6.EE.A.4Common CoreMathExpressions and EquationsGrade 6
6.EE.A.4: Identifying Equivalent Expressions
In plain English: 6.EE.A.4 is the Common Core grade 6 math standard that asks students to identify when two expressions are equivalent, meaning they name the same number no matter which value is substituted for the variable. Students test values, find one value that shows two expressions differ, and use properties to explain why pairs such as y + y + y and 3y always match.
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
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.4 · Official standard
Students learn how to tell whether two expressions are the same in disguise. Two expressions are equivalent when they name the same number no matter which value is substituted for (put in place of) the variable. The official example is y + y + y and 3y: for y = 2 both are 6, for y = 10 both are 30, and they match for every other number too.
Students use two tools. The first is substitution: put the same number into both expressions and compare. One value that gives different results, called a counterexample, proves that the expressions are not equivalent. Matching results for a few values are not a proof, because some pairs agree at one value and disagree at others. The second tool is the properties of operations (commutative, associative, distributive), which show why a pair matches for every value. Numbers stay positive and friendly, as expected in grade 6. Writing new equivalent forms is the focus of 6.EE.A.3; here students judge pairs they are given.
Learning Objectives
By the end of this lesson, students will be able to:
Explain what it means for two expressions to be equivalent, using the words "for every value of the variable"
Substitute values into two expressions, organize the results in a table and compare them
Use one counterexample to show that two expressions are not equivalent
Explain why matching values for a few numbers do not prove that two expressions are equivalent
Use the properties of operations to justify that two expressions are equivalent
Prior Knowledge Required
Students should already be comfortable with:
Writing simple expressions that record calculations with numbers 5.OA.A.2
Evaluating expressions at specific values of their variables, following the order of operations 6.EE.A.2
Rewriting expressions with the distributive, commutative and associative properties 6.EE.A.3
Evaluating whole-number exponents such as 3² = 9 6.EE.A.1
Read the situation aloud and let pairs test each expression before anyone explains.
Warm-Up Prompt
"Each friendship bracelet uses 4 blue beads and 2 white beads. For n bracelets, Ana writes the total number of beads as 4n + 2n, Ben writes 6n, and Cara writes n + 5. Test n = 1, n = 2 and n = 5. Who could be right?"
Record the results on the board. For n = 1, all three expressions give 6. For n = 2, Ana and Ben get 12, but Cara gets 7. For n = 5, Ana and Ben get 30, and Cara gets 10. Ask: "Cara's expression worked for 1 bracelet. Why is it still wrong?" The goal is a class sentence: an expression for the beads must be right for every number of bracelets, so one bad value rules it out. Ana's and Ben's expressions look different but always give the same number. Name the idea: they are equivalent expressions.
Direct Instruction20-25 minutes
Part 1: What equivalent means. Two expressions are equivalent when they name the same number regardless of which value is substituted into them, as the standard says. To substitute means to replace the variable with a number and then evaluate. Diagram 1 shows two tables. In the first, y + y + y and 3y match in every row. In the second, 4(m + 3) and 4m + 3 never match.
Part 2: One counterexample is enough. A counterexample is one value of the variable that gives different results. A single counterexample proves that two expressions are not equivalent, because an equivalent pair can have no exceptions at all.
Part 3: Matching is not proof. Some pairs match at a few values by coincidence. Diagram 2 plots x · x and 2x: they match at x = 0 and x = 2, but not at x = 1, 3 or 4. To be sure a pair is equivalent, students rewrite one expression into the other with the properties of operations. Then the match is guaranteed for every number.
Testing and explaining (official example)
Are y + y + y and 3y equivalent?
Equation: For y = 2: 6 and 6. For y = 7: 21 and 21. They always match because y + y + y = 1y + 1y + 1y = (1 + 1 + 1)y = 3y, so they are equivalent
A counterexample
Are 4(m + 3) and 4m + 3 equivalent?
Equation: For m = 1: 4(1 + 3) = 16, but 4 × 1 + 3 = 7. One value disagrees, so they are not equivalent (4(m + 3) is really 4m + 12)
A match that is not proof
Are x · x and 2x equivalent?
Equation: Both equal 4 when x = 2, but for x = 3, x · x = 9 and 2x = 6. They are not equivalent
Deciding with properties
Are 6k + 9 + 2k and 8k + 9 equivalent?
Equation: Commutative property: 6k + 2k + 9. Distributive property: (6 + 2)k + 9 = 8k + 9. Equivalent for every k
Equivalent expressions in a context
A pizza costs $11 and the tip is $2 per pizza. For p pizzas, Kai writes 11p + 2p, Mia writes 13p and Lee writes 11 + 2p. Which are equivalent?
Equation: 11p + 2p = (11 + 2)p = 13p, so Kai and Mia agree for every p. For p = 1, Lee also gets 13, but for p = 2, Lee gets 15 and the others get 26, so Lee's expression is not equivalent
Part 4: A decision routine. Post these three steps for the rest of the lesson:
Test: substitute two or three values, including 0 and one number bigger than 1. Keep the results in a table.
If any row differs: stop. That value is a counterexample, and the expressions are not equivalent.
If every row matches: the pair is probably equivalent. Prove it by rewriting one expression into the other and naming each property.
Guided Practice15 minutes
Pairs work through four problems with the routine, one problem at a time. Start with the table below.
Problem 1: complete the table for 2(a + 4) and 2a + 8, then decide.
a
0
1
3
10
2(a + 4)
?
?
?
?
2a + 8
?
?
?
?
Answers: both rows are 8, 10, 14 and 28, and the distributive property shows why: 2(a + 4) = 2a + 8, so they are equivalent. Problem 2: are 7 + 3b and 10b equivalent? (For b = 1, both are 10, but for b = 2 they are 13 and 20, so no.) Problem 3: are 5c + c and 6c equivalent? (Yes: 5c + 1c = (5 + 1)c = 6c.) Problem 4: are 2 · q · 6 and 12q equivalent? (Yes: by the commutative and associative properties, 2 · 6 · q = 12q.) After Problem 2, ask who stopped after b = 1, and why that was not enough.
Independent Practice10-15 minutes
Students decide on their own whether each pair is equivalent. They give a counterexample for every "no" and a property for every "yes". (1) 9w + w and 10w. (Yes: 9w + 1w = 10w.) (2) 3(2p + 1) and 6p + 1. (No: for p = 0, the values are 3 and 1.) (3) 8 + 4r and 4(2 + r). (Yes, by the distributive property.) (4) 20 - 2z and 18z, for whole numbers z from 0 to 10. (No: they match at z = 1, where both are 18, but for z = 2 they are 16 and 36.) (5) Pencils cost $0.25 each. Jo writes the cost of n pencils as 0.25n and Sam writes n ÷ 4. (Yes: dividing by 4 is the same as multiplying by 0.25, so for 12 pencils both give $3.)
Closure5 minutes
Exit ticket: (1) Give one value of k that shows 2(k + 5) and 2k + 5 are not equivalent. (Any value works; for k = 0, the results are 10 and 5.) (2) Are 4y + 3y and 7y equivalent? Name the property. (Yes, by the distributive property: (4 + 3)y = 7y.) (3) Tom tested x = 1 and found that 3x + 1 and x + 3 both equal 4. Is that enough to say they are equivalent? (No: for x = 2, they are 7 and 5.)
Differentiation Strategies
For Struggling Students
Provide a blank two-row table for every problem with the values 0, 1 and 2 already filled in, so students focus on substituting and comparing
Have students circle the variable in each expression and write the substituted number above it before they compute
Pair each non-equivalent example with a paper-strip model, so students can see that one strip is always longer
For Advanced Students
Ask students to invent a pair of expressions that are not equivalent but match at exactly one whole number, such as 3x + 4 and 4x + 3, which match only at x = 1
Ask why testing x = 1 alone is a weak test (multiplying by 1 hides the difference between 4x and x + 3, for example)
Ask students to decide whether a · a · a and 3a are equivalent and to find every whole number from 0 to 5 where they match (only 0)
Assessment Guidance
What to Look For
Listen for the phrase "for every value" in students' explanations. Check that students stop at the first value that gives different results and name it as a counterexample, and that they do not call a pair equivalent after a single matching value. When a pair is equivalent, look for a property-based explanation, not only a table. Watch for evaluation errors, especially forgetting the order of operations in expressions such as 4 + 3x.
02
Classroom Activities
3 Activities
1
Equivalent or Not? Card Sort
20 minPairs
Pairs sort 12 expression cards into families of equivalent expressions. Four cards are decoys that belong to no family. Pairs must test values and name a property for every family.
Expression Cards (12 cards)
Family A (3 cards): 3(w + 2), 3w + 6, 6 + 3w
Family B (3 cards): 4k + k, 5k, k · 5
Family C (2 cards): 2(3 + 4m), 6 + 8m
Decoys (4 cards): 3w + 2, k + 5, 6m + 8, 14m
Print the cards in random order, without the family labels.
Procedure
Group the cards by their variable (w, k or m)
Inside each group, substitute 0, 1 and 3 and record the results in a table
Put cards whose rows all match into one family, and set aside any card with a counterexample
For each family, write one sentence that names a property to prove the match
Discussion Questions
Which decoys match a Family C card when m = 1? (Both 14m and 6m + 8: each equals 14, and so does 6 + 8m)
Is there any value of w where 3w + 2 equals 3w + 6? (No, 3w + 6 is always 4 more)
Why is testing 0 useful for the decoy 6m + 8? (For m = 0, it gives 8 while 6 + 8m gives 6)
Modification for Distance Learning
Put the 12 cards on a shared slide. Pairs drag them into three boxes labeled Family A, B and C and a fourth box for decoys, and type their test values in a table on the same slide.
2
Table Detectives
20 minGroups of 3-4
Each group gets a worksheet with 4 pairs of expressions and a table for x = 0, 1, 2, 3 and 4. Groups fill in every row, mark each row "same" or "different", and give a verdict for each pair.
The 4 Pairs
Pair 1: x + x + x + x and 4x
Pair 2: 2x + 3 and 5x
Pair 3: x + 6 and 4x
Pair 4: 6(x + 1) and 6x + 6
Procedure
One student substitutes, one computes, one checks, and one records; rotate roles after each pair
Color the "same" rows green and the "different" rows red
Write the verdict: equivalent (with a property) or not equivalent (with a counterexample)
Discussion Questions
Pairs 2 and 3 each match at exactly one value. Which value is it for each pair? (Pair 2 at x = 1, where both are 5; Pair 3 at x = 2, where both are 8)
If you had tested only x = 1, which pair would have fooled you? (Pair 2)
Pairs 1 and 4 match in all five rows. What makes you sure they match for x = 100 too? (The properties: x + x + x + x = 4x and 6(x + 1) = 6x + 6)
Modification for Distance Learning
Share the table as a spreadsheet. Students type each value, and the teacher adds a column that shows whether the two results in each row are equal.
3
Paper Strip Test
20 minPairs
Pairs model expressions with paper strips and a centimeter ruler. The variable y is the length of one strip, and pairs repeat the test with three different lengths to see which models always match.
Materials for Each Pair
Paper strips about 2 cm wide, scissors, tape and a centimeter ruler
A recording table with columns for y = 3 cm, 5 cm and 7 cm
The 3 Tests
Test 1: 3(y + 2) and 3y + 6. Tape three copies of (a y strip plus a 2 cm strip), and compare with three y strips plus a 6 cm strip. (15, 21 and 27 cm for both)
Test 2: 3(y + 2) and 3y + 2. (15, 21 and 27 cm against 11, 17 and 23 cm)
Test 3: y + 4 + y and 2y + 4. (10, 14 and 18 cm for both)
Discussion Questions
In Test 2, by how much does the longer model beat the shorter one each time? Will that change for other lengths? (4 cm every time; no, because 3(y + 2) = 3y + 6 is always 4 more than 3y + 2)
Which property lets you slide the second y strip next to the first in Test 3? (The commutative property of addition)
Why can strips only test some values of y, and how do the properties help?
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Substitution Tables
Left: y + y + y and 3y give the same number for y = 0, 1, 2 and 3, and the properties of operations show they match for every y. Right: 4(m + 3) and 4m + 3 give different numbers in every row. A single row that differs is a counterexample, so these two are not equivalent.
Diagram 2: A Match That Is Not Proof
The squares show x · x and the circles show 2x for x = 0 to 4, drawn to scale. The two expressions give the same value at x = 0 and x = 2, where the marks overlap, but different values at x = 1, 3 and 4. Matching at some values is not enough: equivalent expressions match at every value.
04
Homework Assignment
~30 min
6.EE.A.4 Homework: Are They Equivalent?
Directions: For every pair, decide whether the expressions are equivalent. If they are not, give a counterexample and show the two different results. If they are, name the property that proves it. Show your substitutions.
Part 1: Testing with Substitution (Problems 1-2)
Make a table for the expressions 5(b + 1) and 5b + 5 with b = 0, 2, 4 and 9. Are the expressions equivalent? Name the property that explains your answer.
Nia says that 2g + 6 and 8g are equivalent, because both equal 8 when g = 1. Test two more values of g. Is Nia right? Explain what her test missed.
Part 2: Deciding with Properties (Problems 3-4)
Decide whether each pair is equivalent: (a) 7 + 2x and 2x + 7 (b) 4(3a) and 12a (c) 3(n + 5) and 3n + 5 (d) h + h + h + h + h and h + 5.
Write one expression that is equivalent to 6(2y + 3) and one expression that is not equivalent to it but gives the same value when y = 0. Give a value of y that shows your second expression is not equivalent.
Part 3: Equivalent Expressions in Context (Problems 5-6)
At the movies, each friend buys an $8 ticket and a $4 snack. For f friends, Leo writes the total cost as 8f + 4f, Mae writes 12f, and Tia writes 8 + 4f. Test f = 1 and f = 3. Which expressions are equivalent? Explain.
Carlos earns e dollars per hour walking dogs. He works 3 hours on Saturday and 5 hours on Sunday. His friends write his weekend earnings as 3e + 5e, 8e and 15e. Test e = 10 and e = 12, and decide which expressions are equivalent. Name a property that explains your answer.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Substitution
Values substituted and evaluated correctly, with tables
One evaluation error
No substitution shown, or several errors
Counterexamples
Every "not equivalent" answer has a correct counterexample with both results
Correct verdict but no counterexample
Pair called equivalent after one matching value
Properties
Every "equivalent" answer names a correct property
Correct verdict, property missing or misnamed
No reasoning for equivalent pairs
Context
Explains which expressions fit the situation and why
Correct choice with little explanation
Incorrect choice
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
What does it mean for two expressions to be equivalent?
Answer: B
Equivalent expressions name the same number no matter which value is substituted, so they must match for every value. Choice A is not enough: 2x + 5 and 3x match at x = 5 (both are 15) but not at x = 0, so they are not equivalent. Choice C fails because 4k + k and 5k use different numbers but are equivalent. Choice D fails for the same pair: one has two terms and the other has one.
Question 2 of 20 · Multiple Choice
Which expression is equivalent to 5x + 2x?
Answer: D
By the distributive property, 5x + 2x = (5 + 2)x = 7x. For x = 3, both give 21. Choice A multiplies the coefficients 5 × 2 instead of adding them. Choice B multiplies x by x, but adding like terms keeps the variable as it is. Choice C adds the coefficients and then adds x instead of multiplying by it: for x = 3, it gives 10, not 21.
Question 3 of 20 · Multiple Choice
For which value of n do the expressions 3n + 2 and 5n give the same result?
Answer: B
For n = 1, 3 × 1 + 2 = 5 and 5 × 1 = 5. Choice A gives 2 and 0, choice C gives 8 and 10, and choice D gives 17 and 25. Since the pair matches at n = 1 but not at the other values, the expressions are not equivalent: a match at one value is only a coincidence.
Question 4 of 20 · Multiple Choice
Which pair of expressions is equivalent?
Answer: D
7r + r = 7r + 1r = (7 + 1)r = 8r, so choice D matches for every r. Choice A multiplies only the x by 2: 2(x + 7) is 2x + 14, and x = 0 gives 14 and 7. Choice B mixes up repeated addition and repeated multiplication: x = 3 gives 6 and 9. Choice C adds a constant to a coefficient: y = 2 gives 10 and 14.
Question 5 of 20 · Multiple Choice
Jay substitutes a = 1 into 4a + 4 and 8a. He gets 8 both times. What should he conclude?
Answer: C
For a = 2, 4 × 2 + 4 = 12 but 8 × 2 = 16, so a = 2 is a counterexample and the pair is not equivalent. Choice A treats one match as proof. Choice B looks at the digits instead of the values. Choice D misreads Jay's test: a = 1 gives 8 for both expressions.
Question 6 of 20 · Multiple Choice
A table shows two expressions. For x = 0, 1, 2 and 3, expression P gives 0, 1, 4 and 9, and expression Q gives 0, 3, 6 and 9. What can you conclude?
Answer: A
Equivalent expressions match for every value, and these differ at x = 1 (1 and 3) and at x = 2 (4 and 6). Either row alone is a counterexample. Choice B uses two matching rows as proof, but matches can be coincidences. Choice C relies on a single row. Choice D ignores that one row that differs already settles the question.
Question 7 of 20 · Multiple Choice
Which expression is NOT equivalent to 12k + 8?
Answer: A
4(3k + 8) = 12k + 32, so for k = 0 it gives 32 instead of 8. It comes from dividing only 12k by 4 and leaving the 8 as it was. Choice B reorders the terms (commutative property). Choices C and D expand to 12k + 8 with the distributive property.
Question 8 of 20 · Multiple Choice
Which expression is equivalent to y + y + y + 4?
Answer: C
The three y terms combine into 3y, and the 4 stays a constant: 3y + 4. For y = 5, both give 19. Choice A adds the constant to the coefficients (1 + 1 + 1 + 4 = 7) and gives 35 for y = 5. Choice B swaps the coefficient and the constant and gives 23. Choice D turns repeated addition into repeated multiplication and gives 129.
Question 9 of 20 · Multiple Choice
How do the values of 2(x + 1) and 2x + 1 compare for every value of x?
Answer: D
By the distributive property, 2(x + 1) = 2x + 2, which is always 1 more than 2x + 1. For x = 4, the values are 10 and 9. Choice A would make them equivalent, but every value gives a difference of 1. Choice B reverses which one is larger. Choice C compares 2x + 2 with 2x and forgets the + 1.
Question 10 of 20 · Multiple Choice
Each of b boxes holds 6 red markers and 4 blue markers. Which expression does NOT give the total number of markers?
Answer: B
Choice B counts 4 blue markers in all instead of 4 in each box. For b = 3, the total is 30 markers, but 6b + 4 gives 22. Choices A, C and D are equivalent: 6b + 4b = (6 + 4)b = b(6 + 4) = 10b, and each gives 30 for b = 3.
Question 11 of 20 · Multiple Choice
Which expression is equivalent to 12 + 3d?
Answer: A
3(4 + d) = 3 × 4 + 3 × d = 12 + 3d by the distributive property. Choice B adds the constant 12 to the coefficient 3, which combines unlike terms. Choice C divides only 3d by 3 and gives 36 + 3d. Choice D divides 12 by 4 but divides 3d by 3, so it expands to 12 + 4d.
Question 12 of 20 · Multiple Choice
Kim substitutes w = 5. She finds that 3w + 10 gives 25 and 5(w + 1) gives 30. What can Kim conclude?
Answer: C
w = 5 gives 25 and 30, so it is a counterexample, and one counterexample is enough to show the pair is not equivalent. Choice A looks at the letters, not the values. Choice B compares a property of the results instead of the results themselves. Choice D would be right after a match, but after a difference no more tests are needed.
Question 13 of 20 · Multiple Choice
Which expression is equivalent to 0.5 × z × 10?
Answer: D
The commutative and associative properties let you multiply the numbers first: (0.5 × 10) × z = 5z. For z = 4, both give 20. Choice A adds 0.5 and 10 instead of multiplying. Choice B treats 0.5 as 5. Choice C adds z to 5 instead of multiplying: for z = 4 it gives 9.
Question 14 of 20 · Multiple Choice
Which pair of expressions gives the same value at x = 2 but is NOT equivalent?
Answer: C
At x = 2, 3x = 6 and x + 4 = 6, but at x = 0 they give 0 and 4, so they are not equivalent. Choices A and B are equivalent pairs, so they match at x = 2 and at every other value. Choice D does not match at x = 2: it gives 7 and 10.
Question 15 of 20 · Short Answer
Complete the table for 4(t + 2) and 4t + 8 with t = 0, 3 and 6. Are the expressions equivalent? Explain with a property.
Both expressions give 8, 20 and 32. They are equivalent: by the distributive property, 4(t + 2) = 4 × t + 4 × 2 = 4t + 8, so they match for every t, not only the three tested.
Question 16 of 20 · Short Answer
Find one value of p that shows 6p + 1 and 7p are not equivalent, and one value of p where they happen to give the same result.
Any value other than 1 is a counterexample, for example p = 0, which gives 1 and 0. They give the same result only at p = 1, where both equal 7. So the pair is not equivalent.
Question 17 of 20 · Short Answer
Are 2(3y + 4) and 6y + 8 equivalent? Justify your answer with a property, not only with a table.
Yes. By the distributive property, 2(3y + 4) = 2 × 3y + 2 × 4 = 6y + 8. A table (for y = 1, both give 14) supports this, but the property proves it for every y.
Question 18 of 20 · Short Answer
Ria says that 8 + a and 3a are equivalent, because both equal 12 when a = 4. Is she right? Explain.
No. A match at one value is not enough. For a = 1, 8 + a = 9 but 3a = 3, so a = 1 is a counterexample. The two expressions agree only when a = 4.
Question 19 of 20 · Short Answer
Write two different expressions that are equivalent to 5n + 10 and one expression that is not. Give a value of n that proves your third expression is not equivalent.
Answers vary. Equivalent: 5(n + 2) and 10 + 5n. Not equivalent: for example 5n + 2, because n = 0 gives 10 for 5n + 10 but 2 for 5n + 2.
Question 20 of 20 · Short Answer
A garden has 3 rows. Each row has k tomato plants and 2 pepper plants. Omar writes the total number of plants as 3k + 2, Pia writes 3(k + 2), and Quinn writes 3k + 6. Test k = 4. Which expressions are equivalent, and which one is wrong?
For k = 4, Omar gets 14, Pia gets 18 and Quinn gets 18. Pia's and Quinn's expressions are equivalent by the distributive property: 3(k + 2) = 3k + 6. Omar's is not: he counted only 2 pepper plants in all instead of 2 in each of the 3 rows.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does 6.EE.A.4 mean?
6.EE.A.4 means students can tell when two expressions are equivalent: when they give the same number for every value of the variable. The official example is y + y + y and 3y, which match whatever number y stands for. Students also show that a pair is not equivalent by finding one value where the results differ.
What grade is 6.EE.A.4, and what comes after it?
6.EE.A.4 is a grade 6 standard in Expressions and Equations. In grade 7, 7.EE.A.2 asks students to see how rewriting an expression in a context shows how quantities are related. In Algebra I, students use the structure of expressions to rewrite them (HSA.SSE.A.2).
How do you check if two expressions are equivalent?
Start by substituting a few values into both expressions. If any value gives different results, they are not equivalent. If all the values match, use the properties of operations to rewrite one expression into the other; that proves they match for every value.
Is testing one value enough to show two expressions are equivalent?
No. Some pairs match at one value by coincidence. For example, 2k + 4 and 3k + 2 both equal 8 when k = 2, but for k = 0 they give 4 and 2. A property-based rewrite is the only way to be sure a pair matches for every value.
How many values do you need to test to show expressions are not equivalent?
Just one. A single value that gives different results is a counterexample, and it proves the expressions are not equivalent. Testing 0 is often a quick way to find one, because it removes every term with a variable and leaves only the constants.
Why are y + y + y and 3y equivalent?
Adding y three times is the same as 3 groups of y, which is 3 times y. With properties: each y is 1y, and 1y + 1y + 1y = (1 + 1 + 1)y = 3y by the distributive property. So they name the same number whatever y is: for y = 8, both are 24.
What is the difference between equivalent expressions and an equation?
An equation, such as 2x + 1 = 9, is a statement that may be true for some values and false for others; solving it means finding the values that make it true (6.EE.B.5). Equivalent expressions are always equal: if you write them with an equal sign between them, the statement is true for every value of the variable.
What are common mistakes when deciding if expressions are equivalent?
A common mistake is calling a pair equivalent after one matching value. Others are multiplying only the first term inside parentheses, treating x · x as 2x, and combining a constant with a variable term, as in 5 + 2t = 7t. Evaluation errors with the order of operations can also make an equivalent pair look different.
How is 6.EE.A.4 different from 6.EE.A.3?
6.EE.A.3 asks students to produce equivalent expressions, for example to expand or factor with the distributive property. 6.EE.A.4 asks them to recognize equivalence: given two expressions, decide whether they always name the same number and explain how they know. The two standards are usually taught together.
How can parents help with equivalent expressions at home?
Use shopping. If notebooks cost $3 and pens cost $1, ask your child to write the cost of n notebooks and n pens in two ways, such as 3n + n and 4n, and to test them for 2 and 5 of each. Then ask whether 3 + n would also work, and to find a number of items that shows it does not.
07
Related Standards
6 standards
These standards connect to 6.EE.A.4: 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 numerical expressions and interpret them without evaluating
Lesson coming soon
6.EE.A.2Prerequisite
Write, read and evaluate expressions in which letters stand for numbers
