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Planning to Implement CCSS-M Function Cluster:

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Planning to Implement CCSS-M

Function Cluster:

Interpret functions that arise in applications in terms of the context

Lynn Aring

OCTM VP-Secondary

Bay High School, retired

Lynn.Aring@gmail.com

2012 OCTM Annual Conference

October 18-19

Columbus, Ohio

What do the Standards for Mathematical Practice mean in the context of the conceptual category: Functions?

Students proficient in this standard

·know that solving a problem doesn't always mean solving word problems

·look at a problem verbally, numerically, graphically, and/or symbolically providing different entry points into solving a problem

·plan a solution pathway, rather than just jumping into a solution attempt

·transform algebraic expressions into a more useful form for graphing functions

·check answers to see if they make sense especially in contextual problems

·understand other solution/graphing methods and can see similarities and differences in the methods of others to their own solution/graphing method

What do the Standards for Mathematical Practice mean in the context of the conceptual category: Functions?

Students proficient in this standard

·have the ability to decontextualize-to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents

·have the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved

·pay attention to the units involved, checking that the final answer is not only numerically reasonable but that the algebraic operations used in solving an equation produce the correct units for the final answer

·know and flexibly use different properties of operations and objects

What do the Standards for Mathematical Practice mean in the context of the conceptual category: Functions?

Students proficient in this standard

·can listen to or read arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments

·can compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and if there is a flaw in the argument, explain what it is

·can understand and use stated assumptions, definitions, properties, postulates and previously established results in constructing solution methods, arguments, and proofs

Students proficient in this standard

·can create functions that model situations in everyday life, society, and the workplace

·routinely interpret functions in the context of the situation and reflect on whether the function make sense

The following standards in the conceptual category of Functions have been marked as modeling standards:

·Interpreting Functions 4,5,6,7

·Building Functions 1,2

·Linear, Quadratic, and Exponential Models-All

·Trigonometric Functions 1

Students proficient in this standard

·use estimation skills to estimate the output of a function(e.g. f(3))

·use mental math or paper and pencil for simpler calculations

·use paper and pencil for simpler algebraic manipulations and when writing a function in an alternative form.

·use graph paper and pencil to graph basic functions

·use a graphing calculator to graph more complex equations and to solve equations numerically or graphically

·use spreadsheets to look at both explicit and recursive functions numerically and graphically

·Use dynamic graphing software with sliders to explore transformations of functions(e.g. f(x+k) versus f(x)+K)

Students proficient in this standard

·communicate precisely to others

·use mathematical terminology such as, functions, relations, inverses, properly

·read and write symbolic expressions correctly(e.g. f(x) and f-1(x))

·label axes with appropriate scales and units

·round appropriately based on the context of the problem

Students proficient in this standard

·look closely to discern a pattern or structure

·can see complicated things, such as algebraic expressions, as single objects or as being composed of several objects

·can see the value of different forms of a function or expression(e.g.,quadratic equations in standard form, factored form, or vertex form will reveal different properties of the graphs of the functions)

Students proficient in this standard

·notice if calculations are repeated, and look for both general methods and for shortcuts

For example, after performing long division of polynomials multiple times, students may develop or at least understand synthetic division

From the Common Core State Standards Document

One variable is dependent on the other

Numerical inputs and outputs

Domain

Multiple Representations

Modeling

Linear

Exponential

Technology

From the Common Core State Standards Document

Recursion

From the Common Core State Standards Document

Conceptual Category

Domain

Cluster

From the Common Core State Standards Document

Conceptual Category: Functions

Function

Interpreting

Functions

Domain

Cluster

Standard

Standard

Standard

From the Common Core State Standards Document

Related Grade 8 Standards

Ohio Department of Education Website

Model Curriculum

Ohio Department of Education Website

Model Curriculum

Ohio Department of Education Website

Model Curriculum

Ohio Department of Education Website

Model Curriculum

Ohio Department of Education Website

Model Curriculum

Ohio Department of Education Website

Resources

Ohio Department of Education Website

Resources

Ohio Department of Education Website

Resources

Ohio Department of Education Website

Resources

Ohio Department of Education Website

Resources

From Appendix A

From Appendix A

Traditional Pathway

From Appendix A

Integrated Pathway

From the PARCC Model Content Frameworks

From the PARCC Model Content Frameworks

From the PARCC Model Content Frameworks

In Algebra 1, this cluster is classified as major. Standards 4, 5, and 6 are taught/tested in this course.

Assessment tasks

i. have a real world context

II. are limited to linear functions, square root functions, cube root functions. piecewise-defined functions(including step functions and absolute value functions) and exponential functions with domains in the integers

From the PARCC Model Content Frameworks

In Algebra 2, this cluster is also classified as major. Only standards 4 and 6 are taught/tested in this course.

Assessment tasks

i. have a real world context

II. tasks may involve polynomial, exponential, logarithmic, and trigonometric functions

From the PARCC Model Content Frameworks

From the PARCC Model Content Frameworks

In Mathematics 1, this cluster is classified as major. All 3 standards are taught/tested in this course. -------------------------------------------------------------------------------------------------------------

For Standard 4

i. Tasks have a real-world context

II. Tasks are limited to linear functions, square root functions, cube root functions, piecewise-defined functions(including step functions and absolute value functions), and exponential functions with domains in the integers.

For Standard 5

i. Tasks have a real-world context

II. Tasks are limited to linear functions, square root functions, cube root functions, piecewise-defined functions(including step functions and absolute value functions), and exponential functions with domains in the integers.

For Standard 6

i. Tasks have a real-world context

II. Tasks are limited to linear functions, square root functions, cube root functions, piecewise-defined functions(including step functions and absolute value functions), and exponential functions with domains in the integers.

From the PARCC Model Content Frameworks

In Mathematics 2 this cluster is classified as major. All three standards are taught/tested in this course.

For standard 4

i. Tasks have a real-world context

II. Tasks are limited to quadratic and exponential functions.

For standard 5

i. Tasks have a real-world context

II. Tasks are limited to quadratic functions.

For standard 6

i. Tasks have a real-world context

II. Tasks are limited to quadratic and exponential functions.

From the PARCC Model Content Frameworks

In Mathematics 3, this cluster is also classified as major. Only standards 4 and 6 are tested in this course

For Standard 4

I. Tasks have a real-world context

II. Tasks may involve polynomial, logarithmic, and trigonometric functions

For Standard 6

I. Tasks have a real-world context

II. Tasks may involve polynomial, logarithmic, and trigonometric functions

Domain: all reals between 0 and 7 inclusive

Range: All reals between 0 and 120 inclusive

120

Degrees

0

7

Time(secs)

Quadratic

Door is closing or the number of degrees is decreasing

Door is opening or the number of degrees is increasing

The graph appears to have a horizontal asymptote, so the door would never close

Opening, graph and table indicate number of degrees is increasing

0

100

100

75

50

31.3

18.8

10.9

Opening, Rate of change is positive indicating # of degrees is increasing

6.3

3.5

2.0

Cubic polynomial

You would need 4 points

(0,0)

(7,0)

(time, max degree)

one other point