#### Math - 2018-19

# 5.19 - Variables

**The student will**

a) **investigate **and **describe **the concept of variable;

b) **write **an equation to represent a given
mathematical relationship, using a variable;

c) **use **an expression with a
variable to represent a given verbal expression involving one operation; and

d) **create **a
problem situation based on a given equation, using a single variable and one
operation.

*Adopted: 2016*

### BIG IDEAS

- So that I can make a story problem when given an equation
- So that I can figure out the missing piece of a problem (i.e How much gas can I get if I have $25 and it costs $2.09 a gallon?)
- So that I have a foundation of knowledge for a career in engineering, mathematics, chemistry, physics, and finance.
- So that I can make good financial decisions (i.e comparing offers from two phone companies when signing a long term contract; comparing the price of similar items in the grocery store based on price per unit)
- So that I can improve my critical thinking and problem solving skills
- So that I can win at game of Yahtzee, Math Boggle, Battleship, or Chess

### UNDERSTANDING THE STANDARD

- A variable is a symbol that can stand for an unknown number (e.g.,
*a*+ 4 = 6) or for a quantity that changes (e.g., the rule or generalization for the pattern for an input/output table such as*x*+ 2 =*y*). - An algebraic expression, an expression with a variable, is
like a phrase; a phrase does not have a verb, so an expression does not have an
equal symbol (=).
- A verbal expression describing a relationship involving one
operation can be represented by an expression with a variable that
mathematically describes the relationship. Numbers are used when quantities are
known; variables are used when the quantities are unknown. For example, when
*b*stands for the number of cookies in one full box, “the number of cookies in a full box and four extra” can be represented by*b*+ 4; “three full boxes of cookies” by 3*b*; “the number of cookies each person would receive if a full box of cookies were shared among four people” by b/4 . - An equation is a statement that represents the relationship
between two expressions of equal value (e.g., 12 × 3 = 72 ÷ 2).
- A problem situation about two quantities that are equal can
be expressed as an equation.
- An equation may contain a variable and an equal symbol (=).
For example, the sentence, “A full box of cookies and four extra equal 24
cookies.” can be written as
*b*+ 4 = 24, where*b*stands for the number of cookies in one full box. “Three full boxes of cookies contain a total of 60 cookies” can be written as 3*b*= 60. - Another example of an equation is
*b*+ 3 = 23 and represents the answer to the word problem, “How many cookies are in a box if the box plus three more equals 23 cookies?” where*b*stands for the number of cookies in the box? - Teachers should consider varying the letters used (in
addition to
*x*) to represent variables. The symbol x is often used to represent multiplication and can be confused with the variable*x.*In addition to varying the use of letters as variables, this confusion can be minimized by using parentheses [e.g., 4(*x*) = 20 or 4*x*= 20] or a small dot raised off the line to represent multiplication [4 •*x*= 20]. - By using story problems and numerical sentences, students
begin to explore forming equations and representing quantities using variables.
- An equation containing a
variable is neither true nor false until the variable is replaced with a number
and the value of the expressions on both sides are compared.

### ESSENTIALS

**The student will use
problem solving, mathematical communication, mathematical reasoning,
connections, and representations to**

- Describe the concept of a variable (presented as boxes,
letters, or other symbols) as a representation of an unknown quantity. (a)
- Write an equation with addition, subtraction,
multiplication, or division, using a variable to represent an unknown quantity.
(b)
- Use an expression with a variable to represent a given
verbal expression involving one operation (e.g., “5 more than a number” can be
represented by
*y*+ 5). (c) - Create and write a word problem to match a given equation
with a single variable and one operation. (d)

### KEY VOCABULARY

*Updated: Mar 06, 2019*