Download a worksheet with 10 non-calculator questions on basic number work
Access students will have had a half term break filled with child-care and essays and probably plenty of reading. This simple 10 question quiz is designed to jog a few memories and provide a check of skills and attainment before launching into percentages and metric units.
xtraordinary numbers of Turpin – When drinking bury head above eyes – Will drink when a person is within 2 yards of them about 10 gulps in minute.
noise during cohabitation
Page 37b of notebook EH1.7, Galapagos Otaheite Lima, part of the Beagle field notebook sequence.
The whole of Darwin’s writings is online – Cambridge University and the Darwin family have launched Darwin Online complete with transcripts of the Beagle field notebooks. You can pull up scans of the notebooks recovered from microfilms taken some time ago. This site is a superb and absorbing resource, but I can’t help thinking that concentrating on the work of one historical figure might distort the perception of evolutionary thought – we have moved a long way from Darwin now.
The site has a retro feel, complete with use of frames to provide persistent navigation. The search feature works well and the navigation scheme encourages browsing. Links to the notebooks and other publications themselves are simple text links – no icons as used in the Galileo project at Rice university. I shall include a full comparison of these extensive hypertexts after the half term break. My main finding so far is that it does not seem possible to link directly to a given page of a notebook, there are anchors on the page but these do not figure in the URL.
I spent about 6 hours of lesson time on fractions, and students will have had access to a couple of hours of support time on the topic. I have ‘front-loaded’ the fractions for the following reasons…
When students can use ‘cancelling’ to multiply fractions like 8 / 9×15 / 16 in an efficient way, they have broadened their schema for common factors and extended the range of applicability.
If you can do calculations like 3 3/4 + 2 5/9 then you must understand skills like converting fractions to top heavy, finding common denominators, expressing fractions over a new base, and finally converting from top heavy to mixed format. This bringing together of a range of skills that we have rehearsed separately is valuable for students. As I am teaching adults, we can reflect easily on the process of complex application of the skills and examine how to make notes that will remind students about the sequence and processes.
In the last 10 minutes of a lesson, I simply put the following up on the whiteboard; 3:4 = 9:12. Then I tried 5:6 = 30:? and I had 36 back as the answer instantly. I then explained what a ratio was (I use the vodka and orange for one or for twenty – still tastes the same – analogy). I expect to cover ratio problems quickly next week.
I need to explain what I am doing, and I need to reassure students that they will find that percentages and ratios are easier to understand. I also think that when students see that one piece of Maths can explain another so that the second topic is learned much more quickly, the power of Maths is being demonstrated albeit in a restricted and ‘elementary’ context.
The Birmingham Rep is producing Pravda, a play by Howard Brenton and David Hare billed as a comedy in the main house. We have tickets for Friday.
I’ve just finished Press Gang by Roy Greenslade. This brick of a book weighs in at 300, 000 words and chronicles the history of the national press in the UK (mainly England, based in London) from 1945 to the present. It is interesting to plot the developments in mass circulation newspapers, as we are witnessing what looks like a shift in the market away from print. Greenslade’s book has a huge amount of facts and some reflection on the pressures and processes, including the effect of the emerging middle classes on newspaper markets. A joint review will follow when I have had time to chew on the book for a bit.
The shop offers Internet access at PCs for those without PCs at home. Many of these shops also provide international phone facilities using pre-paid cards. I always scan the screens to see what people are doing: e-mail, screen based chat (in Arabic), and even homework.
I hope the successor to the Red Sea cafe opens again soon.
The Flash Workshop page has examples and tutorials for teaching basic (and not so basic) maths through Flash animations. For some of these animations, the FLA files are available.
The adding fractions animation will come in handy on a projector next week. The numerators of the fractions to be added are limited to 1 or 2, but the animation does get across the idea of finding the highest common factor of the denominators and re-writing both fractions over this denominator.
Many students find moving between ‘mixed’ and ‘improper’ (top heavy) fractions hard. Another animation illustrates the transition between mixed and top heavy very well.
I have uploaded the SWF files to bodmas so that I can link to them directly and have a larger scale animation for projecting. The originals have had a small screen size set in the HTML file, and this small size will not be clear on a projected screen.
If I write 15 over 45 down on a whiteboard and ask about common factors or cancelling down, most people think of 5 as a common factor and then will spot 3. A few will go for the highest common factor of 15 directly.
I have had some success in two lessons now by stressing the common factors approach to cancelling fractions to their lowest terms, and in solving puzzles like 25 / 35 = 5 / ? and 2 / 3 = 12 / ?.
By ‘knowing your tables’, I mean being able to spot that 63 and 49 both have something to do with 7. More on errors and the stories behind what students write when they are trying to solve fractions questions later.