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This PowerPoint is from Day 1 of Math Week. It covers…1. An overview of GPS 2. An overview of Standards-Based Instruction2. How the frameworks are set up3. An overview of Unit 1of Math I4. An overview of Part 1 of Unit 4

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High School MathThe Standards Based Way

Day 1

Nicole Spiller

West Georgia RESA

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Problem of the Day

• The following question refers to the following pattern of dot-figures.

 

If this pattern of dot-figures is continued, how many dots will be in the 100th figure? 

a)100 b) 101 c) 199 d) 200 e) 201

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Essential Questions

• How will teaching math be different under GPS? What is standards-based instruction all about?

• What content is in Unit One of Math I?

• What content is in part one of Unit Four?

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Housekeeping

• Breaks

• Cell Phones

• Restrooms

• Parking Lot

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NameplatesNameplates

• Fold your cardstock lengthwise (like a hot dog).

• On the front, write your name, position, and school or agency.

• On the back, design a vanity plate. It could be one you have now or one you would like to have.

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Activator

• Divide into teams of two

• Partner A needs to face away from the screen

• Partner B needs to face the screen

• When time begins, Partner B will have one minute to try and get Partner A to say 6 words/phrases

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Round One• Any questions?• Ready…..

• Essential Question• Task• Direct Instruction• Transformation• Function• Fiona

Set……. GOOOOOOO…

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Round Two

• Any questions?• Ready…..

• Standard• Assessment• Rate of Change• Pattern• Hypothesis• Alice

Set…. GOOOOO….

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Pre-Assessment

• Take a moment and complete the pre-assessment on your own.

• Does this assessment give you an idea of our goals for the day? Does it match our EQ?

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GPS

• Adapted the following characteristics from the Japanese mathematics curriculum:– Fewer topics at each level– More rigor and depth– An integrated curriculum– A clear, focused path to higher (college)

mathematics

Math I GPS Research and Resource Manual

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Characteristics of the GPS

• Rigor

• Relevance

• Relationships, and

• Reasoning

Math I GPS Research and Resource Manual

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Standards Based InstructionWhat it is not!

• Elimination of Teaching• Passive Educator• Playing Games• Loss of Rigor

Read pages 2-5 of: What is a Standards Based Curriculum and highlight three key points

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Standards Based InstructionWhat it is!

• Relevant to Students

• Student Engagement

• Rigorous

• Shared Decision Making with Students

• A mix of Instructional Techniques

Review handout on SBC and SB Math

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Georgia Math Frameworks

• The BIG Picture

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GPS Standards

UnitsOverview

EU/EQ

Standards Conceptsand Skills to Maintain

Selected Terms and

Symbols

Evidence of Learning

Strategies forTeaching and

Learning

Tasks

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Unit Overview

• Describes the primary focus of the Unit

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Enduring UnderstandingsEssential Questions

• The goal of the unit

• What you want the students to know and be able to do when the lesson or unit is complete

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Standards

• Key Standards –Standards addressed in the unit.

• Related Standards – Standards that support the unit.

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Concepts/Skills To Maintain

• Previously Covered Topics that…– Should have been mastered in previous grades– Are used in this unit in more complex situations

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Selected Terms and Symbols

• New vocabulary introduced in this unit

• New symbols introduced in this unit

• There is an expectation that these terms/symbols will be on state tests

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Evidences of Learning

• A list of competencies that should be mastered by the end of the unit

• Competencies are a delineation of what students should know and be able to do based on the key standards

• Evidences of Learning can be teaching activities OR Culminating assessments

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Evidences of LearningExamples

• Student Writing• Observation• Conferences• Portfolios• Tests/Quizzes• Formative Assessments• Summative Assessments• Performance tasks• TOTD

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Strategies for Teaching and Learning

• Are common to all units

• Used throughout the Curriculum to encourage Mathematical Literacy

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Types of Strategies• Gallery Walk

• Peer Interviews

• Reciprocal teaching

• Jigsaw

• Centers/Stations

• Lecture/Notes

• Scavenger Hunt

• Scaffolding/Tiered Assignments

• Venn Diagrams

• Graphic Organizers

• Word Assoc – Picture Cards

• Activators3-2-1ClozeThink, Pair Share5 – 3- 1Quick TalkWord SplashGive 1 /Get 1

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Tasks

• Tasks represent the depth, rigor, and complexity expected of all students.

• Tasks DO NOT represent a complete curriculum

• May be used for assessment or as teaching and learning activities

• Pre-Assessment critical component to success

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Fiona’s FunctionsAn Exploration Task

• Key Points:– Function Notation

– Domain, range

– Represent functions in a variety of ways

– Use of technology

– Thought process of when and why points on a graph are connected

– Using a pattern to complete a table and write a function equation

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Fiona’s Functions An Exploration Task

Note the following….– What math topics/standards are covered?

– What are appropriate manipulatives for this task?

– How are multiple representations made available?

– What questions do you think students will have?

– What questions would a teacher have?

– Is there a need for whole group instruction and if so, when?

– What would you want previewed/reviewed in Math support?

– What parts of the task are critical? What parts could be eliminated?

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Unit Four Spinning Tasks

• These tasks develop the idea of what random and fair mean.

• They also develop the concept of experimental and theoretical probability

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Unit 1 – Function Families

• Prerequisites – Students need to have worked extensively

with operations on integers, rational numbers, and square roots of non-negative numbers

– Students are assumed to have a deep understanding of linear relationships between variable quantities

– Students should know how to find basic areas and volume of rectangular prisms

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Overview of Unit 1

• Intensive work with functions– Function notation– Tabular, graphical, and Algebraic form– Distinction between discrete and continuous

domain– View of graphs as whole objects– Use standard techniques to draw graphs with

unbounded domains

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Overview of Unit 1

• Logic– Introduction to Propositional Logic

• Conditional statements

• Converses

• Inverses

• Contrapositives

• Use of logic to teach Absolute Value Graph and transformations

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Overview of Unit 1

• Basic Function Families– Real-World Contexts– Work with vertical transformations

• Shifts

• Stretches

• Shrinks

• Reflections

• Change in graph as related to change in formula

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Overview of Unit 1

• Key Points– Use a table to introduce a new function, if the

domain includes negative numbers or fractions, be sure they are included in the table

– Do extensive graphing by hand– Be extremely careful In the use of language

• Example: Always use the name of the function f, to refer to the entire function, and f(x) to refer to output when the input is x.

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Enduring UnderstandingsEssential Questions

• Functions have three parts– Domain– Range– A rule or statement about input/output

• The Domain and rule determine the range• Graphs are geometric representations of functions• Functions are equal if they have the same domain and rule• Function notation is an efficient way to define and

communicate functions• Variables are arbitrary – changing a variable does not

change the function

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Enduring UnderstandingsEssential Questions

• Rate of Change– Average rate of change as a a function– Extends to average rate of change of revenue– Contrast constant rates of change to variable

rates of change (i.e. linear vs. non-linear)

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Enduring UnderstandingsEssential Questions

• Logical Equivalence is a concept that applies to the form of a conditional statement

• A conditional statement and its contrapositive are logically equivalent

• Neither the converse nor inverse of a conditional statement is logically equivalent to the statement

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Key Standards

• MM1A1 – Students will explore and interpret the characteristics of functions using graphs, tables, and simple algebraic techniques (parts a-g)

• Note: Transformations are previewed in this unit

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Key Standards

• MM1G2: students will understand and use the language of mathematical argument and justification (parts a-b)

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Related Standards

• MM1P1: Students will solve problems (using appropriate technology)

• MM1P2: Students will reason and evaluate mathematical arguments

• MM1P3: Students will communicate mathematically

• MM1P4: Students will make connections among mathematical ideas and to other disciplines

• MM1P5: Students will represent mathematics in multiple ways

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Concepts/Skills to Maintain

• Students will…– Apply and extend the Grade 7-8 standards

relating to writing algebraic expressions,– evaluating quantities using algebraic expressions,– understanding inequalities in one variable, and– understanding relations and liner functions

…as they develop much deeper and more sophisticated understanding of relationships between to variables

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Selected Terms and Symbols

• Need to create for Unit I

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Evidence of Learning*

• Students will be able to use graphs, tables, and algebra to represent functions.

• Students will be able to translate between a situation and function notation.

• Students will be able to determine the ‘truth’ of an argument.

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Strategies of Teaching and Learning

• Jigsaw

• Gallery Walk

• Observation

• Pre-Assessment

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Tasks• Task 1: Fiona’s Functions: Intended to Launch the

Unit. Its primary focus is introducing function notation and a more formal approach to functions

• Tasks 2 thru 7: Learning tasks that extend students knowledge of functions through in depth consideration of domain, range, average rate of change, and other characteristics of functions

• Task 8: Designed to demonstrate the type of assessment activities students should be comfortable with by the end of the unit.

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Fences and FunctionA Learning Task

• Key Points:– Boundaries of Domains– The effect input values have on output– Application of functions

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From Wonderland to FunctionlandA Learning Task

• Key Points:– Introduction to concept of logic– Idea of converse, inverse, contrapositive– Idea of conditional Statement– Absolute Value function is embedded within

this task

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Sequences as FunctionsA Learning Task

• Key Points:– Finite and infinite series – Domain and Range of Sequences

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Walking, Falling, and Making MoneyA Learning Task

• Linear (constant) rate of change compared to varied rates of change

• Introduction of Quadratic Curve

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Southern Yard and GardenA Learning Task

• Introduction of Inverse Function

• Introduction of Square Root Function

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Painted CubesA Learning Task

• Stretch and Flip of Quadratic Function

• Introduction to Cubic Function

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Ye Old Village ShoppesCulminating Task

1/2. Assessment of basic function notation and application

3. Assessment of Quadratic Function4/5. Assessment of Absolute Value Graph and

Transformations6/7. Assessment of Rate of Change8. Assessment of sequences9. Assessment of Cubic Function10/11. Assessment of Logic

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End of Day 1