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❶Remember the goal problem is a problem in which we want the students to be able to solve or simplify after teaching each of the scaffold lessons.

Simplifying Rational Expressions

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This lesson will be broken down into 4 lessons. This will serve as a great tool for students who struggle with combining like terms, simplifying expressions and equations, and the use of distributive property.

These objectives have been scaffold down for you into smaller lessons to reach students who may not be able to simplify expressions with multiple variables, exponents, and several operations.

The goal of these lessons will be for students to eventually simplify an expression involving nested parentheses and integers. These lessons have scaffold example problems like this down so that students are equipped with the proper understanding to simplify such expressions.

Students must understand the distributive property, order of operations, how to distribute negatives, and combining like terms. I will include common mistakes on a teacher resource page. Give students about 5 minutes to work out a goal problem. Remember the goal problem is a problem in which we want the students to be able to solve or simplify after teaching each of the scaffold lessons. You may choose the above problem listed in the pre lesson notes. Distribute the bell ringer as the students walk in the room.

Once the students have had 5 minutes to grapple through the problem, MP 1, and 2, allow the students to work with a partner or group to discuss their work. Students will grapple through this problem without the calculator showing their work. This will be a way for you to assess their prior understanding with distributive property, and order of operations. Students should show each step of their thinking. When students are given the opportunity to work as a group, or in pairs, this allows them to practice MP 3.

Students should discuss their thinking, their starting point, and if they were to get stuck, why and what could their partner do to help them. I allow students 10 minutes to discuss their thinking. For day one of this lesson, we will break the problem down together. We will discuss student work, their thinking, misconceptions, and common mistakes.

It is important for us as educators to make sure students understand their mistakes. For this, I like for students to keep their mistakes on their work. The explanation of work is crucial. Students must understand what they did wrong, and how to correct the mistake accurately. This will allow students to practice MP 6. For this particular problem, students should start with what is in parentheses.

This is a good time to remind students of P. A common mistake that students make with this mnemonic device is that if they have only multiplication and division in the problem, or only addition and subtraction they want to still follow the order of the mnemonic device. Students should realize that these are grouped operations.

Multiplication is grouped with Division and Addition is grouped with Subtraction. When left with one of these groups, you will go left to right. With the bell ringer, we have parentheses, multiplication, addition, and division.

This problem is written as a fraction, thus students will need to know that the fraction bar is a symbol of division.

However, you must solve what is represented as the numerator before you can divide. Students should understand that the brackets are there because there is a quantity identified within the expression that needs to be solved.

Now, students must understand that once you solve what is in the parentheses you now have a value that must be multiplied. Divide 27 by 3. With this direct instruction, you want to be sure to explain each step. Take questions, go through their work with each step. I do this with each step. It is a way for me to formatively assess where the breakdown in understanding is and to scaffold the upcoming lessons accordingly. Give the students a similar problem to the problem given during the bell ringer.

However, now the students will have a step by step guide to help them through problem similar to the problem we did together. We have taken appropriate security measures to protect you against loss, misuse or alteration of the information we have collected from you.

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