Download Topic: Equivalent Expressions

Topic: Equivalent Expressions
COMMON CORE STATE STANDARDS
• Domains Expressions and Equations, The Number System
• Clusters Compute fluently with multi-digit numbers and find common factors
and multiples; apply and extend previous understandings of arithmetic to
algebraic expressions.
• Standards for Mathematical Content 6.NS.B.4, 6.EE.A.2c, 6.EE.A.3,
6.EE.A.4
• Standards for Mathematical Practice All of the standards are addressed,
with an emphasis on MP2, MP3, MP4, and MP5. For the full text of the
Standards for Mathematical Practice, see the Unit pages of the Teacher Guide.
DOMAIN Expressions and Equations
6.NS.B.4 Find the greatest common factor of two whole numbers less than or equal
to 100 and the least common multiple of two whole numbers less than or equal to 12.
Use the distributive property to express a sum of two whole numbers 1−100 with a
common factor as a multiple of a sum of two whole numbers with no common factor.
6.EE.A.2c 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).
6.EE.A.3 Apply the properties of operations to generate equivalent expressions.
6.EE.A.4 Identify when two expressions are equivalent (i.e., when the two
expressions name the same number regardless of which value is substituted into
them).
Looking Back
Looking Ahead
Grade 6
Grade 5
5.OA.A.1 Use parentheses, brackets, or
braces in numerical expressions, and
evaluate expressions with these
symbols.
Grade 6
6.EE.A.1 Write and evaluate numerical
expressions involving whole-number
exponents.
6.EE.A.2a Write expressions that
record operations with numbers and with
letters standing for numbers.
6.EE.A.2b 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.
6.EE.B.5 Understand solving an
equation or inequality as a process of
answering a question: which values from
a specified set, if any, make the equation
or inequality true? Use substitution to
determine whether a given number in a
specified set makes an equation or
inequality true.
6.EE.B.7 Solve real-world and
mathematical problems by writing and
solving equations of the form x + p = q
and px = q for cases in which p, q and x
are all nonnegative rational numbers.
Grade 7
7.EE.A.1 Apply properties of operations
as strategies to add, subtract, factor, and
expand linear expressions with rational
coefficients.
– grade 6 • Teacher Guide
Topic: Equivalent Expressions continued
MATH BACKGROUND
Students learned about properties of numerical expressions with parentheses in
Grade 5, under the Operations and Algebraic Thinking domain of the Common Core
State Standards. Students have also had extensive experience with the properties
pertaining to 0 and 1. They will now learn how to apply the same properties to
algebraic expressions. Seeing the full list of properties all in the same topic will help
students distinguish one from the other and appropriately apply each one.
The Greatest Common Factor lesson on is necessary to prepare students for The
Distributive Property lesson. Because prime factorization is also a method for finding
least common multiples, the topic also includes a lesson addressing that concept.
ESSENTIAL QUESTION
What are properties? Why are properties useful?
FOCUS QUESTIONS
The Focus Questions in this topic emphasize the usefulness of properties. Properties
about 0 and 1 are special because of their usefulness as identities. Some lessons
focus on using properties to rewrite expressions by reordering, regrouping, or factoring
out a common factor. The Problem Solving lesson emphasizes that you can use
properties to rewrite an expression, which may help you see a solution pathway or see
a real-life problem situation in a new way.
TOPIC PLANNING
Topic: Equivalent
Expressions
Single
Period
Block
Schedule
Tools
Readiness Lesson
1 day
1
2
day
The Identity and Zero
Properties
1 day
1
2
day
Think-Write
The Commutative Properties
1 day
1
2
day
Integer Chips
Place Value Blocks
The Associative Properties
1 day
1
2
day
Words to Expression
Greatest Common Factor
1 day
1
2
day
Venn Diagram
The Distributive Property
1 day
1
2
day
Area Models
Words to Expression
Least Common Multiple
1 day
1
2
day
Venn Diagram
Problem Solving
1 day
1
2
day
Think/Write
1 day
1
2
day
1 day
1
2
day
Topic Review
Topic Assessment
10 days
5 days
– grade 6 • Teacher Guide