Metro RESA...Building leaders of teaching and learning Keys to CCGPS Coordinate Algebra Units 1 & 2 Sarah Ledford 1

Metro RESA...Building leaders of teaching and learning Fluency Task: x = -6 Write an equation that involves two different operations and has the solution x = -6. Source: - Middle – Patterns, Functions, & Algebra – Solving Equationshttp://books.heinemann.com/math/ 2

Metro RESA...Building leaders of teaching and learning What is fluency? What does fluency look like in middle school and high school? GADOE CCGPS Webinar 3

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Introductions and Expectations? Introduce yourself: – name, school, grade level AND What are your expectations for today? 5

Metro RESA...Building leaders of teaching and learning 6 Group Norms and Housekeeping Group Norms: Participate and share Participate with an open mind Ask questions Work toward solutions Housekeeping: Phone calls Rest rooms Breaks Lunch or Leave

Metro RESA...Building leaders of teaching and learning Objectives: examine the standards to determine what students should know, understand, and be able to do work tasks aligned to standards, including tasks from the Framework units determine the Standards for Mathematical Practice (SMPs) to be integrated in tasks aligned to the standards Identify teacher actions to address TKES 7

Metro RESA...Building leaders of teaching and learning Agenda LiveBinder TKES aligned to SMPs Learning Intentions/Outcomes Tasks related to the concept/unit – Alignment to CCGPS content and SMPs Preparing for GA Milestones Resources 8

Metro RESA...Building leaders of teaching and learning TKES - Standards 1 – Professional Knowledge 2 – Instructional Planning 3 – Instructional Strategies 4 – Differentiated Instruction 5 – Assessment Strategies 6 – Assessment Uses 7 – Positive Learning Environment 8 – Academically Challenging Environment 9 – Professionalism 10 - Communication 9

Metro RESA...Building leaders of teaching and learning Collaborative Planning “Planning can be done in many ways, but the most powerful is when teachers work together to develop plans, develop common understandings of what is worth teaching, collaborate on understanding their beliefs of challenge and progress, and work together to evaluate the impact of their planning on student outcomes.” John Hattie from Visible Learning for Teachers, page 41

Metro RESA...Building leaders of teaching and learning Learning Intentions/Outcomes “Two powerful ways of increasing impact is to know and share both the learning intentions and success criteria of the lesson with students.” John Hattie from Visible Learning for Teachers, page 75

Metro RESA...Building leaders of teaching and learning Learning Intentions/Outcomes “Good learning intentions are those that make clear to the students the type or level of performance that they need to attain, so that they understand where and when to invest energies, strategies, and thinking, and where they are positioned along the trajectory towards successful learning.” John Hattie from Visible Learning for Teachers, page 52

Metro RESA...Building leaders of teaching and learning Content Standards We will now take a few minutes to look at the content standards addressed in units 1 & 2 so that we can develop common understandings as to what students should be able to do in these units.

Metro RESA...Building leaders of teaching and learning Leaky Faucet Watch Dan Meyer videos found at: Make a list of questions you could ask. What other information would be needed to answer your questions. Create & carry out computations. 14 REFERENCE THE source (GaDOE

Metro RESA...Building leaders of teaching and learning Leaky Faucet - GA Framework Kim estimates that the faucet in her kitchen drips at a rate of 1 drop every 2 seconds. Erik wants to know how many times the faucet drips in a week. Help Erik by showing your calculations. Kim estimates that approximately 575 drops fill a 100 milliliter bottle. Estimate how much water her leaky faucet wastes in a year. 15 REFERENCE THE source (GaDOE

Metro RESA...Building leaders of teaching and learning Task Review What CCGPS (content) was addressed? 16

Metro RESA...Building leaders of teaching and learning Algebra Seeing Structure in Expressions A-SSE Interpret the structure of expressions. 1.Interpret expressions that represent a quantity in terms of its context.  a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r) n as the product of P and a factor not depending on P. 2.Use the structure of an expression to identify ways to rewrite it. For example, see x 4 – y 4 as (x 2 ) 2 – (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 – y 2 )(x 2 + y 2 ). Write expressions in equivalent forms to solve problems. 3.Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15 t can be rewritten as (1.15 1/12 ) 12t ≈ t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. 4. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments. Format of High School Standards Code Domain StandardA.SSE.2StandardA.SSE.2 Conceptual Category (5+M) Modeling Symbol Cluster Heading Bibb County 17

Metro RESA...Building leaders of teaching and learning Domains for K-8 / Conceptual Categories for High School 18

Metro RESA...Building leaders of teaching and learning Number & Quantity AlgebraFunctionsGeometry Statistics & Probability The Real Number System Seeing Structure in Expressions Interpreting Functions Congruence Interpreting Categorical and Quantitative Data Quantities Arithmetic with Polynomials & Rational Expressions Building Functions Similarity, Right Triangles, and Trigonometry Making Inferences and Justifying Conclusions The Complex Number System Creating Equations Linear, Quadratic and Exponential Models Circles Conditional Probability and the Rules of Probability Vector and Matrix Quantities Reasoning with Equations and Inequalities Trigonometric Functions Expressing Geometric Properties with Equations Using Probability to Make Decisions Geometric Measurement and Dimension Modeling with Geometry Domains Conceptual Categories & Domains M o d e l i n g 19

Metro RESA...Building leaders of teaching and learning Task Review What CCGPS (content) was addressed? 20

Metro RESA...Building leaders of teaching and learning What was addressed in the task? In grade level groups, chart the following: If more than one domain is addressed, choose the one that is the focus. Identify the standards in your grade level that lead to or build on this. Grade Level: Domain: Cluster: Standard(s) addressed: Including the transition standards; include the code and the “gist” of the standard What needs clarification in the standard: 21

Metro RESA...Building leaders of teaching and learning What SMPs were addressed? 22 GaDOE 7th grade CCGPS Overview Presentation

Metro RESA...Building leaders of teaching and learning What considerations need to be made in order to meet different student learning needs and address individual learning differences? – SWD – ELs – others 23

Metro RESA...Building leaders of teaching and learning SMPs aligned… 24

Metro RESA...Building leaders of teaching and learning Task Review What SMPs were addressed? Examine the TAPS associated with the SMPs for students Examine the TAPS associated with the SMPs for teachers What considerations need to be made for struggling students? – SWDELsOthers 25

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Metro RESA...Building leaders of teaching and learning Assessment What question could you ask students to formatively assess their understanding of the standard(s): that requires them to communicate their reasoning and builds their confidence in providing answers on extended-response items – Georgia Milestones? 27

Metro RESA...Building leaders of teaching and learning Ask This Not That Instead of: How many ounces in a pound? Or 3 lbs = ____ oz Ask: Are these claims reasonable? Justify. My math teacher weighs 2400 ounces. My math teacher drinks 70 ounces of water a day. from Good Questions 6 – 8, pg

Metro RESA...Building leaders of teaching and learning Ask This I know that 500 lbs is a quarter of a ton. Decide which of the following equations best represents how I determined this. Justify  4 = n2000  n =  4 = n2000  n = 4 from Good Questions 6 – 8, pg

Metro RESA...Building leaders of teaching and learning Ask This One cup of uncooked rice weighs about ________ ounces. One cup of dry beans weighs about _______ ounces. Would 1 cup of dry beans equal 1 cup of dry rice in capacity? In weight? Explain. from Good Questions 6 – 8, pg

Metro RESA...Building leaders of teaching and learning Same Solutions? Which of the following equations have the same solution? Give reasons for your answer that do not depend on solving the equations. x + 3 = 5x − 4x − 3 = 5x + 4 2x + 8 = 5x − 310x + 6 = 2x − 8 10x − 8 = 2x x/10 = 1/2x − 0 From Illustrative Mathematics 31 REFERENCE THE source (GaDOE

Metro RESA...Building leaders of teaching and learning Task Review What CCGPS (content) was addressed? – Domain, cluster, and standards What SMPs were addressed? 32

Metro RESA...Building leaders of teaching and learning Who is Correct? Students were asked to solve the future simple interest equation (A = P(1 + rt)) for t. Sam and Ella got two different answers. Which is correct? Explain. Sam’s solution: t = (A-P)/Pr Ella’s solution: t = (A/P – 1) ÷ r 33

Metro RESA...Building leaders of teaching and learning Task Review What CCGPS (content) was addressed? – Domain, cluster, and standards What SMPs were addressed? 34

Metro RESA...Building leaders of teaching and learning Ask this not that Instead of just asking: Solve the equation for t. Ask: These two equations are equivalent. 2x + 5y = 400 & x = -5/2 y Explain how you know that they are equivalent. 35

Metro RESA...Building leaders of teaching and learning Ask this not that 2x + 5y = 400 & x = -5/2 y Liam says that both equations model this situation: I have some $5 bills and two identical piles of $1 bills. Altogether, I have $400. Which equation do you think is a better description? Why? From More Great Questions – Differentiating pg 39 36

Metro RESA...Building leaders of teaching and learning Balancing Equations Play with this app. See if you can figure out what it does & why you might want to use it! Try y = 2x – 3 & y = 5 – 2x Create 2 equations that have the solution (1, 1). 37

Metro RESA...Building leaders of teaching and learning Task Review What CCGPS (content) was addressed? – Domain, cluster, and standards What SMPs were addressed? 38

Metro RESA...Building leaders of teaching and learning Solving 2 Equations in 2 Unknowns Lisa is working with the system of equations x + 2y = 7 and 2x − 5y = 5. She multiplies the first equation by 2 and then subtracts the second equation to find 9y = 9, telling her that y = 1. Lisa then finds that x = 5. Thinking about this procedure, Lisa wonders… From 39

Metro RESA...Building leaders of teaching and learning Solving 2 Equations in 2 Unknowns There are lots of ways I could go about solving this problem. I could add 5 times the first equation and twice the second or I could multiply the first equation by -2 and add the second. I seem to find that there is only one solution to the two equations but I wonder if I will get the same solution if I use a different method? What is the answer to Lisa's question? Explain. 40

Metro RESA...Building leaders of teaching and learning Task Review What CCGPS (content) was addressed? – Domain, cluster, and standards What SMPs were addressed? 41

Metro RESA...Building leaders of teaching and learning Proof that the Elimination Method Works Handout 42

Metro RESA...Building leaders of teaching and learning Task Review What CCGPS (content) was addressed? – Domain, cluster, and standards What SMPs were addressed? 43

Metro RESA...Building leaders of teaching and learning Ask this not that Instead of just asking: Solve this system of equations graphically OR by substitution OR by elimination. Also ask: Sabina earns money by baby-sitting. She offers her clients two different payment options and presents them in the graph on the next slide. What do you think each payment option is? How did you figure it out? Explain which option you would choose and why. 44

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Metro RESA...Building leaders of teaching and learning System of Equations from EOCT Released Items Look at the system of equations. ax + by = c dx + ey = f The system has a unique solution, (x, y). Which system of equations has the same solution? A ax + by = c C ax + by = c dx − ey = f (a+d)x + (b−e)y = c + f B ax + by = c D ax + by = c (a+e)x + (b+d)y = c + f (a+2d)x + (b+2e)y = c + 2f

Metro RESA...Building leaders of teaching and learning GA DOE Implementation Resources – Common Core Tools – Schedule of Unit webinars – Recordings: Standards for Mathematical Practices Grade level overviews Unit webinars – List Serve (subscribe to receive s from DOE) – Learning Village

Metro RESA...Building leaders of teaching and learning GA DOE GaDOE Wiki – Coordinate Algebra & Analytic Geometry Please visit to provide feedback, ask questions, and share ideas and resources. Multi-Grade Resources: 10.wikispaces.com/Multi+Grade+Resources 10.wikispaces.com/Multi+Grade+Resources Secondary Mathematics Specialists Brooke Kline – James Pratt – 48

Metro RESA...Building leaders of teaching and learning Implementation Resources Progressions – “offer explanations for the sequence of the standards, potential cognitive difficulties, and pedagogical solutions which may be useful in teacher preparation and professional development, organizing curriculum, and writing textbooks.” 49

Metro RESA...Building leaders of teaching and learning Implementation Resources Illustrative Mathematics Project – “illustrates the range and types of mathematical work” 50

Metro RESA...Building leaders of teaching and learning Implementation Resources The Mathematics Common Core Toolbox – “ This site is a resource designed to support districts working to meet the challenge and the opportunity of the new standards. Here you will find tools and instructional materials that help you to better understand and to implement the CCSSM. …created through a collaboration of the Charles A. Dana Center at the University of Texas at Austin and Agile Mind with partial funding from the Bill & Melinda Gates Foundation.” 51

Metro RESA...Building leaders of teaching and learning Implementation Resources PARCC Content Frameworks – “voluntary resources offered by PARCC to help curriculum developers and teachers as they work to implement the standards in their states and districts. They are designed with the following purposes in mind: – Supporting implementation of the Common Core State Standards, and – Informing the development of item specifications and blueprints for the PARCC assessments in grades 3–8 and high school.” 52

Metro RESA...Building leaders of teaching and learning PARCC Released Test Items Initial Set of Test Items and Task Prototypes Released and-task-prototypes-released and-task-prototypes-released 53

Metro RESA...Building leaders of teaching and learning Implementation Resources Inside Mathematics – “a professional resource for educators passionate about improving students' mathematics learning and performance. This site features classroom examples of innovative teaching methods and insights into student learning, tools for mathematics instruction that teachers can use immediately, and video tours of the ideas and materials on the site.”classroom examplestools for mathematics instructionvideo tours 54

Metro RESA...Building leaders of teaching and learning Implementation Resources Math Common Core Coalition – “The Mathematics Common Core Coalition works to provide expertise and advice on issues related to the effective implementation of the Common Core State Standards for School Mathematics (CCSSM).” 55

Metro RESA...Building leaders of teaching and learning Implementation Resources Achieve the Core Free resources Founded by one of the contributing authors of the CCSS (Student Achievement Partners), now devoted to successful implementation 56

Metro RESA...Building leaders of teaching and learning Objectives: examine the standards to determine what students should know, understand, and be able to do work tasks aligned to standards, including tasks from the Framework units determine the Standards for Mathematical Practice (SMPs) to be integrated in tasks aligned to the standards Identify teacher actions to address TKES 57

Metro RESA...Building leaders of teaching and learning LIVEBINDER link 58

Metro RESA...Building leaders of teaching and learning Now What? What does this mean for me and my students? Please complete the evaluation. –