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Unit 4: One-Step Equations

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Unit 4: One-Step Equations The Georgia Performance Standards Website * – PowerPoint PPT presentation

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Title: Unit 4: One-Step Equations


1
Unit 4 One-Step Equations
The Georgia Performance Standards Website
2
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.

3
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.

4
One-Step Equation Key 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.

5
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.

6
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.

7
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.

8
One-Step Equations Essential 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?

9
One-Step Equations Enduring 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.

10
One-Step Equations Terms 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.

11
Fractions, Decimals, Ratios Percents Framework
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

12
Model Lesson Unit 4 One-Step Equations
  • Using the Equation c/d p

13
Pre-lesson Reflective 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

14
Pre-lesson Reflective 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?

15
Engage Lesson Opener
  • Use www.xtranormal.com to create a lesson opener

16
Explore Stations
Hands-On Circumference Mystery Ratio
The Shop Ms. Fumble
The Task Using the Equation
17
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.

18
Extend MARS Task
  • Historic Bicycle
  • Rubric

19
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
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