Unit+One+Chapter+Three+Math+2013

= =
 * **Unit of Study: Equations and Functions ** ||
 * **Grade: **Sixth |||| **Topic: **Expressions and Equations || **Length of Unit: **2.5 Weeks ||
 * **Focus of Learning ** ||
 * **__Common Core Standards:__**
 * __Expressions and Equations 6.EE __**

Apply and extend previous understandings of arithmetic to algebraic expressions. 1. Write and evaluate numerical expressions involving whole-number exponents. 2. Write, read, and evaluate expressions in which letters stand for numbers. a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2. 3. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. 4. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.


 * Reason about and solve one-variable equations and inequalities.**

5. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. 6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. 7. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers. 8. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.


 * Represent and analyze quantitative relationships between dependent and independent variables.**

9. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. |||| **__Standards for Mathematical Practice: __** 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. <span style="font-family: Calibri,sans-serif; font-size: 8pt; line-height: 1.5;">4. <span style="font-family: Calibri,sans-serif; font-size: 11pt; line-height: 1.5;">Model with mathematics. <span style="font-family: Calibri,sans-serif; font-size: 8pt; line-height: 1.5;">5. <span style="font-family: Calibri,sans-serif; font-size: 11pt; line-height: 1.5;">Use appropriate tools strategically. <span style="font-family: Calibri,sans-serif; font-size: 8pt; line-height: 1.5;">6. <span style="font-family: Calibri,sans-serif; font-size: 11pt; line-height: 1.5;">Attend to precision. <span style="font-family: Calibri,sans-serif; font-size: 8pt; line-height: 1.5;">7. <span style="font-family: Calibri,sans-serif; font-size: 11pt; line-height: 1.5;">Look for and make use of structure. <span style="font-family: Calibri,sans-serif; font-size: 8pt; line-height: 1.5;">8. <span style="font-family: Calibri,sans-serif; font-size: 11pt; line-height: 1.5;">Look for and express regularity in repeated reasoning. || <span style="font-family: Calibri,sans-serif; font-size: 9pt;">Formulas help represent problems that follow a pattern (add 3 to find out how many is y = x=3) <span style="font-family: Calibri,sans-serif; font-size: 9pt;">Solving or evaluating an equation can be a complex task, but follows mathematical rules || <span style="font-family: Calibri,sans-serif; font-size: 9pt;">What is the pattern? How could you show this for different amounts || Understand solving an equation or inequality as a process of answering a question Evaluate expressions at specific values of their variables. |||| **__<span style="font-family: Calibri,sans-serif;">Application: __** //<span style="font-family: Calibri,sans-serif; font-size: 10pt;">Students will be able to… //
 * **__<span style="font-family: Calibri,sans-serif;">Enduring Understanding(s): __**//<span style="font-family: Calibri,sans-serif; font-size: 9pt;">Students will understand that… //
 * **__<span style="font-family: Calibri,sans-serif;">Guiding Questions: __**//<span style="font-family: Calibri,sans-serif; font-size: 9pt;">These questions will guide student inquiry. //
 * **<span style="font-family: Calibri,sans-serif;">Student Performance ** ||
 * **__<span style="font-family: Calibri,sans-serif;">Knowledge: __** //<span style="font-family: Calibri,sans-serif; font-size: 10pt;">Students will understand/know ////<span style="font-family: Calibri,sans-serif; font-size: 9pt;">… //

<span style="font-family: Calibri,sans-serif; font-size: 10pt;">See examples under Standards || ||
 * **<span style="font-family: Calibri,sans-serif;">Assessments **
 * **__<span style="font-family: Calibri,sans-serif;">Assessments: __**<span style="font-family: Calibri,sans-serif; font-size: 9pt;"> //pre-assessment, formative, and post-assessment/culminating task//

__<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Pre-Assessment: __<span style="font-family: Calibri,sans-serif; font-size: 11pt;"> An assessment of what was learned in Chapter 1

__<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Formative Assessments: __<span style="font-family: Calibri,sans-serif; font-size: 11pt;"> from Text

__<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Post-Assessment (Culminating __<span style="font-family: Calibri,sans-serif; font-size: 11pt;"> Task): from Text w/adjustments ||

//<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will know… // Terms/vocabulary related to expressions and equations (review) //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Write verbal phrases and sentences as simple algebraic expressions and equations. ||  || //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will know… // Terms/vocabulary related to subtraction and addition Subtraction and Addition Property of Equality //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Solve addition and subtraction equations. ||  || //<span style="font-family: Calibri,sans-serif; font-size: 11pt; line-height: 1.5;">Students will know… // Division Property of Equality //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Solve multiplication equations. ||  || //Students will know...// How to discuss and create algebraic expressions and equations //Students will be able to...// Work with algebra tile manipulatives to illustrate problems ||  || //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will know… // The steps for solving a two-step equation //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Solve two-step equations. ||  || //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will know… // The formula for perimeter and area of a rectangle and square //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Find the perimeter and area of figures. ||  || //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will know… // Terms/vocabulary for functions, function tables, and graphs/coordinate plane (review) //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Graph data to demonstrate relationships. ||  || //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will know… // How to represent measurement relationships on a graph //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Graph data to demonstrate the relationship between the dimensions and the perimeter of a rectangle. ||  ||
 * **<span style="font-family: Calibri,sans-serif;">Learning Experiences **<span style="font-family: Calibri,sans-serif; font-size: 9pt;"> (Lesson Plans Attached)  ||
 * **__<span style="font-family: Calibri,sans-serif;">Days __** ||||  **__<span style="font-family: Calibri,sans-serif;">Lesson Sequence __**  ||  **__<span style="font-family: Calibri,sans-serif;">Materials __**  ||
 * |||| **<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Lesson 3-1 Writing Expressions and Equations (pp. 128–133) **
 * |||| **Lesson 3-2 Solving Addition and Subtraction Equations (pp. 136–141)**
 * |||| **<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Lesson 3-3 Solving Multiplication Equations (pp. 142–146) **
 * |||| **Mid Chapter Quiz and Math Workshop**
 * |||| **Lesson 3-5 Solving Two-Step Equations (pp. 151–155)**
 * |||| **Lesson 3-6 Measurement: Perimeter and Area (pp. 156–161)**
 * |||| **Lesson 3-7 Functions and Graphs (pp. 163–167) **
 * |||| **Math Workshop: Measurement Lab**
 * |||| **Review of Chapter** ||  ||
 * **<span style="font-family: Calibri,sans-serif;">Resources ** ||
 * **<span style="font-family: Calibri,sans-serif;">Online ** ||||  **<span style="font-family: Calibri,sans-serif;">Text **  ||