Maths Skills
Before we start we need to lay some ground work. The first is understanding the mathematical principles involved in physics, the second is understanding the scientific process.
Mathematics is the language of physics. When scientists conduct experiments they measure. Establish relationships. So it is important to know how we measure and how we establish those relationships. Following few lessons examine some important principles in
Mathematics is the language of physics. When scientists conduct experiments they measure. Establish relationships. So it is important to know how we measure and how we establish those relationships. Following few lessons examine some important principles in
- what we measure
- how we measure
- how we represent our values and
- how we establish relationships.
1. Dimensions and Units, and the SI system
Into to units and SI
the electron volt
atomic mass unit
Into to units and SI
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This is a brief summary as to what dimensions and units are and why we use a standard set of units called SI units.
The tabs refer to to specific types of units which, although our non-SI units, are two types of units used in physics on a regular basis. |
the electron volt
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Why is this here you ask? The electron volt is a non-SI is a unit that is often used in nuclear and particle physics. It is sometimes used as a unit for energy, and in particle physics it appears to be used as a unit for mass. These two videos examine the electron volt, in both contexts.
atomic mass unit
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The SI or MKS unit for mass is the kilogram. However, it's inappropriate as a unit when the masses are extremely small, such as individual atoms. This is because the values we get are so small that we do not appreciate how small they really are.
The atomic mass unit is a non-SI unit which allows you to appreciate the relative sizes masses of objects at the atomic scale. |
2. Simplifying the maths -scientific notation, prefixes, Significant figures, Orders of Magnitude
In physics, we make measurements. In many cases, those measurements may involve extremely large values, or extremely small values. To negotiate those values we use various mathematical tools to make meanings of those numbers. The following videos examines four different tools we use to allow us to manipulate numbers more effectively.
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worksheets
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In this video, as part of my skills series, I look at what scientific notation and engineering notation is, how they are different. I also use a few examples to demonstrate them
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How are prefixes used in science? They are small additions to units that give a scope of the size of that unit. This video runs through the different prefixes and how to use them.
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Significant figures, or digits, allow you to assess the precision of your measurements. But what are the rules for determining the number of significant figures? Watch the video and find out.
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Order of Magnitude is a useful tool for estimation, but what are they? In this video I explain what they are and how you can use them.
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worksheets
The following are various worksheets as well as answers
- Prefixes - [answers]
- Prefix Fun - [answers] - This worksheet is a bit of fun and not the be used in SERIOUS discussions
- Scientific Notation- [answers]
- Significant digits - [answers]
3. Graphing
When we collect data, whether it is two sets of variables where we are trying to establish relationships between them , or we collect multiple variables and were trying to identify various correlations between those samples, will use graphs to visualise those relationships.
However, it's important to know what type of data you are collecting and how you will represent that data in the form of graphs. It's also important to use those graphs to allow you to determine the mathematical relationships between the data sets you collect.
The following two videos are designed to elaborate on these points.
However, it's important to know what type of data you are collecting and how you will represent that data in the form of graphs. It's also important to use those graphs to allow you to determine the mathematical relationships between the data sets you collect.
The following two videos are designed to elaborate on these points.
videos
resources
videos
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Determine the appropriate graph types based on what type of variable you are analysing: nominal vs ordinal, discrete vs continuous: and thus bar graphs vs line graphs vs histograms.
This video examines the different types of variables you encounter in data collection and then explains why certain graph types are used to represent that data. |
When we graph variables that have a relationship, the graph allows us to determine their mathematical relationship
For example if we graph y vs x, and it is linear, the slope will be the constant of proportionality ie y = mx.
If we then extrapolate the line through to the y axis, we can determine the coefficient
If the graph gives what appears to be parabola, then if we graph y vs x^2, (as opposed to y vs x), we will also get a straight line, and thus the slope will give us its coefficient of proportionality ie y = mx^22
Many relationships in physics are relatively straightforward forward
For example if we graph y vs x, and it is linear, the slope will be the constant of proportionality ie y = mx.
If we then extrapolate the line through to the y axis, we can determine the coefficient
If the graph gives what appears to be parabola, then if we graph y vs x^2, (as opposed to y vs x), we will also get a straight line, and thus the slope will give us its coefficient of proportionality ie y = mx^22
Many relationships in physics are relatively straightforward forward
- linear y=mx
- square, y = mx2
- inverse y = m/x or y = mx-1
- inverse square. y = m/x2 or y=mx-2
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Linearizing data is about determining the relationship between variables, specifically, the independent and dependent variables. In this video I show you how to turn non linear graphs to linear graphs and thus determine the mathematical equation that describes the variable.
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resources
The Scientific Process of Measurement
When scientists make measurements I have to consider a number of things. They need to use appropriate tools for their measurement.They need to be aware of any possible errors that may exist in what they measure which can contribute to any uncertainties as well as how accurate their final answers are. I also need to ensure they conduct the experiments in such a way that measures what they testing and ignores other factors. And they need to ensure that if they do research, the information they gather is correct.
Following videos examines some important considerations if you want to understand the process of science. Terms such as precision and accuracy, uncertainty and error, reliability and validity – these all have very specific meanings which may be different to what the general population might think.
Following videos examines some important considerations if you want to understand the process of science. Terms such as precision and accuracy, uncertainty and error, reliability and validity – these all have very specific meanings which may be different to what the general population might think.
4. Understanding Precision, Accuracy and Uncertainty
When scientist make measurements they have to be aware of the precision of the instruments, how accurate they are with their measurements and aware that there will always be some uncertainty in the measurements they make.
These three terms have very specific definitions in the domain of science and the following video examines them and how to use them appropriately.
These three terms have very specific definitions in the domain of science and the following video examines them and how to use them appropriately.
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5. Understanding Errors
We all make errors, even in science! When scientists measure and collect data, they need to be aware that Errors can exist in their data. The following video examines the two basic types of error and ways that they are reduced.
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problems
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6. Validity, Reliability and Accuracy
in first hand investigations
in research
in first hand investigations
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What does validity, reliability and accuracy mean in experiments?
If you want to understand how scientific process works you need to know what those terms mean, either in the case where you are doing firsthand investigations, or when you are doing secondary investigations or research. |
in research
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How do you ensure your sources are valid, reliable and accurate? What do those terms mean? What's a useful easy to remember the criteria? This videos covers those terms and then explains the CRAAP test to hep you evaluate your sources. Go to 8:05 if you just want the CRAAP test
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