Embed Size (px)
Citation preview
FFuueell LLaannee Rigorous Assessments
December 4, 2014
Presenter: Erica Pifer and Regine Childs
Track Your Progress: Common Core State Standards for Mathematics in Action
Shade each rectangle to show your current understanding of each learning target.
I can describe strategies for increasing theDepth of Knowledge levels.
I can create assessments that reflect thebalanced rigor of the CCSS.
Next Steps…
Starting Getting There Got It!
Starting Getting There Got It!
1
2
Rigorous Assessments Grades 6‐10
Erica Pifer, Regine Childs, & Doug Barsotti
Common Core ‐Whattya know?
① Determine who is A, and who is B.② Partner A begins rolling the die.③ Partner B works as quickly as possible to
complete his/her version of the alpha grid bywriting in words and ideas associated withCCSS.
④ As soon as Partner A rolls a six, the roleschange.
⑤ Partner A works on his/her grid. Partner B rollsthe die.
⑥ Continue the process until time is called.⑦ The goal is to complete your individual grid with
an idea or word for every letter. January 2014
Depth of Knowledge (DOK)• Level 1: Recall and Reproduction
– Requires eliciting information such as a fact, definition, term, or a simple procedure, as well as performing a simplealgorithm or applying a formula.
• Level 2: Basic Skills and Concepts– Requires the engagement of some mental processing beyond a
recall of information.
• Level 3: Strategic Thinking and Reasoning– Requires reasoning, planning, using evidence,
and explanations of thinking.
• Level 4: Extended Thinking– Requires complex reasoning, planning, developing,
and thinking most likely over an extended period of time.
3
DOK Seat Time Guide
Level 125%
Level 325%
Level 250%
Recall and Reproduction
Strategic Thinking and Reasoning
Basic Skills and Concepts
Level 4Extended Thinking (Performance Task)
Claims Used in SBAC Test Specifications
Claim #1Concepts & Procedures
Claim #2Problem Solving
‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐Claim #4Modeling & Data
Analysis
Claim #3Communicating
Reasoning
Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency.
Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.
Students can solve a range of complex well‐posed problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐Students can analyze complex, real‐world scenarios and can construct and use mathematical models to interpret and solve problems.
40%
60%
4
Assessment Item Types• Selected Response (SR)
– Variety of multiple choice and true/false
• Technology Enhanced (TE)
– Technology embedded intoitems
• Constructed Response (CR)
– Free response questions in the Adaptive portion of the test
• Extended Response (ER)
– Non‐computer gradedconstructed response item
• Performance Tasks (PT)
– Rich, real‐world scenarios where multiple math topics are addressed
http://sbac.portal.airast.org/practice-test/
DOK MatchupIn groups of two or three, sort the SBAC questions into DOK levels (1, 2 or 3).
When you are finished, compare your sort with another group sorting the same level of questions.
DOK Matchup Share OutChoose one to two questions to share with the group.
• What did you notice about the question(s)?
• What surprised you?
• Are you incorporating these styles of questionsinto your tests?
5
Create higher level DOK tasks by asking students to:
• Write a word problem for a given expression.• Write a word problem with a given answer or range of
answers.• Use more than one strategy to solve.• Find the error in a student solution and correct.• Solve multi‐step problems.• Explain how you know your answer is correct.• Explain wrong answer choices (distractors) in selected
response items.• Solve open‐ended tasks with multiple possible
responses.
• Write a word problem for a given expression.
• Use more than one strategy to solve.
• Explain how you know your answer is correct.
Rigor is a balanced combination
Application
Fluency
Conceptual Understanding
RIGOR
If you shorten a leg, the stool falls over.If you shorten all the legs, you just can’t reach as high.
Rigor Component #1:Conceptual Understanding
12
• Teach more than “how to get the answer” andinstead support students’ ability to access concepts from a number of perspectives and paths
• Students are able to see math as more than a setof mnemonics or discrete procedures
• Conceptual understanding supports the otheraspects of rigor (fluency and application)
6
Rigor Component #2:Fluency
The NCTM Principles and Standards of Mathematics (2000) defines computational fluency as having
EFFICIENT, FLEXIBLE,
methods of computing.
andACCURATE
Rigor Component #3:Application
• Students can use appropriateconcepts and procedures for application even when not prompted to do so.
• Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations, recognizing this means different things in K‐5, 6‐8, and HS.
14
Rigor & DOK LevelsIn your binder on pages we have included two sample 8th or 9th grade exam.
Determine which exam reflects the rigor and ofthe CCSS.
Using the more rigorous assessment, determinethe DOK level of each question.
Also look at the assessment item types.
Does this exam include an appropriate sampling of DOK levels and assessment item types?
7
Assessment Peer ReviewIn your binders we have included an original and revised exam for 8th grade, Algebra, and Geometry.
Individually spend 5 minutes comparing theoriginal to the revised.
What do you notice about the DOK levels?
What do you notice about the types of questions?
In your table groups, share your findings.
Peer Review – Work Time• Exchange your unit exam with someonesitting at your table.
Assess the DOK level of each question.
Is there a variety of assessment item types?
Make recommendations for improvement.
Share resources.
Peer Review – Work TimeUse the Fuel Lane Unit Development guide to help you design a rigorous assessment for an upcoming unit.
Unit Assessments (Pre‐, Post‐, During Unit)
Essential Element
Represent Blend of Selected‐Response (Multiple Choice) and Constructed‐Response (Short‐ and Extended‐)
Valid (Measure What Intended to Measure); Reliable (Produce Consistent Student Responses Over Time)
Includes Depth of Knowledge (DOK) 1‐3 questions for each priority standard.
Match Format and Rigor of Common Core Sample Assessment Items (SBAC)
Progress Monitoring Checks: Create Short, Ungraded “Checks For Student Understanding” to Administer Throughout Unit of Study; Directly Aligned to Post‐Assessment Questions (Selected‐, Short‐, Extended‐Response); Coincide with Learning Progressions—the “Building Block Chunks” of Instruction.
Authentic Performance Tasks
Essential Element
Task(s) for Unit of Study
Includes Depth of Knowledge (DOK) 1‐4 for each task.
As a table group, choose a modified assessment to share with the whole group.
8
• NOTE: Few resources are aligned completely to ALL components of an SBAC performance task.
• http://balancedassessments.concord.org/ (all grades)
• http://www.nctm.org/rsmtasks/ (High School)
• http://schools.nyc.gov/Academics/CommonCoreLibrary/TasksUnitsStudentWork/default.htm (all grades)
• http://palm.sri.com/palm/ (Grades 3‐HS)
• http://insidemathematics.org/index.php/mathematical‐content‐standards (all grades)
• http://map.mathshell.org/materials/tasks.php (Grades 6‐12)
• https://www.georgiastandards.org/Common‐Core/Pages/Math.aspx (all grades)
Performance Task Resources
Contact Information
Doug Barsotti, SMc Curriculum
Erica Pifer
Regine Childs
9
10
A B C D
E F G H
I J K L
M N O P
Q R S T
U V W X
Y Z
Common Core - Whattya know?
11
12
Depth of Knowledge (DOK)
Source: www.smarterbalanced.org Mathematics Content Specifications
A “Snapshot” of the Cognitive Rigor Matrix (Hess, Carlock, Jones & Walkup, 2009) Depth of Thinking (Webb) + Type of Thinking (Revised Bloom)
DOK Level 1
Recall & Reproduction
DOK Level 2
Basic Skills & Concepts
DOK Level 3
Strategic Thinking & Reasoning
DOK Level 4
Extended Thinking
Remember Recall conversations,
terms, facts
Understand
Evaluate an expression
Locate points on agrid or number on number line
Solve a one-stepproblem
Represent math relationships inwords, pictures, or symbols
Specify, explainrelationships
Make basic inferences or logical predictions from data/observations
Use models/diagrams to explain concepts
Make and explainestimates
Use concepts to solve non-routine problems
Use supporting evidence to justify conjectures, generalize, or connect ideas
Explain reasoning when more than one response is possible
Explain phenomena in terms of concepts
Relate mathematical concepts to other content areas, other domains
Developgeneralizations of theresults obtained andthe strategies usedand apply them to new problem situations
Apply
Follow simpleprocedures
Calculate, measure, apply a rule (e.g., rounding)
Apply algorithm or formula
Solve linear equations Make conversions
Select a procedure and perform it
Solve routine problem applying multipleconcepts or decision points
Retrieve information to solve a problem
Translate between representations
Design investigation for a specific purposeor research question
Use reasoning, planning, andsupporting evidence
Translate between problem & symbolic notation when not a direct translation
Initiate, design, and conduct a project that specifies a problem, identifies solution paths, solves theproblem, and reports results
Analyze
Retrieve information from a table or graph to answer a question
Identify apattern/trend
Categorize data, figures
Organize, order data Select appropriate
graph and organize & display data
Interpret data from asimple graph
Extend a pattern
Compare information within or across datasets or texts
Analyze and draw conclusions from data, citing evidence
Generalize a pattern Interpret data from
complex graph
Analyze multiplesources of evidence or data sets
Evaluate
Cite evidence anddevelop a logical argument
Compare/contrast solution methods
Verify reasonableness
Apply understanding in a novel way, provide argument or justification for the new application
Create
Brainstorm ideas, concepts, problems, or perspectives related to a topic or concept
Generate conjectures or hypotheses basedon observations or prior knowledge and experience
Develop an alternativesolution
Synthesizeinformation withinone data set
Synthesizeinformation across multiple sources or data sets
Design a model to inform and solve a practical or abstract situation.
13
Level One Activities
Recall elements and details of story structure, such as sequence of events, character, plot and setting.
Conduct basic mathematicalcalculations.
Label locations on a map.
Represent in words or diagrams a scientific concept or relationship.
Perform routine procedures like measuring length or using punctuation marks correctly.
Describe the features of a place or people.
Level Two ActivitiesIdentify and summarize the major events in a narrative.
Use context cues to identify themeaning of unfamiliar words.
Solve routine multiple-step problems.
Describe the cause/effect of a particular event.
Identify patterns in events or behavior.
Formulate a routine problem given data and conditions.
Organize, represent and interpret data.
Level Three ActivitiesSupport ideas with details and examples.
Use voice appropriate to the purpose and audience.
Identify research questions and design investigations for a scientific problem.
Develop a scientific model for a complex situation.
Determine the author’s purpose and describe how it affects the interpretation of a reading selection.
Apply a concept in other contexts.
Level Four ActivitiesConduct a project that requiresspecifying a problem, designing and conducting an experiment, analyzing its data, and reporting results/solutions.
Apply mathematical model toilluminate a problem or situation.
Analyze and synthesizeinformation from multiple sources.
Describe and illustrate how commonthemes are found across texts fromdifferent cultures.
Design a mathematical model toinform and solve a practical or abstract situation.
Level Two(Skill/Concept)
Level One
(Recall)
Level Three
(Strategic Thinking)
Level Four(ExtendedThinking)
Arrange
Calculate
DefineDraw Identify
Illustrate
LabelList
Match
Measure
Memorize
Name
QuoteRecall
ReciteRecognize
Repeat ReportState
TabulateTell Use
Who, What, When, Where, Why
DescribeExplain
Interpret
Categorize
Cause/Effect
Collect and Display
Classify
Compare
Construct
Distinguish
Estimate
GraphIdentify Patterns
Infer
Interpret
Make Observations
Modify
Organize
Predict
Relate
Separate
Show
Summarize
Use Context Cues
Apprise
Assess
Cite Evidence
Compare
Construct
Critique
Develop a Logical Argument
DifferentiateDraw Conclusions
Explain Phenomena in Terms of ConceptsFormulate
Hypothesize
Investigate
Revise
Use Concepts to Solve Non-Routine Problems
Apply Concepts
Design
Connect
Prove
Synthesize
Critique
Analyze
Create
Depth of Knowledge (DOK) Levels
Webb, Norman L. and others. “Web Alignment Tool” 24 July 2005. Wisconsin Center of Educational Research. University of Wisconsin-Madison. 2 Feb. 2006. <http://www.wcer.wisc.edu/WAT/index.aspx>.
14
Which Chapter Test (G or H) meets the Rigor of the CCSS?
Test G (8th or 9th grade systems test)
Rigor and Balance: Materials and tools reflect the balances in the Standards and help students meet the Standards' rigorous expectations (conceptual understanding, procedural skill and fluency, and application).
15
16
Which Chapter Test (G or H) meets the Rigor of the CCSS?
Test H (8th or 9th grade systems test)
1. How can graphing a system of equations help you find its solution?
Solve the linear system.
2. 7x + 4y = 5 3. x – 6y = -19 4. 4x + 3 = 2y -7
-3x + 6y = 24 𝑦 = −23𝑥 − 1 2(2x – y) = -10
5. 2x + 4y = 12 6. 3(x + 4) = y 7. ½ x – 4 = ¾ y + 2
5 + 2(x -5) = y – 3.5 2y – 2x -10 = 4x 13𝑥 + 2 = 2
3𝑦 − 1
Check your solutions for two of the systems from #2-#6 above by graphing them below.
8. 9.
10.
a. Draw a line that intersects this line.
b. Write a system of equations that is represented by these two lines.
c. What is the solution to the system?
Rigor and Balance: Materials and tools reflect the balances in the Standards and help students meet the Standards' rigorous expectations (conceptual understanding, procedural skill and fluency, and application).
17
11. Olivia said she can solve the system 2x + 5y = 12 and 2x + 5y = 4 in her head without doing any written work. Explain what youthink she did, what you think her solution was and how you know you are right.
12. Your grandparents are going to get a new cell phone and need to choose between two cell phone companies. They havenarrowed their choice to two plans. Bell Phone Company charges $40 per month. It offers unlimited calling and $0.05 per text sent. Ring Phone Company charges $60 per month. It costs $0.01 per text sent. How many texts would they have to send for the two plans to cost the same? Show the steps you used to solve this.
13. You have been selected by the members of your eighth-grade team (Team A) to participate in a one-mile race (5280 ft.) on FieldDay. Another student from Team B will race against you. You are able to run 12 feet per second. Since the student from Team B runs 10 feet per second, you have been asked to let him have a 1000-ft. head start. If both of you maintain the estimated rates (12 feet per second and 10 feet per second), would you be able to beat your opponent? Show how this can be solved using a system of equations.
14. “Give me 8 sheep and then we will have an equal number,” said Shepherd Sam to Shepherd Pat. “No, you give 8 sheep andthen I will have twice as many as you,” replied Shepherd Pat. How many sheep did each shepherd have to start with? Show your work.
18
Test (Original) ~ Using Linear Equations Name__________________________________________ Period______ Date____________
1. Which of the following linear equations hasa negative slope?
A. 52 −= xy B. xy 74 −= C. 3−=y D. 1−=x
2. What is the slope-intercept equation for thegraph shown below?
A. 221 += xy
B. 22 += xy C. 12
1 −= xy D. 12 −= xy
3. What is the slope-intercept equation of theline with a slope of 4
3 and a y-intercept of 4?
A. 434 += xy
B. 443 += xy
C. 0443 =+ yx
D. xy 434=
4. What is the slope-intercept equation of theline that goes through the points (3, 5) and (−1, 13)?
A. 12 −= xy B. 12 +−= xy C. 2
121 3+= xy
D. 112 +−= xy
5. Which of the following equations isequivalent to 7)2(3 +−= xy ?
A. 13 += xy B. 133 −= xy C. 13 −= xy D. 53 += xy
6. Convert the following equation to slope-intercept form:
1423 =+ yx
A. 1432 +−= xy B. 73
2 += xy C. 72
3 += xy D. 72
3 +−= xy
7. The graph below shows the height of aflower based on the number of weeks since it was planted. What is the linear equation representing this situation?
A. xy 22 +=B. 12 += xy C. xy 2= D. 2+= xy
8. Which of the following equations is NOT alinear function?
A. xy −= 6 B. 4)1(5 −+= xy C. 22 −= xy D. xy 5
28 +−=
19
Write an equation in slope-intercept form given information about each line.
9. slope = 53 , y-intercept = 6 Answer: ____________________
10. slope = −3, goes through the point (1, 2) Answer: ____________________
11. goes through the points (4, 9) and (2, 8) Answer: ____________________
Convert each equation to slope-intercept form. Box your answer.
12. )1(43 −+= xy 13. 632 −=+− yx 14. )10(2 21 +=+ xy
15. Is the point (−5, 1) on the line 92 −−= xy ? Support your answer with work.
16. A bike rental company rents beach bikes. They charge an initial fee plus $1 for each hour thebike is rented. Chet rented a bike for 6 hours and was charged $10. Let x represent the numberof hours and y represent the total cost of the rental.
a. Identify the slope and one ordered pair from the information given.
Slope: _____ Ordered Pair: ________
b. What is the slope-intercept equation of the line that fits this information?
c. If another customer rents a bike for 4 hours, how much should he expect to pay?
20
PPrroobblleemm SSoollvviinngg
At 3 weeks old, Sam’s puppy weighed 2 pounds. When the puppy was 7 weeks old, he weighed 4 pounds. If the puppy continues to grow at this rate, how much will it weigh when it is 12 weeks old?
21
22
Test ~ Using Linear Equations Name__________________________________________ Period______ Date____________ 1. Which of the following linear equations has a negative slope? Select all that apply. A. 52 −= xy E. 𝑦𝑦 = −7 − 2𝑥𝑥 B. xy 74 −= F. 𝑦𝑦 = 2
3𝑥𝑥 + 11
C. 3−=y G. 𝑦𝑦 = −3𝑥𝑥 D. 1−=x H. 𝑦𝑦 = 14𝑥𝑥 2. What is the slope-intercept equation for the graph shown below? A. 22
1 += xy B. 22 += xy C. 12
1 −= xy D. 12 −= xy 3. What is the slope-intercept equation of the line with a slope of 4
3 and a y-intercept of 4?
A. 434 += xy
B. 443 += xy
C. 0443 =+ yx
D. xy 434=
4. What is the slope-intercept equation of the line that goes through the points (3, 5) and (−1, 13)?
A. 12 −= xy B. 12 +−= xy C. 2
121 3+= xy
D. 112 +−= xy
5. Which of the following equations is equivalent to 7)2(3 +−= xy ? Select all that apply A. 13 += xy E. 𝑦𝑦 = 3𝑥𝑥 − 1 B. )1(313 −=+ xy F. −1 + 𝑦𝑦 = 3𝑥𝑥 C. 339 =+ yx G. 𝑦𝑦 = 3(𝑥𝑥 + 4) − 11 D. 53 += xy H −2𝑦𝑦 = −6𝑥𝑥 − 2 6. Convert the following equation to slope-intercept form:
1423 =+ yx A. 1432 +−= xy B. 73
2 += xy C. 72
3 += xy D. 72
3 +−= xy 7. Which of the following equations is NOT a linear function? A. xy −= 6 E. 𝑦𝑦 = 4
𝑥𝑥
B. 4)1(5 −+= xy F. 𝑦𝑦 = −5𝑥𝑥 C. 22 −= xy G. 4𝑥𝑥 + 2𝑦𝑦 = −10 D. xy 5
28 +−= H. 9 + 2𝑦𝑦 = √𝑥𝑥 − 7 8. The graph below shows the height of a flower based on the number of weeks since it was planted. What is the linear equation representing this situation? A. xy 22 += B. 12 += xy C. xy 2= D. 2+= xy 9. Interpret the slope from question 8 in the context of the situation.
23
Write an equation in slope-intercept form given information about each line. 10. slope = −3, goes through the point (1, 2) Answer: ____________________ Circle the step with the error. Then correctly write the equation in slope intercept form. 11. a line goes through the points (4, 9) and (2, 8)
1. 𝑚𝑚 = 9−84−2
2. 𝑚𝑚 = 12
3. 2 = 12
(8) + 𝑏𝑏 4. 2 = 4 + 𝑏𝑏 5. −2 = 𝑏𝑏 6. 𝑦𝑦 = 1
2𝑥𝑥 − 2
Convert each equation to slope-intercept form. Box your answer. 12. 632 −=+− yx 14. )10(2 2
1 +=+ xy 13. Is the point (−5, 1) on the line 92 −−= xy ? Support your answer using two methods.
24
14. A bike rental company rents beach bikes. They charge an initial fee plus $1 for each hour the bike is rented. Chet rented a bike for 6 hours and was charged $10. Let x represent the number of hours and y represent the total cost of the rental. a. Identify the slope and one ordered pair from the information given. Slope: _____ Ordered Pair: ________ b. What is the slope-intercept equation of the line that fits this information?
c. If another customer rents a bike for 4 hours, how much should he expect to pay? Justify your answer. d. If a customer had $21, for how many hours could they rent a bike? Explain your answer.
15. At 3 weeks old, Sam’s puppy weighed 2 pounds. When the puppy was 7 weeks old, he weighed 4 pounds.
a. If the puppy continues to grow at this rate, how much will it weigh when it is 12 weeks old?
b. Determine the weight of the puppy in 8 years and explain your process. Does this answer make sense? Why or why not?
25
26
Test Chapter 3 Part 1 – NO CALCULATOR ALLOWED Name:____________________________________________ Period:________________ Date:_______________ Use the figure at right for Problems 1–5, suppose a || b and c || d. 1. ∠2 and ∠10 are what kind of angles? ______________________________________________ 2. ∠3 and what angle are alternate interior angles? ______________________________________________ 3. If m ∠6 =
50°, then find m ∠11. ______________________________________________ 4. If m ∠2 =
70°, then find m ∠5. ______________________________________________ 5. If m ∠1 =
130°, then find m ∠12. ______________________________________________ Use the given information to find the equation of the line. 6. slope 3, y-intercept -1 ____________________________
7. passes through points (0,3) and (1, 4) ____________________________
8. passes through points (1, 3) and (–4, 8) ____________________________
In a triangle, ∠1, ∠2, and ∠3 are interior angles, and ∠4 is an exterior angle with remote interior angles ∠2 and ∠3. Find the missing angle measures. 10. m∠2 =
50° and m∠3 =
80° ∠1 =_______________ ∠4 =_______________
11. m∠4 =
100° and m∠2 =
50° ∠1 =_______________ ∠3 =_______________
12. m∠1 =
75° and m∠3 =
20° ∠2 =_______________ ∠4 =_______________
13. m∠4 =
110° and m∠2 =
70° ∠1 =_______________ ∠3 =_______________
Determine whether the following pairs of lines are PARALLEL, PERPENDICULAR, or NEITHER Identify the slopes of line 1 and line 2 (
m1 and
m2)
14.
y = 2x +12x + y = 7
_____________________
m1 = _______
m2 = ______
15.
3x + y = 2
y =13
x + 4 _____________________
m1 = _______
m2 = ______
16.
y = −4 x +14x + y = −3
_____________________
m1 = _______
m2 = ______
17.
y = 3x − 2−3x + y = 5
_____________________
m1 = _______
m2 = ______ 27
18. What is the equation of the line parallel to
y − x = −1 that contains the point
1,2( )?
19. What is the equation of the line perpendicular to
y =12
x +1 that contains the point
−2,1( )?
20.
AB contains the points
−2,1( ) and
−1,8( ). What is the equation of the line parallel to
AB that contains point
0,2( )?
28
29
30
RADICALS TEST Name ___________________ Period _____ Please box your final answers. SHOW ALL WORK. All answers should be in reduced radical form (no decimals!) Reduce each radical. 1. 2. 3. Simplify each radical expression. Answers with radicals should be in reduced radical form.
4. 5. 6. 7.
8. 9. 10.
11. 12. 13.
31
Solve each equation using the square root method. 14. 15.
16. 17.
Solve each equation algebraically. Check your solution(s). 18. 19. 20. Use Pythagorean Theorem to find the value of x. 21. 22. 23.
24. A 26-ladder leans up against a building. The base of the ladder is 10 feet from the building. How far does the ladder reach up the building
2
6 15
x x 12
x
32
Find the distance between the points. Use the distance formula to find the
distance between the points: 25. 26.
27. 28.
33
34
RADICALS TEST Name ___________________ Period _____ Please box your final answers. SHOW ALL WORK. All answers should be in reduced radical form (no decimals!) Reduce each radical. 1. 2. 3. Simplify each radical expression in two different ways. Answers with radicals should be in reduced radical form.
4. 5.
6. Explain why = 144. Be clear and complete in your explanation.
Simplify each radical expression. Answers should be in reduced radical form. 8. 9.
35
10. Is it possible to add the terms in the following radical expression 7811473 −+ Yes No Justify your answer. Be clear and precise. Simplify each radical expression . Answers should be in reduced radical form.
11. 12. 13.
Solve each equation using the square root method and check your solution.
14. 15.
36
16. Compare and contrast the next two equations. a) What is different and what is the same. b) Categorize each equation c) Solve each equation 3x + 5 = 65 Solve each equation algebraically. Check your solution(s). Show your work 17. 18. 19. Assume the following triangle is a right triangle. Explain how to find the value of x.
15
x 12
37
20. You are trying to reach a window that is 15 feet off the ground at a building. You lean a 26
foot ladder up against the building so that the base of the ladder is 10 feet from the building. Does the ladder reach the window? If not how what can the person do so that the ladder
will reach the window- Prove mathematically.
21. Use two different methods to find out how far apart the following coordinates are. ( ) ( )1612 −− ,,,
38
Fuel Lane - Unit Development Guide 1.0 The following criteria are provided for use when designing units of study. Please check off each essential element that is included and complete. Provide any comments or feedback that will enable the unit designer to make any necessary adjustments or revisions in the notes section at the bottom. Grade Level/Subject: _____________________________ Approximate Number of Instruction Days (including buffer, remediation, and enrichment):_________________
Unit Standards – Priority & Supporting Essential Element Lists Bolded, Full Text and Coding of Targeted Priority Standards for Unit Lists Full Text and Coding of Supporting Standards for Unit Limits Total Number of Unit Standards to Ensure Depth of Instruction and Student Understanding
Unit Identifying Information Essential Element Includes Identifying Unit Information (i.e., Subject, Grade/Course, Name Of Unit) Pacing Includes Number of Instruction Days and Number of “Buffer” Days (for Remediation and Enrichment)
Unit Assessments (Pre-, Post-, During Unit) Essential Element Represent Blend of Selected-Response (Multiple Choice) and Constructed-Response (Short- and Extended-) Valid (Measure What Intended to Measure); Reliable (Produce Consistent Student Responses Over Time) Includes Depth of Knowledge (DOK) 1-3 questions for each priority standard. Match Format and Rigor of Common Core Sample Assessment Items (SBAC) Progress Monitoring Checks: Create Short, Ungraded “Checks For Student Understanding” to Administer
Throughout Unit of Study; Directly Aligned to Post-Assessment Questions (Selected-, Short-, Extended-Response); Coincide with Learning Progressions—the “Building Block Chunks” of Instruction.
Materials / Resources/Vocabulary Essential Element Include Suggested and/or Required Lists of Needed Instructional Materials and Where Obtained (e.g., Articles,
Websites, Text Selections, Teacher-Created Resources, Technology Hardware and Software, Etc.) Identifies Both Academic Vocabulary of Standards and Additional Content Vocabulary Specific to Unit
Pacing Includes Number of Instruction Days and Number of “Buffer” Days (for Remediation and Enrichment)
Authentic Performance Tasks Essential Element Task(s) for Unit of Study Includes Depth of Knowledge (DOK) 1-4 for each task.
Notes:
39
40
Rigorous Assessments Workshop
InPresenters: Regine Childs, Erica Pifer Job Title: TOSAs Location: Date:
Mapleton12/5/14
Ratings Poor Fair Satisfactory Good Excellent
Content & Presentation – Comments:
Applicability of Content Comments:
Use of Time Comments:
Materials/Handouts Comments:
Workshop Design Comments:
Evaluation/Next Steps
Additional Comments:
I would like additional support with the following topics:
41
