3 + 2(x + y) = 9He is having difficulty solving equations that require him to distribute a negative:
3 - 2(x + y) = -3I remember C. having trouble distributing a negative, and I remember stumbling over minus signs myself when I was a kid. At some point, I solved my problems by deciding to treat minus signs as either a -1 or the addition of a negative, depending on the expression I was dealing with.
Thus -x became (-1)(x) and x-8 became x + (-8).
I don't think anyone ever told me to translate expressions in this manner. Quite the contrary; I have vague memories of reasoning it out for myself on more than one occasion.
Here's the way a sheet I have from Glencoe says to teach distribution of the negative:
Use the Distributive Property to write each expression as an equivalent algebraicUnfortunately, this sequence doesn't solve the problem. My student can simplify 3(w-7); what he can't do is simplify 3–2(x+y).
a. 3(w – 7)
= 3[w + (-7)] Rewrite w – 7 as w + (-7).
= 3w + 3(-7) Distributive Property
= 3w + (-21) Simplify.
= 3w – 21 Definition of subtraction
Today I tried having him draw huge brackets around 2(x+y), then simplify the 2(x+y), and then simplify the remaining expression:
3–2(x+y)In effect, I was turning the problem into two distributions: first the 2, then the negative sign.
This approach always worked for me, but the logic of it wasn't obvious to my student.
One more thing: this student probably had Everyday Math in elementary school, and his current class seems to be intensely procedural. The only textbook his teachers are using seems to be a NY state test prep book.
I'm eager to hear any thoughts you have both about procedural teaching (including mnemonics) and about how I might help this student make some sense of the math he's learning. Moreover, and I hate to say this, but if I'm going to help him make some sense of it, I have to do it on the fly. Our time together is extremely limited.
If anyone knows of a good set of "instructional worksheets," that would be fantastic. I'm combing through my own collection.
Last but not least, what do you think of this video?