# A.B1B - Linear Functions - Texarkana Independent School District # Focus Plan

Texarkana Independent School District

PERIOD:

1 st six weeks

Teacher: Ronda Jameson

PLAN CODE:

Course/subject:

Time allotted for instruction:

M11.1.1

Math 11

2 class periods on block

Title: Linear Functions I

Lesson TOPIC:

TAKS Objective:

FoCUS TEKS and

Student Expectation:

Students will understand that a function represents a relationship in which one quantity is dependent upon the value of another quantity.

Functions can be represented in a number of ways (graphs, equations, tables, etc.) Students will identify functions, represent functions, and translate among various representations of functions. They will recognize and name independent and dependent variables in a functional relationship.

Objective 1: The student will describe functional relationships in a variety of ways.

A. B1 (B) The students uses data sets to determine functional relationships between quantities

Supporting TEKS and

Student Expectations:

A. B1 (A) The student understands that a function represents a dependence of one quantity on another and can be described in a variety of ways.

Concepts

Identify the difference between a relation and a function

Use data sets to determine functional relationships between quantitites

Use properties and attributes of functions and apply functions to problem situations.

Enduring Understandings/Generalizations/Principles

The student will understand that

A function is a relation that assigns exactly one value of the dependent variable to each value of the independent variable.

Describe functional relationships by selecting an equation or inequality that describes one variable in terms of another variable

The student in solving problems, collects data, records results, organizes the data, makes a graph, and interprets the results.

Division of Curriculum and Instruction

School Improvement Department

Texarkana Independent School District

I. Sequence of Activities (Instructional Strategies)

A. Focus/connections

Understanding functional relationships is an essential skill for student success on 11 th

grade TEKS. More than half (52%) of the student expectations which are tested on

TAKS at the exit level are connected to functions or functional relationships.

B. Instructional activities

(demonstrations, lectures, examples, hands-on experiences, role play, active learning experience, art, music, modeling, discussion, reading, listening, viewing, etc.)

Overhead sheet sequence will trace the evolution of the understanding of functional relationships from grades 611. Teacher will build a “ladder” for understanding functional relationships as she guides students through the TAKS released test items for grades 6-

C.

11. As teacher works through the sequence of overhead sheets, he should teach/review concepts which build a foundation for understanding functions. These concepts include:

Vertical line test, mapping, “x” and “y” values in a table.

Guided activity

Activity #1: (Introduction to Functions I)

Introduce this lesson by giving “real-life” examples of dependent relationships. Students write a sentence which describes a dependent relationship and identify the independent and dependent quantities.

Example: My grade in this class depends on the number of hours I study.

My moth er’s mood depends on the cleanliness of our house.

Activity #2: Height vs. Distance: Toy Cars Activity

In order for students to have a clear and lasting understanding of functional relationships, it is imperative that they become proficient in recording data in which the relationship between two variables is demonstrated. Students will work in groups of 2-4 to set up a clarifying activity (Height vs. Distance: toy cars). Students will record data, make a table, create a graph, and summarize their data for the class. Teacher will guide understanding by circulating between groups, facilitating cooperation, and checking for understanding.

D. Accommodations/modifications

E.

Some students will need more help than others on the instructional activities. These students may be paired with a partner or given extra guidance from the instructor.

Enrichment

Activity #3: Swinging Functions: Pendulum Activity

Students make pendulums and measure the period of the pendulums, using different lengths of string. Students record their data, make a table, and create a scatter plot.

Using their findings, students predict the period for any given string length.

Division of Curriculum and Instruction

School Improvement Department

Texarkana Independent School District

Activity #4: Crickets – Nature’s thermometer

Students determine and use functions to examine the relationship between the number of chirps of three different types of crickets and the temperature.

II. STUDENT PERFORMANCE

A. Description

Students will complete Activity 1 as a class. Students should be able to determine whether a dependent relationship exists between 2 given variables. Students will be able to discuss variables which do NOT have a functional relationship (example: Day of the week and number of cavities).

Students will complete Activity 2 in groups of 2-4. They will set up the activity, gather data, record the data in a table, assign variables, record data on a grid, label the x and y axes, analyze the data, and make predictions.

Accommodations/modifications B.

Students with modifications should have answer choices reduced to 3 (instead of 4) on the quiz. Enrichment activities might not be appropriate for these students. iii. Assessment of Activities

A. Description

The teacher should circulate among the students to make sure the activities are

Set up and completed correctly.

Quiz over Functions I should be administered in the last 30 minutes of Day 2.

Activities:

Criteria

Contribution to the

Group

Points

0-25 Points

Possible

Table/ Graph

Activity planning, prep, and completion

Make predictions based on data

Specifics

Cooperation

Participation

Engaged in the activity

Correctly label the axis

Correctly assign the variables

Record data

Plot data

Set up and carry out instructions of activity

Was a prediction written on activity sheet?

Was prediction clearly connected to data

0-25 points

0-25 points

0-25 points

.

100 points

Division of Curriculum and Instruction

School Improvement Department

Texarkana Independent School District

C. Accommodations/modifications

Students should be active participants on activities 1 and 2.

D. Enrichment

Bonus points should be given to any students completing enrichment activity correctly.

Students enrolled in AP courses should complete Enrichment activities as regular classroom activities.

IV. TAKS Preparation

A. Transition to TAKS context

B. Sample TAKS question:

(TAKS 2004, #31)

Which equation best describes the relationship between x and y shown in the table below? x

1 y

3

2

4

6

9

12

48

108

243

A y = 3x

B x = 3y

C x = 3y 2

D y = 3x 2

Students should be familiar with examples of how this concept has been assessed on

TAKS in the past. Students should be proficient in the following:

Look at a table and identify the dependent and independent variables.

In matching a table of values to a function rule, know that the correct function rule will be written with the depend ent variable isolated (example: y = …)

In matching a table of values to a function rule, eliminate answer choices in which the dependent variable is NOT the variable we are solving for.

Given one representation of a function, match it with a different representation using

“plug & chug” (substitution) OR the table function of the graphing calculator.

V. Key Vocabulary

Dependent variable, independent variable, function, function rule, variable, equation, vertical line test, X axis, Y axis

Division of Curriculum and Instruction

School Improvement Department

Texarkana Independent School District