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Transcript
AGENDAS FOR THE WEEK:
February 10th – February 14th
MONDAY
TUESDAY
WEDNESDAY
THURSDAY
FRIDAY
Review
Objective(s): SWBAT
*Review interval notation,
finding intersections and
unions of intervals, and linear
inequalities.
Formative Assessment
Objective(s): SWBAT
*Testing for understanding of
Interval Notation,
Intersections and Unions, and
Linear Inequalities.
NGSSS:
MA.912.A.3.4: Solve and
graph simple and compound
inequalities in one variable
and be able to justify each
step in a solution.
NGSSS:
MA.912.A.3.4: Solve and
graph simple and compound
inequalities in one variable
and be able to justify each
step in a solution.
CCSS:
MACC.7.EE.2.4b: Solve
word problems leading to
inequalities of the form
px+q>r or px+Q<r, where p,
q, and r are specific rational
numbers. Graph the solution
set of the inequality and
interpret it in the context of
the problem.
MACC.912.A-CED.1.1:
Create equations and
inequalities in one variable
and use them to solve
problems. Include equations
arising from linear and
quadratic functions,
MACC.912.A-REI.2.3: Solve
linear equations and
inequalities in one variable,
including equations with
coefficients represented by
letters.
CCSS:
MACC.7.EE.2.4b: Solve
word problems leading to
inequalities of the form
px+q>r or px+Q<r, where p,
q, and r are specific rational
numbers. Graph the solution
set of the inequality and
interpret it in the context of
the problem.
MACC.912.A-CED.1.1:
Create equations and
inequalities in one variable
and use them to solve
problems. Include equations
arising from linear and
quadratic functions,
MACC.912.A-REI.2.3:
Solve linear equations and
inequalities in one variable,
including equations with
coefficients represented by
letters.
Go over yesterday's
homework.
Go over yesterday's
homework.
(5 Minutes)
Engage: Display the first slide
of the Power-Point with the
(10 Minutes)
Engage: Display the first
slide of the Power-Point with
Pass out the Quiz: The quiz
will test the students on
interval notation, intersections
and unions, and linear
inequalities they learned
about this week. When they
Interval Notation
Objective(s): SWBAT
*Use interval notation.
*Learning new vocabulary.
Intersections and Unions
Objective(s): SWBAT
*Find intersections and unions
of intervals.
Linear Inequalities
Objective(s): SWBAT
*Solve linear inequalities (one
variable).
NGSSS:
N/A
CCSS:
N/A
NGSSS:
N/A
CCSS:
N/A
NGSSS:
MA.912.A.3.4: Solve and
graph simple and compound
inequalities in one variable and
be able to justify each step in a
solution.
MA.912.A.3.5: Symbolically
represent and solve multi-step
and real-world applications
that involve linear equations
and inequalities.
CCSS:
MACC.7.EE.2.4b: Solve
word problems leading to
inequalities of the form px+q>r
or px+Q<r, where p, q, and r
are specific rational numbers.
Graph the solution set of the
inequality and interpret it in
the context of the problem.
MACC.912.A-CED.1.1:
Create equations and
inequalities in one variable and
use them to solve problems.
Include equations arising from
linear and quadratic functions,
MACC.912.A-REI.2.3: Solve
linear equations and
inequalities in one variable,
including equations with
coefficients represented by
letters.
P
Pass back and go over last
Friday's Quiz.
(5 Minutes)
Engage: Display the first slide
of the Power-Point with a 2
Go over yesterday's homework.
(5 Minutes)
Engage: Display the first slide
of the Power-Point with interval
notations (1,4) and [2,8] and ask
L
problems that have graphs on
number lines and ask students
what they think the graphs
mean.
the students what the graphs
have in common and how they
differ.
inequality 2x + 5 < 17 and ask
the students to solve it. After
ask them write the solution in
interval notation.
a real-world word problem.
The students should solve the
two inequalities, graph them,
write the solutions in interval
notation.
(5-10 Minutes)
Explore: Display Explore slide
of the Power-Point with
problems asking students how
they could graph the 2 different
situations.
(5-10 Minutes)
Explore: Display Explore slide
of the Power-Point with 2 graphs
and ask students what they have
in common and what they have
that is different. Then ask how
they could write that using
interval notation.
(5-10 Minutes)
Explore: Display the Explore
slide of the Power-Point with a
linear inequality word problem
asking the students to solve the
inequality and graph it.
(40 Minutes)
Elaborate: Give the students
their review worksheet. The
worksheet covers all of the
concepts learned this week,
which include: Interval
notation, set-builder notation,
graphing an interval, finding
the intersection or union of
sets, and solving linear
inequalities. Any problems
the students do not finish in
class should be completed for
homework.
(25-35 Minutes)
Explain: Go over the answers
to the problems on the Explore
slide. After going over the
answers ask the students if they
know what interval notation is.
**
It is a form of notating the
solution sets of inequalities.
**
Discuss how it is used to
represent an interval for an
inequality. Do examples.
A
**
Examples from Power-Point:
Given the problem -2 < x < 3
and the corresponding graph.
Given the problem -2 ≤ x ≤ 3
and the corresponding graph.
Given the problem -2 < x ≤ 3
and the corresponding graph.
**
Discuss how the brackets and
parentheses determine if they
use the symbols <, or ≤. Have
the students guide the teacher
through 3 problems.
**
Examples from Power-Point:
Given (-1,4] what will the
(20-25 Minutes)
Explain: Go over the answers to
the problems on the Explore
slide. After going over the
answers ask the students if they
remember what intersections and
unions are in mathematics.
**
Intersections are the set of
elements common to both set A
and set B. Unions are the set of
elements in set A or in set B or
in both sets.
**
Since intervals represent sets we
can find their intersections and
unions. The steps to find the
intersections and unions of two
intervals are:
1) Graph each interval on a
number line.
2) a. For intersections, take the
portion of the number line that
the two graphs have in common.
2) b. For unions, take the portion
of number line representing the
total collection of the numbers in
the two graphs.
Do 2 examples, to help solidify
the concept. Have the students
(25-30 Minutes)
Explain: Go over the answers
to the problems on the Explore
slide. After going over the
answers discuss inequalities
and how multiplying and
dividing by negative numbers
changes the direction of the
signs in the problem (called the
Negative Multiplication
Property of Inequality). Do 2
examples with students.
**
Examples from Power-Point:
3 – 2x ≤ 11
[Answer: -4 ≤ x]
-2x -4 > x + 5
[Answer: x < -3]
**
Ask students how is solving
inequalities similar to solving
equations. Ask them how it is
different. Discuss how to solve
linear inequalities containing
fractions. Do 2 examples with
the students.
**
Example from Power-Point:
x+ 3 x− 2 1
≥
+
5
3
4
[Answer: x ≤ 14]
finish they must sit quietly at
their seat. They may work on
homework or assignments for
other classes, read a book, or
just sit quietly.
graph look like?
Given [2.5, 4] what will the
graph look like?
Given (-4, ∞ ) what will the
graph look like?
**
Discuss that there is a second
way that is often used as well
called set-builder notation.
Show example of set-builder
notation.
**
Example from Power-Point:
for -2 < x < 3 the notation
would be {x|-2 < x < 3}. Thus
the graph, the interval notation
and the set-builder notation all
represent the same thing.
**
Have the students lead the
teacher through the 3 previous
examples changing the interval
notation to set-builder notation.
**
Example from Power-Point:
Given (-1,4] what will the setbuilder notation be?
[Answer: {x| -1 < x ≤ 4}]
Given [2.5, 4] what will the
set-builder notation be?
[Answer: {x| 2.5 ≤ x ≤ 4}]
Given (-4, ∞ ) what will the
set-builder notation be?
[Answer: {x| -4 < x < ∞}]
**
Display slide with table
showing the different kinds of
notations and their graphs.
Inform the students the table
can be found on page 174 in
their textbook.
guide the teacher through the
problem.
**
Examples from Power-Point:
Given [1,3], (2,6) graph and
write in interval notation what
the union and intersections are.
Given (-3,1], [0,5) graph and
write in interval notation what
the union and intersections are.
**
(10 Minutes)
Elaborate: (Optional)
Give students worksheet that
uses intersections and unions
with real-world examples. Have
them graph and write the sets
using interval notation.
x− 4 x− 2 5
≥
+
2
3
6
[Answer: 13 ≤ x]
**
(10-15 Minutes)
Elaborate: (Optional)
Give the students worksheet
that has 3 linear inequalities
and a word problem on it. The
students will need to make a
graph and give the inequalities
solutions in interval notation.
(10 Minutes)
Elaborate: Give students
worksheet. Any parts they
don't finish in class should be
finished for homework.
N
Resources:
Evaluate and Summary:
Homework is the Worksheet
called Interval Notation
Practice.
Evaluate and Summary:
Homework is from the textbook
Page 185, #s 15-26
Evaluate and Summary:
Homework is from the
textbook Page 185, #s 27-41
odd only
Evaluate and Summary:
Study for tomorrows quiz on
section 1.7! Finish review
worksheet from class.
Evaluate and Summary:
Quiz on Section 1.7
Objectives 1-3 today!
Elaboration/Homework
Worksheets
Power-Point
Power-Point
Power-Point
Review Worksheets
Power-Point
Quizzes