An Overview Read the following curriculum development overview.

What's the big picture? Every computer device you have ever used, from your school computers to your calculator, has been using algorithms to tell it how to do whatever it was doing. Algorithms are a very important topic in Computer Science because they help software developers create efficient and error free programs.

The most important thing to remember about algorithms is that there can be many different algorithms for the same problem, but some are much better than others! Click an image to play sorting animations Selection sort Animations provided by David Martin from www.

However the amount of data computers use is often so large that it doesn't matter how fast the computer is, it will take it far too long to examine every single piece of data companies like Google, Facebook and Twitter routinely process billions of things per day, and in some cases, per minute!

This is where algorithms come in. If a computer is given a better algorithm to process the data then it doesn't matter how much information it has to look through, it will still be able to do it in a reasonable amount of time. If you have read through the Introduction chapter you may remember that the speed of an application on a computer makes a big difference to a human using it.

If an application you create is too slow, people will get frustrated with it and won't curriculum based assessment writing companies it. It doesn't matter if your software is amazing, if it takes too long they will simply give up and try something else!

Algorithms, Programs and Informal Instructions At this stage you might be thinking that algorithms and computer programs kind of sound like the same thing, but they are actually two very distinct concepts.

They are each different ways of describing how to do something, but at different levels of precision: Often you can get away with describing a process just using some sort of informal instructions using natural language; for example, an informal instruction in a non computing context might be "please get me a glass of water".

A human can understand what this means and can figure out how to accomplish this task by thinking, but a computer would have no idea how to do this! Click to load High Score Boxes Use the interactive online at http: Informal instructions like this aren't precise; there's no way that a computer could follow those instructions exactly, but a human could probably get the general idea of what you mean if they know what you're trying to achieve.

This sort of description is only useful for quickly giving another human the general idea of what you mean, and even then there's a risk that they won't properly understand it. For our previous non-computing example, the algorithm might be 1 Go to the kitchen. A human could follow these instructions easily, but it's still using general English language rather than a strict list of computer instructions.

Algorithms are often expressed using a loosely defined format called pseudo-codewhich matches a programming language fairly closely, but leaves out details that could easily be added later by a programmer.

Pseudocode doesn't have strict rules about the sorts of commands you can use, but it's halfway between an informal instruction and a specific computer program. With the high score problem, the algorithm might be written in pseudo-code like this: The other important thing with this level of precision is that we can often make a good estimate of how fast it will be.

For the high score problem above, if the score table gets twice as big, the algorithm will take about twice as long. If the table could be very big perhaps we're tracking millions of games and serving up the high score many times each secondthat might already be enough to tell us that we need a better algorithm to track high scores regardless of which language it's going to be programmed in; or if the table only ever has 10 scores in it, then we know that the program is only going to do a few dozen operations, and is bound to be really fast even on a slow computer.

The most precise way of giving a set of instructions is in the form of a programwhich is a specific implementation of an algorithm, written in a specific programming language, with a very specific result for any particular input. This is the most precise of these three descriptions and computers are able to follow and understand these.

For the example with getting a drink, we might program a robot to do that; it would be written in some programming language that the robot's computer can run, and would tell the robot exactly how to retrieve a glass of water and bring it back to the person who asked for the water.

With the high-score problem, it would be written in a particular language; even in a particular language there are lots of choices about how to write it, but here's one particular way of working out a high score don't worry too much about the detail of the program if the language isn't familiar; the main point is that you could give it to a computer that runs Python, and it would follow the instructions exactly: Both of the above programs are the same algorithm.

In this chapter we'll look in more detail about what an algorithm is, and why they are such a fundamental idea in computer science.

Because algorithms exist even if they aren't turned in to programs, we won't need to look at programs at all for this topic, unless you particularly want to. Algorithm cost When Computer Scientists are comparing algorithms they often talk about the 'cost' of an algorithm.

The cost of an algorithm can be interpreted in several different ways, but it is always related to how well an algorithm performs based on the size of its input, n.

In this chapter we will talk about the cost of an algorithm as either the time it takes a program which performs the algorithm to complete, or the number of steps that the algorithm makes before it finishes.

For example, one way of expressing the cost of the high score algorithm above would be to observe that for a table of 10 values, it does about 10 sets of operations to find the best score, whereas for a table of 20 scores, it would do about twice as many operations. In general the number of operations for a table of n items will be proportional to n.

Not all algorithms take double the time for double the input; some take a lot more than double, while others take a lot less. That's worth knowing in advance because we usually need our programs to scale up well; in the case of the high scores, if you're running a game that suddenly becomes popular, you want to know in advance that the high score algorithm will be fast enough if you get more scores to check.

The most common complexity is the "time complexity" a rough idea of how long it takes to runbut often the "space complexity" is of interest - how much memory or disk space will the algorithm use up when it's running? There's more about how the cost of an algorithm is described in industry, using a widely agreed on convention called 'Big-O Notation', in the "The whole story!

The amount of time a program which performs the algorithm takes to complete may seem like the simplest cost we could look at, but this can actually be affected by a lot of different things, like the speed of the computer being used, or the programming language the program has been written in.The status quo was maintained in this district because the curriculum team didn't have any discussions on the best instructional practices.

Ann had assumed that the team members already had a solid foundation on these practices, so they jumped right into writing the curriculum. I’ve been meaning to let you know about the Illustrative Mathematics blog, which launched a few weeks ago. It has blog posts by members of the IM community about our grades 6–8 curriculum and about teaching practice, including a whole series on the 5 practices framework of Smith and Stein.

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Mathematical Musings | standards, curriculum, and teaching