# Coordinate Algebra Unit 3 Sarah Ledford

## Presentation on theme: "Coordinate Algebra Unit 3 Sarah Ledford"— Presentation transcript:

Coordinate Algebra Unit 3 Sarah Ledford sarah@SarahLikesMath.com
Keys to CCGPS Coordinate Algebra Unit 3 Sarah Ledford

LEGO Code 15 minutes total 5 min. naming; 10 minutes discussing it

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

Introductions and Expectations?
Introduce yourself: name, school, grade level AND What 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.

Group Norms and Housekeeping
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 This 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.

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 2 min. Read each objective. Go back to the list of expectations to identify those that will be addressed in the session.

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?
In Out aardvark a giraffe hippo o otter ? e Complete 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).

From Good Questions 5-8 Complete the chart. What is the rule?
In Out 5 8 10 13 3 6 ? 45 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, … 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).

From Good Questions 5-8 Complete the chart. What is the rule?
In Out 1 2 -1 1/2 4 ? 128 5 32 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, … 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).

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.

Format of High School Standards
Conceptual Category (5+M) Domain Algebra Seeing Structure in Expressions A-SSE Interpret 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. Code Cluster Heading Modeling Symbol Standard A.SSE.2 High school organization Hide 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 students Bibb County

Conceptual Categories & Domains
Number & Quantity Algebra Functions Geometry 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 M o d e l i n g High school organization Hide 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…

Another representation by Bill McCallum, lead writer of the Mathematics CCSS Handout GaDOE 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

SMPs aligned… MRESA staff aligned the College and Career Readiness Anchor Standards (ELA) and considerations for ELs to the Standards for Mathematical Practice. Handout

TKES - Standards 2 – Instructional Planning
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 The 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

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?

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 Explain the meaning of the following statements. A. f(10) = B. f(a) = 20 f(20) = b D. n = f(t) Problem from Illustrative Mathematics Problem from Illustrative Mathematics

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. f(0) = 65 B. f(5) < f(10) f(40) = f(45) D. f(45) > f(60) Problem from Illustrative Mathematics Problem from Illustrative Mathematics

What are the Questions?

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?

Paper Folding Fold a piece of paper….

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?

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. 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.

Domain, cluster, and standards What 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.

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.

Ask This Not That Imagine 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?

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?

Ask This Not That 5, 7, 9, 11, 13, … is a sequence.
Zack said that the formula is t1 = 5, tn = tn 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] You can also ask basic conversion questions like how much would 1 quart of dry rice weigh?

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

Domain, cluster, and standards What 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.

Implementation Resources
Mathematics Assessment Project 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) This is a great site for tasks for middle grades and high school professional 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 The “Laws of Arithmetic” is a concept development

Comparing Investments
Making Money - pre-assessment Odd One Out? - powerpoint slides Matching Game Double Your Money - powerpoint slides Making Money (revisited) 15 minutes total 5 min. naming; 10 minutes discussing it

Odd One Out? Investment 1 \$100 Simple Interest Rate: 5% Investment 2
\$400 Simple Interest Rate: 5% How are these investment options similar/different? Investment 3 \$200 Simple Interest Rate: 10%

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 3 A = 500 × 1.032

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.

Comparing Investments Solutions
P1 F6 P2 F3 P3 F2 P4 F5 P5 F1 P6 F4 15 minutes total 5 min. naming; 10 minutes discussing it

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 15 minutes total 5 min. naming; 10 minutes discussing it

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 15 minutes total 5 min. naming; 10 minutes discussing it

Double Your Money Investment 1 A = 500 × 1.06n Which two investments will take exactly the same time to double the money? Investment 2 A = 250 × 1.06n Investment 3 A = 500 × 1.03n

Domain, cluster, and standards What 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.

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 s from DOE) Learning Village Begin 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.

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 Specialists Brooke Kline – James Pratt –

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.”

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.

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.”

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.”

PARCC Released Test Items
Initial Set of Test Items and Task Prototypes Released

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.

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).”

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

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 2 min. Read each objective. Go back to the list of expectations to identify those that will be addressed in the session.

LIVEBINDER link All materials from today including the ppt can be found at access key: RESACA

Now What? What does this mean for me and my students?