When it comes to writing out the explanation of how you solved the problem, many of you are doing a great job of listing out the steps that you took, but then stopping there. The explanations of why you took those steps are still unclear. But this is probably the most important part of the response so I want to make sure that we get it right. :)
During class the last week of school before break in December, when we were working on these in class, I showed you a sample of how I would solve a similar problem. I want to post that here.
The main thing that I want you to focus on is that in your explanation, you need to include the specifics of the problem. You need to make sure that you include the important information that you need to know in order to solve the problem. Include the what the problem is asking you to solve for. And most importantly, include how you solved the problem. Walk the reader through every step of the way. Explain all of your computations.
I Important Information in the Introduction
S Say what you are solving for
A Always explain what you did and why
T Then answer the question in a full sentence
Notice how for each step, I give an explanation of why I did that step. And notice for Step 5, I explain the way that I solved the actual problem. First I found the LCM that both denominators share; the LCM of 4 and 5 is 20, etc. THIS is what is missing from your work samples, and this is what the ISAT test is looking for you to know how to do.
After reading the problem and underlining the important information, I know Henry bought 1/4 pound of screws and 2/5 pound of nails. I need to find out what is the total weight of the screws and the nails. First, I read the problem to understand the information given to me. Second, I found what I need to solve for - what is the total weight of the screws and nails - so I can figure out how to set up the equation. Third, I identified the important information that I need to use to solve the problem - 1/4 pound of screws and 2/5 pound of nails. Fourth, I set up an equation to solve: 1/4 + 2/5 = ?. I used addition because the problem is asking me what the total weight is. I know to find the total weight of something, I need to add the parts together. Fifth, I solved the problem by finding the LCM that both denominators share. I found the LCM of 4 and 5 by listing the first few multiples of each number and looking for the lowest number that each number shares.The LCM of 4 and 5 is 20. Once I had a common denominator, I made equivalent fractions by doing to the numerator what I did to the denominator to get the common denominator of 20. To find an equivalent fraction for 1/4. I multiplied by 5/5 and I got 5/20 To find an equivalent fraction for 2/5, I multiplied it by 4/4 and I got 8/20. I added the two numerators together (5+8) and I got 13/20. Sixth, I checked my work to make sure that my answer was reasonable and free of errors. After working out the problem, I now know the total weight of the nails and screws is 13/20 pounds.
Below is my full example of how to solve an extended response problem:
As I mentioned in class when going over my example, I can appreciate more greatly how difficult this task is. I did not have to do this when I was your age. That being said, as a teacher, I understand why they are asking you to do this. But I can appreciate that this is not easy to do. We don't normally think about math in this way, and it is even less common for us to write about math in this way. I am a firm believer that practice makes perfect (or as one student put it, practice makes proficient). So we will continue to practice this skill. Keep in mind: I don't expect perfection, but I do expect that you will try your best.