talks relate to a lot of ground, much of it having little to with string theory. Michael Douglas's talk surveys that related to find non-Perturbative formulations of quantum field theory hold that one could hope to have something to say about it exactly, but it contains many more questions than answers. I am most curious about David Ben-Zvi talk tomorrow, so hope that slides or video of that will be available.

The circle of ideas on gauge theory, geometric Langlands, TQFTs and representation theory gets even more attention than the mathematics of string theory this summer. In a few weeks will start with a two-part program on Luminy and then Cargese on double affine Hecke Algebras, the Langlands program, affine varieties of the flag, Conformal Field Theory, Super Yang-Mills theory. I do not know who the author is, but some person or group has written for the occasion a wonderful summary of the current activity in these and related areas of mathematics, see here. Next month, will be hosting a program KITP on non securities and dualities in QFT and Integrable systems that relate to some of the same topics will have.

In some other non-related news, if you understand French, you can listen to an interesting series of interviews with Pierre Cartier here. Finally, it was recently announced that $ 1 million this year is to share my colleague Richard Hamilton Shaw Prize for Mathematics with Demetrios Christodoulou. Richard Congratulations!

The Quantum story

Jim Baggott of The Quantum Story: A History in 40 moments is now here and I have already starting to see it in the bookstore. I read most of it a year or two ago, when he sent me a draft of the manuscript questions if I had a look at it, and very much enjoyed getting the chance to see it than would take. If you are looking for an excellent popular level physics book to read, I recommend that you consider this one, that is accessible for just about everyone, no matter what their background.

The subject of the book is in General, the story of quantum physics told historical with a structure of 40 vignettes. The first three chapters deal with mainly dramatic events of the period of the mid-1980s to the early 1930s during which physicists the basic structures of the quantum theory discovered struggled to get some sense of them. The following two takes the late 40s to mid-70s during which a long sequence of discoveries about elementary particle physics reed theoretical progress in quantum field theory and measure theory, culminating in the standard model fall into place in 1973. The material that Baggott works here is the subject of many other books, but he did a wonderful job of bringing together in a quick but very clear and entertaining story. Along the way, the individual stories he often tells contain fascinating details I never heard before, although I thought this was a subject I already knew too well.

The next last chapter starts with the 1950s and David Bohm, picking up the thread of subsequent debates and discoveries in connection with the general problem of interpretation of quantum mechanics. It brings this story on the pitch, explain some of the current questions that are still being discussed. The last chapter gives an appropriate short discussion of speculative ideas in quantum gravity and string theory which theoretical research have dominated the last few decades, make clear that they still have a long ways from the solid science which is the main subject of the book.

The LHC and the search for the Higgs makeup a final epilogue or 41st vignette, accurately describing the high expectations and the drama surrounding the last period of the long wait for new data that finally put an end this year. The story of quantum theory is not ready, and we all hope that very soon we will have some clues about where the next will go.

This week's Hype

The latest New Scientist has a much larger dose of M-theory/multiverse hype than I in one place have seen in a while. There is a four-part series on M-theory (here, here, here and here) by Mike Duff. It tells the story of the progress of modern physics in the last century, according to the dominant ideology: general relativity Kaluza-Klein extra dimensions, super-symmetry, Superstrings, branes, ends in the apotheosis of M-theory more than fifteen years ago. For the current state of affairs, Duff describes his "M-theory" predictions about the real world (that 4 qubits 31 different ways can be entangled, something discussed here). He ends with the M-theory multiverse and the following comments on whether this can ever be tested:

So is M-theory the final theory of everything? With rival attempts falsifiable predictions are hard to come by. Some generic functions such as supersymmetry or extra dimensions can be displayed on the collider experiments or in astrophysical observations, but the diversity of the possibilities offered by the multiverse allows precise predictions difficult.

Are all the laws of nature that we set theory of fundamental theory perceive? Or are some mere accidents? The jury is still out.

In my opinion, many of the important issues remain unresolved for quite some time. Finding a theory of everything is perhaps the most ambitious scientific undertaking in history. No one said that it would be easy.

Here he makes clear that, at least while he is still around and enjoy academic notoriety because of M-theory, there is no danger that it will be faced with a kind of test can not. He answered the critics of M-theory by claiming that the failures not important. It is the dominant paradigm, and as such will reign until someone comes up with a different theory of everything that is not a failure.

Elsewhere in the magazine there is a fawning article on the recent Bousso-Susskind paper (see here):

TWO of the strangest ideas in modern physics – that the Cosmos continually in parallel universes in which every conceivable outcome of each event happens splits, and understanding that our universe is part of a larger multiverse is-have are grouped in a single theory. This has lost a bizarre but fundamental problem in Cosmology and physics circles buzzing with excitement, as well as some bewilderment.

No critics of the idea were by the writer, with the discussion about blogs described as:

The paper has caused a flurry of excitement on Physics blogs and in the wider physics community. "It's a very interesting document that a lot of new ideas," says Don page, a theoretical physicist at the University of Alberta in Edmonton, Canada. Sean Carroll, a cosmologist at the California Institute of Technology in Pasadena and author of the blog Cosmic Variance, thinks that the idea has some merit. "I have a confused skeptic a believer for the time being," he wrote on his blog. "I realized that these ideas fit very well with other ideas that I've been thinking about myself!"

One way or the other of Lubos "them on crack" to take on the subject was missed.

Finally, the meaning of it all summarized in an editorial that States that Bousso-Susskind finally pulls the plug on religion and replaces it with the Science:

Cosmologists can now begin to take God seriously, precisely because they him (or her) can explain away.

Year 3 Mathematics worksheet: time and calendars

An aspect to learn over time that is often neglected is the use of a calendar. They don't need any explanation for children who do not come across them before and they come in different formats. The month appears in this spreadsheet starts the week on Monday, although many start on Sunday. It may seem puzzling to children as to why there are some ' empty ' days at the beginning of the first week so it's a good idea to have a calendar with available all year.

This can lead to much discussion, such as the number of days in each month, why birthdays on any other day of the week every year etc.

Using a calendar (1)

Carroll diagrams: 2 year treatment of data

Carroll diagrams are named after the famous writer, Lewis Carroll and are a way of grouping things in a ' yes or no ' way. They can be as simple as just two boxes but usually they are seen as four boxes with two attributes. In this case the two characteristics are swimming and cycling and the children may or may not each.

Carroll diagrams were introduced in year 2 as a means of sorting, but it is not until at the end of the year or 3 years where she would meet these types of diagram. The second page has a number of questions about the diagram and suggesting that children go about trying to collect their own data and their own Carroll diagram of this data.

Thanks to urbrainy.com for this specific set of pages and they have a large selection of the treatment of data resources on their site.

Carroll diagrams 1