Algebra Goal 4 – To Graph and Interpret Linear Models
Learning Outcomes
Differentiated Instructional Activities
Text Book
References*
A game of battleship is a nice way to introduce
plotting points in a coordinate plane. Main
emphasis is the concept of ordered pair with
horizontal – vertical as the required order.
Making pictures from sets of ordered pairs is
also motivational to students. Students can
make their own pictures and ask a partner to plot
the points to determine the picture.
Points on the axes are possibly troublesome to
students.
On pages 210 – 212, do examples 3, 2, 1 and 4
in that order.
Solving equations for y needs much practice and
is a follow-up from work in 3.7
Pg.203—205
Ex. 1-10
Pg. 206-207
Ex. 1-35
Pg. 210-212
Ex. 1-5
Pg. 213-215
Ex. 1-56
Stressing that the relationship between x and y is
a key to understanding equations and makes
horizontal and vertical lines easy. The algebraic
model is a constant relation of one variable. For
example, x =2 means x is always 2 and y can be
anything.
Graphing lines by using intercepts is useful and
may be the easiest approach for students who
become confused with the slope – intercept
approach
Pg. 216-218
Ex. 1-9
Pg.219-220
Ex. 1-34
Chapter Resource Book
References
Assessments#
4.1 To graph linear equations
(relations and functions) using:
Point plotting from a table of
values
Chapter References 4.1, 4.2
Intercepts
Chapter References 4.3, 4.4
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WT: pg. 30^
HQ: pg. 30^
WT: pg. 31
HQ: pg. 31
Pg. 222-224
Ex. 1-8
Pg. 225-227
Ex. 1-54
WT: pg. 32
HQ: pg. 32
Chapter 4 Quiz 1
Pg. 44
WT: pg. 33
HQ: pg. 33
The examples noted are for reference only. Teacher has the decision to assign number of examples to meet the needs of the different abilities of students in the class.
These references can be found in the Warm-up Transparencies (WT) and Daily Homework Quiz (HQ) booklet.
End of Chapter Assessments as well as periodic quizzes are to be determined by the teacher
Page 1
Learning Outcomes
Differentiated Instructional Activities
Text Book
References*
Chapter Resource Book
References
Assessments#
Slopes
Handicap ramps are a nice introduction to
slopes. Question: What makes a ramp a
straight line? The answer illumines the
concept of slope.
Pg. 229-232
Ex. 1-9
Pg. 233-235
Ex. 1-42
Alternative Assessment and
Math Journal pg. 114 ex: 2
WT: pg. 34^
HQ: pg. 34^
The activity on page 228 is a good start.
Students should be able to use a pencil to
demonstrate what is meant by positive,
negative, zero and no slope. Ski slope
reference is also good recognition device.
Stressing that a whole number can be written
as a fraction or ratio is important.
Working in pairs through this section will be
helpful. Color coding slope and y-intercept in
equations is useful.
Pg. 243-245
Pg. 1-5
Pg. 246-247
Ex. 1-55
Chapter References 4.5, 4.7
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Ch. 4 Quiz 2 pg. 80
SAT/ACT Chapter Test
Pg. 113 1 – 4; 5 - 9
WT: pg. 35^
WT: pg. 36
HQ: pg. 35
HQ: pg. 37
The examples noted are for reference only. Teacher has the decision to assign number of examples to meet the needs of the different abilities of students in the class.
These references can be found in the Warm-up Transparencies (WT) and Daily Homework Quiz (HQ) booklet.
End of Chapter Assessments as well as periodic quizzes are to be determined by the teacher.
Learning Outcomes
4.2 To develop the equation of a
line from:
The slope and y-intercept
Chapter Reference 5.1
A point and the slope
Chapter Reference 5.2
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Differentiated Instructional Activities
Text Book
References*
The y = mx + b form of a linear equation has
to be completely understood by students at this
point. Color coding the slope and y-intercept
in equations written in form y = mx + b should
be continued.
It has to be understood that m and b are
constants and x and y are variables.
Students can work in pairs, one drawing lines
on coordinate axes, the other stating the
equation. Be sure to have students have lines
pass through two identifiable points. Include
horizontal and vertical lines.
Pg. 269-271
Ex. 1-8
Pg. 272-274
Ex. 1-43
Finding slopes of lines that pass through two
points, one point expressed in the form of
(x, y) has to be practiced before this section is
introduced.
Spend some time on changing equation in
point – slope form to one in slope – y-intercept
form.
Pg. 278-280
Ex. 1-6
Pg. 281-283
Ex. 1-48
Chapter Resource Book
References
Assessments#
WT: pg. 39^
HQ: pg. 39^
Ch. 5 Quiz pg. 31
WT: pg. 40
HQ: pg. 40
The examples noted are for reference only. Teacher has the decision to assign number of examples to meet the needs of the different abilities of students in the class.
These references can be found in the Warm-up Transparencies (WT) and Daily Homework Quiz (HQ) booklet.
End of Chapter Assessments as well as periodic quizzes are to be determined by the teacher.
Learning Outcomes
4.2 continued;
Two points
Chapter Reference 5.3
Differentiated Instructional Activities
Text Book
References*
Chapter Resource Book
References
Assessments#
This section reinforces all skills on writing
equations.
A good exercise is to have students place two
points on a coordinate plane, draw a line
through them that clearly intersects both axes,
then estimate the slope and y-intercept and
write an equation based on the estimate.
Finish problem by actually calculating slope
and y-intercept.
Pg. 285-287
Ex. 1-6
Pg. 288-289
Ex, 1-39
Ch. 5 Quiz pg. 54
WT: pg. 41^
HQ: pg. 41^
SAT/ACT Chapter Test
Pg. 86 ex: 1 – 9
Alternative Assessment and
Math Journal
Pg. 87 ex: 2 - 3
4.3 To use linear models to solve
real-life problems
WT: pg. 42
HQ: pg. 42
Chapter Reference 5.5
It is essential that the students are allowed to
explore several methods for solving
applications. All the work to this point leads
to using linear equation models to solve these
application problems but some may be solved
by other problem solving strategies. Let the
students loose and see what happens.
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Pg. 298-300
Ex. 1-4
Pg.301-303
Ex. 1- 34
The examples noted are for reference only. Teacher has the decision to assign number of examples to meet the needs of the different abilities of students in the class.
These references can be found in the Warm-up Transparencies (WT) and Daily Homework Quiz (HQ) booklet.
End of Chapter Assessments as well as periodic quizzes are to be determined by the teacher.
Learning Outcomes
CAPT Practice
*
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Differentiated Instructional Activities
Text Book
References*
Chapter Resource Book
References
Biology, pg. 207
Triathlon, pg. 214
Railroad, pg. 227
Road Grade, pg.
235
Cable Cars, pg. 247
Basketball, pg. 303
Assessments#
Additional CAPT Practice
Tips for Waitress and
Cook(CCL)
Bicycle Factory(Handbook
2001 pg 62)
Phone Plans(Handbook2001
pg63)
Milk Prices(Handbook 2001
pg64)
College Savings(Handbook
pg 66)
The Case for
Recycling(2002)
The examples noted are for reference only. Teacher has the decision to assign number of examples to meet the needs of the different abilities of students in the class.
These references can be found in the Warm-up Transparencies (WT) and Daily Homework Quiz (HQ) booklet.
End of Chapter Assessments as well as periodic quizzes are to be determined by the teacher.