# Relationships Between Quantities

Everyone loves math until there are letters (known as variables) in problems!! Do students complain about reading when they come to a number in a book? So why do students become frustrated when they see letters (known as variables) in math problems. Variables represent numbers . . . This seems like a simple statement, but it is very powerful when you can understand variables are nothing more than numbers. Variables can be used in problems when we do not know the value of a number. In this unit, we will look at variables and how we can use them to solve and simplify expressions, equations, inequalities, and formulas.

### Essential Questions

• Why are units and scale important when you are working to solve math problems?
• Why is it important to know and consider the different terms (or parts) of a mathematical expression?
• How are variables used in equations, inequalities, and formulas?

### Module Minute

When working math problems, it is important to consider the units of your answer. Many problems deal with finding an unknown value (variable), so it is important to consider what the answer (number equal to variable) represents. Graphs help us visualize data. To ensure everyone views the data the same, it is important to label the graph's axes and their scales. Expressions, equalities, inequalities, and formulas have different components or parts. By recognizing these different parts (or pieces) and what they represent, is it easy to understand the whole expression. Instead of being afraid of letters in math, we need to understand why they are being used, what they represent, and how to solve for them. Finally, we can substitute our answer/s in for the variable/s to see if they work.

### Key Terms

• Algebra- The branch of mathematics that deals with operations on sets of numbers and relationships between them.
• Equation- A statement that describes the equality of two expressions by connecting them with an equals sign.
• Function- A kind of relation in which one variable uniquely determines the value of another variable.
• Linear Equation- An equation that describes a straight line.
• Coefficient- Number used to multiply a variable.
• Factor- Number you multiply by to get another number.
• Variable- A symbol that represents an unknown value.
• Scale - The spacing of numbers on the axes of a graph.
• Units of Measurement -A quantity used as a standard of measurement. (Example: Units of time are second, minute, hour, day, week, month, year and decade.)
• Unit Rates - The rate of one item. (Example: 1 foot = 12 inches)
• Modeling - Using a picture, equation, or system of equations to represent real-world phenomena. Models also represent patterns found in graphs and/or data. Usually models are not exact matches the objects or behavior they represent. A good model should capture the essential character of whatever is being modeled.
• Quantity - The amount of something.
• Proportion - The result of dividing one number or expression by another. Sometimes a ratio is written as a proportion, such as 3:2 (three to two). More often, though, ratios are simplified according to the standard rules for simplifying fractions or rational expressions.
• Precision - The level of detail in a number or estimate. A precise number has many significant digits. Note: An answer may be precise without being accurate. (Example: Numerous shots at a bulls eye being in the same area (not necessarily near the bulls eye).)
• Accuracy - How close an approximation is to an actual value. (Example: Numerous shots at a bulls eye being near the center of the bulls eye but not necessarily around each other.)

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