Appleby White Pre-Algebra Module 34
Unit 2:Proportional and Nonproportional Relationships and Functions / September 12-November 126-October 14Math Florida Standard(s): / MAFS.8.F.1.2 (DOK 2): Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. MAFS.8.EE.2.6 (DOK 2): Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. MAFS.8.EE.2.5F.1.3 (DOK2): Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.Interpret the equation y=mx+b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. MAFS.8.F.2.4 (DOK 3): Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Learning Goal: / The student is expected to create and analyze different models of functions, interpreting the unit rate, constant of proportionality and slope from those models.The student is expected to make and interpret tables, write equations, and draw graphs to model real-world non-proportional relationships.
Assessments / Pre Assessment Quiz on real numbers, exponents, and scientific notation.
Formative Assessments Cornell Notes
Collaborative Assignments
Homework
Exit Slips
Summative Assessment Unit 1 – Begins 9/12
Quiz
Unit test
Essential Question(s): / How can you use tables, graphs, and equations to represent proportional situations? How do you find a rate of change or a slope? How do you interpret the unit rate as slope?How can you determine the slope and y-intercept of a line? How can you graph a line using the slope and y-intercept? How can you distinguish between proportional and nonproportional situations?
Progress Monitoring/ Feedback Loop / If student has a low pre assessment or formative assessment, the teacher will monitor and possibly suggest before or after school tutoring to insure he is learning the unit adequately.
If the student has a 70 or below on a quiz he can study more and retake it within a 7 day period for full credit. If the student has below a 70, the instructor will provide real time remediation.
Higher Order Question(s) / How would a diagram, graph, table…help?
What patterns do you find in…?How has your model served its purpose? In what way does this problem connect to other mathematical concepts? How do you know your answer is correct/reasonable?
Key Vocabulary / Proportional Relationship, Constant of Proportionality, Rate of Change, Unit RateLinear equation, slope-intercept form of an equation, y-intercept
Monday
September 12October 3, 2016 / Module 43: Non-Proportional Relationships / Rigor Level:
Conceptual & Application
Daily Agenda
Daily Objective: / Students will graph a line using the slope and y-intercept.Students will add, subtract, multiply and divide using scientific notation.
Bell Ringer: / Take out your exit slip from yesterday. Share your real-world problem with a neighbor.Explain how you will graph a line if you only have the slope and y-intercept.
I Do: / Review bell ringer, homework, revisit lesson 2-4assess
We Do: / Cornell NotesCornell Notes 4-3
You Do: / Lesson 2-4 A/BPL (must do: WS a,b,c and book) (student choice: book or reteach)
Homework: / Scientific Notation WorksheetFinish work to remain at teacher pace
EXIT TICKET: / Which direction do we move the decimal in a scientific notation problem with a positive exponent?Create a real-world problem that would use proportional relationships.
Tuesday
September October 46, 2016 / Module 4: Non-Proportional Relationships Unit 1: Real Numbers, Exponents, & Scientific Notation / Rigor Level:
ConceptualRigor Level:
Conceptual & Application
Daily Agenda
Daily Objective: / Students will graph a line using the slope and y-intercept. Students will add, subtract, multiply and divide using scientific notation.
Bell Ringer: / When graphing always go which direction for the run?How is scientific notation used in the real-world?
I Do: / Review bell ringer, assessReview bell ringer, homework, introduce 2-4.
We Do: / Cornell Notes 4-3Cornell notes and guided practice page 54
You Do: / 4-3 Student Choice work Independent Practice page 55-56 all problems
Homework: / Complete student choice workFinish 55-56
EXIT TICKET: / Graph y = 3x+2Create a real-world problem using scientific notation.
Wednesday
September October 57, 2016 / Module 4: Non-Proportional Relationships Unit 1: Real Numbers, Exponents, & Scientific Notation / Rigor Level:
Conceptual & Application
Rigor Level:
Conceptual
Daily Agenda
Daily Objective: / Students will add, subtract, multiply and divide using scientific notation.Students will distinguish between proportional and nonproportional situations.
Bell Ringer: / Take out your exit slip from yesterday. Share your real-world problem with a neighbor.If slope is a whole number, what number do we place underneath it for the run?
I Do: / Review bell ringer, homework, revisit lesson 2-4
We Do: / Cornell Notes 4-4
You Do: / PL (must do: WS a,b,c) (student choice: book or reteach)Lesson 2-4 A/B
Homework: / Scientific Notation WorksheetFinish work to remain on teacher pace
EXIT TICKET: / Which direction do we move the decimal in a scientific notation problem with a positive exponent? What is the difference in a proportional and nonproportional relationship?
Thursday
September 8October 6, , 2016 / Module 4: Non-Proportional Relationships Unit 1: Real Numbers, Exponents, & Scientific Notation / Rigor Level:
Conceptual & ApplicationRigor Level
Rigor Level:
Conceptual & Application
Daily Agenda
Daily Objective: / Students will distinguish between proportional and nonproportional situations.Students will show mastery of Unit 1 by reviewing the content.
Bell Ringer: / Convert each number to scientific notation.
0.003 5,432,000 6,506,000,000 0.00895378Create an equation that is a proportional relationship.
I Do: / Review bell ringer, homeworkReview bell ringer, assess
We Do: / Review for test in groupsCornell Notes 4-4
You Do: / 4-4 Student Choice work Worksheet created as Review
Homework: / Complete student choice workFinish Worksheet
EXIT TICKET: / Create a word problem that deals with slope. What is equivalent to 1/216?
Friday
September 9October 7, 2016 / Module 4: Non-Proportional Relationships Unit 1: Real Numbers, Exponents, & Scientific Notation / Rigor Level
Rigor Level:
Conceptual & Application
Daily Agenda
Daily Objective: / Students will distinguish between proportional and nonproportional situations.Students will show mastery of Unit 1 by taking a test.
Bell Ringer: / Complete a table and graph y=3x+2Write a problem based on scientific notation.
I Do: / Bell ringer, assessReview bell ringer and homework
We Do: / Review 4-1/4-4Answer questions
You Do: / 4-4 Student Choice WorkUnit 1 Assessment Readiness
Homework: / Enjoy your weekend!No homework! Enjoy your weekend!
EXIT TICKET: / Turn in all of Module 4 work.Find the square root of 49.
Note: Learning Scales and Accommodations are below.
Scale / Learning Goals Scale:Real NumbersProportional and NonProportional Relationships and Functions
4.0 / Ø Know when numbers are rational and irrational. Understand that every number has a decimal formation.Graph, compare and interpret proportional relationships.
Ø Use rational approximations of irrational numbers to compare and locate on a number line and estimate the value of expressions.Find the slope of a line, analyze patterns and derive an equation of the form y=mx+b.
Ø Know and apply properties of integer exponents.Identify functions algebraically, using graphs and tables, compare and contract functions and draw conclusions.
Ø Use numbers expressed in the form of a single digit times an integer power of 10 to estimate large or small quantities.Recognize that the slope is determined by rate of change, determine the rate, construct a function to model a linear relationship and relate the rate of change to real-world quantities.
3.5 / In addition to 3.0 skills, I can do some of the 4.0 skills.
3.0
(GOAL)
With no help, I can do all these skills. / Ø Graph, compare and interpret proportional relationships. Know when numbers are rational and irrational. Understand that every number has a decimal formation.
Ø Find the slope of a line, analyze patterns and derive an equation of the form y=mx+b. Use rational approximations of irrational numbers to compare and locate on a number line and estimate the value of expressions.
Ø Identify functions algebraically, using graphs and tables, compare and contract functions and draw conclusions.Know and apply properties of integer exponents.
2.5 / In addition to all 2.0 skills, I can do some of the 3.0 skills.
2.0
With no help, I can do all these skills. / Ø Graph, compare and interpret proportional relationships. Know when numbers are rational and irrational. Understand that every number has a decimal formation.
Ø Find the slope of a line, analyze patterns and derive an equation of the form y=mx+b.Know and apply properties of integer exponents.
1.5 / On my own, I can do some of the 2.0 and 3.0 skills.
1.0 / With help, I can do some of the 2.0 and 3.0 skills.
0.5 / With help, I can do some of the 2.0 skills.
0.0 / Even with help, I have no success.
WICR Strategies used during each unit.
Writing
Writing activities that help
students understand the
content / Inquiry
Questioning strategies
that help students
understand the content / Collaboration
Working together with a
partner or in a group of
students to understand, to
problem solve, or to
complete a task/project / Reading
Any strategies in reading
that help students
understand
Writing-to-Learn
• summaries
Process writing
• using a rubric as evaluation
On-demand/Timed writing
• writing that is completed in class within a set amount of time
• grade is evaluated using a rubric
Cornell Notes
• taking notes on the most important information
• summarizing
• using the notes to study
Reflective writing
• students write about what they have learned and what they still need / Higher level questioning
in classes
• Costa’s Level 1: Students
find the answers right there
in the text.
• Costa’s Level 2: Students
must figure out the answer
from information in the
text.
• Costa’s Level 3: Students
apply what they have
learned or use what they
have learned to evaluate or
create. / Think Pair Share
Sharing ideas with a
partner or in a group
Carousel/Gallery Walk
Problem solving in groups
Projects in groups / Before reading activities
• vocabulary activities
• accessing prior knowledge
• making predictions
During reading activities
• marking the text
• Cornell notes
• graphic organizers
After reading strategies
• summarizing
• group projects
Accommodations used daily on an individual basis in accordance with IEP and 504 plans and ELL Students
· Read directions for the student
· Check for understanding
· Allow to leave class for assistance
· Extra time for exams
· Daily agenda / · Allow student time to step out to de-escalate
· Testing in small groups
· Use of a planner/binder for organization
· English Language Dictionary / · Extended time on assignments =1 day
· Preferential seating
· Written direction given
· Break directions into chunks / · Read Aloud to Students
· Visual manipulatives
· Cooperative Learning,
· Vocabulary, Description, Introduction,
.
Student Friendly Mathematical Practice Statements
MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them.
• Make a plan!
• Try different approaches when your problem is hard.
• Solve your problem in more than one way.
• Check whether your solution makes sense.
MAFS.K12.MP.2.1 Reason abstractly and quantitatively.
• Explain the meanings of the numbers, words, pictures, symbols, and objects you and others use
MAFS.K12.MP.3.1 Construct viable arguments and critique the reasoning of others.
• Explain both what to do and why it works.
• Work to make sense of others’ mathematical thinking.
MAFS.K.12.MP.4.1 Model with mathematics.
• Apply math to real-world situations.
• Use models such as graphs, drawings, tables, symbols, numbers, and diagrams to solve problems.
MAFS.K12.MP.5.1 Use appropriate tools strategically.
• Choose appropriate tools for your problem.
• Use mathematical tools correctly and efficiently.
• Estimate and use what you know to check the answers you find using tools.
MAFS.K12.MP.6.1 Attend to precision.
• Communicate your mathematical thinking clearly and precisely.
• Use the level of precision you need for your problem.
• Be accurate when you count, measure, and calculate.
MAFS.K12.MP.7.1 Look for and make use of structure.
• Find, extend, analyze, and create patterns.
• Use patterns and structures to solve problems.
MAFS.K12.MP.8.1 Look for and express regularity in repeated reasoning.
• Use patterns and structures to create and explain rules and shortcuts.
• Use properties, rules, and shortcuts to solve problems.
• Reflect on your thinking before, during, and after you solve a problem.