Mathematics Pacing Resource Document
6.AF.2
Standard: 6.AF.2:Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear
expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is
substituted into them.
Teacher Background Information: Students use the distributive property to write equivalent expressions. Using their understanding of area models from
elementary students illustrate the distributive property with variables. Properties are introduced throughout elementary grades (3.OA.5); however, there has
not been an emphasis on recognizing and naming the property. In 6th grade students are able to use the properties and identify by name as used when
justifying solution methods. Students demonstrate an understanding of like terms as quantities being added or subtracted with the same variables and
exponents. For example, 3x + 4x are like terms and can be combined as 7x; however, 3x + 4x2 are not like terms since the exponents with the x are not the
same. This concept can be illustrated by substituting in a value for x.
Lesson Plans/Print Activities:
Web-based Practice:

https://www.engageny.org/resource/grade-6-mathematics-module-4topic-overview (Lessons 1-4)

https://www.engageny.org/resource/grade-6-mathematics-module-4topic-c-overview (Lessons 7-8)

https://www.engageny.org/resource/grade-6-mathematics-module-4topic-d-overview (Lessons 9-14)




https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6thexpressions-and-variables/cc-6th-equivalentexpressions/e/equivalent-forms-of-expressions-1 Equivalent forms
of expressions

https://learnzillion.com/lessons/648-write-equivalent-expressionsusing-the-additive-identity-property-of-zero-and-themultiplicative-identity-property-of-one Learnzillion videos
http://www.rsm.rcs.k12.tn.us/teachers/Robertsont/6.3.4%20%26%206.EE
.3%20%26%204%20~%20Equivalent%20M%26M%27s.pdf Lesson

https://learnzillion.com/lessons/650-write-equivalent-expressionsusing-the-additive-inverse-property Learnzillion videos
https://grade5aglcommoncoremath.wikispaces.hcpss.org/file/view/6.EE.3
%20CONJECTURES%20ABOUT%20PROPERTIES%20Task%20Georgia.pdf/4
42332554/6.EE.3%20CONJECTURES%20ABOUT%20PROPERTIES%20Task%
20Georgia.pdf Conjectures about properties. Georgia DOE Lesson

https://learnzillion.com/lessons/649-write-equivalent-expressionsusing-the-distributive-property-of-multiplication-over-addition
Learnzillion video

https://learnzillion.com/lessons/651-write-equivalent-expressionsusing-the-multiplicative-inverse-property Learnzillion Lesson

https://learnzillion.com/lessons/374-write-equivalent-expressionsusing-distributive-property Learnzillion Lesson
http://map.mathshell.org/materials/lessons.php?taskid=221#task221
Algebraic Expression Lesson Plan-MARS
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
Indianapolis Public Schools

https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6thexpressions-and-variables/cc-6th-equivalentexpressions/e/equivalent-forms-of-expressions-1 Khan Academy

http://nrich.maths.org/5864 Online Game

https://learnzillion.com/lessonsets/238-identify-when-twoexpressions-are-equivalent Learnzillion video

http://www.bbc.co.uk/schools/mathsfile/shockwave/games/equat
ionmatch.html Equation Game
Curriculum & Instruction
Mathematics Pacing Resource Document
6.AF.2
Standard: 6.AF.2:Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear
expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is
substituted into them.
Item Bank:
[louisianabelieves.com]
[louisianabelieves.com]
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
6.AF.2
Standard: 6.AF.2:Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear
expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is
substituted into them.
Item Bank:
[louisianabelieves.com]
[louisianabelieves.com]
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
6.AF.2
Standard: 6.AF.2:Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear
expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is
substituted into them.
Item Bank:
[louisianabelieves.com]
…continued on next page…
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
6.AF.2
Standard: 6.AF.2:Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear
expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is
substituted into them.
Item Bank:
a. Which expressions represent the number of boxes of popcorn that Jonna, Cedric, Miles, and Alysha sold both days? Choose all that apply.
a.) 2(8) + 2(6) + 19 + 12
b.) 9 + 8 + 5 + 6
c.) 19 + 16 + 2(12)
d.) 9 + 10 + 2(6) + 2(8) + 5 + 7
e.) 8 + 8 + 6 + 6 + 9 + 7
b. The expression 2(8+6) can be used to find the amount of popcorn sold by Alisha and Cedric. Identify the factors used in the expression.
c. The student council realized not everyone would like the same type of popcorn, so Cedric sold butter popcorn, and Alysha sold caramel popcorn. Cedric sold
his butter popcorn for x dollars, and Alysha sold her caramel popcorn for y dollars. Write two equivalent expressions that could be used to find the total amount
of money collected by Cedric and Alysha on Thursday and Friday. One of the expressions must demonstrate the distributive property. Explain how you know the
expressions you have written are equivalent.
[louisianabelieves.com]
[NAEP 2007]
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
6.AF.2
Standard: 6.AF.2:Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear
expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is
substituted into them.
Item Bank:
[NAEP 2005]
Some of the students at Kahlo Middle School like to ride their bikes to and from school. They always ride unless it rains.
Let d be the distance in miles from a student's home to the school. Write two different expressions that represent how far a student travels by bike in a four
week period if there is one rainy day each week.
[illustrativemathematics.org]
a.
b.
c.
d.
e.
Which of the following expressions are equivalent? Why? If an expression has no match, write 2 equivalent expressions to match it.
A. 2(x+4)
B. 8+2x
C. 2x+4
D. 3(x+4)−(4+x)
E. x+4
[illustrativemathematics.org]
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
6.AF.2
Standard: 6.AF.2:Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear
expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is
substituted into them.
Item Bank:
The students in Mr. Nolan's class are writing expressions for the perimeter of a rectangle of side length ℓ and width w. After they share their answers, the
following expressions are on the board:
 Sam: 2(ℓ+w)
 Joanna: ℓ+w+ℓ+w
 Kiyo: 2ℓ+w
 Erica: 2w+2ℓ
[illustrativemathematics.org]
Identify which are true.
y + y + y + y = 4y
True
False
6 (3x + 9) = 18x = 9
True
False
3x = 3x + 3x + 3x
True
False
4 + 7y = 7y + 4
True
False
8t – 4 = 4 (2t – 1)
True
False
Choose 2 statements from above to explain how you decided if they were true or false.
[Howard County Public Schools, Maryland]
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
6.AF.2
Standard: 6.AF.2:Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear
expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is
substituted into them.
Item Bank:
Circle whether each of the following pairs of expressions are equivalent or not equivalent:
6y + 12 and 6(y + 2)
equivalent
not equivalent
3x + y and y + 3x
equivalent
not equivalent
3x + 2 and 3(x + 2)
equivalent
not equivalent
5x2+ 15 and 5(x2+ 3)
equivalent
not equivalent
3y2+ 6x2 and 3(y2+ 2x2)
equivalent
not equivalent
Pick 2 from above. Justify why you identified them as equivalent or not equivalent.
[Howard County Public Schools, Maryland]
John’s formula for finding the perimeter of a rectangle is l + l + w + w.
Kay’s formula for finding the perimeter of a rectangle is 2 l + 2w.
Heather’s formula for finding the perimeter of a rectangle is 2(l + w)
They all insist that they are correct. Are their formulas equivalent? _____
Justify your answer.
[Howard County Public Schools, Maryland]
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
6.AF.2
Standard: 6.AF.2:Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear
expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is
substituted into them.
Item Bank:
Grade 6 Math: Grocery Shopping and the Quilt of a Math Teacher (This unit contains a curriculum-embedded Common Core–aligned task and instructional
supports. The task is embedded in a 2–3 week unit on expressions.) http://schools.nyc.gov/NR/rdonlyres/F7DD52E7-FD7E-44DC-B09990301CAC9025/140802/NYCDOE_G6_Math_GroceryShopping_FINAL1.pdf
Grade 6 Math: Elk Street (This unit contains a curriculum-embedded Common Core–aligned task and instructional supports. The task is embedded in a 2–3 week
unit on expressions.) http://schools.nyc.gov/NR/rdonlyres/9BC415CE-0FC0-4C97-9795-78A42276615B/140504/NYCDOE_G6_Math_ElkStreet_FINAL.pdf
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
6.AF.2
Standard: 6.AF.2:Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear
expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is
substituted into them.
Item Bank:
(Readiness I)
Indianapolis Public Schools
Curriculum & Instruction
Mathematics Pacing Resource Document
6.AF.2
Standard: 6.AF.2:Apply the properties of operations (e.g., identity, inverse, commutative, associative, distributive properties) to create equivalent linear
expressions and to justify whether two linear expressions are equivalent when the two expressions name the same number regardless of which value is
substituted into them.
Item Bank:
(Readiness II)
Indianapolis Public Schools
Curriculum & Instruction