Unit+One+Math+2013

= = Expressions and Equations 6.EE
 * **Chapter 1: Algebra and Functions ** ||
 * **Topic: **Intro to Algebra and Functions || **Length of Unit: **2 weeks ||
 * **Focus of Learning ** ||
 * ===Common Core Standards: ===

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.

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 nonnegative 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.

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. 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;">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;">Application: __** //<span style="font-family: Calibri,sans-serif; font-size: 10pt;">Students will be able to… // ||
 * **<span style="font-family: Calibri,sans-serif;">Assessments **<span style="font-family: Calibri,sans-serif; font-size: 9pt;">(Attached)  ||
 * **__<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;"> BoY assessment of basic skills (multiplication, division, fractions)

__<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Formative Assessments: __ Chapter Quizzes (1-4); Mid-Chapter Test

__<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Post-Assessment (Culminating Task): __<span style="font-family: Calibri,sans-serif; font-size: 11pt;"> Initial Assessment Chapter Test Form 1, re-test Chapter Test Form 2 ||

//<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will know… // Terms/vocabulary related to powers and exponents Identify the parts of an exponent //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Use powers and exponents to evaluate expressions where they are used ||  || //<span style="font-family: Calibri,sans-serif; font-size: 11pt; line-height: 1.5;">Students will know… // Terms/vocabulary related to squares and square roots Identify parts of a square or square root //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Find squares of numbers and square roots of perfect squares ||  || //<span style="font-family: Calibri,sans-serif; font-size: 11pt; line-height: 1.5;">Students will know… // Terms/vocabulary related to order of operations //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Evaluate expressions using the order of operations ||  || //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will know… // Identify the parts of an algebraic expression //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Evaluate simple algebraic expressions ||  || //Assessment:// Mid Chapter Test //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will know… // Formula for perimeter and area of rectangular quadrilaterals //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Working in groups, come up with quadrilaterals, and calculate the area or perimeter for them ||  || //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will know… // Definitions of the Commutative, Associative, Identity, and Distributive properties //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Use Commutative, Associative, Identity, and Distributive properties to solve problems. ||  || //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will know… // What a mathematical sequence is and what it looks like //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Describe the relationships and extend terms in arithmetic sequences ||  || //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will know… // What is a function (input/output) and how to express these mathematically //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // Make function tables and write equations. ||  || Go through Chapter Review with students //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will know… // That functions and sequences can be expressed in a variety of formats (numeric/symbolic, physical/manipulatives) //<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Students will be able to… // <span style="font-family: Calibri,sans-serif; font-size: 11pt;">Express sequences and functions with manipulatives, and write formulas to express patterns ||  ||
 * **<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;">Extra Materials __**  ||
 * 1 |||| **<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Lesson ** 1-2 Powers and Exponents (pp. 30–33)
 * 1 |||| **<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Lesson ** 1-3 Squares and Square Roots (pp. 34–37)
 * 1 |||| **<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Lesson ** 1-4 Order of Operations (pp. 38–41)
 * 1 |||| **<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Lesson **1-6 Algebra: Variables and Expressions (pp. 44–47)
 * 1 |||| **Mid-Chapter Review and Math Workshop**
 * 1 |||| **<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Lesson ** 1-8 Algebra: Properties (pp. 53–56)
 * 1 |||| **<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Lesson ** 1-9 Algebra: Arithmetic Sequences (pp. 57–61)
 * 1 |||| **<span style="font-family: Calibri,sans-serif; font-size: 11pt;">Lesson ** 1-10 Algebra: Equations and Functions (pp. 63–67)
 * 1 |||| **Chapter Review and Math Workshop**
 * **<span style="font-family: Calibri,sans-serif;">Resources ** ||
 * **<span style="font-family: Calibri,sans-serif;">Online ** ||||  **<span style="font-family: Calibri,sans-serif;">Text **  ||