The students will be looking at several expressions and determining whether or not they are algebraic. They can circle or put a check mark by the expressions they recognize as algebraic. Then, I want them to tell my why they chose those expressions. Students should be able to tell you that it is algebraic because it has a variable, operations and a number. This is a recall activity that is designed to get them thinking about what an algebraic expression is. Students can share their responses with a table to mate to check solutions and justifications (SMP 1 and 3)
This section has the students using substitution to evaluate an expression. Some common misconceptions that you will want to address are the variable can be any number we want it to be. Just because the table gives a sampling of variables, it can be anything we want it to be. Also, students need to be aware that when substituting, the number is placed where the variable is in the expression. I like the students to do this, even with addition and multiplication, because they forget that subtraction and division are not commutative. Finally, since this is an expression, it needs to be solved using the orders of operations when more than one operation is present.
If you keep these ideas in mind while teaching, the students should be successful when substituting.
I will be going through the 4 examples with them. I will be substituting and re-writing the expression, showing the substitution and then working the math using orders of operations. I will be asking students after the first few substitutions to tell me what to do to find the value of the expression.
Students will be working through 4 tables independently. As they are working, I will be watching for the common misconceptions (explained above) and address this as needed. When students have completed their tables, they can do a HUSUPU to share answers and justifications with a partner. Students should prove to their partner that their answer is correct (MP 3 and 6)
This will be a whole group discussion. For the first problem, the students will have to understand the expression to get the constant and the variable. If the students understand that this is a multiplication problem then comprehension is there. It is not necessary to actually write the expression. Students just need to understand that the changing piece is the variable and what it stands for and the part that never changes is the constant. In the next problem, the students need to correct the error. If students are struggling you can ask them what the relationship between 12, 4 and 8 are?(SMP 2) Once they see that this should have been a subtraction problem, they can change it one of two ways, 12-4 = 8 or 12 ÷ 4 = 3. This would be a good problem to share strategies out loud. The next two problems are substitution problems with an inverse variable. Students struggle with this and if addressed correctly during the demonstration, you should see them working it properly. As a whole class, I would ask them if it’s ok to reverse the order of the numbers? Would it result in the same answer? (SMP 3)
The round table I have created is a great way to differentiate. There are four forms: A,B,C, and D. A is the easiest and D is the hardest. My students are sitting in mixed ability groups. At each table, I have a High, Medium-High, Medium –Low, and Low level learner. The High and Low level learner will always sit diagonally across from each other. This eliminates the High student from getting annoyed or taking over for the Low level learner. Give all the High students a D form, Medium-High a C form, Medium-Low a B form and Low an A form. Each student will start out with a problem based upon their ability and they will feel successful. As the forms are passed, you will notice that at the top of the form there are directions. One of the directions is to check and coach. Peer tutoring will play an important role in this round table. (SMP1,2,3,6)
The students will be completing a connect 3. The terms that they will be making a connection with are: term, algebraic expression, constant. Students should make a connection on each line of the triangle and then create a brief summary of learning inside the triangle. Students can share with a tablemate if time permits. Reflecting on learning helps to deepen the understanding of the concepts taught. (SMP 1 and 6)