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When the student arrives, take a few moments to tell them what you’re going to cover. Make sure they don’t have homework to do or a quiz to prepare for that may be more pressing. Even though you took a great deal of time to prepare for the session, be flexible and accommodate your students whenever possible.  An example may be saying something such as, “I remember you said you were having trouble with absolute value equations. I thought we could work a few of those together. Then, I’d like you to work a few independently.” If the student agrees, you can follow up with something like, “Before we get started, what specific questions about absolute value do you have?” You should also double check that there isn’t a more pressing topic they need to cover, “Is absolute value still a topic you’re concerned about now, or do you have upcoming assignment you want to look at first?” You may think you’re doing a great job of explaining everything but it’s important to periodically ensure your student is on the same page. Asking students if they have questions, and taking time to answer them seriously is important. Try not to get annoyed or frustrated, if it seems like you’ve answered the same questions for your student. Just encourage them to keep trying. They’ll get there.  Establish early on that the student should stop you anytime they need to ask a question. Avoid saying things like, “Does that makes sense, or do you understand?” This may discourage students who want to impress you or those who don’t want to take more time with the subject by asking for more information. Instead, try something like, “Do you have questions?” Better yet, say, “What questions do you have?” This tells the student you expect them to have questions. Now that you’ve established the plan for the day, start by working through a problem together. You can do this a number of different ways, but the goal is to improve students’ confidence in their ability to do the problems, and find out where they will likely need your help. Try:  Asking the student to tell you what needs to be done, and attempt the problem based on their instructions. Then, make corrections as needed. For instance, in the equation: 8|x + 7| + 4 = -6|x + 7| + 6, the first step should be getting the variables of |x + 7| on the same side of the equation. If the student starts out by saying you need to divide each of the variables by the multiplier, i.e. -6|x + 7|/-6, explain that the equation may be easier if you instead have both 8|x + 7| and -6|x + 7| on the same side of the equation. Walking the student through the problem. Let them do the actual figuring on paper or computers as this helps them remember, but tell them each step. In the sample problem above, you would give them the equation and say "The first step is to get both 8|x + 7| and -6|x + 7| on the same side of the equation. How would you do that?" Trading the problem back and forth. You start the student down the right track. Then, let them determine what they need to do next. Using the same absolute value equation above, you would get both 8|x + 7| and -6|x + 7| on the left side of the equation. Then, ask the student to complete the next step, getting the +4 and +6 on the same side of the equation by subtracting 4 from both sides. If they do this, you can move forward. If not, explain what they should have done, and continue to the next step. You can trade the problem back and forth in this manner, until it’s done. When you’re done working through one or more problems together, give the student one to work on independently. Let them take as much time as they need to find the solution. Try not to help them with the problem. Even if they get frustrated, just encourage them to keep going until they get an answer (it doesn’t have to be the right answer). Once the student solves their problem, review it with them. Let them know where they got off course, tell them what the correct method would have been, and make sure to ask them if they have questions for you. This allows them to build independence when it comes to solving problems while continuing to help them improve their algebra skills. Take the sample absolute value equation 8|x + 7| +4 = -6|x + 7| + 6. If the student begins the problem by dividing each side by -6 rather than adding 6|x + 7| to each side, they end up with a very different result (x = -6 or -15/2 rather than the correct x = -7 or -50/7), but they can achieve an answer. Let the student solve the problem. Then, walk them back through the equation the correct way. After your student has completed the problem and you’ve reviewed and corrected it, have them start over from the beginning and walk you through how to solve the problem. This gives them the opportunity to rehash what they just learned from a different perspective. If they can accurately explain how to complete the process, they are more likely to retain the information. Have your student work problems until they can solve two or more in a row without error. When they reach this point, you can move on to something new, if you still have time. Otherwise, ask them if they have any questions, and begin planning for your next session. They might hate their homework, but you really want to make sure they understand the material. If they have an assignment in their class that’s covering the same subject, this may be adequate, so make sure you ask them what their homework is for class. Inform the parent/guardian about their assignment too. If their parents know they have homework from you, they may be more likely to get the work done.  Even if the students have a great deal of homework, assign them two or three extra equations. Ask the student to text or email you a photo of their completed equations as they finish. You can then send feedback letting them know whether or not they’ve gotten the correct answer or need to make another attempt. Before the student leaves, schedule your upcoming study time. Ask if there are any tests or assignments coming up that they would like to focus on. If the student pays you directly, you can also obtain payment at this time.
Walk students through your lesson plan. Encourage questions. Work through a problem together. Let your student attempt a problem. Guide them through corrections. Ask the student to walk you through the problem. Repeat as needed. Assign homework. Plan your next session.