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]]>During a class discussion on square roots, Johnny wrote this equation on the board.

It was obviously wrong, and the teacher was about to cross it out, but on second thought it looked *almost* right. Is the equation correct? Almost correct? Or is it completely wrong?

Here is the answer.

]]>Dragon Box is sneaky because the students begin learning how to solve algebraic equations without even knowing it. The application is done so well, that very little instruction is needed. It begins solving equations using picture cards and without using hardly any words or instructions; the students figure out very intuitively that to solve the equations (or win the “games”) they need to make the constants zero, and then the coefficient one. Brilliant!! So now in class, when we are solving equations, I can relate to the Dragon Box ideas to help them understand the pencil/paper steps for doing the same thing. If you haven’t checked it out yet, hurry. You’ll be amazed.

]]>I’ve been teaching this topic for years, and this year I did a few things differently. I think a few ideas were good, and others still need work.

The good:

- I introduced 2-step equations and how to solve them with a demonstration. I showed the students 3 cups. I told them that the cups hold exactly the same number of paper clips. The number of paper clips in those cups along with the 6 in my hand total 18 paper clips. How many paper clips in each cup? This was awesome; in each class, the student I called on to explain their thinking on solving the problem, solved the problems exactly how we normally solve 2-step equations: “First I subtracted 6 from 18 and got 12. Then I divided by 3 since there are 3 cups. So each cup has 4 paper clips.” Sweet. I then went and explained their thinking using the variable, c, for cup and so on… Where did I get the idea for this demonstration? In the most unlikely place: their Holt texbook. Ha, who would have thunk?
- After we concluded that a good way to solve an equation was to zero-out the constant term that is on the same side as the variable, and then to make the coefficient 1, we created a flow map (thinking map) for their notes. I think this is a great time to emphasize the vocabulary: constant, coefficeint, and term.
- I had students come to the board and work out the homework problems twice this week. Students love it, and I get to see where they are having problems.

Things needing work:

- Many students are having a difficult time with equations like 2m-3=-9. They are not seeing the 3 as negative, so they are subtracting 3. Previous years I would have them immediately change the subtraction sign to adding the opposite. This year I was trying to get them to use inverse operations instead. Instead of subtracting 3, lets add 3. I *thought* they were getting it, and I think they sort of did. But this is where most of the mistakes were made on the quiz. More practice with this on Monday!
- I had my students check their work, by substituting their answer into the variable. We practiced this again and again. However, I am still seeing students work where they get the answer incorrect, and then they check their work, and they rush to believe that their check is true. I somehow want them to slow down and do the check as objectively as possible…yah right. This is driving their teacher crazy. Maybe some multiple choice problems would help here.