[Download O Level Maths Green Book Free
Addison Mauldin
What is it? A 132-page document called 'Building Our Industrial Strategy', published on 23rd January. It is a government Green Paper, which means it is a consultation document asking for feedback from both inside and outside government. Anyone can respond - the closing date for feedback is 17 th April 2017, and you can reply here .
What does it say? The report links the future of the UK's industry success to both a plan for Brexit and a need to develop education, infrastructure and funding structures. There are six key points for those working in STEM education:
The report identifies that UK workers are less productive than France, Germany and the US, and that there are significant disparities in worker production in different parts of the country, citing lack of numeracy, literacy and digital skills as the reason why. According to the report, 'England remains the only OECD country where 16-24 year-olds are no more literate or numerate than 55-64 year-olds' and that the skills levels around the country show large differences between regions. The fact that many students retake GCSEs in English and maths and continue to fail them is mentioned, alongside the assurance that government is reviewing current policy in this area, including supporting FE colleges to become centres of excellence in teaching English and mathematics and asking the Education Endowment Foundation to expand their remit to consider post-16 issues. There is also mention of a 'transition year', already proposed in the 'Skills Plan' published last summer, to provide intensive support in numeracy and literacy and other basic skills to help young adults prepare for employment and stop them leaving education at 16.
It is noted that, while the UK has more Nobel Laureates than any other country outside the US, we spend only 1.7% of GDP on research and development (compared to OECD average of 2.4%) - and that funding is heavily focused on the 'golden triangle' of Oxford, Cambridge and London, with a need to expand this to other areas of the country. The report suggests that innovation - not only in terms of breakthrough, but also adoption of technology and new ways of providing services - is crucial to the economic future of the UK and will be invested in by the government (around an additional 4.7 billion, or 20%, by 2020-2021). Views are sought on the priorities for this investment. It is also suggested that, while the UK has 'world-class universities', they are lagging behind in terms of 'creating innovation and commercialisation'.
While acknowledging that the UK has a high proportion of adults with degrees and some of the best universities in the world, the report suggests serious issues with our system of technical ('non-academic') education, and that industry now needs to help shape qualifications and curriculum to ensure the skills being developed are useful to future employers. The report suggests the progression paths in technical education are unclear and the choices 'bewildering', and that a clear and simple framework needs to be put in place, including 15 'core' technical routes, leading to 'full professional competence'. Institutes of Technology will be created in order to provide these opportunities. A course-finding process will be organised in a similar model to UCAS and careers advice will be improved.
The report suggests the UK has 'particular skills shortages in subjects that depend on STEM subjects', and suggests we need to 'boost STEM skills at all levels', by increasing the uptake of STEM subjects studied at university, creating more specialist maths schools (using Kings and Exeter Free schools as model) to further increase take-up of A-Level Mathematics, and improving basic numeracy levels. Even though the number of STEM graduates has been increasing over the last few years, industry demand is still unmet.
There is 'support' shown for the creation of new education institutions and the strengthening of local networks of universities 'to improve commercial opportunities'. In particular, a new research institution is being considered by Sir Mark Walport, with a focus on 'battery technology, energy storage and grid technology'. The report acknowledges the need for global collaboration among scientists: it says despite leaving the EU 'we will welcome agreement to continue to collaborate with our European partners on major science, research and technology initiatives'. A new forum has been established on 'EU Exit, Universities, Research and Innovation'.
The report places importance on 'building the pipeline of talent for an innovative economy', citing PhD students in STEM subject as significant contributors but suggesting programmes for post-doctoral and PhD programmes are oversubscribed and under-funded. Comparisons are made with other countries who have active programmes to attract leading talented academics who act as 'stars' and similarly attract others.
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Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz).
When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024.
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This unit introduces the idea that fractions come from equi-partitioning of one whole. Therefore, the size of a given length can be determined with reference to one whole. When the size of the referent whole varies, then so does the name of a given length.
Some equal partitioning of the one is needed to create unit fractions with one as the numerator. For the size of the brown rod to be named accurately, those unit fractions need to fit into it exactly. We could choose to divide the orange rod into tenths (white rods) or fifths (red rods). By aligning the unit fractions we can see that the brown rod is eight tenths or four fifths of the orange rod.
Note that eight tenths and four fifths are equivalent fractions and the equality can be written as 8/10 = 4/5. These fractions are different names for the same quantity and share the same point on a number line. The idea that any given point on the number line has an infinite number of fraction names, is a significant change from thinking that occurs with whole numbers. For the set of whole numbers, each location on the number line matches a single number. Some names are more privileged than others by our conventions. In the case of four fifths, naming it as eight tenths aligns to its decimal (0.8) and naming it as eighty hundredths aligns to its percentage (80/100 = 100%).
If the blue rod is one then the dark green rod is two thirds, as the light green rod is one third. If the dark green rod is one then the blue rod is three halves since the light green rod is now one half.
Re-unitising and norming are not just applicable to defining a part to whole relationships like this. In this unit students also consider how to use re-unitising to find the referent one and to name equivalent fractions. For example, below the crimson rod is named as two fifths. Which rod is the one (whole)? If the crimson rod is two fifths, then the red rod is one fifth. Five fifths (red rods)form the whole. Therefore, the orange rod is one.
What other names does two fifths have? If the red rods were split in half they would be the length of white rods, and be called tenths since ten of them would form one. The crimson rod is equal to four white rods which is a way to show that 2/5 = 4/10. If the red rods were split into three equal parts the new rods would be called fifteenths since 15 of them would form one. The crimson rod would be equal to six of these rods which is a way to show 2/5 = 6/15. The process of splitting the unit fraction, fifths in this case, into equal smaller unit fractions, produces an infinite number of fractions for the same quantity.
The contexts for this unit can be adapted to suit the interests and cultural backgrounds of your students. Cuisenaire rods (rakau) are often used in the introduction of te reo Māori, meaning they may be familiar to some students. Knowing the relationships between rods of different colours, without having assigned number names to the rods, is very helpful in easing cognitive load. Other contexts involving fractions of lengths might also be engaging for your students. For example, the fraction of a race or journey that has been covered at different points is practically useful. This could be linked to the early journeys of Māori and Pasifika navigators to Aotearoa, or to current journeys your students have experienced (e.g. a bus ride to camp, running a lap of the playground). Consuming foods that are linear, such as submarine sandwiches, bananas, or sausages, might motivate some learners. Board games that have a particular number of steps from start to finish provide opportunities to look at a fraction as an operator.
Students may have mixed experiences with using Cuisenaire rods. When introducing the Cuisenaire rods, ask students to think about what they could be used to represent in mathematics. Value the contributions of all students.
This week students will be learning about fractions, like three quarters and two thirds. We will be using some materials called Cuisenaire rods which are lengths of plastic or wood. They look like this:
If $c \ne 0$, then we can rewrite the level curve equation $c=x^2-y^2$ as\beginalign* 1 = \fracx^2c - \fracy^2c.\endalign*If you remember you conic sections, you'll recognize this as theequation for a hyperbola. If $c$ is positive, the hyperbolas open tothe left and right. If $c$ is negative, the hyperbolas open up anddown.
Level curves of a hyperbolic paraboloid. When the green point on the slider is to the left, as it is in the default view, the figure shows a standard level curve plot of $f(x,y)=x^2-y^2$, though it is floating in a three dimensional space. When you drag the green point to the right, each level curve $f(x,y)=c$ moves to the height $z=c$, so that they are in the same position as in the graph of $z=f(x,y)$. In this way, the figure demonstrates the correspondence between the level curve plot and the graph of the function.
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