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This PowerPoint is from Day 2 of Math Week. It covers…1. A comparison of QCC vs. GPS2. The Process Standards3. The math of Unit 24. The math of Part 2 of Unit 4

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High School MathThe Standard Based Way

Day 2

Nicole Spiller

West Georgia RESA

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Problem of the Day

  This question requires you to show your work and explain your reasoning. You may use drawings, words, and numbers in your explanation. Your answer should be clear enough so that another person could read it and understand your thinking. It is important that you show all your work.

One plan for a state income tax requires those persons with income of $10,000 or less to pay no tax and those persons with income greater than $10,000 to pay a tax of 6 percent only on the part of their income that exceeds $10,000. A person's effective tax rate is defined as the percent of total income that is paid in tax. Based on this definition, could any person's effective tax rate be 5 percent? Could it be 6 percent? Explain your answer. Include examples if necessary to justify your conclusions.

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Essential Questions

• What is the Math of Unit Two?• What is the Math of part two of Unit Four?• What level of factoring is expected by the

end of unit two?• How are the GPS standards different from

the QCC’s?• What are the process standards and why are

they important?

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Housekeeping

• Breaks

• Cell Phones

• Restrooms

• Parking Lot

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Activator

• On your own, write down the 5 most words or phrases that define or describe the Math I standards compared to the QCC’s

• Work with a partner and combine your work into 3 words or phrases

• Now as a table, choose the 1 one word or phrase that best defines/describes this transition

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Pre Assessment

• Question 1:

• What percent of traditional Algebra I is now taught before students reach high school?

a) 20% b) 40% c) 60% d) 80%

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Pre Assessment

• Question 2:

• What percent of traditional Geometry is now taught before students reach high school?

a) 20% b) 40% c) 60% d) 80%

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Pre-Assessment

• Question 3:

• Factoring Quadratics is taught in Unit two of Math I.

a) True b) False

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Pre-Assessment

• Question 4:

• The Quadratic Formula is taught in Unit two of Math I?

a) True b) False

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Pre-Assessment

• Question 5:

• The process standards are the same K-12.

a) True b) False

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What Has Changed in 9th grade Math

• There is a stack of cards on your table– Blue (algebra I QCC’s)– Yellow (Geometry QCC’s) and– Green (Algebra II QCC’s)

Using your GPS standards for grades 6-9 place QCC cards under the grade level where you feel the standard is now taught

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What does this mean?

• Look at the color coded wall.

• Discuss at your table what this means for you as a teacher and what this means for our students.

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“No matter how lucidly and patiently

teachers explain to their students,

they cannot understand for their students.”

Deborah Schifter & Cathy Fosnot

Reconstructing Mathematics Education:

Stories of Teachers Meeting the Challenge of Reform

Teachers College Press: 1993

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Process Standards• If the Content Standards are “the what” then

the Process Standards are “the how”

• Every lesson should focus on one or more content standards as well as incorporating one or more of the process standards

• These standards encourage student engagement and understanding!

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The Process 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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MM1P1. Students will solve problems (using appropriate technology).

a. Build new mathematical knowledge through problem solving.

b. Solve problems that arise in mathematics and in other contexts.

c. Apply and adapt a variety of appropriate strategies to solve problems.

d. Monitor and reflect on the process of mathematical problem solving.

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MM1P2. Students will reason and evaluate mathematical arguments

a. Recognize reasoning and proof as fundamental aspects of mathematics. b. Make and investigate mathematical conjectures. c. Develop and evaluate mathematical arguments and proofs. d. Select and use various types of reasoning and methods of proof.

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MM1P3. Students will communicate mathematically.

a. Organize and consolidate their mathematical thinking through communication. b. Communicate their mathematical thinking coherently and clearly to peers, teachers, and others. c. Analyze and evaluate the mathematical thinking and strategies of others. d. Use the language of mathematics to express mathematical ideas precisely

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MM1P4. Students will make connections among mathematical ideas and to other

disciplines.

a. Recognize and use connections among mathematical ideas.

b. Understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

c. Recognize and apply mathematics in contexts outside of mathematics.

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MM1P5. Students will represent mathematics in multiple ways.

a. Create and use representations to organize, record, and communicate mathematical ideas.

b. Select, apply, and translate among mathematical representations to solve problems.

c. Use representations to model and interpret physical, social, and mathematical phenomena.

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Multiple Representations

• Read article “Representation: Show Me the Math”.

• Find one statement you agree with and one that you disagree with

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Pictures

ManipulativeModels

Symbols/Formal Notation

Tables/ChartsGraphs

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Tiling Learning Task

• Key Points:– Turning patterns into algebraic expressions– Writing algebraic expressions– Justifying mathematical thinking– Determining relationships between expressions

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Unit Four Part 2

• Testing Learning Tasks

• These tasks use the graphing calculator

• Use formal expressions for combinations and permutations

• Review mean deviation and IQR

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Unit 2 – Algebra Investigations

• 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 area of basic figures and use the Pythagorean Theorem

– Students will apply the basic function concepts of domain, range, rule of correspondence, and interpreting graphs of functions learned in Unit One.

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Overview

• Intensive work in writing linear and quadratic expressions to represent quantities in a real-world context

• An initial focus of developing students abilities to read and write meaningful statements using the language of Algebra

• A study of the special products (NO FACTORING)

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Enduring UnderstandingsEssential Questions

• Algebraic Equations can be identities that express properties of operations

• Equivalence of algebraic expressions means that they have the same numerical values

• Equivalent expressions are useful tools in computation and problem solving

• It takes only one counterexample to show that a general statement is not true

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Key Standards

• MM1A2 – Students will simplify and operate with radical expressions, polynomials, and rational expressions

• MM1A3 – Students will solve simple equations

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Related Standards

• MM1G2 – Students will understand and use the language of mathematical argument and justification

• 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 6-8 standards relating to:– writing algebraic expressions,– Performing operations with algebraic

expressions, and– Working with relationships between variable

quantities

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Selected Terms and Symbols

• We will create this list

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Tasks

• Task 1: Tiling Task: This tasks launches the unit. • Tasks 2 – 5: Activities are designed to allow

students to build their own algebraic understanding through exploration.

• Task 6: Culminating task: Should demonstrate the type of assessment activities students should be comfortable with by the end of the unit.

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Tiling Pools A Learning Task

• Key Points: – A continuation of how different ways of

reasoning can lead to different, but equivalent expressions

– A continuation of mathematical justification

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I’ve Got Your NumberA Learning Task

• Key Points:– An introduction to algebraic identities– Introduction to factoring

• This task is tiered

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Just JoggingA Learning Task

• Key Points:– Writing Algebraic Expressions– Writing Algebraic Equations using formulas

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LaddersA Learning Task

• Key Points– Writing Functions– Basic Analysis of Functions

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Planning for the PromA Culminating Task

• Four questions that incorporate all tasks in this unit.

• This could be done as a portfolio or as an summative assessment at then end of the unit.

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End of Day 2