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Unit 4 One-Step Equations

The Georgia Performance Standards Website

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.

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.

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.

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.

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.

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.

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?

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.

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.

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

Model Lesson Unit 4 One-Step Equations

- Using the Equation c/d p

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

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?

Engage Lesson Opener

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

Explore Stations

Hands-On Circumference Mystery Ratio

The Shop Ms. Fumble

The Task Using the Equation

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.

Extend MARS Task

- Historic Bicycle
- Rubric

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