math for educators

Question

1. Students sometimes mistakenly think that the expression 4x–x is equivalent to 4.
2. Why might a student make such a mistake?
3. Use Algebra tiles to explain why this is not correct and show another expression
4. that is equivalent to 4x – x

Answer 1

4x-x looks a lot like 4 followed by x-x, viewed as 4 + (x-x) which does = 4

the x's cancel leaving just 4

4x-x = x(4-1) = x(3) = 3x is correct.

or if there were parentheses such as 4(x-x) then it equals 4(0) = 0, since x-x=0 and 4 times 0 = 0

4, 3x, or 0 are what students might come up with. especially if it's a time pressure test or homework and no real advance notice, with little time to think it through.

use 4 tiles where each tile has an x on it. each tile = x

take one tile away, and you're left with 3 times x = 3x