Question

What're some basic things an incoming 7th grader Pre-AP Math should know about algebra?

Answer 1

See Below:

Explanation:

Kudos to you for reaching out to learn more! Education is an amazing thing that many people take for granted. Anyways:

It's hard to say. I don't particularly remember what I learned in 7th Grade Algebra, I simply remember Algebra in general. In general though, the most important thing about Algebra is manipulating equations! So I'd start studying how to manipulate equations. In higher math, calculus for example, Algebra is heavily used in order to manipulate equations to suit the needs of the problem.

If you'd like to begin with practice in this, I'd head over to Khan Academy's Algebra section and study the material listed there! Or, you can get a book and go at it!

Other than that, just remember that Math is just a set of RULES. Don't get confused because you don't understand a concept, just accept the rules as is, and continue forward. With time, you'll understand the underlying foundations of the rules with ease.

Answer 2

Letters!

Explanation:

The biggest change in mathematics when entering algebra is the use of variables. Variables are able to represent more general ideas in mathematics, which can allow for problems to be solved more easily.

Let's look at an example of how algebra is useful to us. Consider a scenario where you have apples. You want the following 3 conditions to be true.

[1] You want to be able to give half of your apples to your first sibling.

[2] You also want your second sibling to have `2` less apples than the first sibling.

[3] The total number of apples you want to buy at the store is `10`.

How many apples does each person get?

The "not algebra" approach would be to randomly guess how many apples each person gets and check that all 3 conditions are met. This might work, but for complicated problems it becomes difficult. Algebra helps us out by allowing us to logically reach the solution.

The algebraic approach is the write down a set of equations using variables. Let's do that. Let's call the number of apples you have `a`, the number of apples your first sibling has `b`, and the number of apples your second sibling has `c`. We can write the equations corresponding to each condition as:

[1] `=> 1/2a = b`

[2] `=> c = b - 2`

[3] `=> a+b+c = 10`

Let's solve this system of equations.

[2] `=> b = c+2`

Substituting [2] into [1]:

[4] `=> a = 2c+4`

Substituting [2] into [3]:

[5] `=> a+2c=8`

Substituting [4] into [5]:

`=> 2c+4+2c=8`

`=> 4c + 4 = 8`

`=> 4c = 4`

`=> color(blue)( c = 1)`

Using this result in [2]:

`=>1 = b - 2`

`=> color(blue)(b = 3)`

Using this result in [1]:

`=>1/2a = 3`

`=> color(blue)(a = 6)`

What we have found is that if you purchase `10` total apples, you would keep `6` apples, your first sibling would get `3`, and the second sibling would get `1`.

This solution is the only solution! It was logical to get to it using algebra while randomly guessing the three numbers would have taken some time. Problems can get much more complicated than the one I showed here, so you can begin to understand the importance of solid algebra skills.

Hope this helps to give you an idea of what you will work towards learning when you get into your algebra course. Best of luck!