Algebra stuff

[happycc]

So two of my daughter were having problems putting the like terms together and placing one type on one side of the equal side and the other on the other side. We have used hands on equations but to no avail.

 

So I came up with an idea and i really hope this doesn't mess with them as they were not able to see any other way. 

 

So I basically said any term that has a variable is a like a cat and the ones with just numbers is like a dog and you have to separate them. Cats on the left side of the equal side or fence. Dogs on the other side. And you have to unwrap the package ---basically do the opposite of what was done to make it equal to zero on one side and what you do on one side you have to do on the other side. 

 

To make zero, I did what that guy did in that movie Stand and Deliver. You dig a hole and it is -2, then you fill it up +2 and it is flat zone which is zero. I drew a picture to show this. 

 

Now the next part is hard for them ...they see something like 5x and they think they should subtract the 5 to get the x by itself. and I keep telling them that 5x really means multiply and what is the opposite of multiplying---divide....

 

Thoughts on this anyone?

[mathmarm]

Not sure the ages or grade levels of the students but I would be sure that they are clear on the underlying math. Its okay to use, teach and require proper terminology of kids and hammer away at the concepts. Its okay--and better to do 5 problems explicitly, step by step, in slow motion so that kids can take in the process and break it down, rather than bumble along through 10 or 20 problems. Sometimes you have to go slow in the beginning and pick up speed later.

 

As an upper level math teacher I can tell you with certainty that as a teacher you don't want to rely on cute euphemisms and slogans in math, but they can help to perfect the execution and jog the memory after some degree of understanding about what is supposed to be happening is achieved.

 

Typically, in my experience, if a child is struggling with basic polynomial operations they are not understanding what they are supposed to be doing or why.

 

It can help to relate each basic polynomial skill right back to basic arithmetic so that they can see that the principles have NOT changed, only the form in which we express the numbers.

 

It can help to start with basic arithmetic to illustrated the point. When we say 2 + 2 = 4 (two and two more make four total) what we actually mean to convey is that TWO of a particular thing and TWO more of that particular thing make a total of FOUR of that particular thing. This is so "obvious" that we take it for granted and students will too, but they usually don't have the insight or motivation to see how being that explicit is even needed. Until they meet polynomials in Algebra class :)

 

 

If you have 2 dogs and someone gives you two 2 cats you do not suddenly own a total FOUR dogs or cats or four dog-cat hybrids.

You have to say that you have 2 dogs, 2 cats and a total of 4 pets. (Provided that you don't own any more animals of course.)

 

Yes, you have 4 pets, but not 4 dogs and not 4 cats and not 4 dog-cat hybrids. (This isn't the most eloquent example, but this type of hyper vagueness mixed with specific expectations leads to all sorts of confusion in mathematics education.)

 

When you look at "23" you should be able to think both 2-groups of ten and 3-units of the same thing and know that it is the 'meaning' of "twenty-three".

Hold on, my kid is doing something...brb.

 

[kiana]

This might sound silly, but I would recommend that they say "five times x" instead of "five-x" for some time. 

[regentrude]

I suggest you take a step back: it sounds as if you are already trying to solve linear equations, when your kids have not yet grasped the concept of combining like terms.

So, before you solve equations and have them think about separating terms with x and "undoing" operations, they need to understand combining of terms and simplifying expressions. If they get confused with things like 5x, I would first have them work on simplifying algebraic expressions, until they internalize this concept.

Only after they have a thorough grasp of this and have understood and practiced how to combine "like" terms would I move on to solving linear equations.

 

I recommend having them narrate every step they perform.

I also found it helpful to have my kids use colored pencils and use different colors for terms with the variable and constants, respectively. (We also found it immensely useful to use colors for plus and minus signs to eliminate mistakes when expanding parentheses.)

[happycc]

Ok so they are in 7th and 5th grade using Math In Focus 5th grade and Course 2. My other 7th grader totally gets it and has moved forward. 

 

I think their issue is still trying to figure what the like terms are. Does that make sense? 

 

I like the different colors. I will use that idea.

 

Ok I will back track a little bit and slow down to illustrate this point. I like the 2+2= example too. 
 

 

 

[regentrude]

I think their issue is still trying to figure what the like terms are. Does that make sense?

 

Yes, that makes sense - and that is what you need to work on until they get it. Any attempt to make them do equations at this stage is futile. There's no rush, give them the time they need.

[go_go_gadget]

This might sound silly, but I would recommend that they say "five times x" instead of "five-x" for some time. 

 

This is my advice as well, though I teach mine to say ''of'' instead of ''times''.  Have you tried the HOE or DragonBox apps?

[BusyMom5]

Could you have them put parenthesis around the 5 and the x, to show they are being multiplied-    (5)(x)  So that they know to do the opposite (divide).  I had my DD do this a few times, and it helped! 

[happycc]

Yes, I was using the dogs and cats thing to kind of help with the sorting issue. I noticed they had problems sorting. To them it is just a jumble of numbers/letters on a line. 

[EndOfOrdinary]

If they are having trouble sorting, then you need to take it all the way back. No equations. No expressions. Basic variable, coefficient, number correlation. There is no way that word problems are going to have any meaning, and all algebra is are word problems. It sounds like they are not ready for the abstract nature of algebra.

 

It is much like when parents get so excited that their toddler can count to ten. All the toddler is doing is speaking words. Without one to one correspondence then ten means the same thing as four as seven as eighty two. Without place value eighty two is just a number that follows eighty one.

 

You can also speak of the variables in terms of something they might understand. X's are text messages, x^2's are pix messages (like a text only to the next level), numbers are just straight phone calls, y's are emails. If you wanted to count how many texts you got over the last three days, you wouldn't be looking at your email.

 

If each text cost 10 cents, you wouldn't add text plus 10. That makes no sense. You would multiple the number of texts times 10.

 

You could also do it in terms of money. X is loads of laundry, y is sinks of dishes washed, and numbers are the amount of stray cash they have lying around. If every load of laundry is worth three dollars and every sinful of dishes washed is worth four dollars, how much would six loads of laundry be worth? What if you had fifteen dollars in your pocket, how much woukd you have now? What if you did four sink full, but your sister washed five loads of laundry, who has more money?

 

More than likely they can do these sorts of problems because the problems have meaning to them. The numbers are too abstract to sort. They cannot see the situation being represented.

[daijobu]

When combining like terms in a big busy equation, I like to underline the terms as I combine them into the new equation.  That way I can keep track of what has already been combined, and what I may have forgotten in the process.