Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Students will learn how to distribute with variables and how to factor linear expressions. For example, distribute \(2(2x + 5),\) or factor \(4x + 10.\) Both of these skills can be done with algebra tiles before moving on to the abstract method. Here's an example of distributing, and here are two examples of factoring. After students are comfortable with these types of problems, move on to problems involving like terms as well. For example, distribute and combine like terms to simplify \(4(3c - 4) - 12 - 4c.\) You can see an explanation of the solution here. We can pose similar problems which involve factoring. For example, combine like terms and factor to simplify \(12c - 16 - 12 - 4c.\) After that, do similar problems with multiple variables. For example, distribute and combine like terms to simplify \(2(2z - 3x) + 4z + 8 - 2.\) Next, give your students this challenge. For students who are stuck and frustrated, provide the hint of drawing the rectangle around the triangle. Finally, give your students this challenge.