Subject(s)

High School Mathematics

Grade/Course

Math I

Unit of Study

Unit 1:  Patterns of Change

Unit Type(s)

❑Topical  ❑ X Skills-based  ❑  Thematic 

Pacing

15 days for Semester Block & A-Day/B-Day; 20 days for Middle School

Unit Abstract

Understanding relationships between variables is key to the study of algebra and is the focus of this unit of study. Exploring a wide variety of relationships between variables from real-world situations introduces students to the broad idea of rate of change.  Connecting rates of change to patterns found in graphs, tables, and algebraic rules gives students an opportunity to think about representing the relationship between two variables in a variety of ways.  Students are introduced to iterative or recursive change, using the words NOW and NEXT to get a sense of recursive change.  Students also focus on how to write symbolic rules for relations among variables.  This unit also explores the use of the table-building and graphing capabilities of their calculators to study linear and nonlinear relationships.

Common Core Essential State Standards

Conceptual Category:  Number and Quantity; Functions

Domain:    1) Quantities (N-Q)

                  2) Interpreting Functions (F-IF)

                  3) Building Functions (F-BF)

Cluster:     1) Reason quantitatively and use units to solve problems. (N-Q)

                  2) Understand the concept of a function and use function notation. (F-IF)

                      Analyze functions using different representations. (F-IF)

                  3) Build a function that models a relationship between two quantities. (F-BF)

                      Build new functions from existing functions. (F-BF)

Standards:   N-Q.1  USE units as a way to understand problems and to guide the solution

                                of multi-step problems; CHOOSE and INTERPRET units consistently

                                in formulas;  CHOOSE and INTERPRET the scale and the origin in

                                graphs and data displays.

         N-Q.2  DEFINE appropriate quantities for the purpose of descriptive

                     modeling.

                    N-Q.3  CHOOSE a level of accuracy appropriate to limitations on

                                measurement when reporting quantities.

                    F-IF.3  RECOGNIZE that sequences are functions, sometimes DEFINED

                               recursively, whose domain is a subset of the integers. For example,

                               the Fibonacci sequence is defined recursively by f(0) = f(1) = 1,

                               f(n+1)  = f(n) + f(n-1) for n ≥ 1.

F-IF.9  COMPARE properties of two functions each represented in a

                                 different way (algebraically, graphically, numerically in tables, or by

                                 verbal descriptions).

Note: At this level, focus on linear, exponential and quadratic functions.

t straight up into the air

                    F-BF.1a  WRITE a function that DESCRIBES a relationship between two

                                  quantities.

a)    Determine an explicit expression, a recursive process, or steps for calculation from context.

Note:  At this level, limit to addition or subtraction of constant to linear, exponential or quadratic functions or addition of linear functions to linear or quadratic functions.

         F-BF.2  WRITE arithmetic and geometric sequences both recursively and

                       with an explicit formula, USE them to model situations, and

                       TRANSLATE  between the two forms.

Note:  At this level, formal recursive notation is not used.  Instead, use of informal recursive notation (such as NEXT=NOW+5 starting at 3) is intended.

         F-BF.3  IDENTIFY the effect on the graph of replacing f(x) by f(x) + k, k f(x),

                       f(kx), and f(x + k) for specific values of k (both positive and negative);

                       FIND the value of k given the graphs. EXPERIMENT with cases and

                       ILLUSTRATE an explanation of the effects on the graph using

                       technology.  

Note: At this level, limit to vertical and horizontal translations of linear and exponential functions.  Even and odd functions are not addressed.