Complex Fractions and Some Polynomial Functions
Teacher: Labor
CA Standard(s):
Date: 8/19 - 23
Subject/Course: Pre-Calculus
Grade: 11th/12th
Alg 1 1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers,
including closure properties for the four basic arithmetic operations.
Alg 1 6.0 Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2x + 6y = 4). They are also able to sketch
the region defined by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).
Alg 1 7.0 Students verify that a point lies on a line, given an equation of the line. Students are able to derive linear equations by using
the point-slope formula.
Alg 1 8.0 Students understand the concepts of parallel lines and perpendicular lines and how those slopes are related. Students are
able to find the equation of a line perpendicular to a given line that passes through a given point.
Alg 2 25.0 Students use properties from number systems to justify steps in combining and simplifying functions.
Learning Objective (s):
Given a complex fraction, the learner will simplify the expression, by performing the necessary arithmetic operation – addition, subtraction,
multiplication and/or division.
Given a constant function, the learner will graph the equation by evaluating it at various points on the coordinate plane.
Given a linear equation or function, the learner will graph the equation by either evaluating it at various points on the coordinate plane or using the
slope and/or intercepts of the function.
Given two or more linear equations, the learner will determine if the lines are parallel or perpendicular by examining their slopes and y-intercepts.
Essential Question(s):
What is a complex fraction?
What is the main arithmetic operation involved in a complex fraction?
What is a constant function? How does its graph look like?
What are the different ways of graphing a linear function?
When is a rational number undefined? What is undefined slope?
Looking at the equations of two lines, when will the lines be parallel? perpendicular?
Assessment:
Homework quiz on day 1, quick check on all days.
Do Now: Writing prompts:
Day 1: “The process of dividing complex numbers starts with…”
Day 2: “A complex fraction is a fraction…”
Day 3: “The set of whole numbers in NOT closed under division because…”
WHOLE GROUP
Do Now: Writing Promts
Lesson: Note-taking (I Do, You Do, We Do): Complex Fractions, Constant Function and Some Polynomial Functions
Quick Check
DIRECT INTRUCTION STATION
Unit 2: Polynomial Functions
Notes: Students use their composition
notebooks to copy notes. Students then answer
guided exercises and then answer problems on
their own.
Activities:
*Note-taking
*Pair-share
*Mini-whiteboards
*Thumbs up, thumbs down
*I Do, You Do, We Do
*Quick checks
COLLABORATIVE STATION
Exploration: Students will be assigned to groups
of 3 or 4 depending on the result of quick checks
or verbal assessments. Students will be working
on complex fractions.
Group Roles:
Leader: Moderates the whole group and
ensures that each member is doing his/her role
Time Keeper: Ensures that each member is on
efficiently on track to accomplish the task
INDEPENDENT STATION
Homework Quiz #4: On day 1, students will be
given problems from assigned homework from
the previous day to check for comprehension.
Activity: Each student is going to create a
student-friendly brochure on complex numbers.
Individual work: Each student is assigned
homework to build on the concepts discussed in
class.
Recorder: Records all responses and makes
sure every one in the group shares the same
data
Day 1 HW:
pA44 #28 - 32
Day 3 HW:
p41 #46 – 70 (even only)
Reporter: Shares what the group learned from
the activity
*All HW answers need to be in a composition
notebook
Address possible misconceptions:
Adding or subtracting fractions with different
denominators.
Slope of a vertical line versus slope of a
horizontal line.
Division by zero error.