5/3/07
Okay, so today was one of those days when I felt like nothing I did got through! It was frustrating! I gave a mini-quiz yesterday, based on class discussion and entrance/exit slips that we've been working on. I figured this quiz was a guaranteed success for my students. There were 10 questions total, all related to solving equations. But there were three questions in there that were different from the one-step or two-step equations we've been doing.
- 22 (3+p) = 88
- 40 = c + 2c - 101
- 4x + x - 2x + 3 = 54
These should look familiar, because in my last blog entry I said that I was going to give this quiz the next day. However, we took some more time to go through the more confusing equations, so that students would be able to master this.
They have been kicking butt on all of this! Almost all of them have aced the past one or two exit slips, which were on solving equations using distribution, as well as simplifying before they solve the equation.
My plan for this quiz was to make the second and third questions listed above count for extra credit (without telling them, so that they would all try it). To my amazement, these kids bombed on this quiz. Two of my students did pretty well, but there was one student who only got one question correct, and was confused as to how to even begin solving the questions. And one student didn't get any of the questions correct. I was so surprised! I really didn't expect this.
Today I handed back the quizzes. They were not really graded. Instead, I put a star next to the questions that were correct. When I handed the quizzes back, the first thing I did was ask what happened, and I was pleasantly surprised at the feedback I received.
There were two or three students who did not like how the quiz was set up. They said that it was overwhelming to them. It made them nervous. (The quiz was set up with the 10 questions in 2 columns — 5 questions in each.) Another student said they got a little confused because they had a sub for the beginning of class. Unfortunately, I had to be out of the building for a meeting, so another 7th grade math teacher covered the start of my class. They reviewed for the quiz, but apparently the way she went through things confused a few students. I never would have thought about this, so it was great to hear their true thoughts and feelings.
We then went through the quiz, answered questions, and reviewed how to distribute and simplify.
Today I decided to pull out the algebra tiles, and it worked really well with this class. Normally I would have used them before this point, if students were having trouble, but this group seemed to be doing pretty well.
I LOVE algebra tiles! The tiles that we use are the yellow squares, red squares, green rectangles, and red rectangles. We began by "naming" each of the tiles:
The yellow square = +1
The red square = -1
The green rectangle = +X
The red rectangle = -X
Next, we started exploring the zero principle. I asked students to tell me what the picture would equal if I had 4 yellow squares and 4 red squares. We practiced making zero with both our number and X tiles. We then moved on to solving expressions with integers.
For example: 4 + -3
Students would pull out 4 yellows and 3 reds. They would then "zero out" 3 of the yellows with the 3 reds. They would be left with 1 yellow (or +1). They had a packet to be working on while solving, so in their packet they would draw a picture of the situation they set up, and then show how they solved it.
After some practice with integers, we moved on to equations. One equation they needed to set up was: X + 3 = 8. On their desks they put 1 green rectangle and 3 yellow squares; then, on the other side of the equation, they would put 8 yellow squares. To solve this problem, students needed to take 3 reds and put them on the left side of the equation to "zero out" the +3. Then they would take 3 reds and put them on the right side, to zero out 3 of the 8 yellow squares. In the end, they would have 1 X on the left and 5 yellows on the right. So their answer is X=5.
My kids loved using the tiles. Not only did it help some of them better understand the process of solving equations, it also was a fun change of activity for them. We'll continue this activity tomorrow, moving on to two-step equations.
Depending on how far we get, students may be taking a new and improved quiz tomorrow. The new quiz will still have both one-step and two-step equations, as well as at least one distribution problem and at least one simplifying problem. I'm going to set it up so that it seems less intimidating than the first quiz. I think I'll leave a space under each problem, so that the students can draw an illustration of how they solved it. I'll accept a picture like the algebra tiles, a picture of the coins and pouches from Investigation 3, or a picture they create that makes sense to them. Hopefully this will help reduce some of their confusion and anxiety about this quiz. I'm confident they will rock this quiz!
