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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.
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
• 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
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