6.EE.A.2Common CoreMathExpressions and EquationsGrade 6
6.EE.A.2: Writing, Reading and Evaluating Expressions with Variables
In plain English: 6.EE.A.2 is the Common Core grade 6 math standard that asks students to write, read and evaluate expressions in which letters stand for numbers. Students turn words such as "subtract y from 5" into 5 - y, name the parts of an expression (sum, term, product, factor, quotient, coefficient), and evaluate expressions and formulas such as V = s³ using the order of operations.
Write, read, and evaluate expressions in which letters stand for numbers.
a.Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract y from 5" as 5 - y.
b.Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
c.Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s³ and A = 6 s² to find the volume and surface area of a cube with sides of length s = 1/2.
Common Core State Standards for Mathematics · Domain: Expressions and Equations (EE) · Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions. Also written as 6.EE.2 · Official standard
Students learn to use letters in place of numbers. A variable is a letter, such as n or s, that stands for a number. An expression is a math phrase made of numbers, variables and operation signs, such as 5 - y or 3(k + 2); it has no equal sign. Students write expressions from words and situations (standard a), for example the official example "Subtract y from 5", which is 5 - y. They read expressions aloud in words, too.
Next, students name the parts of an expression with the words the standard lists (standard b): sum (the result of adding), term (a part of an expression that is added to other parts), product (the result of multiplying), factor (a number or group that is multiplied), quotient (the result of dividing) and coefficient (the number that multiplies a variable, such as 3 in 3k). They learn to see a group in parentheses, such as (8 + 7) in 2(8 + 7), as one single thing and also as a sum of two terms. Finally, they evaluate expressions (standard c): they replace each variable with a given number and find the value, following the order of operations (parentheses, then exponents, the small raised numbers that tell how many times a factor is used, then multiplication and division, then addition and subtraction). This includes formulas (rules that use variables for real quantities) from real life, such as the official example V = s³ for the volume and A = 6s² for the surface area (the total area of all 6 faces) of a cube with sides of length s = 1/2. Students do not solve equations in this lesson; that comes in 6.EE.B.7.
Learning Objectives
By the end of this lesson, students will be able to:
Write expressions with numbers and variables from words and simple situations, and read expressions aloud in words
Identify the terms, sums, products, factors, quotients and coefficients in an expression
Describe a part in parentheses both as a single entity and as a sum or difference of terms
Evaluate expressions, including real-world formulas, at given values of their variables
Use the order of operations, including whole-number exponents, when an expression has no parentheses to show the order
Prior Knowledge Required
Students should already be comfortable with:
Using the area and perimeter formulas for rectangles 4.MD.A.3
Evaluating expressions with parentheses 5.OA.A.1
Writing simple expressions that record calculations, such as 2 × (8 + 7) 5.OA.A.2
Multiplying fractions 5.NF.B.4
Writing and evaluating expressions with whole-number exponents 6.EE.A.1
Write the price on the board and ask students to write a calculation for each question, without finding the totals yet:
Warm-Up Prompt
"Movie tickets cost $9 each. Write a calculation for the cost of 2 tickets, then 5 tickets, then 11 tickets. How could you write the cost for any number of tickets?"
Collect 9 × 2, 9 × 5 and 9 × 11. Ask what stays the same (the 9) and what changes (the number of tickets). Introduce a variable: let t stand for the number of tickets, so the cost is 9 × t, written 9t. Explain that a number written right next to a letter means multiplication, which avoids confusing the × sign with the letter x. Then ask for the cost if t = 4. (9 × 4 = 36 dollars.)
Direct Instruction20-25 minutes
Part 1: Writing and reading expressions (standard a). Show that order matters for subtraction and division. "Subtract y from 5" starts with 5 and takes y away, so it is 5 - y. "5 less than y" starts with y, so it is y - 5. Key words: sum (the result of adding), difference (subtracting), product (multiplying) and quotient (dividing). A quotient can be written with a fraction bar, so "n divided by 3" is n/3. Use parentheses to keep a group together: "twice the sum of x and 7" is 2(x + 7). To read an expression, say what happens to the numbers: 4(m - 1) is "4 times the difference of m and 1".
Writing from words (official example a)
Express the calculation "Subtract y from 5" as an expression. Then write "5 subtracted from y".
Equation: "Subtract y from 5" is 5 - y; "5 subtracted from y" is y - 5, a different expression
A product of two factors (official example b)
Describe 2(8 + 7) as a product of two factors, and describe (8 + 7) in two ways.
Equation: 2(8 + 7) is the product of the factors 2 and (8 + 7). (8 + 7) is one single entity, the second factor, and it is also a sum of the two terms 8 and 7. Its value is 2 × 15 = 30
Naming the parts of an expression
Name the parts of 6a + b/4 + 9.
Equation: It is a sum of 3 terms: 6a, b/4 and 9. The term 6a is a product with coefficient 6 and factors 6 and a; b/4 is a quotient; 9 is a number term (a term with no variable)
Evaluating formulas (official example c)
Use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2.
Equation: V = (1/2)³ = 1/8 cubic unit; A = 6 × (1/2)² = 6 × 1/4 = 3/2 square units (Diagram 2)
Part 2: The parts of an expression (standard b). Use Diagram 1. A term is a part of an expression that is added to other parts, such as 5a, 2(b + 6) and c/3 in 5a + 2(b + 6) + c/3. A factor is a number or group that is multiplied. A coefficient is the number that multiplies a variable, such as 5 in 5a. Work the official example 2(8 + 7) above: it is a product of two factors, and the factor (8 + 7) is both a single entity and a sum. To decide what a whole expression is, ask which operation you would do last.
Part 3: Evaluating expressions (standard c). To evaluate an expression, replace each variable with its value, then follow the order of operations: parentheses, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right. Write the substitution with parentheses or a × sign: if a = 4, then 5a is 5 × 4 = 20, not 54. Work the official cube example with Diagram 2: the exponent comes before the multiplication by 6. A formula is a rule that uses variables for real quantities, such as P = 2l + 2w for the perimeter of a rectangle with length l and width w.
Guided Practice15 minutes
Pairs work three short sets, and the class checks after each one. Write: "the quotient of p and 6" (p/6); "8 more than 3 times w" (3w + 8); "the product of 5 and the sum of a and 2" (5(a + 2)).
Name the parts: fill in the number of terms, any coefficient, and what the whole expression is.
Expression
Number of terms
Coefficient
The whole expression is
9 + 4t
2
4
a sum of 9 and 4t
5(p - 2)
1
none
a product of 5 and (p - 2)
(x + 1)/3
1
none
a quotient of (x + 1) and 3
Show the first row filled in and have pairs complete the other two before revealing them. Evaluate: 2a + b² when a = 6 and b = 3 (12 + 9 = 21). A garden bed is a rectangle with l = 12 feet and w = 7 feet. Use P = 2l + 2w. (2 × 12 + 2 × 7 = 24 + 14 = 38 feet.) Listen for students who write 2l as 212 when l = 12, and ask them to write 2 × 12.
Independent Practice10-15 minutes
Students work alone on six problems. (1) Write "7 fewer than twice n". (2n - 7.) (2) In 3r + s/8 + 11, name the coefficient, the quotient and the number of terms. (3; s/8; 3 terms.) (3) Evaluate 20 - 3m when m = 4. (20 - 12 = 8.) (4) Evaluate k³ + 2k when k = 3. (27 + 6 = 33.) (5) A cyclist rides at r = 12 miles per hour for t = 1.5 hours. Use d = rt to find the distance. (18 miles.) (6) Evaluate x/y + 4 when x = 18 and y = 6. (3 + 4 = 7.)
Closure5 minutes
Exit ticket: (1) Write "the sum of c and 9, divided by 2". ((c + 9)/2.) (2) Name the two factors of 6(w + 1), and describe (w + 1) in two ways. (6 and (w + 1); (w + 1) is a single factor and a sum of two terms.) (3) Evaluate 4h² - h when h = 6. (4 × 36 - 6 = 144 - 6 = 138.)
Differentiation Strategies
For Struggling Students
Give a word bank card: sum = add, difference = subtract, product = multiply, quotient = divide, with one example of each
When evaluating, have students rewrite the expression with empty parentheses where each variable was, then write the number inside, for example 5a becomes 5( ) and then 5(4)
Have students circle each term in a different color before they name coefficients and factors
For Advanced Students
Ask students to write two different expressions that each have 3 terms, one quotient and a coefficient of 7, then trade with a partner who names every part
Ask for the value of a in 4a + 3 when the expression equals 23, by trying values in a table (a = 5); solving equations formally comes in 6.EE.B.7
Give the formula F = 9C/5 + 32 and ask students to find the Fahrenheit temperature for 0, 10, 20 and 30 degrees Celsius and describe the pattern (32, 50, 68, 86: each step adds 18)
Assessment Guidance
What to Look For
Check that students write subtraction and division in the right order ("subtract y from 5" is 5 - y) and use parentheses when a sum or difference is multiplied or divided. When they name parts, listen for the right words: a term is added, a factor is multiplied, a coefficient is the number in front of a variable. Ask them to describe a group in parentheses in two ways. When they evaluate, look for a × sign or parentheses at every substitution, exponents done before multiplication, and units written with the answers to formula problems.
02
Classroom Activities
3 Activities
1
Words and Expressions Match
15 minPairs
Pairs match 8 phrase cards to 8 expression cards (standard a). Several pairs of cards use the same numbers and letters in a different order, so students must read carefully. Then each pair reads two new expressions aloud in words.
Cards (16 cards: 8 phrases and 8 expressions)
"4 less than t" and t - 4
"4 minus t" and 4 - t
"the product of 6 and b" and 6b
"b divided by 6" and b/6
"3 times the sum of k and 2" and 3(k + 2)
"2 more than 3 times k" and 3k + 2
"the quotient of 10 and z" and 10/z
"1 more than z squared" and z² + 1
Procedure
Shuffle the cards and lay them face up in two groups, phrases and expressions
Take turns matching a phrase to an expression and explaining the order of the numbers
When all 8 matches are made, write each of these in words on a blank card: 5(q - 1) and 12/(r + 2)
Discussion Questions
Which two cards use t and 4 but in a different order? Why do they not mean the same thing?
Why does "3 times the sum of k and 2" need parentheses, but "2 more than 3 times k" does not?
If t = 10, what are the values of t - 4 and 4 - t? (t - 4 = 10 - 4 = 6, but 4 - t takes 10 away from 4, which gives a number less than zero, so the two expressions give different values)
Modification for Distance Learning
Put the cards on a shared slide and have pairs drag each phrase next to its expression. Each pair records a short voice or video message reading their two new expressions aloud.
2
Expression Anatomy with Colored Pencils
15 minGroups of 3-4
Each group gets 6 expression cards. Students color each term, circle each coefficient, box each factor in a product, and then sort the cards by what the whole expression is (standard b).
Expression Cards (6 cards)
Card A: 8m + 3
Card B: 5(n + 4)
Card C: (a + b)/2
Card D: 7x + y/3 + 1
Card E: 2p² + 9
Card F: 12 - 4w
Procedure
Color every term a different color, and write the number of terms on the card
Circle every coefficient, and box every factor of a product
Sort the cards into four groups by the last operation: the whole expression is a sum, a difference, a product or a quotient
For each card with parentheses, write one sentence that describes the group in parentheses in two ways
Discussion Questions
Which cards are sums as a whole? (A, D and E) Which card is the only product? (B) The only quotient? (C) The only difference? (F)
Which card has the most terms? (Card D, with 3 terms)
On Card B, (n + 4) is a factor. How can it also be a sum?
Challenge Variation
Groups write a new card that is a product of two factors, where one factor is a sum of three terms, and a card that is a quotient whose top is a product. Another group must name every part.
3
Measure and Evaluate Formula Stations
20 minPairs
Pairs rotate through three stations. At each one they measure a real object, substitute the measurements into a formula and evaluate it, writing units with every answer (standard c).
Stations (3 stations)
Station 1, perimeter: measure a sheet of letter-size paper in inches (it is 11 inches by 8.5 inches) and use P = 2l + 2w. (2 × 11 + 2 × 8.5 = 22 + 17 = 39 inches)
Station 2, cube: build a cube from 27 linking cubes, 3 on each edge. Each linking cube is 2 centimeters on an edge, so s = 6 centimeters. Use V = s³ and A = 6s². (V = 216 cubic centimeters, A = 6 × 36 = 216 square centimeters)
Station 3, temperature: read the classroom thermometer in degrees Celsius (C) and use F = 9C/5 + 32 to find degrees Fahrenheit. Classrooms are usually about 20-22 degrees Celsius; for 20, F = 9 × 20 ÷ 5 + 32 = 36 + 32 = 68
Procedure
At each station, write the formula, then rewrite it with the measured numbers in parentheses
Evaluate one step per line and write the units
Before leaving a station, check that the answer makes sense for the object
Discussion Questions
At Station 2, the volume and the surface area have the same number, 216. Are they the same amount? (No: one counts cubic centimeters and the other square centimeters)
Would the numbers still match for a cube 3 linking cubes long, but made of 1-centimeter cubes? (No: s = 3 gives V = 27 and A = 54)
At Station 3, which operation did you do first, and why?
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: The Parts of an Expression
The expression 5a + 2(b + 6) + c/3 is a sum of three terms. The first term, 5a, is a product with coefficient 5. The second term is a product of two factors, 2 and (b + 6), and (b + 6) is both a single entity and a sum of two terms. The third term, c/3, is a quotient.
Diagram 2: The Official Cube Example, s = 1/2
The official example for standard c. A cube has sides of length s = 1/2 unit. Its volume is V = s³ = (1/2)³ = 1/8 cubic unit. Its net (the 6 faces of the cube unfolded flat) shows 6 square faces, each with area s² = 1/4 square unit, so the surface area is A = 6s² = 6 × 1/4 = 3/2 square units. The cube and the net are drawn to the same scale. The exponent is evaluated before the multiplication by 6.
04
Homework Assignment
~30 min
6.EE.A.2 Homework: Expressions with Variables
Directions: Show your work. When you evaluate, rewrite the expression with the numbers in parentheses first, then do one step per line. Write units for every formula answer.
Part 1: Writing and Reading Expressions (Problems 1-2)
Write an expression for each phrase. (a) 9 less than p (b) the quotient of 12 and d (c) 4 times the difference of x and 3 (d) subtract k from 15
(a) Write 7 + 2n and 3(m - 1) in words. (b) Concert tickets cost $8 each, plus a $3 fee for the whole order. Write an expression for the cost of an order of t tickets.
Part 2: Parts of an Expression (Problems 3-4)
Use the expression 5x + y/4 + 12. (a) How many terms does it have? (b) What is the coefficient of x? (c) Which term is a quotient? (d) Name the two factors of the first term.
(a) Describe 3(a + 6) as a product of two factors. (b) Describe (a + 6) in two ways. (c) Write an expression that is a quotient of a sum and 5.
Part 3: Evaluating Expressions and Formulas (Problems 5-6)
Evaluate each expression. (a) 4x² - 10 when x = 3 (b) 2y + 5 when y = 1/2 (c) x³ - x when x = 4 (d) 24/w + w when w = 6
(a) Use V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/4 foot. (b) On a hot summer day the temperature is 35 degrees Celsius. Use F = 9C/5 + 32 to find the temperature in degrees Fahrenheit.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Writing and Reading
All expressions correct, with the right order and parentheses; readings are clear
One or two order or parentheses errors
Most expressions incorrect
Parts of an Expression
Terms, coefficient, quotient and factors named correctly; (a + 6) described two ways
One part misnamed, or only one description of (a + 6)
Most parts misnamed
Evaluating
All values correct, with substitutions shown and the order of operations followed
One or two arithmetic or order errors
Substitution missing or most values wrong
Formulas and Units
Cube and temperature answers correct, with units
Correct numbers but units missing
Formula answers incorrect
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 "subtract 8 from w"?
Answer: B
"Subtract 8 from w" starts with w and takes 8 away, so it is w - 8. Choice A reverses the order: 8 - w means subtract w from 8. Choice C divides instead of subtracting. Choice D adds instead of subtracting.
Question 2 of 20 · Multiple Choice
Which expression means "the product of 7 and the sum of n and 3"?
Answer: C
The sum of n and 3 is one group, (n + 3), and the product multiplies it by 7: 7(n + 3). Choice A has no parentheses, so only n is multiplied by 7. Choice B adds all three numbers. Choice D groups the wrong pair: it multiplies the sum of 7 and n by 3.
Question 3 of 20 · Multiple Choice
A gym charges a $25 sign-up fee plus $15 for each month. Which expression gives the total cost, in dollars, for m months?
Answer: D
The $15 is paid every month, so it is multiplied by m, and the $25 fee is paid once: 15m + 25. Choice A swaps the two amounts, as if the fee were paid every month. Choice B charges both $25 and $15 every month. Choice C adds m instead of multiplying it by 15.
Question 4 of 20 · Multiple Choice
Which phrase describes 3(x - 4)?
Answer: A
The parentheses make x - 4 one group, and 3 multiplies the whole group, so it is 3 times the difference of x and 4. Choice B describes 3x - 4, which has no parentheses. Choice C describes (3 - x) × 4. Choice D describes 3 + x - 4.
Question 5 of 20 · Multiple Choice
How many terms are in the expression 2(x + 5) + 3y?
Answer: B
Terms are the parts that are added: 2(x + 5) and 3y, so there are 2 terms. The group 2(x + 5) is one term because it is a product. Choice A treats the whole expression as one term. Choice C splits 2(x + 5) into two terms because of the plus sign inside the parentheses. Choice D counts 2, x, 5 and 3y as four separate terms.
Question 6 of 20 · Multiple Choice
What is the coefficient in the expression 8p + 15?
Answer: C
A coefficient is the number that multiplies a variable. In 8p, 8 multiplies p, so the coefficient is 8. Choice A is the variable itself. Choice B is a number term with no variable, so it is not a coefficient. Choice D adds 8 and 15, but they are parts of different terms.
Question 7 of 20 · Multiple Choice
Which part of 10 + x/4 is a quotient?
Answer: D
A quotient is the result of dividing. In x/4, x is divided by 4, so x/4 is the quotient. Choice A is a term, but nothing is divided in it. Choice B is only the number being divided. Choice C comes from misreading the expression as (10 + x)/4, but only x is divided by 4, and 10 + x is not a part of the expression.
Question 8 of 20 · Multiple Choice
Which describes the expression 4(9 + 2)?
Answer: A
The last operation is multiplying 4 by the group (9 + 2), so the expression is a product of two factors. Its value is 4 × 11 = 44. Choice B ignores the parentheses and the multiplication. Choice C names division, but nothing is divided. Choice D treats the 4 as added instead of multiplied.
Question 9 of 20 · Multiple Choice
In the expression 3(a + b), what is the part (a + b)?
Answer: B
(a + b) is one of the two factors of the product 3(a + b), so it is a single entity, and inside it a and b are added, so it is also a sum of two terms. Choice A mistakes the plus sign for multiplication. Choice C names division, but nothing is divided. Choice D mixes up the roles: (a + b) does not multiply the 3; it is the group that 3 multiplies.
Question 10 of 20 · Multiple Choice
Evaluate 5x - 7 when x = 4.
Answer: C
Replace x with 4: 5 × 4 - 7 = 20 - 7 = 13. Choice A writes 5x as the number 54 instead of 5 × 4, then subtracts 7. Choice B adds 5 and 4 instead of multiplying. Choice D adds 7 instead of subtracting it.
Question 11 of 20 · Multiple Choice
Evaluate 2n² when n = 3.
Answer: A
The exponent applies only to n: n² = 3² = 9, then 2 × 9 = 18. Choice B squares 2n instead: (2 × 3)² = 36. Choice C treats n² as n × 2: 2 × 3 × 2 = 12. Choice D adds 2 and 9 instead of multiplying.
Question 12 of 20 · Multiple Choice
Evaluate 20 - 12 ÷ k + k when k = 4.
Answer: D
Divide first: 12 ÷ 4 = 3. Then subtract and add from left to right: 20 - 3 = 17 and 17 + 4 = 21. Choice A subtracts before dividing: (20 - 12) ÷ 4 + 4 = 6. Choice B adds 3 + 4 before subtracting: 20 - 7 = 13. Choice C adds k + k before dividing: 20 - 12 ÷ 8 = 18.5.
Question 13 of 20 · Multiple Choice
The perimeter of a rectangle is P = 2l + 2w. Find P for a rectangle with length l = 9 centimeters and width w = 5.5 centimeters.
Answer: C
P = 2 × 9 + 2 × 5.5 = 18 + 11 = 29 centimeters. Choice A multiplies the length by the width, which gives the area in square centimeters, not the perimeter. Choice B adds one length and one width and forgets to double them. Choice D doubles the length but not the width.
Question 14 of 20 · Multiple Choice
The surface area of a cube is A = 6s². Find A for a cube with sides of length s = 4 centimeters.
Answer: A
Exponent first: s² = 4² = 16, then 6 × 16 = 96 square centimeters. Choice B multiplies first and then squares: (6 × 4)² = 576. Choice C treats s² as s × 2: 6 × 4 × 2 = 48. Choice D uses the volume formula s³ = 64, which gives cubic centimeters.
Question 15 of 20 · Short Answer
Lena has d dollars. She spends $6 on lunch and then splits the money that is left equally among herself and 2 friends. Write an expression for the amount each person gets.
The money left is d - 6, and it is split into 3 equal shares, so each person gets (d - 6)/3 dollars, or (d - 6) ÷ 3. The parentheses keep d - 6 together as one quantity; d - 6/3 would divide only the 6.
Question 16 of 20 · Short Answer
Use the expression 7w + 18/z + 3. (a) Name the terms. (b) What is the coefficient of w? (c) Which term is a quotient? (d) Name the two factors of the first term.
(a) The terms are 7w, 18/z and 3. (b) The coefficient of w is 7. (c) 18/z is a quotient. (d) The factors of 7w are 7 and w.
Question 17 of 20 · Short Answer
Describe 6(y + 5) as a product. Then describe (y + 5) in two ways.
6(y + 5) is a product of two factors, 6 and (y + 5). The part (y + 5) is a single entity, the second factor, and it is also a sum of two terms, y and 5.
6.EE.A.2 means students can write, read and evaluate expressions that use letters for numbers. It has three parts: (a) writing expressions such as 5 - y from words, (b) naming the parts of an expression with words like term, factor and coefficient, and (c) finding the value of an expression or formula when the variables are given numbers, using the order of operations.
Is 6.EE.A.2 taught in grade 6 or grade 7?
It is a grade 6 standard. In grade 7, students build on it by adding, subtracting, factoring and expanding linear expressions with rational coefficients, including negative numbers (7.EE.A.1). In grade 6, students evaluate expressions with whole numbers, fractions and decimals; operations with negative numbers come in grade 7 (7.NS.A.1).
What is a variable in math?
A variable is a letter that stands for a number. In the expression 9t for the cost of movie tickets, t stands for the number of tickets. The same expression works for any number of tickets, so a variable lets one expression describe many calculations.
What is the difference between a term, a factor and a coefficient?
Terms are added, factors are multiplied, and a coefficient is the number factor of a term with a variable. In 4k + 10, the terms are 4k and 10. The term 4k has the factors 4 and k, and its coefficient is 4.
Why is "subtract y from 5" written 5 - y and not y - 5?
Because you start with 5 and take y away from it. The official example of 6.EE.A.2 uses exactly this phrase. Subtraction and division depend on order, so students should picture the action: "subtract y from 5" means 5 is the starting amount. "5 less than y" means y - 5.
What does it mean to view part of an expression as a single entity?
It means treating a group, usually in parentheses, as one thing. In 10(q + 1), the group (q + 1) is one factor that 10 multiplies, so the whole expression is a product of two factors. The same group is also a sum of two terms, q and 1. Seeing both views helps students later when they expand and factor expressions (6.EE.A.3).
How do you evaluate an expression with variables?
Replace each variable with its number, then follow the order of operations. For example, for 3m + 2 when m = 10: 3 × 10 + 2 = 30 + 2 = 32. Writing the × sign or parentheses at the substitution prevents the error of reading 3m as the number 310.
Why do we write 3n instead of 3 × n?
Writing a number next to a variable is the usual way to show multiplication, and it avoids mixing up the × sign with the letter x. So 3n means 3 times n. A dot can also show multiplication: 3 · n. When a number replaces n, the × sign or parentheses come back: 3(2) = 6.
Which formulas do grade 6 students use for 6.EE.A.2?
Common ones are the area and perimeter of a rectangle (A = lw and P = 2l + 2w), the volume and surface area of a cube (V = s³ and A = 6s², the official example), and distance traveled at a constant speed (d = rt). Students evaluate these formulas; they do not need to derive them.
How can parents help with expressions at home?
Turn everyday prices into expressions. If apples cost $2 a pound, ask for an expression for p pounds (2p), then ask for the cost of 6 pounds. When cooking, ask your child to name the parts of a recipe rule, such as "3 cups of flour for every batch, plus 1 cup for the pan", written as 3b + 1.
07
Related Standards
6 standards
These standards connect to 6.EE.A.2: 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 without evaluating
Lesson coming soon
6.EE.A.1Prerequisite
Write and evaluate numerical expressions involving whole-number exponents
