Maryland Math 6.AT.B.7
The Standard
Apply the properties of operations (e.g., distributive, associative, commutative, etc.) to generate equivalent algebraic expressions and to identify when two expressions are equivalent (e.g., apply the distributive property to the expression 3(2 + ๐ฅ) to produce the equivalent expression 6 + 3๐ฅ; apply the distributive property to the expression 24๐ฅ +18๐ฆ to produce the equivalent expression 6(4๐ฅ + 3๐ฆ); apply properties of operations to ๐ฆ + ๐ฆ + ๐ฆ to produce the equivalent expression 3y.)
Maryland College and Career Ready Standards for Mathematics (2025) ยท APPLY AND EXTEND PREVIOUS UNDERSTANDINGS OF ARITHMETIC TO ALGEBRAIC EXPRESSIONS.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students expand, factor, and combine terms using the rules for addition and multiplication. They decide whether two expressions have the same value for every value of the variable.
What Mastery Looks Like
- A student can rewrite 4(x+2) as 4x+8 and 10a+15 as 5(2a+3). They can explain why each pair gives the same result for any value of the variable.
Common Misconceptions
- Students may multiply only the first term inside parentheses. They may combine unlike terms, such as x and 3, into one term. Some think getting the same answer for one value proves two expressions are equivalent.
How to Assess It
- Exit ticket: Rewrite 5(n+2) without parentheses and decide whether 5n+2 is equivalent. Explain your answer using a rule for multiplication.
Lesson moves
Ways to Teach It
Give pairs algebra tiles to build three groups of x+2, then rearrange the tiles to show 3x+6.
Ask: Does 2(y+5) equal 2y+5 for every y? Write a reason using groups or multiplication.
Play a matching game with cards showing 2(a+4), 2a+8, 6b+9, and 3(2b+3); students defend each match.
Have students price four lunches, each with a $3 sandwich and a drink costing d dollars, using 4(3+d) and 12+4d.
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Related Standards
- 4.NOS.C.7.c
Use properties of operations (e.g., to solve 8 ร 7, think of (5 ร 7 + (3 ร 7)) to multiply.
- 2.NOS.C.9.c
Use properties of operations, and/or the relationship between addition and subtraction to add and subtract.
- 5.NOS.B.7.d
Use properties of operations and/or the inverse relationship between multiplication and division to multiply and divide.
- 3.NOS.C.4
Identify and apply the Commutative Property of Multiplication, Associative Property of Multiplication, and Distributive Property of Multiplication as strategies...
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