4251
0011 0010 1010 1101 0001 0100 1011
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
42510011 0010 1010 1101 0001 0100 1011
High School MathThe Standard Based Way
Day 2
Nicole Spiller
West Georgia RESA
4251
0011 0010 1010 1101 0001 0100 1011
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.
4251
0011 0010 1010 1101 0001 0100 1011
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?
4251
0011 0010 1010 1101 0001 0100 1011
Housekeeping
• Breaks
• Cell Phones
• Restrooms
• Parking Lot
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
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%
4251
0011 0010 1010 1101 0001 0100 1011
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%
4251
0011 0010 1010 1101 0001 0100 1011
Pre-Assessment
• Question 3:
• Factoring Quadratics is taught in Unit two of Math I.
a) True b) False
4251
0011 0010 1010 1101 0001 0100 1011
Pre-Assessment
• Question 4:
• The Quadratic Formula is taught in Unit two of Math I?
a) True b) False
4251
0011 0010 1010 1101 0001 0100 1011
Pre-Assessment
• Question 5:
• The process standards are the same K-12.
a) True b) False
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
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.
4251
0011 0010 1010 1101 0001 0100 1011
“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
4251
0011 0010 1010 1101 0001 0100 1011
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!
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
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.
4251
0011 0010 1010 1101 0001 0100 1011
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.
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
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.
4251
0011 0010 1010 1101 0001 0100 1011
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.
4251
0011 0010 1010 1101 0001 0100 1011
Multiple Representations
• Read article “Representation: Show Me the Math”.
• Find one statement you agree with and one that you disagree with
42510011 0010 1010 1101 0001 0100 1011
Pictures
ManipulativeModels
Symbols/Formal Notation
Tables/ChartsGraphs
4251
0011 0010 1010 1101 0001 0100 1011
Tiling Learning Task
• Key Points:– Turning patterns into algebraic expressions– Writing algebraic expressions– Justifying mathematical thinking– Determining relationships between expressions
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
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.
4251
0011 0010 1010 1101 0001 0100 1011
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)
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
Key Standards
• MM1A2 – Students will simplify and operate with radical expressions, polynomials, and rational expressions
• MM1A3 – Students will solve simple equations
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
Selected Terms and Symbols
• We will create this list
4251
0011 0010 1010 1101 0001 0100 1011
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.
4251
0011 0010 1010 1101 0001 0100 1011
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
4251
0011 0010 1010 1101 0001 0100 1011
I’ve Got Your NumberA Learning Task
• Key Points:– An introduction to algebraic identities– Introduction to factoring
• This task is tiered
4251
0011 0010 1010 1101 0001 0100 1011
Just JoggingA Learning Task
• Key Points:– Writing Algebraic Expressions– Writing Algebraic Equations using formulas
4251
0011 0010 1010 1101 0001 0100 1011
LaddersA Learning Task
• Key Points– Writing Functions– Basic Analysis of Functions
4251
0011 0010 1010 1101 0001 0100 1011
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.
4251
0011 0010 1010 1101 0001 0100 1011
End of Day 2