Presentation on theme: "Coordinate Algebra Unit 3 Sarah Ledford"— Presentation transcript:
1 Coordinate Algebra Unit 3 Sarah Ledford sarah@SarahLikesMath.com Keys to CCGPSCoordinate AlgebraUnit 3Sarah Ledford
2 LEGO Code15 minutes total5 min. naming; 10 minutes discussing it
3 LEGO Code 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?The source of this code was my son’s LEGO Club magazine from Aug (Not sure about the date!)Handout coding that is deciphered to be: “Welcome to MRESA. My name is Sarah Ledford. Today we will be discussing functions in CA unit 3. Fun!!”Discuss function, 1-1 function, function notation [ie., f(>) = t], domain & range, input/output table, etc.Standards: F.IF.1 and F.IF.2
4 Introductions and Expectations? Introduce yourself:name, school, grade level ANDWhat are your expectations for today?15 min.As people introduce themselves, have them state their expectations for the day. Someone should record the expectations as they are mentioned.Option: As they introduce themselves go to the perimeter of the room and group themselves according to their expectations.Keep a record of the number of teachers at each grade level as information for getting into grade level groups in the afternoon to work on specific grade level tasks.
5 Group Norms and Housekeeping Participate and shareParticipate with an open mindAsk questionsWork toward solutionsHousekeeping:Phone callsRest roomsBreaksLunch or Leave
6 Agenda LiveBinder TKES aligned to SMPs Learning Intentions/Outcomes Tasks related to the concept/unitAlignment to CCGPS content and SMPsPreparing for GA MilestonesResourcesThis just gives the outline for the day.If it is a grade band, have 3 or 4 tasks that teachers can work at their grade level. Get same grade level teachers to sit together.
7 Objectives:examine the standards to determine what students should know, understand, and be able to dowork tasks aligned to standards, including tasks from the Framework unitsdetermine the Standards for Mathematical Practice (SMPs) to be integrated in tasks aligned to the standardsIdentify teacher actions to address TKES2 min.Read each objective. Go back to the list of expectations to identify those that will be addressed in the session.
8 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
9 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
10 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
11 From Good Questions 5-8 Complete the chart. What is the rule? InOutaardvarkagiraffehippoootter?eComplete the chart.What is the rule?Add three more pairs of In and Out values.Source: Good questions for math teaching: Why ask them and what to ask grades 5–8. Math Solutions Publications: Sausalita, CA. Schuster, L. and Andeson, N.C. (2005).
12 From Good Questions 5-8 Complete the chart. What is the rule? InOut58101336?45Complete 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, …Source: Good questions for math teaching: Why ask them and what to ask grades 5–8. Math Solutions Publications: Sausalita, CA. Schuster, L. and Andeson, N.C. (2005).
13 From Good Questions 5-8 Complete the chart. What is the rule? InOut12-11/24?128532Complete 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, …Source: Good questions for math teaching: Why ask them and what to ask grades 5–8. Math Solutions Publications: Sausalita, CA. Schuster, L. and Andeson, N.C. (2005).
14 Task Review What CCGPS (content) was addressed? Handout standards for CA Unit 3.Show this slide, but before having them actually find the content, go over the next several slides to go over the organization and format of the CCGPS. For some it will be a review; for others it may be completely new.Use the slide in the next several that is pertinent to the grade levels in the PL.
15 Format of High School Standards Conceptual Category (5+M)DomainAlgebraSeeing Structure in Expressions A-SSEInterpret the structure of expressions.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.Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).Write expressions in equivalent forms to solve problems.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 1.15t can be rewritten as (1.151/12)12t ≈ t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.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.CodeCluster HeadingModeling SymbolStandardA.SSE.2High school organizationHide the slide not appropriate for your grade band.The high school standards are formatted in a similar way to the grade-level standards, indicating the conceptual category, domain and cluster headings. The code begins with the conceptual category followed by the domain. The modeling standards are integrated into the other conceptual categories and are indicated by a star.The + symbol indicate additional mathematics that students should learn in 4th year courses or advanced courses such as calc, adv stats…may also occur in courses intended for all studentsBibb County
16 Conceptual Categories & Domains Number & QuantityAlgebraFunctionsGeometryStatistics & ProbabilityThe Real Number SystemSeeing Structure in ExpressionsInterpreting FunctionsCongruenceInterpreting Categorical and Quantitative DataQuantitiesArithmetic with Polynomials & Rational ExpressionsBuilding FunctionsSimilarity, Right Triangles, and TrigonometryMaking Inferences and Justifying ConclusionsThe Complex Number SystemCreating EquationsLinear, Quadratic and Exponential ModelsCirclesConditional Probability and the Rules of ProbabilityVector and Matrix QuantitiesReasoning with Equations and InequalitiesTrigonometric FunctionsExpressing Geometric Properties with EquationsUsing Probability to Make DecisionsGeometric Measurement and DimensionModeling with GeometryDomainsM o d e l i n gHigh school organizationHide the slide not appropriate for your grade band.The high school standards are organized around five conceptual categories: number and quantity, algebra, functions, geometry, and statistics and probability.The high school standards emphasize mathematical modeling—Ask participants what they think mathl modeling is…
17 What SMPs were addressed? Another representation by Bill McCallum, lead writer of the Mathematics CCSSHandoutGaDOE 7th grade CCGPS Overview Presentation
18 What considerations need to be made in order to meet different student learning needs and address individual learning differences?SWDELsothers
19 SMPs aligned…MRESA staff aligned the College and Career Readiness Anchor Standards (ELA) and considerations for ELs to the Standards for Mathematical Practice.Handout
20 TKES - Standards 2 – Instructional Planning 1 – Professional Knowledge2 – Instructional Planning3 – Instructional Strategies4 – Differentiated Instruction5 – Assessment Strategies6 – Assessment Uses7 – Positive Learning Environment8 – Academically Challenging Environment9 – Professionalism10 - CommunicationThe first two are in red because they seem to be the main focus of our training even though all TKES will probably be discussed in each training.Handouts
22 AssessmentWhat question could you ask students to formatively assess their understanding of the standard(s):that requires them to communicate their reasoningand builds their confidence in providing answers on extended-response items – Georgia Milestones?
23 Ask This Not ThatInstead 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 Explain the meaning of the following statements.A. f(10) = B. f(a) = 20f(20) = b D. n = f(t)Problem from Illustrative MathematicsProblem from Illustrative Mathematics
24 Ask This Not ThatAlso 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.f(0) = 65 B. f(5) < f(10)f(40) = f(45) D. f(45) > f(60)Problem from Illustrative MathematicsProblem from Illustrative Mathematics
28 What are the Questions? Number of regions vs. Area of each region Draw the next step in the patternCreate an in/out tableFind the nth termGraph itWrite the recursive form of the equationIs it arithmetic or geometric?
29 Visual PatternsEach pair/group will be given a picture to study with some information.On chart paperDraw the sequence & next stepcomplete the tablewrite the equation in explicit & recursive formssketch the graphdetermine if you have an arithmetic or geometric sequence.Insert slides for additional tasks.Allow about 1 – 1.5 hours for teachers to do selected tasks from their grade level frameworks related to the topic/concept for the PL.
30 Task Review What CCGPS (content) was addressed? Domain, cluster, and standardsWhat SMPs were addressed?If the session has multiple grade levels, have them identify the standards at their grade level that lead to or build on this task.
31 Ask This Not ThatInstead 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.
32 Ask This Not ThatImagine that the following pattern continues: Row 1: 3 Row 2: 3 6 Row 3: Row 4: Row 5: What questions could we ask?Why use the number 2000? Why use 4? Is there another way to find the answer?
33 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 ]You can also ask basic conversion questions like how much would 1 quart of dry rice weigh?
34 Ask This Not That 5, 7, 9, 11, 13, … is a sequence. Zack said that the formula is t1 = 5, tn = tnEric 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]You can also ask basic conversion questions like how much would 1 quart of dry rice weigh?
35 Graph.tk Free graphing site Color-coded Only graphs functions Explore key features of a graphDomain/range, intercepts, end behavior,Explore transformationsUnit 3 Frameworks: High Functioning
36 Task Review What CCGPS (content) was addressed? Domain, cluster, and standardsWhat SMPs were addressed?If the session has multiple grade levels, have them identify the standards at their grade level that lead to or build on this task.
37 Implementation Resources Mathematics Assessment ProjectTools 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)This is a great site for tasks for middle grades and high school professional learning.
38 MAP FALsLesson 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 WorksheetsThe “Laws of Arithmetic” is a concept development
39 Comparing Investments Making Money - pre-assessment Odd One Out? - powerpoint slides Matching Game Double Your Money - powerpoint slides Making Money (revisited)15 minutes total5 min. naming; 10 minutes discussing it
40 Odd One Out? Investment 1 $100 Simple Interest Rate: 5% Investment 2 $400Simple Interest Rate: 5%How are these investment options similar/different?Investment 3$200Simple Interest Rate: 10%
41 Odd One Out? Investment 1 A = 500 × 1.064 Investment 2 A = 250 × 1.062 How are these investment options similar/different?Discuss how to find compound probability IF needed!!Investment 3A = 500 × 1.032
42 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.
43 Comparing Investments Solutions P1 F6 P2 F3 P3 F2 P4 F5 P5 F1 P6 F415 minutes total5 min. naming; 10 minutes discussing it
46 Double Your MoneyInvestment 1A = 500 × 1.06nWhich two investments will take exactly the same time to double the money?Investment 2A = 250 × 1.06nInvestment 3A = 500 × 1.03n
47 Task Review What CCGPS (content) was addressed? Domain, cluster, and standardsWhat SMPs were addressed?If the session has multiple grade levels, have them identify the standards at their grade level that lead to or build on this task.
48 GA DOE Implementation Resources https://www.georgiastandards.org/Common-Core/Pages/Math.aspxCommon Core ToolsSchedule of Unit webinarsRecordings:Standards for Mathematical PracticesGrade level overviewsUnit webinarsList Serve (subscribe to receive s from DOE)Learning VillageBegin this section about 30 – 40 minutes prior to the end of the session.The following slides provide resources for implementation at the grade level.The Implementation Resources section should just be to show the website and information included. The participants will have access to the ppt. so they can visit the websites themselves later.Be sure to point out the 1st two slides and show the Progressions document related to the concept being addressed in the day.
49 GA DOE GaDOE Wiki – Coordinate Algebra & Analytic Geometry Please visit to provide feedback, ask questions, and share ideas and resources.Multi-Grade Resources:Secondary Mathematics SpecialistsBrooke Kline –James Pratt –
50 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.”
51 Implementation Resources Illustrative Mathematics Project – “illustrates the range and types of mathematical work”This site has illustrated tasks for specific grade levels. Some of the tasks may be used for the multiple grade level sessions.
52 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.”
53 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, andInforming the development of item specifications and blueprints for the PARCC assessments in grades 3–8 and high school.”
54 PARCC Released Test Items Initial Set of Test Items and Task Prototypes Released
55 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.”This is a good site from which to get some tasks that can be used in the multiple grade level sessions.
56 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).”
57 Implementation Resources Achieve the CoreFree resourcesFounded by one of the contributing authors of the CCSS (Student Achievement Partners), now devoted to successful implementation
58 Objectives:examine the standards to determine what students should know, understand, and be able to dowork tasks aligned to standards, including tasks from the Framework unitsdetermine the Standards for Mathematical Practice (SMPs) to be integrated in tasks aligned to the standardsIdentify teacher actions to address TKES2 min.Read each objective. Go back to the list of expectations to identify those that will be addressed in the session.
59 LIVEBINDER linkAll materials from today including the ppt can be found ataccess key: RESACA
60 Now What? What does this mean for me and my students? Please complete the evaluation.Follow us on