6.EE.B.6Common CoreMathExpressions and EquationsGrade 6
6.EE.B.6: Using Variables to Write Expressions for Problems
In plain English: 6.EE.B.6 is the Common Core grade 6 math standard that asks students to use variables to write expressions when they solve real-world and math problems. Students learn that a variable can stand for one unknown number or, depending on the purpose, for any number in a set, such as any number of hours worked. It builds toward writing and solving equations in 6.EE.B.7.
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.
Common Core State Standards for Mathematics · Domain: Expressions and Equations (EE) · Cluster: Reason about and solve one-variable equations and inequalities. Also written as 6.EE.6 · Official standard
Students use letters to stand for numbers and write expressions that describe real situations and math problems. A variable is a letter, such as n or c, that stands for a number. An expression is a combination of numbers, variables and operation signs with no equals sign, such as 4c or 10 + 1.5t. An equation, such as n + 7 = 15, says that two expressions have the same value. Students translate words into expressions, choose what each variable stands for, and evaluate the expression (find its value) for given numbers.
The second half of the standard is about meaning. Sometimes a variable stands for one unknown number: in "Sofia's number plus 7 is 15", n can only be 8. Other times, depending on the purpose, it stands for any number in a specified set (a list or range of allowed values): in "$4 per class, so the cost is 4c", c can be any number of classes, such as 0, 1, 2 and so on up to 20. Students learn to tell the two uses apart and to choose a set that makes sense in the situation. Numbers stay friendly and positive, and formal equation solving waits for 6.EE.B.7.
Learning Objectives
By the end of this lesson, students will be able to:
Choose a variable for an unknown quantity and say in words what it stands for
Write expressions with one or two operations for real-world and mathematical problems
Evaluate an expression they wrote to answer a question about the situation
Explain whether a variable stands for one unknown number or for any number in a specified set
Choose a set of values that makes sense for a variable in a real situation
Prior Knowledge Required
Students should already be comfortable with:
Writing simple numerical expressions that record calculations 5.OA.A.2
Using parentheses and the order of operations 5.OA.A.1
Writing and reading expressions with letters standing for numbers 6.EE.A.2a
Evaluating expressions at specific values of their variables 6.EE.A.2c
Adding, subtracting, multiplying and dividing decimals 6.NS.B.3
Tell a short story and let students answer on mini whiteboards.
Warm-Up Prompt
"Jordan has a box of trading cards, but he has not counted them. He also has 12 cards in his backpack. How could you write the total number of cards he has, without knowing how many are in the box? If the box turns out to hold 30 cards, what is the total?"
Collect answers such as "box + 12" or "? + 12". Explain that mathematicians use a letter instead of a word or a question mark: if b is the number of cards in the box, the total is b + 12. When b = 30, the total is 30 + 12 = 42 cards. Introduce the words variable (the letter b) and expression (b + 12). Ask: could b be any number? Only numbers that make sense for a box of cards: whole numbers, and not too large.
Direct Instruction15-20 minutes
Writing expressions. Model three steps for every problem: (1) say what the variable stands for in words, including the unit, such as "c = the number of classes"; (2) find the operation in the words (more than and plus mean add, less than and decreased by mean subtract, times and per often mean multiply, split equally means divide); (3) write the expression and test it with one easy number. Watch the order in subtraction and division: "10 less than m" is m - 10, not 10 - m.
Variable for one unknown number
Sofia thinks of a number, adds 7, and gets 15. Write an expression for "Sofia's number plus 7" and find the number.
Equation: Let n be Sofia's number. The expression is n + 7, and n + 7 is 15, so n is 8 (8 + 7 = 15). Here n stands for one unknown number.
Variable for any number in a set
A gym charges $4 for each class. Write an expression for the cost of c classes, where c can be any whole number from 0 to 20. Find the cost of 5 classes and of 12 classes.
Equation: The cost is 4c dollars. 4 × 5 = 20, so 5 classes cost $20; 4 × 12 = 48, so 12 classes cost $48. Here c can be any number in the set {0, 1, 2, ..., 20}.
Expression with two operations
A pizza costs $10, plus $1.50 for each topping. Write an expression for the cost of a pizza with t toppings, and find the cost with 3 toppings.
Equation: 10 + 1.5t dollars. With t = 3: 10 + 1.5 × 3 = 10 + 4.5 = 14.5, so the pizza costs $14.50.
Expression with division
A class of s students splits into teams of 4. Write an expression for the number of teams. How many teams are there if s is 20, 24 or 28?
Equation: s ÷ 4 teams. 20 ÷ 4 = 5, 24 ÷ 4 = 6 and 28 ÷ 4 = 7 teams. The set for s holds class sizes that split evenly into teams of 4.
Mathematical problem
An equilateral triangle has three sides of the same length. Each side is s centimeters long. Write an expression for its perimeter (the distance around it), and find the perimeter when s = 7.
Equation: s + s + s, or 3s centimeters. With s = 7: 3 × 7 = 21 centimeters.
What does the variable stand for? Diagram 1 shows the first example as a tape diagram (a bar split into parts whose lengths match the numbers): the whole bar is 15, one part is 7, and the other part, n, must be 8. Only one number works. Diagram 2 shows the second example: the same expression, 4c, gives a cost for every number of classes, so c can be any number in the set. Use this table to sum up the difference:
Two ways a variable can be used
One unknown number
Any number in a specified set
Question it answers
Which number is it?
What happens for each allowed number?
Clue in the words
A fixed result is given, such as "and gets 15"
A rule for many cases, such as "for c classes"
Example
n + 7 when n + 7 is 15, so n = 8
4c for c = 0, 1, 2, ..., 20
Guided Practice15 minutes
Pairs write an expression for each phrase or situation on a mini whiteboard, then say whether the variable stands for one unknown number or any number in a set. Stop after each row to compare.
Guided practice: write the expression
Problem
Words
a
5 more than a number x
b
A number y decreased by 8
c
A tutor earns $20 per hour. Her pay for h hours
d
A dinner bill of m dollars split equally among 4 friends
e
Twice a number k, plus 1, is 19
Answers: (a) x + 5. (b) y - 8. (c) 20h dollars, where h can be any number of hours in a set such as {1, 2, ..., 10}; for 3 hours she earns $60. (d) m ÷ 4 dollars each, where m can be any bill amount; a $72 bill gives $18 each. (e) 2k + 1, and because the result is fixed at 19, k is one unknown number: 9, since 2 × 9 + 1 = 19. Listen for pairs who write 8 - y in (b) or 4 ÷ m in (d).
Independent Practice10-15 minutes
Students work alone. (1) A movie ticket costs $9. Write an expression for the cost of k tickets, and find the cost of 6 tickets. (9k; $54.) (2) Tia had s stickers and gave away 6. Write an expression for the number she has left. How many are left if she started with 20? (s - 6; 14.) (3) A car travels at a steady 55 miles per hour. Write an expression for the distance it travels in h hours, and find the distance in 3 hours. (55h; 165 miles.) (4) A number times 4 is 36. Write an expression for "a number times 4" and find the number. (4n; n = 9, one unknown number.) (5) The area of a rectangle that is 6 feet wide and L feet long is 6L square feet. Does L stand for one number or any number? (Any length, for example any number of feet greater than 0; the expression works for every such rectangle.)
Closure5 minutes
Exit ticket: (1) Write an expression for the number of wheels on b bicycles. (2b.) (2) Find its value for b = 15. (30 wheels.) (3) Mr. Park says, "I bought some $3 notebooks and paid $21 in all. The cost was 3n." Does n stand for one unknown number or any number? Find it. (One unknown number: 7, since 3 × 7 = 21.)
Differentiation Strategies
For Struggling Students
Give a word bank that sorts operation words into four columns (add, subtract, multiply, divide), with one example expression in each column
Have students write "n = ..." in words before every expression, and test the expression with an easy number such as 10
Use tape diagrams on grid paper for the unknown-number problems, one square for each unit
For Advanced Students
Ask students to write two different expressions for the perimeter of a rectangle that is 4 units longer than it is wide, and test that both give the same value
Ask students to write a story for the expression 25 - 3k and choose a set of values for k that makes sense in the story
Ask students to write a situation where the same expression is first used with any number in a set, and then with one unknown number
Assessment Guidance
What to Look For
Check that students define each variable in words with a unit before writing the expression, and that the operation matches the words, especially the order in subtraction and division. When students evaluate, look for correct substitution and order of operations. For the meaning of a variable, students should point to the clue: a fixed result makes the variable one unknown number, while a rule for many cases makes it any number in a set. Ask them to name a set of values that makes sense, such as whole numbers for people or tickets.
02
Classroom Activities
3 Activities
1
Phrase and Expression Match-Up
15 minPairs
Each pair gets 8 phrase cards and 8 expression cards. All 16 cards use the number 7 and the variable p, so pairs must read the words carefully to match them.
Phrase Cards and Matching Expressions (8 pairs)
7 more than a number p: p + 7
7 less than a number p: p - 7
A number p subtracted from 7: 7 - p
7 times a number p: 7p
A number p divided by 7: p ÷ 7
7 divided by a number p: 7 ÷ p
Twice a number p, plus 7: 2p + 7
Twice the sum of a number p and 7: 2(p + 7)
Procedure
Shuffle the expression cards and deal them face up; the phrase cards stay in a stack
One partner reads a phrase and the other finds the expression; switch roles after each card
Test each match by substituting p = 14 and checking that the words and the expression give the same number
Discussion Questions
When p = 7, the expressions p ÷ 7 and 7 ÷ p both equal 1. Are they the same expression? Test p = 14. (No: 14 ÷ 7 = 2, but 7 ÷ 14 = 1/2)
When p = 14, what are the values of 2p + 7 and 2(p + 7)? (35 and 42) What do the parentheses change?
Which words told you the order in 7 less than p?
Modification for Distance Learning
Put the cards on a shared slide. Pairs drag each expression next to its phrase and type the value for p = 14 beside it.
2
Fundraiser Tables: Same Rule, Many Numbers
20 minGroups of 3-4
Groups plan a school fundraiser. Each group gets 3 fundraiser cards, writes an expression for the money raised, and fills in a table for the set {5, 10, 15, 20} sales. At the end, each group solves one mystery question where the variable stands for a single unknown number.
Fundraiser Cards (3 cards)
Bracelets: $3 for each bracelet sold. Expression: 3b. Table: $15, $30, $45, $60
Car wash: $8 for each car washed. Expression: 8c. Table: $40, $80, $120, $160
Bake sale: $2 for each muffin sold, plus $12 a parent already donated. Expression: 2m + 12. Table: $22, $32, $42, $52
Procedure
One student writes the expression, one evaluates it for each number in the set, and one checks with a calculator; rotate for each card
Write what the variable stands for on each table, for example "b = the number of bracelets sold, any number in {5, 10, 15, 20}"
Mystery question: the bracelet table raised exactly $39. How many bracelets were sold? (13, because 3 × 13 = 39) Discuss why b now stands for one unknown number
Discussion Questions
Which fundraiser raises the most money for 10 sales? (The car wash, $80)
For which numbers in the set do bracelets raise more than the bake sale? (15 and 20)
Why does the bake sale raise more than bracelets for 5 and 10 sales, even though a bracelet costs more than a muffin?
Challenge Variation
Groups invent a fourth fundraiser with a price per item and a starting amount, write its expression, and find a number of sales from the set where it raises more than the car wash, if there is one.
3
Write It, Test It: Story Cards
20 minPairs
Pairs work through 4 story cards. For each card, they define a variable in words, write an expression, decide whether the variable stands for one unknown number or any number in a set, and answer the question on the card.
Story Cards (4 cards)
Card 1, bus seats: a school bus has 36 seats, and e seats are empty. Expression for the filled seats: 36 - e. If 9 seats are empty, 27 are filled. (Any number in the set {0, 1, 2, ..., 36})
Card 2, pets: Zoe's dog weighs 4 times as much as her cat. The cat weighs k pounds. Expression for the dog's weight: 4k. The dog weighs 44 pounds, so the cat weighs 11 pounds, because 4 × 11 = 44. (One unknown number, the cat's weight)
Card 3, paint: 1 gallon of paint covers about 350 square feet. Expression for the area covered by g gallons: 350g. Three gallons cover about 1,050 square feet. (Any number of gallons)
Card 4, mystery number: half of a number, plus 5, is 12. Expression: d ÷ 2 + 5. The number is 14, because 14 ÷ 2 + 5 = 12. (One unknown number)
Procedure
Write "variable = ..." in words with a unit before writing each expression
Test each expression with the number on the card and record the result on the recording sheet
Circle "one unknown number" or "any number in a set" and write the clue from the story that decided it
Discussion Questions
On Card 1, why can e not be 40?
Which cards gave a fixed result that made the variable one unknown number? (Cards 2 and 4)
Could Card 3 use a set that includes 2.5 gallons? Why is that different from Card 1?
Modification for Distance Learning
Post one card at a time in a shared document. Pairs type their variable definition, expression and decision in a table, and the class compares clues.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: A Variable as One Unknown Number
A tape diagram for "Sofia's number plus 7 is 15". The bar is drawn to scale: the n part is 8 units long and the 7 part is 7 units, for a total of 15. Because the total is fixed, n stands for exactly one number, 8.
Diagram 2: A Variable as Any Number in a Set
The gym charges $4 per class, so the cost is 4c dollars. The table and the bars, drawn to scale, show the cost for 1 to 6 classes: $4, $8, $12, $16, $20 and $24. The same expression works for every number of classes in the set, so c can be any number in it.
04
Homework Assignment
~30 min
6.EE.B.6 Homework: Variables and Expressions
Directions: For every expression, first write what the variable stands for in words, with a unit. Show your substitution when you evaluate. In Part 2, say whether each variable stands for one unknown number or any number in a set, and explain the clue.
Part 1: Writing Expressions (Problems 1-3)
Write an expression for each phrase: (a) 12 more than a number r; (b) the product of 8 and a number q; (c) a number z divided by 5; (d) 3 less than twice a number w.
A bike rental costs $6, plus $3 for each hour. Write an expression for the cost of renting a bike for h hours. Then find the cost of renting it for 4 hours.
A baker puts 12 muffins in each box. (a) Write an expression for the number of muffins in x boxes, and find it for 7 boxes. (b) Write an expression for the number of boxes needed for m muffins, and find it for 96 muffins.
Part 2: What Does the Variable Stand For? (Problems 4-6)
A bean plant grows about 2 centimeters each week. The expression 2w gives its growth in centimeters after w weeks. Does w stand for one unknown number or any number in a set? Name a reasonable set for w, and find the growth for three numbers in your set.
Marco thinks of a number, multiplies it by 3, and gets 27. Write an expression for "Marco's number times 3". Does the variable stand for one unknown number or any number in a set? What is Marco's number?
Tickets to the school play cost $7 each. (a) Write an expression for the cost of t tickets. (b) Ava bought some tickets and paid $35 in all. What does t stand for now, and what is its value? Explain how the purpose of the variable changed from (a) to (b).
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Defining Variables
Every variable is described in words with a unit
Some variables described, or units missing
Variables not described
Writing Expressions
All expressions match the words, including order in subtraction and division
One or two expressions with an error
Most expressions incorrect
Evaluating
Substitution shown and values correct
Correct values with no work shown, or one error
Values missing or incorrect
Meaning of the Variable
Problems 4-6 correctly identify one unknown number or any number in a set, with the clue
Correct choices but no clue given
Choices incorrect or missing
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Work through the questions in order. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
Which expression means "6 more than a number k"?
Answer: C
"More than" means add, so 6 more than k is k + 6. Test with k = 10: 6 more than 10 is 16, and 10 + 6 = 16. Choice A reads "more" as "times" and gives 60 for k = 10. Choices B and D subtract instead of adding.
Question 2 of 20 · Multiple Choice
Which expression means "9 less than a number m"?
Answer: A
9 less than m means start with m and take away 9: m - 9. Test with m = 25: 9 less than 25 is 16, and 25 - 9 = 16. Choice B writes the numbers in the order they are read, which reverses the subtraction: 9 - 25 is not 16. Choice D adds instead of subtracting.
Question 3 of 20 · Multiple Choice
Grapes cost $3 per pound. Which expression gives the cost, in dollars, of p pounds of grapes?
Answer: D
Each pound costs $3, so p pounds cost 3 × p = 3p dollars. Test with p = 2: 2 pounds cost $6, and 3 × 2 = 6. Choice A divides instead of multiplying, which gives 2 ÷ 3 = 2/3 of a dollar for 2 pounds. Choice B adds the price and the pounds, which gives $5 for 2 pounds instead of $6.
Question 4 of 20 · Multiple Choice
Jen has d dollars. She spends $8 on lunch. Which expression shows how many dollars she has left?
Answer: B
She starts with d dollars and takes away 8, so d - 8 dollars are left. Test with d = 20: 20 - 8 = 12 dollars left. Choice A reverses the order and would give a negative number for d = 20. Choice C adds the lunch price instead of subtracting it.
Question 5 of 20 · Multiple Choice
A class of 28 students splits into groups with g students in each group. Which expression gives the number of groups?
Answer: A
The number of groups is the total divided by the size of each group: 28 ÷ g. Test with g = 4: 28 ÷ 4 = 7 groups. Choice B divides in the wrong order and gives 4 ÷ 28 = 1/7 of a group. Choice C multiplies and gives 112 for g = 4, more groups than there are students.
Question 6 of 20 · Multiple Choice
A phone case costs $12, and each screen protector costs $5. Which expression gives the total cost, in dollars, of one case and s screen protectors?
Answer: C
The case is paid once ($12), and each protector adds $5, so the cost is 12 + 5s. Test with s = 2: 12 + 10 = 22 dollars. Choice A attaches the variable to the wrong price and gives $29 for s = 2. Choice B adds 12 + 5 first and then multiplies, which charges for a case with every protector: $34 for s = 2. Choice D adds s instead of multiplying: $19 for s = 2.
Question 7 of 20 · Multiple Choice
A bowling alley charges $4 for shoes plus $5 for each game. The expression 4 + 5g gives the cost of g games. What does it cost to bowl 3 games?
Answer: B
Substitute 3 for g: 4 + 5 × 3 = 4 + 15 = 19, so it costs $19. Choice A adds 4 + 5 first and then multiplies by 3, which breaks the order of operations: 9 × 3 = 27. Choice C adds all three numbers: 4 + 5 + 3 = 12. Choice D finds only the games, 5 × 3 = 15, and forgets the shoes.
Question 8 of 20 · Multiple Choice
In which situation does the variable n stand for one unknown number?
Answer: D
In choice D, the result is fixed at 20, so n can only be 11. In choices A, B and C, the expression is a rule that works for many values: any number of pencils, any length or any number of players, with no fixed result given. There the variable stands for any number in a set, not one unknown number.
Question 9 of 20 · Multiple Choice
The expression 15w gives the dollars Rosa earns for w hours of babysitting, where w can be any whole number from 1 to 8. What does w stand for?
Answer: B
The problem says w can be any whole number from 1 to 8, so w is any number in that set, and 15w gives Rosa's pay for each one. Choice A would be right only if a fixed total were given. Choice C mixes up the variable with the 15, which is the dollars per hour. Choice D mixes up the variable with the value of the whole expression.
Question 10 of 20 · Multiple Choice
A number is multiplied by 7, and the result is 42. If n is the number, which statement is true?
Answer: C
The result is fixed at 42, so n is one unknown number: 7 × 6 = 42, so n is 6. Choice A ignores the fixed result. Choice B multiplies 42 × 7 instead of asking which number times 7 gives 42. Choice D subtracts 42 - 7.
Question 11 of 20 · Multiple Choice
Which expression means "the sum of a number x and 4, divided by 2"?
Answer: D
The sum x + 4 is found first and then divided by 2, so it needs parentheses: (x + 4) ÷ 2. Test with x = 6: the sum is 10, and half of it is 5; (6 + 4) ÷ 2 = 5. Choice A leaves out the parentheses, so only the 4 is divided: 6 + 2 = 8. Choice C divides in the wrong order.
Question 12 of 20 · Multiple Choice
A rectangle is 5 inches long and w inches wide. Which expression gives its area in square inches?
Answer: B
Area of a rectangle = length × width, so the area is 5 × w = 5w square inches. Test with w = 3: 5 × 3 = 15 square inches. Choice D is the perimeter, the distance around the rectangle: 5 + 5 + w + w = 10 + 2w. Choice A adds the length and width instead of multiplying.
Question 13 of 20 · Multiple Choice
Movie tickets cost $11 for adults and $7 for children. Which expression gives the total cost, in dollars, for a adults and k children?
Answer: A
Each adult ticket costs $11 and each child ticket costs $7, so the cost is 11a + 7k. Test with 2 adults and 3 children: 22 + 21 = 43 dollars. Choice B adds the two prices and charges $18 for every person: $90. Choice C switches the prices and charges children $11: $47. Choice D multiplies everything together.
Question 14 of 20 · Multiple Choice
The expression 60 - 4d gives the dollars left on a $60 cafeteria card after d days of buying a $4 snack. How much is left after 9 days?
Answer: A
Substitute 9 for d: 60 - 4 × 9 = 60 - 36 = 24, so $24 is left. Choice B subtracts first, 60 - 4 = 56, and then multiplies by 9, which breaks the order of operations. Choice C subtracts both numbers: 60 - 4 - 9 = 47. Choice D finds only the amount spent, 4 × 9 = 36, and forgets to subtract it from 60.
Question 15 of 20 · Short Answer
Write an expression for the number of minutes in h hours. Then use it to find the number of minutes in 3.5 hours.
Each hour has 60 minutes, so the expression is 60h. For h = 3.5: 60 × 3.5 = 210 minutes. Here h can be any number of hours.
Question 16 of 20 · Short Answer
Paulo already has $30 saved, and he saves $5 each week. Write an expression for his savings after w weeks. How much will he have after 8 weeks?
He starts with $30 and adds $5 per week: 30 + 5w dollars. For w = 8: 30 + 5 × 8 = 30 + 40 = $70. A common error is (30 + 5) × 8 = $280, which adds the $30 every week.
Question 17 of 20 · Short Answer
The perimeter of any rectangle is 2L + 2W, where L is the length and W is the width. Do L and W stand for one unknown number each, or for any numbers in a set? Explain, and find the perimeter of a rectangle 9 cm long and 4 cm wide.
In the formula, L and W can be any positive lengths: the expression works for every rectangle, so each variable stands for any number in a set (all numbers greater than 0). For L = 9 and W = 4: 2 × 9 + 2 × 4 = 18 + 8 = 26 cm.
Question 18 of 20 · Short Answer
A number t decreased by 15 is 26. Write an expression for "a number t decreased by 15" and find the number. Does t stand for one unknown number or any number here?
The expression is t - 15. Its value is fixed at 26, so t stands for one unknown number: t = 41, because 41 - 15 = 26.
Question 19 of 20 · Short Answer
Each student needs 3 pencils for testing week. Write an expression for the number of pencils needed for s students. Then find how many boxes of 10 pencils a class of 30 students needs.
The expression is 3s pencils. For s = 30: 3 × 30 = 90 pencils, and 90 ÷ 10 = 9 boxes.
Question 20 of 20 · Short Answer
Tacos cost $2.50 each. Write an expression for the cost of n tacos. Choose a reasonable set of values for n, and explain why a number like 2.3 does not belong in it. Then find the cost of 6 tacos.
The cost is 2.5n dollars (or 2.50n). A reasonable set is the whole numbers {0, 1, 2, 3, ...}, perhaps up to 20 for one order, because people buy whole tacos; 2.3 tacos cannot be ordered. For n = 6: 2.5 × 6 = $15.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does 6.EE.B.6 mean?
6.EE.B.6 means students use letters (variables) to stand for numbers and write expressions to solve real-world and math problems. It also asks them to understand two uses of a variable: it can stand for one unknown number, such as the number in "a number plus 7 is 15", or for any number in a set, such as any number of hours in "$15 per hour".
What is the difference between a variable and an expression?
A variable is a single letter that stands for a number, such as h. An expression combines numbers, variables and operations, such as 20h + 5, and it has no equals sign. An equation, such as 20h + 5 = 65, says that two expressions have the same value.
When does a variable stand for an unknown number, and when for any number in a set?
Look at the purpose. If the problem gives a fixed result, such as "he spent $18 on stamps", the variable stands for one unknown number that you can find. If the expression is a rule meant to work for many cases, such as "the cost of s stamps", the variable can be any number in a set that makes sense, such as the whole numbers from 0 to 50.
Is 6.EE.B.6 about solving equations?
Not mainly. 6.EE.B.6 is about writing expressions with variables and understanding what the variable stands for. Students may find an unknown number by reasoning, such as seeing that 8 + 7 = 15. Writing and solving equations such as x + p = q and px = q with a formal method is 6.EE.B.7.
What are common mistakes when writing expressions?
A common mistake is reversing the order in subtraction and division: "5 less than n" is n - 5, not 5 - n, and "n divided by 3" is n ÷ 3. Another is forgetting parentheses, as in "twice the sum of n and 4", which is 2(n + 4), not 2n + 4. Testing the expression with an easy number catches most of these.
Why should students say what the variable stands for?
Writing "h = the number of hours" makes the expression readable and shows which numbers make sense. It also prevents mixing up quantities, such as using the price per hour as if it were the number of hours. Teachers often give credit for a clear variable definition.
How is 6.EE.B.6 tested?
Test items often describe a situation and ask students to choose or write the expression that matches it, sometimes with two operations. Other items ask students to evaluate the expression for a given value, or to explain what the variable represents. Answer choices often include the reversed order or a missing set of parentheses, so reading carefully matters.
What letters can be used as variables?
Any letter can be a variable. Many teachers encourage a letter that reminds students of the quantity, such as c for cost or t for tickets. Students should avoid letters that are easy to confuse with numbers, such as a lowercase l next to 1 or o next to 0, and should not use the same letter for two different quantities in one problem.
How does 6.EE.B.6 connect to later math?
Writing expressions is the first step in setting up equations and inequalities in 6.EE.B.7 and 6.EE.B.8, and in two-step word problems in 7.EE.B.4. The idea that a variable can be any number in a set leads to functions in grade 8 and to writing equations in Algebra I (HSA.CED.A.1).
How can parents help with variables and expressions at home?
Use everyday prices and rates. Ask, "If a game costs $2 per round, what is the cost for r rounds?" (2r), and then try a few values for r. Or give a fixed result: "I spent $10 on rounds. How many did I play?" Talking about why r can be many numbers in the first case but only one in the second builds exactly this standard.
07
Related Standards
6 standards
These standards connect to 6.EE.B.6: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
5.OA.A.2Prerequisite
Write simple expressions that record calculations and interpret them
Lesson coming soon
6.EE.A.2Prerequisite
Write, read and evaluate expressions in which letters stand for numbers
