Algebraic Expressions Intro

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Grade

5th Grade

Duration

60 minutes

Class Size

25 students

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Common Core Standards Addressed

CCSS.MATH.CONTENT.5.OA.A.1
Write and interpret numerical expressions.

• Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

CCSS.MATH.CONTENT.5.OA.A.2
Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

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Learning Objectives

By the end of this lesson, students will be able to:

1. Define and identify key algebraic vocabulary: variable, coefficient, term, and expression.
2. Explain what an algebraic expression is and how it differs from a numerical expression.
3. Write simple algebraic expressions to represent real-world situations.
4. Evaluate simple algebraic expressions for given values of variables.
5. Apply their understanding through collaborative and individual practice.

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Key Vocabulary

Term	Definition
Variable	A symbol (usually a letter) that represents an unknown number.
Coefficient	A number multiplied by a variable in a term.
Term	A single number, variable, or numbers and variables multiplied together.
Expression	A math phrase containing numbers, variables, and operations but no equal sign.

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Materials Needed

• Whiteboard and markers
• Student notebooks or math journals
• Printed expression cards (with simple expressions and real-life scenarios)
• Colored dry erase markers for student groups
• Small whiteboards or tablets for student work (if available)
• Exit tickets (small slips of paper with 2-3 question prompts)

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Lesson Outline

1. Introduction & Motivation (10 minutes)

• Begin with a quick warm-up: Write the numerical expression "5 + 3" on the board.
• Ask: “What does this mean?” “What if we don’t know the numbers and use letters?”
• Introduce the concept of a 'variable' as a “mystery number.”
• Briefly explain what an algebraic expression is: a math sentence with numbers, variables, and operations but no equals sign.
• Use simple examples:
  • Numerical: 5 + 3
  • Algebraic: 5 + x
• Highlight key vocabulary terms on the board.

2. Direct Instruction & Modeling (15 minutes)

• Define each vocabulary word interactively as you write them on the board and invite students to help give examples.
• Write examples of expressions on the board:
  • 3x (read “3 times x”) – identify coefficient and variable
  • x + 7 – identify terms (x and 7)
  • 4y + 2 – break down into terms and coefficients
• Model evaluating expressions by substituting values:
  • Example: Evaluate 3x + 2 when x = 4
  • Calculation: 3×4 + 2 = 12 + 2 =14
• Emphasize the step-by-step approach in evaluating expressions.

3. Guided Practice (15 minutes)

• Distribute expression cards with simple algebraic expressions and real-life contexts. For example:
  • “John has x apples and buys 5 more. Write an expression for the total apples.” (Expression: x + 5)
  • “A pack holds 4 pencils. Write an expression for the number of pencils in p packs.” (Expression: 4p)
• Students work in pairs to write expressions, identify terms, variables, and coefficients.
• Circulate and assist as needed using questioning to scaffold understanding.
• After pairs finish, call on several to share examples and explanations with the class.

4. Independent Practice (10 minutes)

• Students receive a worksheet or notebook prompt with 4-5 problems:
  • Write expressions from word problems.
  • Evaluate expressions for given variable values.
  • Identify coefficients and terms in provided expressions.
• Include a challenge problem for advanced learners, e.g.:
  • Write an expression for “3 fewer than twice a number n.”

5. Formative Assessment and Wrap-Up (10 minutes)

• Collect exit tickets with questions such as:
  1. Write an expression for: a number y minus 7.
  2. Evaluate 2x + 3 when x = 5.
  3. What is the coefficient in 6m?
• Review answers aloud, clarifying misconceptions.
• Summarize key points about expressions and vocabulary.

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Differentiation Strategies

Learner Type	Strategy
Struggling Learners	Provide vocabulary visuals and sentence frames; pair with supportive peer; use manipulatives like algebra tiles.
English Learners	Use gestures and visuals; provide word banks; read text aloud; check comprehension often.
Advanced Learners	Offer multi-step expression writing problems; introduce simple two-step evaluation; encourage creating word problems.
Kinesthetic Learners	Use whiteboards for expressive writing and evaluation; allow movement breaks during pair activity.

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Extensions and Homework

• Extension: Have students create their own short word problem that can be represented by an algebraic expression and exchange with a peer to solve.
• Homework: Worksheet with 5-6 real-life scenario problems asking students to write and evaluate expressions.

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Notes for Teachers

• Keep checking for understanding by asking students to explain in their own words.
• Use positive reinforcement to encourage attempts even if not exact.
• Encourage students to verbalize their thought process when evaluating or writing expressions.
• This foundation prepares students for writing equations and understanding more complex algebra in later grades.

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This lesson plan builds a solid foundation in algebraic expressions consistent with 5th grade Common Core objectives, blending conceptual understanding, vocabulary, and practical application with engaging, differentiated activities targeted for the diverse classroom.