7.EE.A.1Common CoreMathExpressions and EquationsGrade 7
7.EE.A.1: Adding, Subtracting, Factoring and Expanding Linear Expressions
In plain English: 7.EE.A.1 is the Common Core grade 7 math standard that asks students to use the properties of operations to add, subtract, expand and factor linear expressions whose coefficients are fractions, decimals or negative numbers. For example, (5a - 3) - (2a - 7) = 3a + 4 and 4.5k + 3 = 1.5(3k + 2). It extends grade 6 work with equivalent expressions.
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
Common Core State Standards for Mathematics · Domain: Expressions and Equations (EE) · Cluster: Use properties of operations to generate equivalent expressions. Also written as 7.EE.1 · Official standard
Students rewrite linear expressions in new forms that are equal for every value of the variable. An expression is a group of numbers, letters and operation signs with no equal sign, such as 4x - 1.5. It is linear when each variable appears only to the first power: 4x - 1.5 and 2x + 3y are linear, but x² is not. The parts joined by + or - are terms. The number multiplied by a variable is its coefficient, and a term with no variable is a constant. In grade 7 the coefficients are rational numbers: whole numbers, fractions, decimals and their negatives.
Students do four things with these expressions. They add and subtract them by combining like terms (terms with the same variable part, such as 0.6n and 1.5n). They expand, which means multiplying out parentheses with the distributive property, a(b + c) = ab + ac. They factor, which means the reverse: writing a sum as a number times a sum. Two expressions are equivalent when they are equal for every value of the variable. The new grade 7 step is working with negative and fractional numbers, for example subtracting a whole expression by adding the opposite of each term (the same number with the other sign, such as 9 and -9), or factoring out -4 or 1/3.
Learning Objectives
By the end of this lesson, students will be able to:
Add linear expressions with fraction, decimal and negative coefficients by combining like terms
Subtract a linear expression by adding the opposite of each of its terms
Expand expressions such as -3(2y - 1/3) with the distributive property, including negative and fractional factors
Factor a linear expression by a whole number, a negative number, a fraction or a decimal, and check the result by expanding
Name the property of operations used in each step and test equivalence by substituting a number
Prior Knowledge Required
Students should already be comfortable with:
Using the distributive property and combining like terms with whole numbers 6.EE.A.3
Deciding whether two expressions are equivalent by substituting values 6.EE.A.4
Adding and subtracting positive and negative rational numbers, including subtraction as adding the opposite 7.NS.A.1
Multiplying positive and negative rational numbers 7.NS.A.2
Post the four expressions. Half the class substitutes x = 5 and the other half x = 10. To substitute means to put the number in place of the letter.
Warm-Up Prompt
"Find the value of each expression: 2(x - 3), 2x - 3, 2x - 6 and -2(3 - x). Which ones always seem to give the same value?"
Record the results in a table. With x = 5 the values are 4, 7, 4 and 4. With x = 10 they are 14, 17, 14 and 14. So 2(x - 3), 2x - 6 and -2(3 - x) look equivalent, and 2x - 3 does not. Ask: "Two numbers worked. Does that prove they are always equal?" No: a test can only show that two expressions are not equivalent. The properties of operations prove it, and that is today's work. Come back to -2(3 - x) after the examples: -2 × 3 = -6 and -2 × (-x) = 2x, so it equals -6 + 2x, which is 2x - 6.
Direct Instruction20 minutes
Part 1: The properties. Every rewrite in this lesson uses one of these rules. They are true for every rational number, so they work with variables too. Write each rule with numbers first, then with letters.
Properties of operations used in this lesson
Property
With numbers
With letters
Commutative property (order can change)
-2 + 7 = 7 + (-2)
a + b = b + a
Associative property (grouping can change)
(0.5 + 1.5) + 4 = 0.5 + (1.5 + 4)
(a + b) + c = a + (b + c)
Distributive property
-3(4 + 1) = -3(4) + (-3)(1)
a(b + c) = ab + ac
Subtracting is adding the opposite
6 - 9 = 6 + (-9)
a - b = a + (-b)
The opposite of a sum
-(2 + 5) = -2 + (-5)
-(a + b) = -a + (-b)
Part 2: Worked examples. Work each example on the board and name the property at every step. The last example uses an area model: a rectangle whose height is the factor and whose width is split into the parts of the sum.
Adding expressions with decimals
Add (0.6n - 4) + (1.5n + 2.5).
Equation: Regroup like terms (commutative and associative properties): (0.6n + 1.5n) + (-4 + 2.5). Combine: 2.1n + (-1.5), so the sum is 2.1n - 1.5.
Subtracting an expression
Subtract (5a - 3) - (2a - 7).
Equation: Add the opposite of each term in the second group: 5a - 3 + (-2a) + 7. Group like terms: (5a - 2a) + (-3 + 7) = 3a + 4.
Expanding with a negative factor
Expand -3(2y - 1/3).
Equation: Distribute -3 to both terms: -3(2y) + (-3)(-1/3) = -6y + 1. A negative times a negative is positive.
Factoring out a negative number
Factor -8m + 12 by taking out -4.
Equation: Divide each term by -4: -8m ÷ (-4) = 2m and 12 ÷ (-4) = -3, so -8m + 12 = -4(2m - 3). Check: -4(2m) + (-4)(-3) = -8m + 12.
Factoring with a decimal
Factor 4.5k + 3 using the factor 1.5.
Equation: 4.5k ÷ 1.5 = 3k and 3 ÷ 1.5 = 2, so 4.5k + 3 = 1.5(3k + 2). Diagram 1 shows this as an area model.
Part 3: Subtracting a group. The minus sign in front of parentheses applies to every term inside. Think of it as -1 times the group: -(2a - 7) = -1(2a) + (-1)(-7) = -2a + 7. Diagram 2 shows each sign change. A common error is changing only the first sign and writing 5a - 3 - 2a - 7.
Part 4: Factoring. To factor an expression is to write it as a product, such as -4(2m - 3). In grade 6, students took out the greatest common factor (GCF), the largest whole number that divides every coefficient. In grade 7 the factor can also be negative, a fraction or a decimal. The rule is always the same: divide every term by the factor, then check by expanding. The area model in Diagram 1 shows why it works: the area of the whole rectangle equals the sum of the areas of its parts.
Guided Practice15 minutes
Pairs solve one problem at a time on mini whiteboards and name each property. After each problem, one pair explains their steps, and the class checks the answer by substituting a small number.
Guided practice problems with answers
Problem
Answer
Factor (2/3)w - 4 by taking out 2/3
(2/3)(w - 6), because 4 ÷ (2/3) = 6
Expand and combine 2(x + 4) - 3(x - 1)
2x + 8 - 3x + 3 = -x + 11
Subtract (7 - 1.2p) - (3 - 0.8p)
7 - 1.2p - 3 + 0.8p = 4 - 0.4p
Expand -(1/4)(8 - 12c)
-2 + 3c
Listen for these errors: dividing only the first term when factoring, changing only one sign when subtracting a group, and writing -3(x - 1) as -3x - 3. For the second problem, ask: "What does the -3 multiply?" (Both x and -1, so -3 × (-1) = +3.)
Independent Practice10 minutes
Students work alone on six problems. They check each answer by substituting x = 2 (or the letter in the problem) into the first and last forms.
Independent practice problems with answers
Problem
Answer
(3/5)z + 1/5 + (1/5)z - 1
(4/5)z - 4/5
(4q - 9) - (-2q + 5)
6q - 14
Expand 0.5(-6r + 14)
-3r + 7
Factor -10v - 25 by taking out -5
-5(2v + 5)
(2x + 3y) - (x - y)
x + 4y
Expand and combine 4(0.25b - 2) + 3b
4b - 8
Closure5 minutes
Exit ticket: (1) Subtract (6h + 1) - (4h - 2). (Answer: 2h + 3.) (2) Factor -6t + 9 by taking out -3. (Answer: -3(2t - 3).) (3) In one sentence, explain why 7 - (x + 2) is not 5 + x. (The minus sign applies to both terms: 7 - x - 2 = 5 - x.) Sort the tickets into three piles: correct, one sign error, and other errors.
Differentiation Strategies
For Struggling Students
Rewrite every subtraction as adding the opposite before combining, and circle each term with its sign in front of it
Draw an area model on grid paper for each factoring problem, starting with whole-number factors and then using 0.5 and 1.5
Give a checklist for factoring: divide every term by the factor, write the results inside the parentheses, then expand to check
For Advanced Students
Ask students to factor 0.75x - 1.5 in three ways (by 0.75, by -0.75 and by 1/4) and explain which form has the simplest numbers inside
Give expressions with two variables, such as (1.5a - 2b) - (0.5a - 3b), and ask for the shortest equivalent form
Ask students to write an expression that expands to -2x + 5 and has a fraction outside the parentheses
Assessment Guidance
What to Look For
Check that students change the sign of every term when they subtract a group, and that they multiply the factor by every term when they expand. When factoring, look for a check by expanding, not only an answer. Ask students to name a property for each step (commutative, associative, distributive, or adding the opposite). A substitution check with one number is a good habit, but students should say that it can catch a mistake, not prove that two expressions are equivalent.
02
Classroom Activities
3 Activities
1
Match and Spot the Mistake
15 minPairs
Each pair gets 12 index cards: 4 start cards, 4 correct answer cards and 4 mistake cards. Pairs match each start card with its correct answer and with the mistake card that comes from it, then name the error on the mistake card.
Start Cards
S1: (2.5x + 6) - (x - 4)
S2: -2(3y - 4.5)
S3: (1/3)(9m + 6) - m
S4: (5 - 0.4n) + (1.4n - 8)
Answer and Mistake Cards (answer key)
S1: correct 1.5x + 10; mistake 1.5x + 2 (changed the sign of x but not of -4)
S2: correct -6y + 9; mistake -6y - 9 (forgot that -2 × (-4.5) is positive)
S3: correct 2m + 2; mistake 2m + 6 (multiplied only 9m by 1/3)
S4: correct n - 3; mistake 1.8n - 3 (added 0.4n instead of subtracting it)
Discussion Questions
Substitute x = 2 into S1 and into both of its cards. Which card gives the same value as the start card?
S1 and S4 both combine two groups. Why does only S1 need signs to change?
Which property explains the correct answer for S2?
Modification for Distance Learning
Put the 12 cards on a shared slide. Pairs drag each answer card and mistake card next to its start card and type the name of the error in a text box.
2
One Expression, Three Factors
15 minPairs
Pairs factor the same expression in several ways, using a whole number, a negative number and a fraction or decimal. They check every form by expanding it on a mini whiteboard. There are 4 expression cards.
Expression Cards (with the factors to use)
F1: 6x - 9, factor out 3, then -3, then 1/2
F2: -4y + 10, factor out 2, then -2, then -1/2
F3: (1/2)k + 2, factor out 1/2, then 2
F4: 0.8p - 2.4, factor out 0.8, then -0.4
Answer Key
F1: 3(2x - 3), -3(-2x + 3), (1/2)(12x - 18)
F2: 2(-2y + 5), -2(2y - 5), -(1/2)(8y - 20)
F3: (1/2)(k + 4), 2((1/4)k + 1)
F4: 0.8(p - 3), -0.4(-2p + 6)
Discussion Questions
When you factor out a negative number, what happens to the signs inside the parentheses? Check it on F1 and F2.
On F1, factoring out 1/2 made the numbers inside bigger. Why?
Which form of F3 would you use to find the value when k = 6? Why?
Challenge Variation
Pairs write their own expression that can be factored by 1.5 and by -3/4, and trade it with another pair.
3
Error Detective Gallery Walk
15 minGroups of 3-4
Hang 6 posters on chart paper around the room. Each poster shows a worked problem with exactly one wrong step. Groups rotate every 2 minutes, find the wrong step, and leave a sticky note with the correct answer.
Posters
P1: (3x + 2) - (x - 5) = 3x + 2 - x - 5 = 2x - 3
P2: -4(2 - 0.5w) = -8 - 2w
P3: 12a - 18 = 6(2a - 18)
P4: (2/5)c + (1/5)c = (3/10)c
P5: -(2/3)(6d + 3) = -4d + 2
P6: -5r - 15 = -5(r - 3)
Answer Key
P1: -(-5) is +5, so the answer is 2x + 7
P2: -4 × (-0.5w) = +2w, so the answer is -8 + 2w
P3: 18 ÷ 6 = 3, so the answer is 6(2a - 3)
P4: add the numerators and keep the denominator: (3/5)c
P5: -(2/3) × 3 = -2, so the answer is -4d - 2
P6: -15 ÷ (-5) = 3, so the answer is -5(r + 3)
Discussion Questions
Four of the six posters (P1, P2, P5 and P6) have a sign error. Which step in each one should have changed a sign?
How could you catch the mistake on P3 without redoing the problem? (Expand the answer and compare.)
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Area Model for Factoring 4.5k + 3
The rectangle has height 1.5. Its width is split into 3k and 2, so the two parts have areas 4.5k and 3. Reading the model one way expands 1.5(3k + 2) into 4.5k + 3; reading it the other way factors 4.5k + 3 into 1.5(3k + 2). The height and the part of width 2 are drawn to scale (60 pixels per unit); each k is drawn 100 pixels long, since k can be any number.
Diagram 2: Subtracting an Expression Term by Term
To subtract the group 2a - 7, add the opposite of each of its terms: 2a becomes -2a and -7 becomes +7. Then group the like terms and combine them to get 3a + 4. A check with a = 2 gives 10 for both the first and the last form.
04
Homework Assignment
~30 min
7.EE.A.1 Homework: Rewriting Linear Expressions
Directions: Show every step and name the property you use. Check each final answer by substituting a number, such as 2, into the first and the last expression.
Expand and combine like terms: 3(2x - 1) - 2(x - 3.5). Then check your answer by substituting x = 2 into both forms.
Part 3: Factoring (Problems 5-6)
Factor each expression using the factor given: (a) 9w - 12, factor 3 (b) -14z - 21, factor -7 (c) (3/8)t + 9/8, factor 3/8
(a) Factor 2.5a + 10 using the factor 2.5. (b) Write 18 - 6c as a product in two ways: once with a positive factor and once with a negative factor. Expand both to show they are equivalent to 18 - 6c.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Combining Like Terms
Only like terms combined, with correct signs and fraction or decimal sums
One sign or arithmetic error
Unlike terms combined or most answers wrong
Subtracting and Expanding
Every term inside the parentheses changed or multiplied correctly
One term missed
Parentheses ignored
Factoring
Every term divided by the factor and the result checked by expanding
Correct form but no check, or one term not divided
Not a product, or not equivalent
Properties and Checks
Properties named and a substitution check shown
Properties named or check shown, not both
Neither shown
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 is equivalent to (0.7x + 3) + (1.8x - 5)?
Answer: B
Combine like terms: 0.7x + 1.8x = 2.5x and 3 + (-5) = -2, so the sum is 2.5x - 2. Choice A adds 3 and 5 and ignores the minus sign in front of the 5. Choice C subtracts 0.7 from 1.8 instead of adding. Choice D computes 5 - 3 instead of 3 - 5.
Question 2 of 20 · Multiple Choice
Which expression is equivalent to (6y - 4) - (2y + 3)?
Answer: C
Add the opposite of each term in the second group: 6y - 4 - 2y - 3 = 4y - 7. Choice A subtracts the 3 but adds 2y instead of subtracting it. Choice B subtracts 2y but adds the 3: 6y - 4 - 2y + 3. Choice D adds the whole second group: 6y - 4 + 2y + 3.
Question 3 of 20 · Multiple Choice
Which expression is equivalent to 9 - (4 - 2.5n)?
Answer: A
The minus sign changes both terms: 9 - 4 + 2.5n = 5 + 2.5n. Choice B subtracts the 4 but does not change the sign of -2.5n. Choice C adds 4 instead of subtracting it and keeps -2.5n. Choice D computes 4 - 9 instead of 9 - 4.
Question 4 of 20 · Multiple Choice
Which expression is equivalent to -6(0.5x - 2)?
Answer: D
Multiply -6 by both terms: -6(0.5x) = -3x and -6(-2) = +12, so the answer is -3x + 12. Choice A multiplies only the first term. Choice B forgets that a negative times a negative is positive. Choice C drops the negative sign of -6 and expands 6(0.5x - 2).
Question 5 of 20 · Multiple Choice
Which expression is equivalent to (2/5)(10p + 15)?
Answer: A
Multiply each term by 2/5: (2/5)(10p) = 4p and (2/5)(15) = 6, so the answer is 4p + 6. Choice B multiplies only the first term. Choice C divides each term by 2/5 instead of multiplying. Choice D adds 2/5 = 0.4 to each coefficient instead of multiplying.
Question 6 of 20 · Multiple Choice
Which expression is 15m - 20 factored with the greatest common factor?
Answer: B
The GCF of 15 and 20 is 5. Divide each term by 5: 15m ÷ 5 = 3m and 20 ÷ 5 = 4, so 15m - 20 = 5(3m - 4). Choice A divides only the first term. Choice C subtracts 5 from each coefficient instead of dividing. Choice D puts -5 outside without changing the signs inside, and it expands to -15m + 20.
Question 7 of 20 · Multiple Choice
Factor -12k + 8 by taking out -4.
Answer: C
Divide each term by -4: -12k ÷ (-4) = 3k and 8 ÷ (-4) = -2, so -12k + 8 = -4(3k - 2). Check: -4(3k) + (-4)(-2) = -12k + 8. Choice A changes the sign of the k-term but keeps +2, and it expands to -12k - 8. Choice B keeps both original signs inside, which expands to 12k - 8. Choice D divides the first term by -4 but only changes the sign of the 8.
Question 8 of 20 · Multiple Choice
Which expression is equivalent to (1/3)r - 2?
Answer: D
Take out 1/3 by dividing each term by 1/3: (1/3)r ÷ (1/3) = r and 2 ÷ (1/3) = 6, so (1/3)r - 2 = (1/3)(r - 6). Check: (1/3)(6) = 2. Choice A does not divide the 2. Choice B multiplies 2 by 1/3 instead of dividing. Choice C writes 3 outside instead of 1/3, and it expands to 3r - 18.
Question 9 of 20 · Multiple Choice
Which expression is equivalent to 2.4 + 0.6h?
Answer: B
Divide each term by 0.6: 2.4 ÷ 0.6 = 4 and 0.6h ÷ 0.6 = h, so 2.4 + 0.6h = 0.6(4 + h). Choice A does not divide the 2.4. Choice C subtracts 0.6 from 2.4 instead of dividing. Choice D divides 0.6 by 2.4 instead of 2.4 by 0.6.
Question 10 of 20 · Multiple Choice
Which expression is NOT equivalent to 8x - 12?
Answer: A
Expand each one. Choice A gives -8x + 12, the opposite of 8x - 12, so it is not equivalent. Choice B gives 8x - 12. Choice C gives 8x - 12, because factoring out -4 changes both signs inside. Choice D gives 8x - 12 as well; it uses a common factor that is not the greatest one. A student who picks C may think a negative factor always gives a negative result.
Question 11 of 20 · Multiple Choice
Which expression is equivalent to 5(x - 1.2) - 2x?
Answer: C
Expand: 5x - 6 - 2x. Combine like terms: 3x - 6. Choice A multiplies only x by 5 and leaves -1.2. Choice B adds 2x instead of subtracting it. Choice D treats -2x as the constant -2, so it combines -6 and -2 and leaves 5x.
Question 12 of 20 · Multiple Choice
Which expression is equivalent to 5(y + 2) - 3(y - 1)?
Answer: D
Expand both groups: 5y + 10 - 3y + 3. Combine like terms: 2y + 13. Choice A writes -3(y - 1) as -3y - 3, forgetting that -3 × (-1) = +3. Choice B adds the second group: 5y + 10 + 3y - 3. Choice C multiplies -3 by y only and keeps -1: 5y + 10 - 3y - 1.
Question 13 of 20 · Multiple Choice
A garden bed is w feet wide. Its length is (2.5w + 1) feet. Which expression gives the perimeter, the distance around the bed?
Answer: A
Perimeter = 2(length) + 2(width) = 2(2.5w + 1) + 2w = 5w + 2 + 2w = 7w + 2. Choice B adds only one width: 2(2.5w + 1) + w. Choice C adds one length and one width. Choice D doubles the w-terms but not the 1.
Question 14 of 20 · Multiple Choice
Which expression is equivalent to -(3 - 5c)?
Answer: B
The minus sign in front of the parentheses means -1 times each term: -1(3) = -3 and -1(-5c) = +5c, so the answer is -3 + 5c. Choice A changes only the first sign. Choice C changes only the second sign. Choice D ignores the minus sign.
Question 15 of 20 · Short Answer
Simplify (5/6)x - (1/3)x + 4.
Write 1/3 as 2/6: (5/6)x - (2/6)x = (3/6)x = (1/2)x. The answer is (1/2)x + 4.
Question 16 of 20 · Short Answer
Subtract (3.2d - 7) - (1.5d - 2.4).
Add the opposite of each term: 3.2d - 7 - 1.5d + 2.4. Combine like terms: 1.7d - 4.6. Check with d = 2: (6.4 - 7) - (3 - 2.4) = -0.6 - 0.6 = -1.2, and 1.7(2) - 4.6 = -1.2.
Question 17 of 20 · Short Answer
Expand -(3/2)(4a - 6).
-(3/2)(4a) = -6a and -(3/2)(-6) = +9, so the answer is -6a + 9.
Question 18 of 20 · Short Answer
Factor 27q - 18 in two ways: once with the greatest common factor, and once by taking out -9.
The GCF of 27 and 18 is 9: 9(3q - 2). Taking out -9 changes both signs inside: -9(-3q + 2). Both expand to 27q - 18.
Question 19 of 20 · Short Answer
Expand and simplify 6(0.5m + 1) - (2m - 3).
Expand: 3m + 6 - 2m + 3. Combine like terms: m + 9.
Question 20 of 20 · Short Answer
Tyler says 10 - 2(x + 3) = 8(x + 3) = 8x + 24. Explain his mistake and write the correct simplified expression.
Tyler subtracted 10 - 2 first, but the 2 multiplies (x + 3), and multiplication comes before subtraction. Correct: 10 - 2x - 6 = 4 - 2x. Check with x = 1: 10 - 2(4) = 2 and 4 - 2(1) = 2, while Tyler's form gives 32.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does 7.EE.A.1 mean?
7.EE.A.1 means students can add, subtract, expand and factor linear expressions whose coefficients are fractions, decimals or negative numbers. They use the properties of operations, such as the distributive property, to write an equivalent form. For example, (0.6n - 4) + (1.5n + 2.5) = 2.1n - 1.5, and -8m + 12 = -4(2m - 3).
How is 7.EE.A.1 different from 6.EE.A.3?
The skills are the same, but grade 7 adds negative numbers, fractions and decimals. In grade 6 (6.EE.A.3), students expand and factor with whole numbers, such as 3(2 + x) = 6 + 3x. In grade 7 they subtract whole expressions and factor out numbers such as -4, 1.5 or 2/3.
What is a linear expression?
A linear expression is one where each variable appears only to the first power and is not multiplied by another variable. So 4x - 1.5 and 2x + 3y are linear, but x² + 1 and 5xy are not. The name comes from graphs: in grade 8, expressions like these give straight lines.
Why do all the signs change when you subtract an expression in parentheses?
Because you subtract the whole group, not only its first term. Subtracting is the same as adding the opposite, and the opposite of a group is the opposite of each term. So -(4r - 1) = -4r + 1. Leaving the second sign unchanged is a frequent error.
How do you factor out a negative number or a fraction?
Divide every term by that number, write the results inside the parentheses, and expand to check. For example, to take 1/4 out of (1/4)x + 2, divide: x and 2 ÷ (1/4) = 8, so the result is (1/4)(x + 8). Dividing by a negative number changes the sign of every term inside.
Is there only one correct way to factor a linear expression?
No. An expression can be factored with any number that is not zero, so 10x - 4 can be 2(5x - 2), -2(-5x + 2) or 0.5(20x - 8). All of them are equivalent. Teachers often ask for a specific factor, such as the greatest common factor or a negative factor, so read the directions.
How can students check that two expressions are equivalent?
Substitute the same number into both and compare, then use the properties to be sure. If the values differ, the expressions are not equivalent. If they match, the expressions might be equivalent, because one number cannot prove it. Expanding a factored answer is another quick check.
What comes after 7.EE.A.1?
Next, students use these skills to solve equations. In grade 7 they solve equations like p(x + q) = r (7.EE.B.4). In grade 8 they solve equations that need expanding and combining like terms on both sides (8.EE.C.7). In Algebra I, students rewrite expressions by looking at their structure (HSA.SSE.A.2).
How can parents help with 7.EE.A.1 at home?
Ask your child to explain each step out loud and to check an answer by putting in a number. For example, for 2(x - 4) - x, try x = 10: 2(6) - 10 = 2, and the simplified form x - 8 also gives 2. Everyday totals help too, such as the cost of 3 shirts at s dollars each with $1.50 off each shirt: 3(s - 1.50) = 3s - 4.50.
What mistakes should teachers watch for?
Common mistakes are multiplying only the first term, as in writing 4(x - 3) as 4x - 3; changing only the first sign when subtracting a group; and combining unlike terms, such as 3x + 2 into 5x. With fractions, some students add denominators, as in (1/4)x + (1/4)x = (2/8)x instead of (2/4)x, which is (1/2)x.
07
Related Standards
6 standards
These standards connect to 7.EE.A.1: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
6.EE.A.3Prerequisite
Apply the properties of operations to generate equivalent expressions
