In the beginning of the year, I assessed my students for understanding of what equals really means because I wanted to know if they could think algebraically . This concept is essential to master (Karen Falkner) in order for them to fluently solve equations and algorithms. It supports future algebraic concepts,especially as multi-step word problems become more challenging.
With MAP tests on the near horizon, I wanted to revisit this to trigger their memory and help me see if their understanding of this concept has grown. Earlier in the year, it was very poor and I have worked on it in little doses. So, I chose to use the same quiz I had in the fall as a guage.
I administered the "quiz" telling them that it really wasn't a graded quiz, but a quick review of an old concept and that we call that "spiraling".
I had them keep their papers for a quick discussion and celebration of progress in their mathematical understanding. One boy who I had worked with since summer on this concept mastered it easily. He had struggled for so long and I was pleased to see he could solve the equations and explain them to me.
This clip is of the discussion we had about its importance. It's So Important!
Now that they were thoroughly warmed up and ready to think about meanings of equations, I was comfortable giving them their formative assessment. They understood that this assessment was going to be graded. I would use this quiz to determine RTI and if they are mastering writing equations better.
I guided a short review of their homework from the lesson the day before to prepare them for their assessment. They looked at their own work, discussed and corrected it as a whole class. I don't think they get enough exposure to word problems and hope to change that within our curriculum through Better Lesson.
As I brought up the worksheet assigned from the day before on the SB, I developed equations and deliberately did the first one incorrectly on the white board next to the SB. They caught the errors and guided me to solve it correctly. They thought it was hysterical that I didn't write the right equation ( I added) and then didn't notice that it was an estimated problem. I do this purposely so that they are taking responsibility for participating in thinking about their work and keep them engaged. They enjoy it a lot!
We continued until all problems were solved. Rich discussions were taking place about whether or not you would round both numbers in the "bus" problem because some students felt that the 16 buses was a solid number and that the amount of children could change. I was surprised at their thinking and pleased to see that they were starting to think not only about numbers, but about situations involving the word problem. The Common Core learning environment for math develops that logical and multi directional thinking. We celebrated with pats on the back that we had developed equations with variables to solve. Celebrating our equation success! Talking about the standard.Mastery of standards is continually in my dialogue with them to help develop their appreciation for what they are learning.
This formative assessment will tell me if students are able to multiply double digit by double digits using an area model as expected in CCSS 4.NBT.B.5. The standard algorithm is not expected to be mastered at this grade level and I only have one student that thoroughly understands a standard algorithm. He achieved that understanding through learning area model first. I think Common Core is absolutely right on with expecting area model problem solving because it gives students clear understanding of place value's role in the solution. I have taught students to unpack their word problems systematically and logically through the use of a graphic organizer called a KWS chart. I expect them to show this on their daily work in solving word problems and their quizzes. It gives them a controlled way of developing their equations with variables as CCSS 4.OA.A.3 also requires. (We are not measuring that they can use estimation to check reasonableness of answers just yet, even though we are estimating.) And finally, students show me that they understand that every time they multiply by 10 they move a place value as CCSS 4.NBT.A.1 expects.