Math - 2019-20
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.
- 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 3b; “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 3b = 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
- 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 4x = 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.
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.
- 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)