8a Functions

Objectives

Glencoe Mathematics: Pre-Algbra

Chapter 8.1-8.4: Functions and Graphs

(p. 366-431)

Functions

8.1.1 Describe what a function is

8.1.2 Determine whether relations are functions

8.1.3 Use functions to describe relationships between two quantities

8.2.1 Distinguish linear from non-linear graphs and functions

8.2.2 Student make table to determine coordinates which satisfy function

8.2.3 Solve linear equations with two variables

8.2.4 Graph linear equations using ordered pairs

8.3.1 Students manipulate x= equation to solve for y (change to y= equation.)

8.3.2 Students describe and determine x- and y-intercepts

8.3.3 Graph linear equations using x and y intercepts

8.4.1 Find the slope of a line

03.11 Tuesday

Objective:

8.1.1 Describe what a function is

8.1.2 Determine wether relations are functions

8.1.3 Use functions to describe relationships between two quantities

8.2.1 Distinguish linear from non-linear graphs and functions

8.2.2 Student make table to determine coordinates which satisfy function

8.2.3 Solve linear equations with two variables

8.2.4 Graph linear equations using ordered pairs

8.3.1 Students manipulate x= equation to solve for y (change to y= equation.)

8.3.2 Students describe and determine x- and y-intercepts

8.3.3 Graph linear equations using x and y intercepts

Lesson:

(1) Students copy down each objective from list above. Beneath each objective, students should write at least two questions that test knowledge of the objective. Students can invent the question or find the questions in the textbook.

Assignment:

As described in "lesson," students should complete assignment for next class, when they will have summative assessment over all of these objectives.

03.10 Monday

Objective:

8.1.1 Describe what a function is

8.1.2 Determine wether relations are functions

8.1.3 Use functions to describe relationships between two quantities

8.2.1 Distinguish linear from non-linear graphs and functions

8.2.2 Student make table to determine coordinates which satisfy function

8.2.3 Solve linear equations with two variables

8.2.4 Graph linear equations using ordered pairs

8.3.1 Students manipulate x= equation to solve for y (change to y= equation.)

8.3.2 Students describe and determine x- and y-intercepts

8.3.3 Graph linear equations using x and y intercepts

Lesson:

(1) Grade students bringing supplies (summative): ruler, scissors, pencil, pen, eraser. (2) Provide straight lines draw on graphs; student determine slope based on graph-without coordinates provided. (3) Ended explaining pythagorean theorem (got half way through).

Assignment:

(1) Complete slope calculations (in class). (2) Practice test review problems.

03.06 Thursday

Objective(s):

• Practice graphing and slope determination.

Lesson:

(1) Students measure the circumference and diameter of 6 circles: test tubes, beakers, lids, dishes, etc. It does (2) Record their diameters and circumferences in a table with diameter in the left (x) column and circumference in the right (y) column. (3) Graph

Assignment:

(1) Students must bring supplies to class on Monday, March 10: scissors, ruler (marked in mm), pen, pencil, eraser, A4 lined paper. You will be graded summatively on this assignment. (2) Using circle data collected in class today, graph your circle data on a graph. Put paper in portrait orientation, put diameter on x axis and circumference on the y axis. Plot 6 points. Draw straight line that goes through origin and fits all points best. Find slope of line; do calculation on your graph on the front (same side a your graph.)

03.04 Tuesday

Objective(s):

We have been working on unit 8 objectives (see list), but students do not seem to make a connection between algorithmic graphing and slope determination, and the real-life application of this skill and knowledge. Today we will apply graphing and slope determination to find what the "use" of graphing can be in one example.

Lesson:

(1) Students measure the circumference and diameter of 6 circles: test tubes, beakers, lids, dishes, etc. It does (2) Record the six circle diameters and circumferences in a table with diameter in the left (x) column and circumference in the right (y) column. (3) Graph you six data points.

Assignment:

(1) Students must bring supplies to class on Monday, March 10: scissors, ruler (marked in mm), pen, pencil, eraser, A4 lined paper. You will be graded summatively on this assignment. (2) Using circle data collected in class today, graph your circle data on a graph. Put paper in portrait orientation, put diameter on x axis and circumference on the y axis. Plot 6 points. Draw straight line that goes through origin and fits all points best. Find slope of line; do calculation on your graph on the front (same side a your graph.)

03.03 Monday

Objective:

8.1.1 Determine wether relations are functions

8.1.2 Use functions to describe relationships between two quantities

8.2.1 Solve linear equations with two variables

8.2.2 Graph linear equations using ordered pairs

8.3.1 Find the x and y intercepts of graphs

8.3.2 Graph linear equations using x and y intercepts

Lesson:

[Last day we used equations to find x and y intercept; we made data tables for equations; we graphed linear equations]

(1) Today teach slope. (2) Explain four slope types p388-389. (3) Use linear equations to find intercepts (review) and data table (review) and graph (review) and slopes NEW.

Assignment:

Today: p. 384 #16-24 (1st and 3rd column); make data table of ≥ 5 points; graph points; calculate slope (writing EVERY time: slope = ∆y/∆x = (y2-y1)/(x2-x1) = [write final answer as reduced fraction]

Future: Student complete: finding slope for each equation p385 #25-33 (they did intercepts data and graphing last day.) WHen they are done, do Hooke's law graph with paper cups, paper clips, rubber bands, water and graph paper. [container shape graph of water volume and height next?]

02.28 Thursday

Objective:

8.1.1 Determine wether relations are functions

8.1.2 Use functions to describe relationships between two quantities.

8.2.1 Solve linear equations with two variables

8.2.2 Graph linear equations using ordered pairs

8.3.1 Find the x and y intercepts of graphs

8.3.2 Graph linear equations using x and y intercepts

Lesson:

(1) Assess previous days understanding (2) Introduce function equations

Assignment:

Student complete p. 384 #16-24

Student complete p. 385 #25-33 a) solve for both y=... and x=... b) make data table which includes x=0 and y=0; circle and label x intercept and y intercept; c) Graph #25-33 odd only on graph paper

02.26 Tuesday

Objective:

8.1.1 Describe domain, range and function

8.1.2 Determine whether relations are functions

8.2.1 Distinguish linear from non-linear graphs and functions

8.2.2 Use functions to describe relationships between two quantities

8.2.3 Student make table to determine coordinates which satisfy function

8.2.4 Solve linear equations with two variables

8.2.5 Graph linear equations using ordered pairs

Lesson:

8.1.1 Introduce functions: "a function is a special relationship in which each member of the domain (x values) is paired with exactly one member in the range (y values).[Note that functions can have multiple same y values as long the domain of each similar y is unique]" 8.1.2a Review sample questions p 371-372 to determine student understanding. 8.1.2b Students complete handout page 417-419. 8.2.1 Define linear functions: an equation in which the variables appear in separate terms and both variables contains an exponent of only 1 (or do not contain exponents other than 1) 8.2.3-8.2.4 Make table of data points to solve and graph functions 8.2.5 graph functions.

Assignment:

Student complete p. 371-373, #1-31 and 32

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