Metro RESA...Building leaders of teaching and learning Keys to CCGPS Coordinate Algebra Unit 3 Sarah...

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?


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


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


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


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


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

? ?

? ?

? ?





• Write your rule in words and as an equation.


• Create sequence with inputs 1, 2, 3, 4, …

In Out

5 8

10 13

3 6

0 ?

? 45

? ?

? ?

? ?





• Write your rule in words and as an equation.


• Create sequence with inputs 1, 2, 3, 4, …

In Out

0 1

1 2

-1 1/2

4 ?

? ?

? 128

? ?

5 32


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


• 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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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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• 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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• 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



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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)

http://map.mathshell.org/


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


Investment 3$200



Odd One Out?

P-41

Investment 1

A = 500 × 1.064

Investment 2

A = 250 × 1.062

Investment 3

A = 500 × 1.032


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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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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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?


Task Review



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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

https://www.georgiastandards.org/Common-Core/Pages/Math.aspx


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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http://ccgpsmathematics9-10.wikispaces.com/

http://ccgpsmathematics9-10.wikispaces.com/Multi+Grade+Resources

http://ccgpsmathematics9-10.wikispaces.com/Multi+Grade+Resources

mailto:[email protected]

mailto:[email protected]


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



• Illustrative Mathematics Project – “illustrates the range and types of mathematical work” http://illustrativemathematics.org/

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http://illustrativemathematics.org/



• 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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http://www.ccsstoolbox.org/


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


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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http://www.parcconline.org/initial-set-test-items-and-task-prototypes-released

http://www.parcconline.org/initial-set-test-items-and-task-prototypes-released



• 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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http://insidemathematics.org/index.php/classroom-video-visits

http://insidemathematics.org/index.php/tools-for-teachers

http://insidemathematics.org/index.php/video-tours-of-inside-mathematics

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



• 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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http://www.mathccc.org/



• 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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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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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

Please complete the evaluation.http://bit.ly/ref_eval

https://twitter.com/MRESAmath

https://twitter.com/MRESAmath

Date post:	14-Dec-2015
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Metro RESA...Building leaders of teaching and learning Keys to CCGPS Coordinate Algebra Unit 3 Sarah...

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