Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
A letter in an expression can play two roles, and sixth graders learn to tell them apart. Sometimes it stands for one specific unknown, as in 'Maya had some stickers, gave away 8 and has 15 left' where s - 8 = 15 has a single answer. Other times it stands for any number in a set, as in 'the cost of t tickets at $12 each is 12t', where t can be 1, 2, 10 or any whole number of tickets.
The practical skill is writing an expression that models a situation. Students choose a variable, say clearly what it represents (including units), and build the expression from the relationships in the story. If a gym charges $25 to join and $15 a month, the total cost for m months is 25 + 15m. Defining the variable precisely ('m = number of months') is essential, because 'm = months' leaves it unclear whether m counts months or measures money. These expressions become the raw material for equations in 6.EE.B.7 and for the dependent and independent variables of 6.EE.C.9.
Students may write 5a to mean '5 apples'. In algebra, a should stand for a number, such as the number of apples or the cost of one apple.
'Twelve less than the number of students' is s - 12, but students often write 12 - s because 12 comes first in the sentence.
Different letters can take the same value. What matters is that each letter is defined.
A gym charges a $25 joining fee plus $15 per month. Write an expression for the total cost of m months, then find the cost of 8 months.
Answer: Total cost = 25 + 15m dollars; 8 months cost $145.
Have students write 'Let ___ = ___' before every expression. Contrasting two stories, one with a single unknown and one with a general rule, makes the two roles of a variable explicit.
Assessments often ask students to select the expression that models a situation or to write one and use it. Including a fixed fee plus a rate is very common and previews linear functions.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: A) 0.35p
Each pencil adds $0.35, so p pencils cost 0.35 × p = 0.35p dollars.
Answer: D) s - 12
Start with all students, s, and take away the 12 absent: s - 12.
Answer: 21
3 + 2 × 9 = 3 + 18 = 21 dollars.
Answer: B) The side length of any square
The formula works for every square, so s stands for any side length, not one particular unknown.
Answer: 64
3 × 20 + 4 = 60 + 4 = 64 marbles.
A full lesson with slides, activities and an exit ticket on using variables to represent numbers, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 6.EE.B.6 with an answer key, ready in about a minute.
Make a worksheet →Turn using variables to represent numbers into a quiz students answer online that marks itself, with a class summary for you.
Build a test →A variable can stand for one unknown number that makes a statement true, or it can stand for any number in a set, as in a formula or general rule.
Saying exactly what the letter represents, with units, avoids confusion and makes the expression meaningful to someone else reading it.