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Simplifying Expressions
What is an expression?
• An expressions is a mathematical statement that includes terms and coefficients
• Unlike an equation, expressions are simplified NOT solvedThe contents of this content module were developed by special educator Bethany Smith, PhD and validated by content expert Drew Polly, PhD at University of North Carolina at Charlotte under a grant from the Department of Education (PR/Award #: H373X100002, Project Officer, [email protected]). However, the contents do not necessarily represent the policy of the Department of Education and no assumption of endorsement by the Federal government should be made
6y + 4 + 3y +x + 2
Like terms
coefficient
Breaking down the expression
• Expressions have many components called factors– Example: 2(x+5) has two factors
• Factor 1: 2• Factor 2: (x+5)
• Sometimes those factors include exponents– Example: (x+5)2 really means (x+5) (x+5)
The contents of this content module were developed by special educator Bethany Smith, PhD and validated by content expert Drew Polly, PhD at University of North Carolina at Charlotte under a grant from the Department of Education (PR/Award #: H373X100002, Project Officer, [email protected]). However, the contents do not necessarily represent the policy of the Department of Education and no assumption of endorsement by the Federal government should be made
Simplifying Expressions
• When simplifying expressions, it is important to remember the order of operations
– Terms within parenthesis are simplified first– Then exponents– Then terms that are either multiplied or divided– Then terms that are either added to or
subtracted from
The contents of this content module were developed by special educator Bethany Smith, PhD and validated by content expert Drew Polly, PhD at University of North Carolina at Charlotte under a grant from the Department of Education (PR/Award #: H373X100002, Project Officer, [email protected]). However, the contents do not necessarily represent the policy of the Department of Education and no assumption of endorsement by the Federal government should be made
Simplifying Expressions: An example
6(4x + 7x)-16x +14
6(11x)-16x +14
66x-16x +14
50x +14
The contents of this content module were developed by special educator Bethany Smith, PhD and validated by content expert Drew Polly, PhD at University of North Carolina at Charlotte under a grant from the Department of Education (PR/Award #: H373X100002, Project Officer, [email protected]). However, the contents do not necessarily represent the policy of the Department of Education and no assumption of endorsement by the Federal government should be made
Step 1: Simplify terms in parenthesis
Step 2: Simplify terms that are multiplied
Step 3: Simplify terms that are multiplied
This is the simplest version of the expression
Expressions and Word Problems
• In addition to simplifying expressions, students also need to practice generating an expression based on a word problem
• Example: A movie theater charges $6.00 for an adult ticket, plus an additional $2.00 fee if you buy the ticket online. Write an expression to find the total cost of x tickets.
Answer: 6x +2x= 8xThe contents of this content module were developed by special educator Bethany Smith, PhD and validated by content expert Drew Polly, PhD at University of North Carolina at Charlotte under a grant from the Department of Education (PR/Award #: H373X100002, Project Officer, [email protected]). However, the contents do not necessarily represent the policy of the Department of Education and no assumption of endorsement by the Federal government should be made
Ideas for application
• Create personally relevant word problems
• Pair terms with familiar objects to assist with combining like terms. For example a term with an x is paired with a red circle, terms with a y are paired with a yellow square.
The contents of this content module were developed by special educator Bethany Smith, PhD and validated by content expert Drew Polly, PhD at University of North Carolina at Charlotte under a grant from the Department of Education (PR/Award #: H373X100002, Project Officer, [email protected]). However, the contents do not necessarily represent the policy of the Department of Education and no assumption of endorsement by the Federal government should be made
Making connections
• Simplifying expressions addresses the following Core Content Connectors– 6.PRF.2a2 Use variable to represent numbers and write
expressions when solving real world problems– 6.NO.1i2 Solve numerical expressions involving whole
number exponents– 6.SE.1a3 Write expressions for real-world problems
involving one unknown number– H.PRF.2a Translate an algebraic expression into a word
problem– H.NO.2c1 Simplify expressions that include exponents– H.NO.2c2 Rewrite expressions that include rational
exponentsThe contents of this content module were developed by special educator Bethany Smith, PhD and validated by content expert Drew Polly, PhD at University of North Carolina at Charlotte under a grant from the Department of Education (PR/Award #: H373X100002, Project Officer, [email protected]). However, the contents do not necessarily represent the policy of the Department of Education and no assumption of endorsement by the Federal government should be made
