Teaching Notes 3.1: Writing Equations
The purpose of writing equations is to show that two expressions are equal. Common mistakes
students make are writing an expression in a sentence incorrectly and not making sure that the
quantities on each side of the equal sign are in fact equal.- Explain that word phrases can be written as algebraic expressions. For example, three times a
numbercanbewrittenas3n,wherenstands for a number; twice your age can be written 2a,
whereastands for your age; and four more than something can be written ass+4, wheres
stands for something. Depending on the abilities of your students, you may find it helpful
to remind them that a variable is a letter used to represent a number. You may also wish to
review 1.7: ‘‘Writing Expressions.’’ - Explain that in the same way that word phrases can be used to form word sentences, algebraic
expressions can be used to form equations. An equation is a number sentence that shows that
two expressions are equal. - Offer your students this hint: The word ‘‘is’’ often represents the equal sign in an equation.
For example, a number divided by 2 is 3 can be written asn÷ 2 =3. - Review the information and example on the worksheet with your students. Note that when
writing equations, students must identifya variable to represent an unknown quantity. It is
helpful to select a letter that reminds them of the quantity.
EXTRA HELP:
Equations may be true or false, depending on the value of the variable.ANSWER KEY:
Equations and variables may vary.
(1)n=a number;n− 5 = 12 (2)n=a number; 2n= 24
(3)a=Marie’s present age;a+ 3 = 15 (4)n=the number of quarters; 0. 25 n=$2.25
(5)n=a number;n− 12 = 24 (6)a=Quinn’s present age;a− 8 = 6
(7)n=a number; 3+ 2 n= 27 (8)c=cost of a student’s ticket; 10c=$50
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(Challenge)Answers may vary. Jason’s answer was wrong because 4 is less than 5 is an inequality,
not an equation. It should be written as 4<5. (Jason should pay better attention in class.)
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