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. An example goal problem will be [ 4 (13 – 8) + 7] 3 with and without the calculator. 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.
: For the Bell Ringer for lesson 1, give the students an example goal problem. Let’s see where they are. 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. Label it as “MISKTAKE” give an explanation of what the mistake was, and correct it right next to it. 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.E.M.D.A.S. 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. Let’s break this problem down.
[ 4 (13-8) +7]
Step 1. Solve what is in parentheses [ 4 (5) + 7 ] What did you do? (13-8) = 5
Students should understand that the brackets are there because there is a quantity identified within the expression that needs to be solved. (13-8).
Now, students must understand that once you solve what is in the parentheses you now have a value that must be multiplied.
Step 2. Focusing on the numerator portion of the expression, we will now multiply.
4(5) + 7 20 + 7 What did you do? 4 multiplied by 5 = 20
Step 3. Continue to solve for the numerator
20 + 7 = 27 /3 What did you do? 20 + 7 = 27 What does 27/3 mean? Divide 27 by 3.
Step 4. Final answer
27/3 = 9
With this direct instruction, you want to be sure to explain each step. Take questions, go through their work with each step. I like to ask my students, “Show me if you were able to do step 1 on your own”. 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. It will be naïve of us to think our awesome direct instruction over one problem enabled our students to fully understand how to solve these problems. However, now the students will have a step by step guide to help them through problem similar to the problem we did together. This will allow them to practice MP 5. I tell my students that they may use the direct instruction notes as a resource, but it is up to them to navigate through the notes they took to use for their help. I want them to understand the importance of note taking and how this will be a tool they will need to master as they grow in their educational careers. As we know, Common Core has a heavy focus on becoming college and career ready. Effective Note taking is a crucial objective that students will need in order to become college and career ready. Let’s start them early on. You may want to start them early with guided notes, however, students must see that the better their note taking on their own, the better tool they are creating for themselves. If they are not taking effective notes, they will see this when they go to use their notes as a useful resource. (total sidebar)
Walk the room and check for understanding. Are students able to follow appropriate order of operations, do they understand when to distribute, are students distributing properly, are students able to understand when to divide when the division is represented with a fraction bar? These are all things to check for. This will allow you to pick and choose the next lessons within this unit. This will also allow you to choose some of my scaffold lessons, or create lessons on your own to scaffold from your assessments.
Assign the students this one problem, or create several other similar problems to go along with this problem. I like to keep the homework simple, not in rigor, but the amount given. This will allow me ample time to grade and have effective feedback in a timely manner.