DS1 (yr 8) really can't get even basic algebra

[rwepi]

I've known he found it difficult but I didn't realise just how bad it was until he "helped" his 10 yo brother with his homework this weekend and made a real hash of it.

His maths generally isn't that bad - working at 5A according to his last monitoring (so not great either) but this particular subject is a real problem for him and IMO as he progresses there's very little maths that doesn't have some algebraic content, so this will effect other areas. It's those little letters that seem to throw him a,x,n etc

Tell him you've got 3 baskets of apples, you eat 3 and are left with 27 he'll have no trouble telling you that each basket had 10 apples originally.

Express it as 3n-3=27 and he is absolutely flummoxed, even after several minutes spent trying to explain it.

Doesn't help that his teacher has told him she hates algebra too!

Is there anything I can do to help - any resources we can use?

I love algebra

It's the letters bothering him, or is it that he struggles to work it out, instead relies on trial and error.

If it's letters, then try writing them down with a box/space to fill in. So instead of 3n - 3 = 27 You write 3[ ] - 3 =27 and get him to fill in the blanks. All the letter is doing is representing an unknown number.

If it's the working out: There's two ways of looking at it. I think the easiest is to think of the equation as a set of scales. The scales are equal both sides and you want to keep it like that. So what you do to one side, do to the other.
Do one step at a time, and write what that step is:
3n - 3 = 27
You want to get rid of the -3, so add three to both sides:
+3 3n = 27 + 3
3n = 30
Now you just want one n on it's own. So divide both sides by 3.
/3 3n/3 =30/3
n = 10

If he's really not getting it, then I think it would be worth asking the teacher to really go through algebra, or getting a tutor for a few lessons. Because as you say, algebra is a major part of maths.

Some people do take longer to get algebra. I did A-level maths with a lad who had really struggled with it. He had got it by then, but he had to work each thing slowly. So (for example) if he was told he had a circle radius a, what was the area, he couldn't go straight to pi a2, he would write down area of a circle is pi r2. r = a, then he could see the answer.

Try Dragonbox on ipad or iphone - it uses the principles, but is also lots of fun. My primary aged dds play with it (and have no idea it's anything to do with algebra)

There's another good ipad app called hands-on equations, it's for younger children but it sounds like he needs to get back to the basic and then slowly learn the leap from apples to x's!

There's an interesting short TED talk about how it came about that the unknown variable in algebra came to be called "x", maybe if that made sense to him he would be less frightened of the letters.

I'd also advise you to practice a lot with him every day, just do 10 of your apple problems every day and then practice writing it as an equation for each one. Maybe he just needs more practice to build up confidence.

As Elibean said, you need to get dragonbox. My 6 year old can solve 23 stage equations, not because he is particularly clever, but because the app is bloody fantastic. After 4 hours of playing the game, your ds will completely understand algebra. Best £6 you'll ever spend. Seriously.

The Khan Academy has a really good step by step explanation of algebra.

My mother couldn't get algebra, had to struggle thru to get her Uni degree, too (foreign Uni).

just get him to think about is as apples. I know someone who taught simple algebra to first year uni students using mars bars instead of x. And it was amazing how many peoples faces lit up and mutters of "why didn't anyone put it like that before".

It is just getting the idea that x stands for some variable - could be anything. The other key thing is realising it has to balance - if you take 3 from one side you have to take 3 from the other too. If you multiply one side by 5 you have to multiply the other side by 5 too.

Maths teachers who hate algebra shouldn't be maths teachers.

Another vote for Dragonbox. It's brilliant!

Lots of people find it difficult because they can't imagine why it is necessary. The mars bar trick is one way through, the other is the football contract. If you have a contract hat depends on f a set fee with a variable element algebra is really helpful.

I'll play devil's advocate here
there are some people who NEVER get algebra
there are people whose earning capacity will not be affected by that.
PLEASE
not all children are "academic"
if yours is not, find what they are good at and stop torturing them with algebra

Another vote for Dragonbox.

Algebra is the very basis of reasoning (mathematical or verbal). We use it every day. It is indispensable - and very easy!

Another vote for Khan academy. It starts at the very basics and you move on when you fully understand the first, second stages etc. It's free and has helped Ds so much. Not just with Algebra - all maths.
He will get it, it just needs to be explained properly. They are YouTube videos and made total sense to me. Worth a try. Good luck.

These video tutorials on Algebra Basics are very good.

mathantics.com/

I don't really understand it
I'd love to.. but I don't
I'm actually frightened of algebra. I get the same feelings I had a school ( hot, sweaty, embarrassed mind blank) when I see algebra.

I once made DS1 factorise a pile of actual apples and bananas because the letters were bothering him. Once he could pick up a and b and move them around he got it.

I am going to take a look at Dragonbox

I think that if they introduce very basic algebra in primary schools alongside teaching addition and subtraction, fewer children will have problems with it later on.

It's probably something like a mental bock, rather than an inability to understand.

They actually do introduce variables yr4+ , like "a + 4 = 8 solve for a " type of very basic ones.

In yr6, there's skills to write & solve 2 variable equations. It's just not called algebra.

Ds didn't like maths at your Ds age, but is now doing A level. It may take time to click, but go gently.

The equation given in the OP is of the form an + b = c where n is the unknown. If this is too complicated initially, look at simpler equations of the form an = c (e.g. 3n = 27) and n – b = c (e.g. n – 3 = 27) and consolidate on those.

Working with a concrete example like apples in baskets is actually a good idea, I think.

It’s possible to introduce the equation solving method in this concrete setting. This might help DS to identify the sequence of steps he is taking to solve the problem in his head.

The unknown number to figure out is the number of apples in a basket.

3 baskets of (number of apples in a basket) take away 3 apples equals 27 apples. ->

add 3 to each side

3 baskets of (number of apples in a basket) take away 3 apples add 3 apples equals 27 apples add 3 apples ->

3 baskets of (number of apples in a basket) equals 30 apples ->

divide by 3 on each side

1 basket of (number of apples in a basket) equals 10 apples ->

So the number of apples in a basket is 10

I’d then suggest giving several examples illustrating the same equation, so that DS can see that it does not matter if it’s baskets of apples, bunches of flowers or jars of marbles, one abstract equation involving numbers on their own can be extracted from the concrete examples and solved using the same sequence of steps used for the concrete examples:

3 baskets of (n apples per basket) – 3 apples = 27 apples
⇒ 3 x n apples – 3 apples = 27 apples
3 bunches of (n flowers per bunch) – 3 flowers = 27 flowers
3 jars of (n marbles per jar) – 3 marbles = 27 marbles

⇒ 3n – 3 = 27

add 3 to each side

3n = 30

divide by 3 on each side

n = 10

(In this particular example, it would of course be possible to divide both sides by 3 as an alternative first step.)

Having written all this out, I've just realised it's a zombie thread. But I'll post anyway - someone somewhere might get something out of it!