Linear Equation Exploration Lesson Plans
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Reeqquuiissiitteess: The students will need to know the names of the parts of equations
(constant, coefficient, variable) and how to create tables of values
for equations.
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Materials Needed:
• Floor taped off with a coordinate plane, mark the +y, -y, +x, -x.
• Ordered pairs on card stock for student seats. (Sample ordered pairs are attached)
• Timer or timer program on computer
• Coordinate plane review worksheet

Find Your Ordered Pair Seat ~ While they line up outside class
explain they will get a card with an ordered pair printed on it. The ordered
pair corresponds to a seat that follows the coordinate plain taped to the floor.
They are to find their seat from the card for that day. Keep track of the time
it takes each period. Continue the ordered pair seats for a week, keeping
track of the times. Use the seats during the de-briefs and during the
lessons to reinforce the topics and ideas of linear equations.
Debrief ~ What do you notice with the coordinate plain? (Positives
are to the top and to the right, negatives to the bottom and to the left)
Where do you start to find your seat? Raise your hand if you are in
the _____ quadrant?

Coordinate Plain and tables review worksheet
Worksheet Master #1

Homework ~ Make a table of values for the following 5
equations for x ~ -2 to +2.




y=x-2
y = -3x + 1
y = 2x + 2
y=3
 y = -½x + (-4)
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Objective:
Using a graphing calculator or computer-graphing program to discover the characteristics of
linear equations. Beginners will discover what parts of the equations makes “uphill/downhill”
lines, horizontal lines, lines that cross above/below the x-axis and through the origin. This is
just the first introduction to linear equations, so it will start with investigation.
Materials Needed:
• One graphing calculator or Green Globs program/GraphCalc program
• LCD for overhead for calculator or projector system
• Overhead projector if using calculator
• PowerPoint presentation ~ Drawing Linear Equations
Find Your Ordered Pair Seat ~ De-brief by having students stand up in quadrants or
positive/negative x/y coordinates.
WARM UP: PowerPoint slide #3
In the equation y = x + 11
a) What is the coefficient?
b) Is the coefficient positive or negative?
c) What is the constant?
d) Is the constant positive or negative?
e) What is an improper fraction? Give an example?
ACTIVITY: Have the Attention PowerPoint slide (Slide 1) showing as the students come into the room.
Explain that there are several steps to learning linear equations, today they are at the beginner
level and go to the beginner level slide (slide 2) and explain what the beginner level means.
1) Have the students quickly sketch 8 Cartesian planes on the front of their paper or use the premade handout.
2) Type in an equation on the graphing calculator and show on the LCD or use computer-graphing
program.
3) Have students copy the equation on their first plane.
4) Show the graph of the equation on the overhead and have students draw a quick sketch on their
first plane.
NOTE:
Make sure they have the intercept in roughly the correct place.
Make sure the slope is roughly the correct “steepness”.
Remind them that they are just beginners and in a couple of days they will be experts, so just do
a rough sketch of the line. Encourage them to analyze the equations and their lines.
5) When all sketches are complete have students complete the Beginner Level worksheet in pairs.
(Each partner should complete their own paper, which will become their notes).
EQUATIONS: The following are some sample equations to use for their sketches.
Homework
Finish the
beginner level
notes.
1)
2)
3)
4)
y
y
y
y
 3x
 2 / 5 x  6
 6x  3
 2
5)
6)
7)
8)
y
y
y
y




4 x  6
3 / 7x  4
16 / 3 x  5
1 / 4x  2
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Objective:
Using a computer-graphing program to discover the characteristics of linear equations.
Today the students will discover the y-intercept is where the line crosses the y-axis and
it is the constant in the equation.
Materials Needed:
• Projector system and computer
• PowerPoint presentation ~ Drawing Linear Equations
• Novice Level Notes Handout, 8 coordinate planes handout, graph paper
• Rulers
Have the Attention PowerPoint slide (Slide 1) showing as the students come into the room.
Explain, again, that there are several steps to learning linear equations, today they will be leaving the beginner
level and going to the novice level (slide 6) and explain what the novice level means.
Find Your Ordered Pair Seat ~ De-brief by having students stand up in "uphill", "downhill",
steep, flat, horizontal lines.
WARM UP: Beginner Quiz ~ PowerPoint slide #7, then to #8. Answers on slide #9.
ACTIVITY:
1) Pass out novice level notes and rulers.
2) Explain that they are going to start to notice specifics in the equations and their
lines. PowerPoint slide #6
3) Show each PowerPoint slide with the equations graphed, have them draw a rough
sketch as before. Starting at slide #14
NOTE:
Make sure they have the intercept in roughly the correct place.
Make sure the slope is roughly the correct “steepness” and going in the correct
"uphill"/"downhill" direction.
Remind them that they are just 1 step beyond a beginner, so they will not be perfect yet,
but in two days they will be.
4) The students will answer the questions next to the graph and make a prediction for
the equation. Again remind them that they will get better by the end of today’s
lesson.
5) Display the next slide, which has the correct equation, and have them write it
down.
6) After the first 4 lines, start to ask if anyone notices anything about the lines and
where the lines cross the y-axis.
Homework ~ PowerPoint slide #26
Students are to predict, make a table of values, and graph 6 different equations.
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Objective:
Using a computer-graphing program to discover the characteristics of linear equations.
Today the students will discover the slope is rise over run, and the vocabulary of slope
and y-intercept.
Materials Needed:
• Green Globs program or GraphCalc program
• Projector system and computer
• PowerPoint presentation ~ Drawing Linear Equations
• Advanced Level Notes Handout
• Rulers
Have the Attention PowerPoint slide (Slide 1) showing as the students come into the room.
Explain, again, that there are several steps to learning linear equations, today they will be leaving the novice
level and going to the advanced level (slide 27) and explain what the advanced level means.
Find Your Ordered Pair Seat ~ De-brief by having students stand up in lines and check what the
constant will be.
WARM UP:
Create equations that satisfy certain requirements ~ PowerPoint slide #28. Use the
computer-graphing program to test students’ equations. Make it a point to show
various equations on the same graph. Have them realize that the bigger a number’s
absolute value is the steeper the line and the smaller the absolute value is the flatter
the line.
ACTIVITY:
1) Pass out novice level notes and rulers. Explain that they are going to start to get
pretty good at writing the equations after today’s lesson.
2) Show the lines of the equations directly on the white board. Starting at PowerPoint
slide #29
3) Have the students draw an exact line in each grid.
4) The students will answer the questions next to the graph and ask for a prediction of
the equation. Again remind them that they will get it exactly by the end of
today’s lesson.
NOTE:
They should know part of the equation, the constant. They discovered the constant
yesterday and how to find it. Point out that the coefficient is found by knowing how many
up or down from the y-intercept over how many to the right to the next point on the line. If
they went up, equals positive coefficient, if they go down, negative coefficient.
5) Introduce the vocabulary for the parts of the linear equation,
coefficient is the slope and the constant is the y-intercept.
Homework ~ PowerPoint slide #45
Students find the slope of several linear equation lines.
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Objective:
Using a computer-graphing program to discover the characteristics of linear equations.
Today the students will learn and appreciate the expert way of graphing linear equation,
which is by plotting the y-intercept first and then using the slope to plot the next point.
The students will struggle with graphing 2 equation by using a table of values and then
they will learn the expert way.
Materials Needed:
• Projector system and computer
• PowerPoint presentation ~ Drawing Linear Equations
• Binder paper and graph paper
• Rulers
Have the Attention PowerPoint slide (Slide 1) showing as the students come into the room.
Explain, again, that there are several steps to learning linear equations, today they will be experts and experts
use their knowledge to graph equations smarter (slide 46).
Find Your Ordered Pair Seat ~ De-brief by having students stand up in lines and check what the
steepness or flatness of the slope is.
WARM UP:
Create table of values and graphs for equations ~ PowerPoint slide #47.
ACTIVITY:
1) Pass out graph paper and rulers. Explain that they are going to get their equations
exactly after today’s lesson without the teacher’s help.
2) The students will write the y-intercept and the slope on binder paper, then use that
information to write the linear equation. Check that they understand the different
parts of the equation and what it does to the graph.
3) Then have the student create a table of values, using –2 to +2 for x, on binder paper
and draw the lines on graph paper for the 2 equations. PowerPoint slide #52
Have them struggle with the fraction data values.
4) Once the students have struggled with the graphs, explain what an expert would do
to graph the lines. Slide #53 ~ plotting the y-intercept first and then using the
slope to plot the next point. Draw a line through the two points.
5) Use the blank coordinate plane (Slide #54) to show how to graph the equations
quickly and accurately.
Homework ~ Practice 4-4 worksheet
Students use the expert method to graph several linear equations.
Reinforcing linear equation characteristics and vocabulary
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Objective:
Using word mind maps to have the students deepen their knowledge of linear equations
in a graphical form.
Materials Needed:
Word/Mind Map
Word list
ACTIVITY:
1) Pass out mind map and word list.
2) The students will use the word list to fill in the mind/word map, so the
characteristics are presented in a graphic organized form.
3) De-brief mind/word map.
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Objective:
Using linear equations students will deepen their knowledge of linear equations and yintercept in a fun, game form.
Materials Needed:
• Graphs on hard-stock
• Small white boards and markers
• 1 binder paper and pencil per group ~ it is for keeping score
• Prizes for winners of the game, a prize per group
ACTIVITY:
1) Get students into groups of 3.
2) Explain the rules…
• 1 student will get a stack of graphs on hard-stock paper along
with the equations on a separate sheet of paper. There is a
number at the top of each graph. That number corresponds to
the answer number on the answer sheet.
• The other 2 students will get white boards and markers.
• The student with the equations will show 1 at a time and the
other students will write the equation on the white board and
sketch the equation. Students will also be asked to identify the
points and y-intercept of the line.
• The first student with the correct equation gets 1 point.
• After a set number of equations shown, students will rotate
roles ~ therefore, everyone will get a chance to show the
graphs and compete against another.
• The student with the most points at the end gets a prize.