Poly Plug Activities
blackdouglas.com.au
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Introducing Algebra
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Submitted by:
Tony Wright
(Retired)
Bellarine Secondary College
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Preparation
If students have had sufficient experience with Protons & Anti-Protons they will be comfortable with a blue-up plug representing +1 and a yellow-up plug representing -1. They will also be familiar with ideas such as:
Any positive or negative number can be represented by an infinite number of collections, eg:
Each of these is worth 3 Protons (or +3) |
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Adding a negative gives the same answer as subtracting a positive. |
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Algebraic Expressions
- If the yellow and blue plugs can be used to represent any integer, then what shall the red plugs represent? How about x?
- If you want to get really sophisticated perhaps a sticker could be put on one side of the red counter to represent -x.
Now we can make all sorts of expression to factorise and expand. For example:
Make the collection 6x - 12 and sort it into equal groups. You can make:
- 6(x - 2)
- 3(2x - 4)
- 2(3x - 6)
That's what factorising is all about.
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Expanding is asking the reverse question, for example:
We have 5 groups of (x plus 1), ie: 5(x + 1), what is the total collection?
Plenty of practice may be required, but it is more meaningful than drill and kill exercises from the text book.
Linear Equations
Suppose we assign a value to a particular collection. We know the amount each yellow or blue plug contributes to the total value. The remaining amount must come from the red plugs - the x.
So, what is the value of x if 5x - 6 = 4?
- Use the concept of the = sign being a balance...
- Keep the balance level by doing the same thing to both sides...
- Then each step parallels the 'standard' algorithm for solving a linear equation...
- And we get the answer x = 2...
- Now substitute that value back into the original collection to check that it works.
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What happens if there are x plugs on both sides, eg:
3x - 6 = 4 - 2x?
- Return to
- Return to:
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