AAppleby Pre-Algebra Module 310
Unit 4: Transformations and Congruency2:Proportional and Nonproportional Relationships and Functions / September 12-November 1February 13 -22Math Florida Standard(s): / MAFS.8.G.1.1 Verify experimentally the properties of rotations, reflections and translations. A) lines are taken to lines and segments to line segments of the same length MAFS.8.G.1.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. MAFS.8.G.1.3 Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. MAFS.8.G.1.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations and dilations; given two-similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
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.2.5 (DOK2): Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. 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 analyze how real-world objects are affected when they undergo reflections, translations, rotations, and dilations.
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 1/309/12
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 do you describe the properties of orientation and congruence of translations, reflections, rotations? How can you describe the effect of a translation, rotations or reflection on coordinates using an algebraic representation? What is the connection between transformations and figures that have the same shape and size?
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…?What are some other problems that are similar to this one? How would you represent ____? What mathematical consistencies do you notice? What are some problems that similar to this one? What is the relationship between ___ and ____? What evidence will support your solution?
Key Vocabulary / Proportional Relationship, Constant of Proportionality, Rate of Change, Unit Ratecenter of rotation, congruent, image, preimage, line of reflection, reflection, rotation, transformation, translation
Monday
September 12February 13, 20176 / Module 10: Transformations and SimilarityModule 3: Proportional Relationships / Rigor Level:
Conceptual & Application
Daily Agenda
Daily Objective: / The student will describe the property of dilations.Students will add, subtract, multiply and divide using scientific notation.
Bell Ringer: / Grab a pre-test off the back table, a piece of scratch paper and a calculator.Take out your exit slip from yesterday. Share your real-world problem with a neighbor.
I Do: / Collect Pre-testReview bell ringer, homework, revisit lesson 2-4
We Do: / Properties of Dilations (Cornell Notes)Cornell Notes
You Do: / 10-1 Guided Practice Worksheet Lesson 2-4 A/B
Homework: / Finish worksheet Scientific Notation Worksheet
EXIT TICKET: / Which direction do we move the decimal in a scientific notation problem with a positive exponent?
Tuesday
September February 146, 20176 / Module 10: Transformations and Similarity Unit 1: Real Numbers, Exponents, & Scientific Notation / Rigor Level:
ConceptualRigor Level:
Conceptual & Application
Daily Agenda
Daily Objective: / The student will describe the property of dilations.Students will add, subtract, multiply and divide using scientific notation.
Bell Ringer: / How is scientific notation used in the real-world?
I Do: / Go over Bell RingerReview bell ringer, homework, introduce 2-4.
We Do: / Properties of Dilations (Cornell Notes)Cornell notes and guided practice page 54
You Do: / 10-1 A/B/C WorksheetIndependent Practice page 55-56 all problems
Homework: / Finish worksheet Finish 55-56
EXIT TICKET: / Find the cube root of 8, 27, 216, and 704.Create a real-world problem using scientific notation.
Wednesday
September February 15,7, 20176 / Module 10: Transformations and Similarity Unit 1: Real Numbers, Exponents, & Scientific Notation / Rigor Level:
Conceptual & Application
Rigor Level:
Conceptual
Daily Agenda
Daily Objective: / The student will describe the effect of a dilation on coordinates using an algebraic representation.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.
I Do: / Review Bell ringerReview bell ringer, homework, revisit lesson 2-4
We Do: / Algebraic Representations of Dilations (Cornell Notes)Cornell Notes
You Do: / 10-2 Guided PracticeLesson 2-4 A/B
Homework: / Finish Guided Practice for homework Scientific Notation Worksheet
EXIT TICKET: / Explain the effects of a dilation on coordinates.Which direction do we move the decimal in a scientific notation problem with a positive exponent?
Thursday
September 8February 16, , 20176 / Module 10: Transformations and Similarity Unit 1: Real Numbers, Exponents, & Scientific Notation / Rigor Level:
Conceptual & ApplicationRigor Level
Rigor Level:
Conceptual & Application
Daily Agenda
Daily Objective: / The student will describe the effect of a dilation on coordinates using an algebraic representation.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 0.00895378
I Do: / Review Bell ringerReview bell ringer, homework
We Do: / Algebraic Representations of Dilations (Cornell Notes)Review for test in groups
You Do: / 10-2 A/B/C WorksheetWorksheet created as Review
Homework: / Finish A/B/C Worksheet Finish Worksheet
EXIT TICKET: / Explain the effects of a dilation on coordinates.What is equivalent to 1/216?
Friday
September 9February 17, 20176 / Module 10: Transformations and Similarity Unit 1: Real Numbers, Exponents, & Scientific Notation / Rigor Level
Rigor Level:
Conceptual & Application
Daily Agenda
Daily Objective: / The student will review standards EE.1.1, EE.1.2, EE.14 through a class activity. Students will show mastery of Unit 1 by taking a test.
Bell Ringer: / Write a problem based on scientific notation.
I Do: / Review bell ringerReview bell ringer and homework
We Do: / Remediation on standards EE.1, EE.2, EE.1.4Answer questions
You Do: / Participate in activityUnit 1 Assessment Readiness
Homework: / No homework – enjoy your weekendNo homework! Enjoy your weekend!
EXIT TICKET: / How can you start preparing for the FSA in class and at home?Find the square root of 49.
Note: Learning Scales and Accommodations are below.
Scale / Learning Goals Scale:Real NumbersSolving Systems of Linear Equations
4.0 / I can solve and analyze problems involving two linear equations in tow variables with rational coefficients or constants.
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 I can solve and analyze a system of equations in two variables with integer and benchmark fraction coefficients.
Ø I can solve mathematical and real-world systems of two linear equations in two variables with integer coefficients by inspection, algebraically by multiplying only one of the equations by and integer. Know when numbers are rational and irrational. Understand that every number has a decimal formation.
Ø Use rational approximations of irrational numbers to compare and locate on a number line and estimate the value of expressions.
Ø 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 I can interpret mathematical or real-world problems, given the graph, of a system of two linear equations in two variables.Know when numbers are rational and irrational. Understand that every number has a decimal formation.
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.