Unit 4: One-Step Equations

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Unit 4 One-Step Equations
The Georgia Performance Standards Website
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Overview

• Students will investigate relationships between
  two quantities through algebraic representations
  using variables. In Grade 5 Mathematics, students
  studied variables as a placeholder for a specific
  unknown.
• Students will extend and deepen their
  understanding of this concept by also
  understanding variables as quantities that vary
  and as a pattern generator.
• This unit is a building block for analyzing
  relationships between quantities that students
  will continue to study in middle school and high
  school mathematics.

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Overview

• The unit opens with Using Letters to Represent
  Numbers which develops students understanding of
  variables as a pattern generator. Through this
  task, students will write and evaluate algebraic
  expressions, including those with exponents.
• Balancing Act introduces students to generalize
  patterns by writing simple equations using two
  variables and solve simple one-step equations
  using each of the four basic operations.
• Using the Equation c/d p develops students'
  understanding of variables as quantities that
  vary. This task was previously in the "Circles
  and Graphs" unit that was removed during the
  2009-2010 school year.

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One-Step EquationKey Standards

• M6A3. Students will evaluate algebraic
  expressions, including those with exponents, and
  solve simple one-step equations using each of the
  four basic operations.
• M6A2. Students will consider relationships
  between varying quantities.
• a. Analyze and describe patterns arising from
  mathematical rules, tables, and graphs.

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GPS Math Process Standards

• P1. Students will solve problems (using
  appropriate technology).
• a. Build new mathematical knowledge through
  problem solving.
• b. Solve problems that arise in mathematics and
  in other contexts.
• c. Apply and adapt a variety of appropriate
  strategies to solve problems.
• d. Monitor and reflect on the process of
  mathematical problem solving.
• P2. Students will reason and evaluate
  mathematical arguments.
• a. Recognize reasoning and proof as fundamental
  aspects of mathematics.
• b. Make and investigate mathematical conjectures.
  
• c. Develop and evaluate mathematical arguments
  and proofs.
• d. Select and use various types of reasoning and
  methods of proof.

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GPS Math Process Standards

• P3. Students will communicate mathematically.
• a. Organize and consolidate their mathematical
  thinking through communication.
• b. Communicate their mathematical thinking
  coherently and clearly to peers, teachers, and
  others.
• c. Analyze and evaluate the mathematical thinking
  and strategies of others.
• d. Use the language of mathematics to express
  mathematical ideas precisely.

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GPS Math Process Standards

• P4. Students will make connections among
  mathematical ideas and to other disciplines.
• a. Recognize and use connections among
  mathematical ideas.
• b. Understand how mathematical ideas interconnect
  and build on one another to produce a coherent
  whole.
• c. Recognize and apply mathematics in contexts
  outside of mathematics.
• P5. Students will represent mathematics in
  multiple ways.
• a. Create and use representations to organize,
  record, and communicate mathematical ideas.
• b. Select, apply, and translate among
  mathematical representations to solve problems.
• c. Use representations to model and interpret
  physical, social, and mathematical phenomena.

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One-Step EquationsEssential Questions

• Why do we use letters to represent numbers in
  mathematics?
• Why do we need conventions in mathematics?
• How do I evaluate an algebraic expression?
• How can variables be used to describe patterns?
• How do I solve a one step equation?

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One-Step EquationsEnduring Understandings

• In mathematics, letters are used to represent
  numbers.
• There are conventions for using letters to
  represent numbers in mathematics. Algebraic
  expressions are used to represent relationships
  between numbers. Variables can be used to
  generalize patterns.
• Pictures and diagrams are helpful in recognizing
  relationships.
• Inverse operations are helpful in understanding
  and solving problems.

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One-Step EquationsTerms and Symbols

• Equivalent Expressions Expressions that simplify
  to an equal value when numbers are substituted
  for the variables of the expression.
• Equation A mathematical sentence that contains
  an equals sign.
• Addition Property of Equality Adding the same
  number to each side of an equation produces an
  equivalent expression.
• Subtraction Property of Equality States that
  when both sides of an equation have the same
  number subtracted from them, the remaining
  expressions are still equal.
• Multiplication Property of Equality States that
  when both sides of an equation are multiplied by
  the same number, the remaining expressions are
  still equal.
• Division Property of Equality States that when
  both sides of an equation are divided by the same
  number, the remaining expressions are still
  equal.
• Inverse Operation A mathematical process that
  combines two or more numbers such that its
  product or sum equals the identity.

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Fractions, Decimals, Ratios PercentsFramework
Unit Tasks

• Using Letters to Represent Numbers
• Learning the Conventions for Multiplying and
  Dividing Letters and Numbers
• Balancing Act
• Step It Up
• The Ant
• Using the Equation c/d p
• Culminating Task "Building with Toothpicks

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Model LessonUnit 4 One-Step Equations

• Using the Equation c/d p

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Pre-lessonReflective Teacher Questions

• What is the lesson about?
• What prior knowledge do you think the students
  have?
• What unique considerations need to be included
  when planning for this group of students?
• Review the task and use the Anticipation Guide

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Pre-lessonReflective Teacher Questions

• What manipulatives or tools can be used for
  conceptual modeling?
• What do you already know through pre-assessments
  or other formative assessments about their
  misconceptions and/or error patterns related to
  this concept?
• How do you think they will do?

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Engage Lesson Opener

• Use www.xtranormal.com to create a lesson opener

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Explore Stations
Hands-On Circumference Mystery Ratio
The Shop Ms. Fumble
The Task Using the Equation
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Using the Equation c/d p Evaluate/Explain
Model Lesson

• Lesson Summary Closing
• Small groups should share their results with the
  large group. This is an opportunity for students
  to communicate and justify their reasoning in a
  collaborative environment that encourages
  questioning from others, but not evaluation or
  criticism.
• At the very end of the lesson time, the teacher
  provides the whole class feedback on the goals
  accomplished today and discusses the expectations
  for what will be accomplished the next day.

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Extend MARS Task

• Historic Bicycle
• Rubric

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Closing

• Choose one of the 5 prompts to include in your
  Math Journal as your Exit Ticket.

I feel I really understood I am unsure about
I am curious to learn more about. Todays lesson left me wondering about.
The thing I will remember most about this lesson is .. because. I continue to struggle with because