UNIT UNDERSTANDING: UNIT 5 EXPRESSIONS AND EQUATIONS II
SUBJECT/GRADE/YEAR: ALGEBRA/8/2012-2013
STAGE 1 – DESIRED RESULTS (STANDARD)
POWER STANDARD (S): What CCSS/ISBE/National Standard(s) TRANSFER GOAL: Applies the Power Standard to a “novel” real world situation.
T will this unit address? https://ccgps.org/8.EE_DFKO.html
R 8EE.5, 8EE.6
A • Graph proportional relationships, interpreting the unit rate as the
slope of the graph. Compare two different proportional relationships
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represented in different ways. For example, compare a distance-time
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graph to a distance-time equation to determine which of two moving
objects has greater speed.
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• Use similar triangles to explain why the slope m is the same between
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any two distinct points on a non-vertical line in the coordinate plane;
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derive the equation y = mx for a line through the origin and the
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statement of what students should be able to do with the standard knowledge in other
contexts. Students will be able to independently use their learning on a long-term basis to…
•Model a real world situation they observe algebraically and draw conclusions representing their
findings.
equation y = mx + b for a line intercepting the vertical axis at b.
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ESSENTIAL UNDERSTANDINGS:
What specific understandings
can be predicted from the Power Standard(s)?
ESSENTIAL QUESTIONS: What thought provoking questions would foster inquiry,
•Understand the connections between proportional relationships, lines,
and linear equations
• Understand that the slope m is the same between any two distinct
points on a nonvertical line in the coordinate plane. (This is shown using
similar triangles.)
How can proportional and non-proportional linear relationships be represented and compared
in graphs, tables and equations?
understanding, and transfer of learning?
KNOWLEDGE: What should students know as a result of this unit? What can be studied? (Theory/Concepts/Mental Coordination)
 Students will know…
• graphic, symbolic & numerical representations of proportional relationships
• constant rate of change
• unit rate is the slope of a proportional relationship
• proportional relationships start at the origin
• When two quantities vary in such a way that one of them is a constant multiple of the other, the two quantities are “proportional”. Conversely, two quantities are
proportional when they vary in such a way that one of them is a constant multiple of the other, i.e., they have a constant ratio.
• similar right triangles can be used to establish that slope is constant for a
non-vertical line
• graphically derive equations y = mx and
y = mx + b
SKILLS:
What should students be able to do as a result of this unit? What can be practiced? (Application of Theory/Concepts/Physical Coordination)
 Students will be able to…
• Graph a proportional relationship given a table, equation or contextual situation.
• Recognize unit rate as slope and interpret the meaning of the slope in context.
• Recognize that proportional relationships include the point (0,0).
• Compare different representations of two proportional relationships represented as contextual situations, tables, graphs, or equations.
• Explain why the slope is the same between any two distinct points on a line using similar right triangles.
• Write an equation in the form y = mx + b from a graph of a line on the coordinate plane.
• Determine the slope of a line as the ratio of the leg lengths of similar right triangles.
STAGE 2 –EVIDENCE (ASSESSMENT)
SUMMATIVE PERFORMANCE ASSESSMENT (S): Is each standard and transfer goal being assessed? An authentic assessment(s) designed to show how students
demonstrate their understanding of essential questions and transfer goals when applied to a new, varied, or realistic situation. Should be written in the GRASPS format and
reflect the UbD “Six Facets of Understanding.”
•Using graphs of experiences that are familiar to students increases accessibility and supports understanding and interpretation of proportional relationship. Students
are expected to both sketch and interpret graphs.
Example:
 Compare the scenarios to determine which represents a greater speed. Include a description of each scenario including the unit rates in your explanation.
Scenario 1:
Scenario 2:
y = 50x
x is time in hours
y is distance in miles
•Assessments (quizzes)
•Summative Assessment – Direct Variation Task (8.EE.5)
• Graphing Calculator activity (from Sheila)
ASSESSMENT CRITERIA: What criteria will be used in each assessment to evaluate attainment of each desired result? What are the qualities by which learning is judged?
Think rubric components!!! (Content, Process, Product, knowledge, skill)
Constructively aligned assessment criteria begin with a noun that complements the verb in the assessment tasks objective. If the objective is for students to "explain how concepts in the
subject interrelate" one of the criteria might be "Clarity of explanation". That is, the criterion describes the quality in the assessment task that will be judged as an assessment. Other
commonly used quality words used in criteria include: Accuracy, Currency, Depth, Impact, Legibility, Originality, Succinctness, and Relevance.
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FORMATIVE ASSESSMENT EVIDENCE: What daily evidence has been collected to determine goal attainment? Tests, quizzes, discussions, homework, exit slips, graphic
organizers, note-taking, etc…
• Homework – WSQ (Watch, Summarize, Question
 Class notes
 Math talks/Class discussion
 Exit slips
 Warm-ups/closure
 Note-taking and classroom participation
 Teacher observations
 Interactive notebook
• Graphing Calculator activity from Sheila
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STAGE 3 – LEARNING PLAN (ACTIVITY)
PRE-ASSESSMENT: What will be done to determine students’ background knowledge, skill level, and possible misconceptions? (K-W-L) How will students be grouped?
What opportunities for differentiation will take place?
 8.EE.5
 8.EE.6
ALIGNED LEARNING ACTIVITIES: What will be done each day to foster student success at transfer, meaning, and acquisition? How will critical thinking, problem
solving, and systems thinking be incorporated? Consider the “Gradual Release of Responsibility Model” and “WHERETO” format when developing daily experiences linked to
Stages 1 and 2.
DATE(S) “WE WILL…” OBJECTIVE:
How are action verbs used to
link content to the Power
Standard for each learning
experience?
See Math site for detailed
plans
PROCEDURES:
What is the daily lesson plan process? What is the step-by-step path of
learning? How are learning activities prioritized and sequenced in an engaging
and time sensitive manner? How are learning experiences differentiated or
modified to meet assessed learning needs? How are the daily products
connected to Summative Performance Tasks?
PROGRESS MONITORING:
How is progress toward transfer, meaning,
and acquisition regularly monitored?
What are the misunderstandings?
How will students receive relevant
feedback?