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Metro RESA...Building leaders of teaching and learning Keys to CCGPS Coordinate Algebra Unit 3 Sarah Ledford sarah@SarahLikesMath.com 1

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Metro RESA...Building leaders of teaching and learning LEGO Code 2

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Metro RESA...Building leaders of teaching and learning LEGO Code 3 Why did I give this to you? What does it mean? What does it have to do with our unit? What math can we get out of it?

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Metro RESA...Building leaders of teaching and learning Introductions and Expectations? Introduce yourself: – name, school, grade level AND What are your expectations for today? 4

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Metro RESA...Building leaders of teaching and learning 5 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

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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 6

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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

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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

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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

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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

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Metro RESA...Building leaders of teaching and learning From Good Questions 5-8 Complete the chart. What is the rule? Add three more pairs of In and Out values. InOut aardvarka giraffea hippoo otter? ?e ?? ?? ??

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Metro RESA...Building leaders of teaching and learning From Good Questions 5-8 Complete the chart. What is the rule? Write your rule in words and as an equation. Add three more pairs of In and Out values. Create sequence with inputs 1, 2, 3, 4, … InOut 58 1013 36 0? ?45 ?? ?? ??

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Metro RESA...Building leaders of teaching and learning From Good Questions 5-8 Complete the chart. What is the rule? Write your rule in words and as an equation. Add three more pairs of In and Out values. Create sequence with inputs 1, 2, 3, 4, … InOut 01 12 1/2 4? ?? ?128 ?? 532

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Metro RESA...Building leaders of teaching and learning Task Review What CCGPS (content) was addressed? Handout standards for CA Unit 3. 14

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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 ≈ 1.012 12t 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 15

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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 16

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Metro RESA...Building leaders of teaching and learning What SMPs were addressed? 17 GaDOE 7th grade CCGPS Overview Presentation

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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 18

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Metro RESA...Building leaders of teaching and learning SMPs aligned… 19

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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 20

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Metro RESA...Building leaders of teaching and learning 21

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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? 22

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Metro RESA...Building leaders of teaching and learning Ask This Not That Instead of just asking: Here’s a function, find f(3). Also ask: Let f(t) be the number of people, in millions, who own cell phones t years after 1990. Explain the meaning of the following statements. A. f(10) = 100.3B. f(a) = 20 C.f(20) = bD. n = f(t) Problem from Illustrative Mathematics 23

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Metro RESA...Building leaders of teaching and learning Ask This Not That Also ask: You put a yam in the oven. After 45 minutes, you take it out. Let f(t) be the temperature of the yam t minutes after you placed it in the oven. Explain the meaning of the statement in everyday language. A.f(0) = 65 B. f(5) < f(10) C.f(40) = f(45)D. f(45) > f(60) Problem from Illustrative Mathematics 24

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Metro RESA...Building leaders of teaching and learning What are the Questions? 25

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Metro RESA...Building leaders of teaching and learning What are the Questions? Draw the next step in the pattern Create an in/out table Find the nth term Graph it Write the recursive form of the equation Is it arithmetic or geometric? 26

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Metro RESA...Building leaders of teaching and learning Paper Folding Fold a piece of paper…. 27

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Metro RESA...Building leaders of teaching and learning What are the Questions? Number of regions vs. Area of each region Draw the next step in the pattern Create an in/out table Find the nth term Graph it Write the recursive form of the equation Is it arithmetic or geometric? 28

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Metro RESA...Building leaders of teaching and learning Visual Patterns Each pair/group will be given a picture to study with some information. On chart paper – Draw the sequence & next step – complete the table – write the equation in explicit & recursive forms – sketch the graph – determine if you have an arithmetic or geometric sequence. 29

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Metro RESA...Building leaders of teaching and learning Task Review What CCGPS (content) was addressed? – Domain, cluster, and standards What SMPs were addressed? 30

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Metro RESA...Building leaders of teaching and learning Ask This Not That Instead of just asking: Complete the sequence or identify the rule. Also ask: Create your own arithmetic (or geometric) sequence and write the rule in explicit form and recursive form. Then give your sequence to your partner and write the rules for each other’s sequences. 31

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Metro RESA...Building leaders of teaching and learning Ask This Not That Imagine that the following pattern continues: Row 1: 3 Row 2: 3 6 Row 3: 3 6 9 Row 4: 3 6 9 12 Row 5: 3 6 9 12 15 What questions could we ask? 32

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Metro RESA...Building leaders of teaching and learning Ask This Not That What numbers will be in Row 6? What is the last number in Row 10? In which row is 45 the last number? Explain how to find the last number in a row. [from Good questions for math teaching: Why ask them and what to ask by Lainie Schuster and Nancy Canavan Anderson (2005). Pp 98-99.] 33

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Metro RESA...Building leaders of teaching and learning Ask This Not That 5, 7, 9, 11, 13, … is a sequence. Zack said that the formula is t 1 = 5, t n = t n-1 + 2. Eric said that a better way to write the formula is f(n) = 2n + 3. Do you agree or disagree with Eric? Why? [from More good questions: Great ways to differentiate secondary mathematics instruction. Teachers College Press: Columbia University. Small, M. and Lin, A. (2010). Pp. 30] 34

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Metro RESA...Building leaders of teaching and learning Graph.tk Free graphing site Color-coded Only graphs functions Explore key features of a graph – Domain/range, intercepts, end behavior, Explore transformations – Unit 3 Frameworks: High Functioning 35

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Metro RESA...Building leaders of teaching and learning Task Review What CCGPS (content) was addressed? – Domain, cluster, and standards What SMPs were addressed? 36

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Metro RESA...Building leaders of teaching and learning Implementation Resources Mathematics Assessment Project http://map.mathshell.org Tools for formative and summative assessment that make knowledge and reasoning visible, and help teachers to guide students in how to improve, and monitor their progress. – Formative Assessment Lessons (FALs grades 6-11)

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Metro RESA...Building leaders of teaching and learning MAP FALs Lesson Plans – Concept development vs. Problem Solving Process – think independently & jot down ideas/work, work within a group to come up with a better/more efficient solution, discuss student solutions, & discuss provided student solutions PPT slides Worksheets 38

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Metro RESA...Building leaders of teaching and learning Comparing Investments Making Money - pre-assessment Odd One Out? - powerpoint slides Matching Game Double Your Money - powerpoint slides Making Money (revisited) 39

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Metro RESA...Building leaders of teaching and learning Odd One Out? P-40 Investment 1 $100 Simple Interest Rate: 5% Investment 2 $400 Simple Interest Rate: 5% Investment 3 $200 Simple Interest Rate: 10%

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Metro RESA...Building leaders of teaching and learning Odd One Out? P-41 Investment 1 A = 500 × 1.06 4 Investment 2 A = 250 × 1.06 2 Investment 3 A = 500 × 1.03 2

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Metro RESA...Building leaders of teaching and learning Comparing Investments Match pairs in first envelope. If any information is missing, fill it in. Once you are done with envelope 1, open envelope 2 and add to your matched pairs. If any information is missing, fill it in. Once your group feels really good about your matched groups, open envelope 3 and add these cards to your groups. 42

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Metro RESA...Building leaders of teaching and learning Comparing Investments Solutions P1 F6 P2 F3 P3 F2 P4 F5 P5 F1 P6 F4 43

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Metro RESA...Building leaders of teaching and learning Comparing Investments Solutions P1 F6 G6 T6 P2 F3 G4 T4 P3 F2 G3 T5 P4 F5 G5 T2 P5 F1 G1 T1 P6 F4 G2 T3 44

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Metro RESA...Building leaders of teaching and learning Comparing Investments Solutions P1 F6 G6 T6 S4 P2 F3 G4 T4 S1 P3 F2 G3 T5 S2 P4 F5 G5 T2 S1 P5 F1 G1 T1 S5 P6 F4 G2 T3 S3 45

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Metro RESA...Building leaders of teaching and learning Double Your Money P-46 Investment 1 A = 500 × 1.06 n Investment 2 A = 250 × 1.06 n Investment 3 A = 500 × 1.03 n Which two investments will take exactly the same time to double the money?

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Metro RESA...Building leaders of teaching and learning Task Review What CCGPS (content) was addressed? – Domain, cluster, and standards What SMPs were addressed? 47

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Metro RESA...Building leaders of teaching and learning GA DOE Implementation Resources https://www.georgiastandards.org/Common-Core/Pages/Math.aspx – Common Core Tools – Schedule of Unit webinars – Recordings: Standards for Mathematical Practices Grade level overviews Unit webinars – List Serve (subscribe to receive emails from DOE) – Learning Village

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Metro RESA...Building leaders of teaching and learning GA DOE GaDOE Wiki – Coordinate Algebra & Analytic Geometry Please visit http://ccgpsmathematics9-10.wikispaces.com/ to provide feedback, ask questions, and share ideas and resources. http://ccgpsmathematics9-10.wikispaces.com/ Multi-Grade Resources: http://ccgpsmathematics9- 10.wikispaces.com/Multi+Grade+Resources http://ccgpsmathematics9- 10.wikispaces.com/Multi+Grade+Resources Secondary Mathematics Specialists Brooke Kline – bkline@doe.k12.ga.usbkline@doe.k12.ga.us James Pratt – jpratt@doe.k12.ga.usjpratt@doe.k12.ga.us 49

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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.” http://ime.math.arizona.edu/progressions/ 50

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Metro RESA...Building leaders of teaching and learning Implementation Resources Illustrative Mathematics Project – “illustrates the range and types of mathematical work” http://illustrativemathematics.org/ 51

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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.” http://www.ccsstoolbox.org/ 52

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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.” http://www.parcconline.org/parcc-model-content-frameworks 53

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Metro RESA...Building leaders of teaching and learning PARCC Released Test Items Initial Set of Test Items and Task Prototypes Released http://www.parcconline.org/initial-set-test-items- and-task-prototypes-released http://www.parcconline.org/initial-set-test-items- and-task-prototypes-released 54

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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 http://insidemathematics.org/index.php/home 55

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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).” www.mathccc.org 56

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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 57

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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 58

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Metro RESA...Building leaders of teaching and learning LIVEBINDER link All materials from today including the ppt can be found at http://www.livebinders.com/play/play?id=1477 222 access key: RESACA 59

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Metro RESA...Building leaders of teaching and learning Now What? What does this mean for me and my students? Follow us on Twitter @MRESAmathTwitter Please complete the evaluation. http://bit.ly/ref_eval

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