Interpret the Context of Expressions Worksheets
In this section we are working with you to better understand the nature of math expressions that you come across. If you understand all the parts, you will better understand how to manipulate them to improve your ability to be fluid with solving more complex forms of algebra. In this section we are interested specifically in understand the number of terms that exist in expressions and the degrees of the terms that are present. The degree in context of expressions refers to the exponents of the variables that are present. These worksheets and lessons show students how to breakdown and understand all aspects of math expressions including coefficients, factors, and terms. We also go as far to see how these elements interact and affect the outcome of the problem.
Aligned Standard: HSA-SSE.A.1a
- Understanding a Polynomial Step-by-step Lesson- Learn the numbers of terms, degrees, and classification of an expression.
- Guided Lesson - We build on the lesson a great deal and leave you determining your classification of expressions.
- Guided Lesson Explanation - This will give you a solid understanding of the concepts of this section.
- Practice Worksheet - This one might be a bit easy for most, but you surely will know the concept of highest degrees.
- Matching Worksheet - More degree work here. I will diversify the new sheets I add to this section better.
- Answer Keys - These are for all the unlocked materials above.
Homework Sheets
Time to breakdown expressions and their parts. Make sure to review your expression vocabulary first.
- Homework 1 - Each piece of the polynomial is a term, as you see above. This polynomial has 3 terms.
- Homework 2 - Whichever term is to the highest power is also to the highest degree. 2x3 is to the highest degree.
- Homework 3 - The degree of the overall polynomial is represented by the term that is to the highest degree.
Practice Worksheets
Many students still have a problem identifying expressions as mono, bi, or even polynomials at this level.
- Practice 1 - How many terms are in the polynomial?
- Practice 2 - What is the degree of the polynomial?
- Practice 3 - Which would be the best classification of this expression?
Math Skill Quizzes
We only ask you to identify a single part of each expression in the quizzes.
- Quiz 1 - Interpret the polynomial based on each question.
- Quiz 2 - Make sense of each polynomial. Explain the number of terms present and the highest available degree.
- Quiz 3 - More complex terms for you. You need to step back a bit and look at the big picture with these problems.
What Are the Parts of an Expression?
Expressions are a composition of numbers, symbols, variables, and a series of operators that connect it altogether. The things in expression that are not operators are called terms. A term could be a signed number, a variable, a constant, or a mixture of both. If we have multiple terms that share the same variable they often can be combined. Coefficients are the numeric portion of a multiplication expression, that means the number in front. Constants on the other hand are just a value. Constants are constant meaning they never change.
Now that we understand a bit about expressions let’s explain the functional parts of the expression 3x – 2y + 6.
This expression consists of 3 terms: 3x, 2y, and 6. The variables x and y are present. The coefficients are the values in front the variables (3 and 2). The constant present is 6.
How to Determine the Context of Mathematical Expressions
Equations are basically a pure and symbolic expression of mathematical entities, most of the time. The idea of an equation is almost always about finding a solution to a problem through symbol or value manipulation. Every single manipulation, if done according to the conventional rules, can lead to an equivalent equation which is relatively simpler (easier to solve) compared to the previous one. Another way of solving such equations is through making a graphical representation of them. This, however, is a much more symbolic approach to solving a mathematical equation. This doesn't determine the concept of all equations. You can always think of a story for explaining an equation. Work on developing stories that can help enliven the math equations. Allowing the students to make sense of what is happening in the situation that makes up the equation. Make proper distinctions between constants and variables and how their relationship can be changed if assumptions are changed midway.