Unit _2 Expressions Mathematics Grade 6 School Year: 2013-14 Unit Duration: Six Weeks Domains—Students Expressions and Equations (6.EE.1.2.3.4) The Number System (6.NS.4) • Apply and extend previous understandings of • Compute fluently with multi-digit numbers and arithmetic to algebraic expressions. find common factors and multiples. • Reason about and solve one-variable equations • Apply and extend previous understandings of and inequalities. numbers to the system of rational numbers. • Represent and analyze quantitative relationships between dependent and independent variables. Standards for Mathematical Practice Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Overview/Rationale Unit 2 employs the students’ understanding of the concepts involving integers in unit 1 to understand and apply rational number concepts. The standards from the Geometry and Statistics and Probability domains are included as a means of providing real world contexts. Standard(s) (6.EE.1)— Write and evaluate numerical expressions involving whole number exponents. (6.EE.2)— Read, write, 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. (6.EE.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. (6.EE.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.
(6.NS.4)— Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2) Technology Standard(s)
8.1.A The use of technology and digital tools requires knowledge and appropriate use of operations and related applications. 4.A.1: Demonstrate effective input of text and data using an input device. 4.A.2: Create a document with text formatting and graphics using a word processing program. 4.A.3: Create and present a multimedia presentation that includes graphics. 4.A.4: Create a simple spreadsheet, enter data, and interpret the information. 4.A.5: Determine the benefits of a wide range of digital tools by using them to solve problems. Technology Common Core Standards
Interdisciplinary Standard(s)
Common Core Science Grade 6-Grade8 Common Core History & Social Issues Grade 6-8 Common Core Reading Informational Text
Essential Question(s)
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Are mathematical expressions a language? How? How not? What is a pattern? How do you identify a pattern? How are patterns helpful? How can you express a pattern? What are qualities and components of an equation? How does change within the equation affect the other components? What are symbols? Why would you use a symbol? What words or symbols indicate which operation? How do the order of operations and properties help me simplify algebraic expressions? When does order matter and when does it not matter? How does the result change when the value of the variable is changed? How can mathematical symbols model verbal expressions? How is thinking algebraically different from thinking arithmetically? How do I use algebraic expressions to analyze or solve problems? How do the properties contribute to algebraic understanding? What is meant by equality? Can everything that has been done mathematically be undone? How do you represent numbers and their relationships to each other? What does it mean to be “computationally fluent”?
Enduring Understandings
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Daily life is full of variables or things that change. Sometimes there are ways to make sense of and predict change through identifying and extending patterns. Mathematics, as it reflects real-life situations, is often relational. Changing one thing often impacts other things in relation to it (change often does not occur in isolation).
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There are a variety of ways to express or convey a thought or event in a mathematical expression. Unknown numbers, or symbols, are not as mysterious and scary, or as unsolvable as they appear. Variables can be used as unique unknown values or as quantities that vary. Exponential notation is a way to express repeated products of the same number. Algebraic expressions may be used to represent and generalize mathematical problems and real life situations Properties of numbers can be used to simplify and evaluate expressions. Algebraic properties can be used to create equivalent expressions Two equivalent expressions form an equation.
In this unit plan, the following 21st Century themes and skills are addressed.
21
Check all that apply.
st
Century Themes
Indicate whether these skills are E-Encouraged, T-Taught, or AAssessed in this unit by marking E, T, A on the line before the appropriate skill.
Global Awareness
√
21 s t Century Skills
A
Creativity and Innovation
Environmental Literacy
T
Critical Thinking and Problem Solving
Health Literacy
E
Communication
E
Collaboration
Civic Literacy Financial, Economic, Business, and Entrepreneurial Literacy √ Student Learning Targets/Objectives/SLOs
1. Use mathematical language to identify parts of an expression. 2. Write and evaluate numerical expressions involving whole number exponents. 3. Read, write, and evaluate expressions in which letters stand for numbers (Including formulas that arise from real-world contexts). 4. Apply the properties of operations to generate equivalent expressions (Including the distributive property; for example, express 36 + 8 as 4(9 + 2) and y + y + y = 3y. 5. Identify when two expressions are equivalent; for example, Are the two expressions equal? 81 + 18 and 9(9 + 2). 6. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two numbers less than or equal to 12. Assessments
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NWEA--Diagnostic Exit Tickets, Do Nows, skill check list, --Formative (Monitor student progress) Model Curriculum Unit Testing, Unit Project, Extended Response Questions—Summative (evaluate student learning) Authentic Tasks, Math Notebook, Other Evidence
Interactive Assessment Practice CMP2 Testing Activities Grade 6 Instructor Code: amk-5500 Student Code: amk-0099 Grade 6 Math Skill Practice
Interactive math skill builders - Sixth grade at I4C 6th Grade Math Test Skills Practice Portfolio
Authentic Tasks Extended Response Questions Short Response Questions DOL Samples
Enrichment
Test Box
Unit Tests Quiz Samples NWEA Data SAMS Data
Differentiated Activities Prime Time; Connections; pg. 56 #1,2 & 3. Prime Time; Extensions; pg. 45 #37 Prime Time; Extensions; pg. 34 #36 Bits & Pieces II; Extensions; pg. 29 #48 Bits & Pieces II; Applications; pg. 44 #34 Bits & Pieces II; Connections; pg. 59 #35 Covering & Surrounding; Applications; pg. 63 #20 Bits & Pieces III; Applications; pg. 29 #22 & 23 Value Student Backgrounds to Improve Performance Be aware of and draw from your ELL students' prior knowledge. You should: •
Make sure ELL students know that their experiences and culture are valued. This will help their attitudes and increase their motivation.
•
Focus on meaning. When your ELL students share answers and present ideas, remember to focus on the meaning they are conveying, not on their grammar and usage.
•
Be flexible with student use of native language. You may want to have the ELL student record answers or solution steps in their own native language. You can have their work translated, if desired. This will help ELL students focus on the concepts and reasoning involved, without being slowed or hindered by their developing language skills. Readings:
ELL
Helping English Language Learners in the Classroom Intervention
US Department of Education--Intervention--What Works! Strategies to help struggling students Teaching and Learning Actions
Instructional Strategies
Compare & Contrast: Venn diagrams, Number line placement, plot and graph comparison Note Taking: Student organized notebook by unit. Reinforcing Effort & Providing Feedback: Using rubrics to guide student work; display student work with relevant comments. Homework & Practice: Focus practice on difficult concepts; Homework is an extension of class work. Word problems that require student to choose the correct strategy.
Activities/Experiences
Setting objectives & Providing Feedback: Specific objective and DOL for each lesson; Rubrics comparison as feedback. (Given a word problem, the student will be able to complete the division algorithm to find the solution) Generating & Testing Hypotheses: Using a general rule to make a prediction. (Rounding to add/subtract/multiply/divide decimals) Cues, Questions, Advance Organizers: Use of lists, tables to collect data, the efficient use of an algorithm. Creating Equations with Tiles Mathematical Strings (Connect to TE Resource Wiki) Resources
Key Terms
Content Vocabulary Equation Expression Variable Term constant Coefficient Equality Exponent Order of operations Inverse operations
Readings
Progression through the Grades University of Arizona Progression documents to support the Common Core Kansas Assoc. of Teacher of Mathematics--Flip Books “Flip Books” are intended to help teachers understand what each standard means in terms of what students must know and be able to do. It provides only a sample of instructional strategies and examples. The “Flip Books” support a teacher’s goal to guide students in understanding and making sense of mathematics.
Supporting Text Connected Math 2
Supplemental Materials
6.NS.4: Prime Time; Inv. 2; Inv. 3, CC Transition Kit, Inv. 2( Number Properties and Algebraic Equations). 6.EE.1.: Prime Time; Inv. 4; 6.EE.2: Bits & Pieces II; Inv. 2 Adding & Subtracting Fractions; Inv. 3. Multiplying with Fractions; Inv. 4, Dividing with Fractions. 6.EE.3.4: CC Transition It: (Inv. 2 Number Properties and Algebraic Equations)
Academic Vocabulary Compute evaluate Visual Relationship Interpret Value Verbal model
6.EE.2: Bits and Pieces III: Inv. 2, Decimal Times, Inv. 3, The Decimal Divide, CC Transition Kit, Inv. 2 (Number Properties and Algebraic Equations. Prime Time: Inv. 1, 3, 4,5. Bits & Pieces II: Inv. 2,3,4; Bits & Pieces III: Inv. 2: (Number Properties and Algebraic Equations. Covering & Surrounding: Inv. 1,2,3,4,5 (Designing Bumper Cars, Changing Area, Changing Perimeter, Measuring Triangles, Measuring Parallelograms, Measuring Irregular Shapes and circles
Ready Common Core Math 6—Student Workbook Lesson 11: Common Factors and Multiples Lesson 15: Numerical Expressions with Exponents Lesson 16: Algebraic Expressions
Video/Presentation Links
Lesson 17: Equivalent Expressions Math Connects, Course 1: Problem-Solving Practice Homework Book http://www.mathplayground.com/mathvideos.html http://math.pppst.com/ Variables Expressions and Equations | Equation examples for beginners | Khan Academy Expression-Equation PPT. (Connect to TE Resource Wiki)
Teacher Resource Links
CMP2 Transition Kit Pearson Transition Kit Grade 6 Connected Math Online: http://www.phschool.com/cmp2/ Master Codes: CMP2 Student Grade 6: amk 0099 Teacher: amk 5500 Sadlier-Oxford Online Practice & Activities Math.com Algebra Worksheet Generator Quantitles Grade 6 Database (For More Resources Connect to TE Resource Wiki)
Student Resource Links
Expression and Equations Activities Mathsisfun.com Pre-Algebra Model Algebraic Equations with a Balance Scale
Submitted by: ____________________________________
Date:
Curriculum and Instruction Administration:
Approved
Date: March 11, 2014
Board of Education:
Approved
Date: March 25, 2014
