metro resa...building leaders of teaching and learning keys to ccgps coordinate algebra unit 3 sarah...
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Metro RESA...Building leaders of teaching and learning
Keys to CCGPS
Coordinate AlgebraUnit 3
Sarah [email protected]
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LEGO Code
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LEGO Code
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• 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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Introductions and Expectations?• Introduce yourself:
– name, school, grade level AND• What are your expectations for today?
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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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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
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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
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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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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
From Good Questions 5-8
• Complete the chart.
• What is the rule?
• Add three more pairs of In and Out values.
In Out
aardvark a
giraffe a
hippo o
otter ?
? e
? ?
? ?
? ?
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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, …
In Out
5 8
10 13
3 6
0 ?
? 45
? ?
? ?
? ?
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, …
In Out
0 1
1 2
-1 1/2
4 ?
? ?
? 128
? ?
5 32
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Task Review
• What CCGPS (content) was addressed?• Handout standards for CA Unit 3.
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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 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.
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 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t 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
CodeDomain
StandardA.SSE.2
Conceptual
Category (5+M)
Modeling Symbol
Cluster Heading
Bibb County
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Number & Quantity Algebra Functions Geometry Statistics &
Probability
The Real Number System
Seeing Structure in Expressions
Interpreting Functions Congruence Interpreting Categorical
and Quantitative Data
QuantitiesArithmetic with Polynomials &
Rational Expressions
Building FunctionsSimilarity, 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
InequalitiesTrigonometric
FunctionsExpressing Geometric
Properties with Equations
Using Probability to Make Decisions
Geometric Measurement and
Dimension
Modeling with Geometry
Do
mai
ns
Conceptual Categories & Domains
M o d e l i n g
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What SMPs were addressed?
17GaDOE 7th grade CCGPS Overview Presentation
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• What considerations need to be made in order to meet different student learning needs and address individual learning differences? – SWD– ELs– others
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SMPs aligned…
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TKES - Standards 1 – Professional Knowledge 2 – Instructional Planning 3 – Instructional Strategies 4 – Differentiated Instruction 5 – Assessment Strategies 6 – Assessment Uses 7 – Positive Learning Environment8 – Academically Challenging Environment9 – Professionalism10 - Communication
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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?
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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) = 100.3 B. f(a) = 20
C. f(20) = b D. n = f(t)
Problem from Illustrative Mathematics
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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.
A. f(0) = 65 B. f(5) < f(10)
C. f(40) = f(45) D. f(45) > f(60)Problem from Illustrative Mathematics
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What are the Questions?
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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?
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Paper Folding
• Fold a piece of paper….
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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?
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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.
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Task Review
• What CCGPS (content) was addressed?– Domain, cluster, and standards
• What SMPs were addressed?
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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.
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Ask This Not ThatImagine that the following pattern continues:
Row 1: 3Row 2: 3 6Row 3: 3 6 9Row 4: 3 6 9 12Row 5: 3 6 9 12 15
What questions could we ask?
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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.]
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Ask This Not That5, 7, 9, 11, 13, … is a sequence.
Zack said that the formula is t1 = 5, tn = tn-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]
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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
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Task Review
• What CCGPS (content) was addressed?– Domain, cluster, and standards
• What SMPs were addressed?
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Implementation ResourcesMathematics 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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MAP FALsLesson Plans – Concept development vs.
Problem SolvingProcess – 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 slidesWorksheets
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Comparing Investments
Making Money - pre-assessment
Odd One Out? - powerpoint slides
Matching Game
Double Your Money - powerpoint slides
Making Money (revisited)
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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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Odd One Out?
P-41
Investment 1
A = 500 × 1.064
Investment 2
A = 250 × 1.062
Investment 3
A = 500 × 1.032
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Comparing InvestmentsMatch 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.
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Comparing Investments Solutions
P1 F6
P2 F3
P3 F2
P4 F5
P5 F1
P6 F4
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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
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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
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Double Your Money
P-46
Investment 1
A = 500 × 1.06n
Investment 2
A = 250 × 1.06n
Investment 3
A = 500 × 1.03n
Which two investments will take exactly the
same time to double the money?
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Task Review
• What CCGPS (content) was addressed?– Domain, cluster, and standards
• What SMPs were addressed?
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GA DOE Implementation Resourceshttps://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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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.
• Multi-Grade Resources: http://ccgpsmathematics9-10.wikispaces.com/Multi+Grade+Resources
• Secondary Mathematics Specialists• Brooke Kline – [email protected] • James Pratt – [email protected]
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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/
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Implementation Resources
• Illustrative Mathematics Project – “illustrates the range and types of mathematical work” http://illustrativemathematics.org/
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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/
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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
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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
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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.”
http://insidemathematics.org/index.php/home
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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
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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
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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
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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=1477222
access key: RESACA
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Now What?• What does this mean for me and my students?
Follow us on Twitter @MRESAmath
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