1 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. 2

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 = π develops students' understanding of variables as quantities that vary. This task was previously in the "Circles and Graphs" unit that was removed during the school year. 3

4 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. One-Step Equation Key Standards

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.

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? 8

9 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 Enduring Understandings

10 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. One-Step Equations Terms and Symbols

11 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 = π Culminating Task: "Building with Toothpicks” Fractions, Decimals, Ratios & Percents Framework Unit Tasks

Atlanta Public Schools Mathematics and Science Department Model Lesson Unit 4: One-Step Equations Using the Equation c / d = π

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?

Engage: Lesson Opener Use to create a lesson opener: 15

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

17 Using the Equation c / d = π Evaluate/Explain: Model Lesson Lesson Summary – Closing 1.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. 2.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 18

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…. Today’s lesson left me wondering about…. The thing I will remember most about this lesson is ….. because…. I continue to struggle with… because