Date: November 1, 2021 Teacher’s Name: Rossaura De La Cruz
Subject: Mathematics (Algebra) Grade level: 9th Grade
Learning Segment Title:Linear and Inequalities Length of each lesson: 45 minutes
Lesson: 3 Day Lesson Plan
Central Focus: Using linear and inequalities equations and graphing them
Essential Question(s): What is the relationship between linear/inequality equations and graphs
Learning Standards:
1. AI-A.REI
Represent and solve equations and inequalities graphically.
Pre-Assessment: (if applicable): Students will be building on math standards in this lesson, they should
be able to recall previous knowledge on inequality sign
Learning Objectives: Students will: Assessments:
Day 1: Recognize and analyze linear equations Day 1: Students work independently and do a
and be able to solve them in correct worksheet “Slope Intercept Form”. After
slope-intercept form independent practice is done, students will
complete “EXIT TICKET DAY 1” to recognize
Day 2: Recognize and analyze linear inequality components of a linear equations and put them
equations and be able to solve them in correct in terms of y (slope intercept)
slope-intercept form
Day 2: Students work independently and do
Day 3: Recognize linear/linear inequality worksheet “Solving Linear Inequalities (A)”,
equations and be able to understand how to graph after independent practice students will
both equations using graphing paper complete “EXIT TICKET DAY 2” to continue
to recognize components of a linear inequality
equations and put them in terms of y (slope
intercept)
Day 3: Students will be given “Graphing
Equation and Systems Worksheet” as homework
after independent practice. Students will
complete “Exit ticket Day 3”, this will relate
back to all three days of learning
● All assessments will be graded
Differentiation:
Approaching: On level: Beyond:
Students who may not be there Students who demonstrate that Students that are beyond can
yet. They still don't understand they understand the difference complete both equations
the difference between normal between both equations, but still proficiently and understand how
equations and inequality may make a few errors when to graph both equations
equations, and may not be able graphing them. graphically
to graph them.
Academic Language: Students will need to comprehend the words:
Vocab
Inequalities: the relation between two expressions that are not equal, employing a sign such as ≠ “not
equal to,” > “greater than,” or < “less than.”.
Linear: able to be represented by a straight line on a graph; involving or exhibiting directly proportional
change in two related quantities.
Equations: a statement that the values of two mathematical expressions are equal (indicated by the sign
=).
Graphs: a collection of points whose coordinates satisfy a given relation.
Xy-plane: the plane that contains the x- and y-axes; the yz-plane contains the y- and z-axes; the xz-plane
contains the x- and z-axes. These three coordinate planes divide space into eight parts, called octants.
Procedure:
Day 1- Lesson Topic: Linear equations
Anticipatory Set Sponge Activity, Anticipatory Set ,Activating Prior Knowledge
Activating Prior Knowledge:
Do Now: Write at least two examples of linear equations in one variable
After about 4 minutes, at least three students will be asked to share their answers.
Initial Phase: Direct Instruction
To begin, a Slide presentation has been prepared to teach during direct instruction students
1. First slide: Do Now: Write at least two examples of linear equations in one variable
2. Second slide : What you'll learn:
Identify linear equations and functions
Write linear equations in slope intercept form
VOCAB:
1) Linear equations
2) Slope intercept form
3) Constants
4) SCAM Method
3. Third slide: Understanding:
A linear equation has no operations other than:
addition, subtractiction, and multiplication of a variable by a constant
Variables may not be multiplied together or appear in a denominator
A linear equation does not contain variables with exponents other than 1
The graph of a linear equation is always a line
4. Fourth slide: SCAM Method
5. Fifth slide: procedure of linear equations
6. Sixth slide: Linear equations formatting
7. Seventh slide: Stating difference between linear and nonlinear equations
8. Eighth slide: explaining how linear equations are solved
9. Ninth slide: More practice on linear equations!
10. Tenth slide: Check your work!
11. Eleventh slide: Homework
12. Twelfth slide: Exit ticket
Middle Phase
a. Practice (guided, independent)
1. Guided practice
The 10th slide is where students work on guided practice
10th slide: Let's work together! In your notebooks, write down the following problems,
Final answers should be converted into Slope-Intercept Form (y = mx + b)
1. 10x + 2y = 24 4. -3x + 2y = 14
2. -14x + 2y = 28 5. 4x + 3y = 24
3. 24x + 3y = 48 6. -5x + 2y = 50
1. Have students work together in small groups for 10 minutes
2. After about 10 minutes bring the class back to focus
3. Work on problems together as a class
4. Ask students to participate by coming up to boards to answer questions
5. Have each student that comes up explain their thought process and their work
After questions are complete, move on to 11th slide where students can see correct answers and
fix their mistakes
11th slide:
1. 10x + 2y = 24
- Subtract 10x from both sides, then divide by 2
Ans: y = -5x + 12
2. -14x + 2y = 28
- Add 14x from both sides, then divide by 2
Ans: y = 7x + 14
3. 24x + 3y = 48
- Subtract 24x from both sides, then divide by 3
Ans: y = -8x + 16
4. -3x + 2y = 14
- Add 3x from both sides, then divide by 2
Ans: y = 3/2x + 7
5. 4x + 3y = 24
- Subtract 4x from both sides, then divide by 3
Ans: y = -4/3x + 8
6. -5x + 2y = 50
- Add 5x from both sides, then divide by 2
Ans: y = 5/2x + 25
2. Independent Practice
a. Students will receive their independent work as homework, students will complete Slope
Intercept Form worksheet as homework / independent practice and will turn it in for next
class
- Simplify both sides of the equation and combine like terms
- Ensure variable y is isolated so equation can be in correct slope intercept form
- Rewrite equation in proper form
Evaluative criteria: Independent practice, exit ticket
Independent practice:
Full Credit (3 points)
- Uses SCAM Method to solve algebraically
- Shows all steps correctly
- States correct equation
- Correctly has final answer in slope intercept form
Partial Credit (2 Points)
- Uses SCAM Method to solve algebraically but does not include all steps
- Has correct solution but does not include correct work
- Has correct components of equation but not in slope intercept form
No Credit (1 Point)
- Does not use SCAM Method to solve algebraically
- Solution is incorrect
- Slope Intercept form is incorrect or not completed
Exit Ticket:
✓+,✓,✓-
✓+ (3) ✓ (2) ✓- (1)
- Uses SCAM Method - Uses SCAM Method - Does not use SCAM
correctly but doesn't include all Method, uses some
- Clearly states correct parts other strategy
answer - Has correct answer - Solution is incorrect
- Has final answer in but not correct work - Final answer is not in
slope intercept form - Has correct slope intercept form
components but
answer is not in slope
intercept form
Concluding Phase
3. Closure/Summary
Before leaving, students must complete the exit ticket. They will take a piece of paper and write
down exit ticket that is being projected on the board
- Students must solve the linear equation and then follow up by putting it in correct
slope intercept form for complete credit
EXIT TICKET DAY 1:
Given Linear equation: Solve the following linear equation and
put them in correct slope-intercept form.
1. 12x + 3y = 24 → 1.
2. 16x + 2y = 30 → 2.
Students will continue to work on ensuring understanding. Students must show their work and
understanding. All problems that were not completed during class will be done as homework to
keep on practicing.
Follow up: What comes next to reinforce the lesson (HW or supplemental instruction)
For the next class, students who are responsible for finishing their homework (independent
practice) from the worksheet “Slope Intercept Form”. This homework will give them more
practice on computing and finding linear equations.
Materials: (items, technology, etc.)
Direct instruction: Computer; projector for slide presentation
Students will need a computer for worksheets that are emailed before class for homework
(independent practice), extra copies will be provided for students who do not have access to a
computer. Students will need their notebooks for guided practice and a piece of paper (loose
leaf) for exit ticket
Given worksheets, notebooks, paper(loose leaf)
Slide Presentation by Rossaura De La Cruz:
https://docs.google.com/presentation/d/1lExkUT8GgCW76D2vNrO2jht7zt1BC6aj5vPVbqeSMcA
/edit#slide=id.g10136a6b8f7_0_69
Worksheet for independent practice/Homework “Slope Intercept Form”:
https://www.mathworksheets4kids.com/linear-equation/slope-intercept/convert-1.pdf
Day 2 – Lesson Topic: Linear Inequality Equations
Anticipatory Set - Activating Prior Knowledge
1. Do Now: Write at least two inequality signs and examples
After about 4 minutes, at least three students will be asked to share their answers.
Initial Phase: Direct Instruction
To begin, a Slide presentation has been prepared to teach during direct instruction students
13. First slide: SWBAT: Objective
14. Second slide: Do Now: Write at least two inequality signs and examples
15. Third slide : What you'll learn:
Identify linear inequality equations and functions
Write linear inequality equations in slope intercept form
VOCAB:
5) Linear equations
6) Slope intercept form
7) Constants
8) SCAM Method
9) Inequalities
16. Fourth slide: Retrieval Practice
17. Fifth slide: Lets Review!
A linear equation has no operations other than:
addition, subtractiction, and multiplication of a variable by a constant
Variables may not be multiplied together or appear in a denominator
A linear equation does not contain variables with exponents other than 1
The graph of a linear equation is always a line
18. Sixth slide: SCAM Method
19. Seventh slide: procedure of linear inequalities equations
20. Eighth slide: Linear inequalities formatting
21. Ninth slide: Stating difference between linear and nonlinear inequality equations
22. Tenth slide: explaining how linear inequalities are solved
23. Eleventh slide: More practice on linear inequalities!
24. Twelfth slide: Check your work!
25. Thirteenth slide: Homework / independent practice
26. Forutheeth slide: Exit ticket
Middle Phase
b. Practice (guided, independent)
2. Guided practice
The 12th slide is where students work on guided practice
12th slide: More Work! In your notebooks, write down the following problems,
Final answers should be converted into Slope-Intercept Form (inequalities included)
1. 12x + 2y < 24 4. -3x - 2y ≥ 20
2. -15x - 3y > 30 5. 5x + 3y ≤ 24
3. 24x + 3y < 48 6. -5x - 2y ≥ 50
6. Have students work together in small groups for 10 minutes
7. After about 10 minutes bring the class back to focus
8. Work on problems together as a class
9. Ask students to participate by coming up to boards to answer questions
10. Have each student that comes up explain their thought process and their work
After questions are complete, move on to 11th slide where students can see correct answers and
fix their mistakes
13th slide:
1. 12x + 2y < 24
- Subtract 12x from both sides, then divide by 2
Ans: y < -6x + 12
2. -15x - 3y > 30
- Add 15x from both sides, then divide by -3, inequality sign changes
Ans: y < -5x - 10
3. 24x + 3y < 48
- Subtract 24x from both sides, then divide by 3
Ans: y < -8x + 16
4. -3x - 2y ≥ 20
- Add 3x from both sides, then divide by -2; inequality sign changes
Ans: y ≤ -3/2x - 10
5. 5x + 3y ≤ 24
- Subtract 5x from both sides, then divide by 3
Ans: y = -5/3x + 8
6. -5x - 2y ≥ 50
- Add 5x from both sides, then divide by -2; inequality changes
Ans: y ≤ -5/2x - 25
Independent Practice
b. Students will receive their independent work as homework, students will complete
Solving Linear Inequalities (A) worksheet as homework / independent practice and will
turn it in for next class
- Simplify both sides of the equation and combine like terms
- Ensure variable y is isolated so equation can be in correct slope intercept form
- Rewrite equation in proper form
Evaluative criteria: Independent practice, exit ticket
Independent practice:
Full Credit (3 points)
- Uses SCAM Method to solve algebraically
- Shows all steps correctly
- States correct equation
- Correctly has final answer in slope intercept form
Partial Credit (2 Points)
- Uses SCAM Method to solve algebraically but does not include all steps
- Has correct solution but does not include correct work
- Has correct components of equation but not in slope intercept form
No Credit (1 Point)
- Does not use SCAM Method to solve algebraically
- Solution is incorrect
- Slope Intercept form is incorrect or not completed
Exit Ticket:
✓+,✓,✓-
✓+ (3) ✓ (2) ✓- (1)
- Uses SCAM Method - Uses SCAM Method - Does not use SCAM
correctly but doesn't include all Method, uses some
- Clearly states correct parts other strategy
answer - Has correct answer - Solution is incorrect
- Has final answer in but not correct work - Final answer is not in
slope intercept form - Has correct slope intercept form
components but
answer is not in slope
intercept form
Concluding Phase
4. Closure/Summary
Before leaving, students must complete the exit ticket. They will take a piece of paper and write
down exit ticket that is being projected on the board
- Students must solve the linear inequality and then follow up by putting it in
correct slope intercept form for complete credit
EXIT TICKET DAY 2:
Given Linear Inequality: Solve the following linear inequalities and
put them in correct slope-intercept form.
3. 6x + 3y < 9 → 3.
4. 10x + 5y > 20 → 4.
Students will continue to work on ensuring understanding. Students must show their work and
understanding. All problems that were not completed during class will be done as homework to
keep on practicing.
Follow up: What comes next to reinforce the lesson (HW or supplemental instruction)
For the next class, students who are responsible for finishing their homework (independent
practice) from the worksheet “Solving Linear Inequalities A”. This homework will give them more
practice on computing and finding linear inequalities equations.
Materials: (items, technology, etc.)
Direct instruction: Computer; projector for slide presentation
Students will need a computer for worksheets that are emailed before class for homework
(independent practice), extra copies will be provided for students who do not have access to a
computer. Students will need their notebooks for guided practice and a piece of paper (loose
leaf) for exit ticket
Given worksheets, notebooks, paper(loose leaf)
Slide Presentation by Rossaura De La Cruz:
https://docs.google.com/presentation/d/1ea0buwmJv8OBzBGhQnKHJ17m4WBnoRahwg-tWDJ-
X1Q/edit#slide=id.g10136a6b8f7_0_69
Worksheet for independent practice/Homework “Solving linear Inequalities (A)”:
https://www.math-drills.com/algebra/linear_inequality_div2_mult2_add1_side3_ndswitch2_vars
witch3_001.1435603648.pdf
Day 3 – Lesson Topic: Graphing inequalities and linear equations
Anticipatory Set - Anticipatory Set, Activating Prior Knowledge
2. Do Now: Let's brainstorm! Write down any knowledge you have about graphs
After about 2 minutes, at least three students will be asked to share their answers.
Initial Phase: Direct Instruction
To begin, a Slide presentation has been prepared to teach during direct instruction students
27. First slide: Essential Question: How do we graph linear equations
28. Second slide: Do Now: Write down any knowledge you have about graphs
29. Third slide : What you'll learn:
Graph linear lines
Write linear equations in slope intercept form and graph them
VOCAB:
10) Coordinate plane
11) Slope intercept form
12) Slope
13) Independent Variable
14) Dependent Variable
30. Fourth slide: Retrieval Practice
Let's think back to Day 1, what were some things we learned about linear lines?
Do you remember that ….
Linear equations have a constant rate of change.
The slope of a linear graph is a measure of the rate of change of y with respect to x. (Rise over Run)
The y-intercept of the equation is the point at which the graph crosses the y-axis and the value of
x is zero.
Linear equations in two variables can be written in slope-intercept form y = mx + b, where m is
the slope and b is the y-intercept.
31. Fifth slide: Lets Review!
- The independent variable is the quantity that changes based on values you choose. The
independent variable will be labeled on the x-axis
- The dependent variable is the quantity that is based on the input values of the
independent variable. The dependent variable will be labeled on the y-axis.
We have to understand that x = independent variable ; y = dependent variable
32. Sixth slide: Example 1
33. Seventh slide: Procedure of Example 1
34. Eighth slide: Example 1
35. Ninth slide: Understanding Slope Intercept in Graphs (Example 2)
36. Tenth slide: Example 2
37. Eleventh slide: Example 3(Guided Practice)
38. Twelfth slide: Check your work! Example 3
39. Thirteenth slide: Homework / independent practice
40. Forutheeth slide: Exit ticket
Middle Phase
c. Practice (guided, independent)
3. Guided practice
The 11th slide is where students work on guided practice
11th slide: Example 3, In your notebooks take out a piece of graphing paper, write down the
following problem
Graph the line: 3x + 5y = 10.
After students have been giving enough time to work together and asks question on this example,
The 12th slide will allow students to check their work:
Example 6: Graph the line 3x + 5y = 10.
3x + 5y = 10
-3x -3x
5y = -3x + 10
Independent Practice
c. Students will receive their independent work as homework, students will complete
Algebra 1: Graphing Equation and Systems worksheet as homework / independent
practice and will turn it in for next class
- Simplify both sides of the equation and combine like terms
- Ensure variable y is isolated so equation can be in correct slope intercept form
- Rewrite equation in proper form
- Plot points correctly
- Ensure arrow and line are pointing towards the correct direction
Evaluative criteria: Independent practice, exit ticket
Independent practice:
Full Credit (3 points)
- Uses SCAM Method to solve algebraically
- Shows all steps correctly
- States correct equation
- Correctly has final answer in slope intercept form
- Points are plotted correctly
- Lines are straight and coordinates are in correct quadrant
Partial Credit (2 Points)
- Uses SCAM Method to solve algebraically but does not include all steps
- Has correct solution but does not include correct work
- Has correct components of equation but not in slope intercept form
- Points are plotted but not in correct place
- Lines are not straight but points are in correct quadrant
No Credit (1 Point)
- Does not use SCAM Method to solve algebraically
- Solution is incorrect
- Slope Intercept form is incorrect or not completed
- Points are plotted incorrectly
- Lines are not straight and points are not in correct quadrant
Exit Ticket:
✓+,✓,✓-
✓+ (3) ✓ (2) ✓- (1)
- Clearly shows absent - Shows absent student - Does not explain
student what they what they missed but clearly for the absent
missed could be clearer student
- States correct and - States how to graph - Does not explain how
clear process of how linear lines but words linear lines are used
to graph linear lines and explanation could and how to graph
answer be clearer them
- Has creativity and - Includes drawing but - No creativity, no
drawing encapsulates picture may mislead drawing or picture
what us being taught what was taught
Concluding Phase
5. Closure/Summary
Before leaving, students must complete the exit ticket. They will take a piece of paper and write
down exit ticket that is being projected on the board
- Students have 90 seconds to explain to a absent classmate what they learned
about graphing linear lines
EXIT TICKET DAY 3:
Your classmate, Rosa, was absent when we learned how to graph linear
lines. She asks you for your notes. You only have 90 seconds to explain the
notes to Rosa, what do you tell her? (yes you may use an example /
drawing…after all a picture is worth a thousand words)
Students will continue to work on ensuring understanding. Students must show their work and
understanding. All problems that were not completed during class will be done as homework to
keep on practicing.
Follow up: What comes next to reinforce the lesson (HW or supplemental instruction)
For the next class, students who are responsible for finishing their homework (independent
practice) from the worksheet “Algebra 1: Graphing Equation and Systems”. This homework will
give them more practice on graphing linear equations using slope intercept form
Materials: (items, technology, etc.)
Direct instruction: Computer; projector for slide presentation
Students will need a computer for worksheets that are emailed before class for homework
(independent practice), extra copies will be provided for students who do not have access to a
computer. Students will need their notebooks for guided practice and a piece of paper (loose
leaf) for exit ticket
Given worksheets, notebooks, paper(loose leaf), graphing paper
Slide Presentation by Rossaura De La Cruz:
https://docs.google.com/presentation/d/1o_rL3shOb1BI_VBIXE_wd0MRTefBSJFRyzUEaKvhtQ
k/edit#slide=id.gc6f919934_0_0
Worksheet for independent practice/Homework: Algebra 1: Graphing Equation and Systems
file:///C:/Users/Rossaura/Downloads/Day%203%20Worksheet%20Graphing%20Linear%20Equ
ations.pdf
References
Algebra 1 Graphing Equations and Systems Worksheet Slope Intercept. (n.d.). StudyLib. Retrieved
November 15, 2021, from
https://studylib.net/doc/10830847/algebra-1-graphing-equations-and-systems-worksheet--slope…
Algebra Worksheet -- Solving Linear Inequalities Including a Third Term. (n.d.). Math Drills. Retrieved
November 15, 2021, from
https://www.math-drills.com/algebra/linear_inequality_div2_mult2_add1_side3_ndswitch2_vars
witch3_001.1435603648.pdf
Forms of linear equations review (article). (n.d.). Khan Academy. Retrieved November 15, 2021, from
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:forms-of-linear-equations/x2f8b
b11595b61c86:summary-forms-of-two-variable-linear-equations/a/forms-of-linear-equations-revi
ew
Graphing Linear Inequalities. (n.d.). ChiliMath. Retrieved November 15, 2021, from
https://www.chilimath.com/lessons/intermediate-algebra/graphing-linear-inequalities/
How to Solve Multi-Step Equations? (23 Surefire Examples!). (2020, January 20). Calcworkshop.
Retrieved November 15, 2021, from
https://calcworkshop.com/solving-equations/multi-step-equations/
Write each equation in slope-intercept form. 3x + 4y = 8 2y – 6 = –6x y = –(x – 5) 5 3 = 9 3(x – y) 2 –14x
+ y = 7 9. (n.d.). Math Worksheets 4 Kids. Retrieved November 15, 2021, from
https://www.mathworksheets4kids.com/linear-equation/slope-intercept/convert-1.pdf
