Complicated Expressions Worksheets
When students come across a complicated algebraic expression, they get that deer in headlights look about them. Then they immediately jump into “Algebra is too hard!” mood. This does not have to be the case at all, and I encourage teachers to help students see this. Expressions can almost always be rewritten or reformed into much more manageable chunks. If you take the time to help students realize this, you will find that they are much less overwhelmed going forward. I realized this early in my days as an algebra teacher and have that I have been able to help students panic a great deal less about the new material that they come across. These worksheets and lessons teach students to breakdown expressions into understandable parts and rewrite them.
Aligned Standard: HSA-SSE.A.1b
- Rewriting Expressions Step-by-step Lesson- How to split apart like expressions.
- Guided Lesson - Rewrite simple set ups, simplify expressions, and write number sentences.
- Guided Lesson Explanation - I amazed that I got such a solid explanation into one page of writing.
- Practice Worksheet - I made this into a very digestible mix of problems for you.
- Adding and Subtracting Rational Expressions Five Pack - A sweet five page set for you to practice with and hone your skills.
- Matching Worksheet - Find the matching rewritten expressions.
- Answer Keys - These are for all the unlocked materials above.
Homework Sheets
Time to separate those expressions into pieces.
- Homework 1 - The new format that has been presented separates the variable V from the expressions.
- Homework 2 - We need to remember that the easiest way to simplify expressions is to combine like terms.
- Homework 3 - A parenthesis is missing from each expression below. Place the parenthesis in the proper position based on the description of the number sentence given.
Practice Worksheets
These sheets run you through a variety of different directives.
- Practice 1 - Rewrite each expression in the format presented.
- Practice 2 - Simplify the following expression.
- Practice 3 - The number sentence: twenty minus the sum of five and thirteen.
Math Skill Quizzes
I will add more difficult quizzes in the coming months. This format was specifically requested by many teachers.
- Quiz 1 - Solve the following rational fractional expression.
- Quiz 2 - Solve each expression using the techniques we have already learned.
- Quiz 3 - We put the parenthesis around the parts that are directly involved with one another.
How to Approach Working with Complicated Mathematical Expressions
An algebraic expression is any mathematical phrase that includes a combination of constants and variables. We use them to better understand the world around us and model situations where math can provide us with usable data. We can also use the data that we compile to make better decisions. Expressions cannot be solved; they can only be simplified as they do not have an "equals" sign.
Simplify Everything - Any complicated mathematical expression can be simplified, no matter how complicated it may be, by learning the basics. We need to remember that we will often have terms that can be combined, or we can process operators that exist with it.
Suppose you get an expression: 3x2 + 5 + 4x3 - x2 + 2x3 + 9
The first task is to make sure it is arranged in the right order. Like this: 3x2 - x2 + 4x3 + 2x3 + 5 + 9
Now it can be simplified like this: 2x2 + 6x3 + 14. This cannot be solved any further. That is because it is in its simplest terms.
Factor Everything - The second tip for solving a complicated mathematical expression is that you must know how to factor a number. This means that you need to evaluate all of the terms that are positioned within the expression and see if they all share common coefficients our coefficients that can be factored. Coefficients really can be treated as ratios and as we know ratios can be factored.
You will find that by simply keeping these two tips as a habitual approach to working with these types of problems you will find working them to much smoother.