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2010 Alabama Course of Study: Mathematics
College- and Career-Ready Standards
Professional Development: Grades 9 – 12 Phase I
Regional Inservice CenterSummer 2011
PART B
Literacy Standards for Grades 6 – 12
2010 Alabama Course of Study: Mathematics
College- and Career-Ready Standards
“These standards are designed to supplement students’
learning of the mathematical standards by helping them meet
the challenges of reading, writing, speaking, listening, and
language in the field of mathematics.”
APPENDIX CLiteracy Standards for Grades 6 – 12History/Social Studies, Science and Technical Subjects
• select and develop resources that ensure students can connect their curriculum with the real world.
It is essential for educators to:
•provide students with opportunities to participate in mathematical investigations.
• help students recognize and apply math concepts in areas outside of the mathematics classroom.
•help students develop problem-solving techniques and skills which enable them to interconnect ideas and build on existing content.
Basis of Literacy Standards
The Literacy Standards for Reading and Writing
are based on the College and Career Readiness (CCR) anchor standards as outlined in the
English Language Arts (ELA) common core.
Both of which are outlined in Appendix C.
Layout of the Literacy Standards
Appendix C
p. 128 College and Career Readiness Anchor Standards for Reading
p. 129 Reading Standards for Literacy in History/Social Studies 6-12
p. 130 Reading Standards for Science and Technical Subjects 6-12
p. 131 College and Career Readiness Anchor Standards for Writing
p. 132 Writing Standards for Literacy in History/Social Studies, Science and Technical Subjects grades 6-12 (through p. 134)
Snapshot View
Notice that the ten reading
standards are in grade spans.
6-8
9-10
11-12
A great layout to assist
teachers in differentiating instruction!
A closer look:
1.Cite specific textual evidence to support analysis of science and technical texts.
1. Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions.
1. Cite specific textual evidence to support analysis of science and technical texts, attending to important distinctions the author makes and to any gaps or inconsistencies in the account.
Famous Mathematician Cards
(aka: ‘The Baseball Card Project’)
FRONT
BACK
Another Reading Standard:
Grades 6 – 8:Students should be able to read a word problem and create an image of some sort (diagrams, graphs, etc…)
Grades 9 – 10:Students should ALSO be able to reverse this skill: translate diagrams and charts into meaningful problems or equations.
Grades 11 – 12:Finally, they should expand this skill to other sources (video, data) and use it to address questions and solve problems.
Problem: Settlers in the Old West would often fashion tents out of a piece of cloth thrown over tent poles. They would secure it to the to the ground with stakes forming an isosceles triangle for the opening. How long would the cloth have to be so that the opening of the tent was 4 meters high and 6 meters wide?
Grade 8 Mathematics / Standard 22Course Standard:22. Apply the Pythagorean
Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
ELA Standard: Reading Standard 7: Integrate quantitative or technical information expressed in words in a text with a version of that information expressed visually.
Solution:
Teacher/Instructional Leader Notes: • Expressing answers as a complete sentence incorporates routine writing.•Continually express the importance of accuracy and clarity in diagrams. •Assess student ability to translate the word problem into a diagram separately from the ability to solve a problem.•It is vital to include word problems in mathematics instruction. •It is equally important students be given an opportunity to share idea’s or concerns about their work and to receive timely feedback.
6
4
3 (1/2 of 6)
Original Problem: Settlers in the Old West would often fashion tents out of a piece of cloth thrown over tent poles. They would secure it to the to the ground with stakes forming an isosceles triangle for the opening. How long would the cloth have to be so that the opening of the tent was 4 meters high and 6 meters wide?
The vertical pole forms 2 right triangles, so I am using the Pythagorean Theorem. a2 + b2 = c2
32 + 42 = c2
9 + 16 = c2
25 = c2
5 = cBut, there are two sides to the tent, so the material needs to be 10 meters long.Answer: The cloth needs to be 10 meters long.
Problem: Identify the word problems below as linear, quadratic, simple rational or exponential stating evidence for your choice. Then, write an equation using variables when appropriate. Solve your equation. 1. A car travels 125 miles in 3 hours. How far would it travel
in 5 hours?2. At a concert, Nabila purchased three t-shirts and a concert
program that cost $15. In total, Nabila spent $90. Find the cost of a single t-shirt if they were all the same price.
3. The product of two consecutive positive even integers is 14 more than their sum. Find the integers.
Algebra I / Standard 11Course Standard: 11. Create equations
(inequalities) in one variable and use them to solve problems (linear, quadratic, simple rational, exponential) .
ELA Standard:Reading #4: Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to their grade level.
Solution:
1. The first problem is a simple rational equation. It compares miles and hours:
so, 3x = 625 and x = 208.3 miles * Answer: The car would travel 208.3 miles in 5 hours.
2. The second problem is linear because it has one unknown, the price of the t-shirts. Let x be the number of t-shirts 3x+15 = 90 so, x = 25Answer: The cost of each t-shirt is $25.
3. The final problem is quadratic because it has two unknowns but the second one is related to the first.Let x be the initial even number; (x+2) is the next consecutive even integerx(x+2) = 14 + x + (x+2)
x2 + 2x = 16 + 2x x2 = 16, Answer: The first number is 4 and the second number is
6 . x = 4. Proof: 6+4 = 10 and 6(4) = 24 which is 14 more than 10.
Teacher/Instructional Leader Notes: •Assess for student logic and ability to pull key vocabulary used in mathematical text.
•Reading problems provide the teacher with tremendous insight into students understanding.
Snapshot View : Writing Standards (page 1 of 3)
Original Problem: Identify the word problems below as Linear, quadratic, simple rational or exponential stating evidence for your choice. Then, write an equation using variables when appropriate. Solve your equation.
1. A car travels 125 miles in 3 hours. How far would it travel in 5 hours?
2. At a concert, Nabila purchased three t-shirts and a concert program that cost $15. In total, Nabila spent $90. Find the cost of a single t-shirt if they all had the same price.
3. The product of two consecutive positive even integers is 14 more than their sum. Find the integers.
REVISITING: Algebra I, Standard 11
Original Standard: 11. Create
equations (inequalities in one variable and use them to solve problems (linear, quadratic, simple rational, exponential) .
NEXT Standard: Writing Standard #1: Write arguments focused on discipline-specific content.
NEW ASSIGNMENT: The teacher presents problems from the original assignment
which were labeled incorrectly, had faulty logic and/or incorrect solutions. Randomly distribute and direct students to write a brief argument for each problem to either defend or dispute the logic used.
Snapshot View : Writing Standards p. 2
Close-up:2. Write informative/explanatory
texts, including the narration of historical events, scientific
procedures/ experiments, or technical processes:
• Introduction
• Development of ideas• Transitions• Vocabulary
• Style• Conclusion
Writing Standard #3
In science and technical subjects, students must be able to write
precise enough descriptions of the step-by-step procedures they use in
their investigations or technical work so others can replicate them
and (possibly) reach the same results.
Snapshot View : Writing Standards p. 3
A closer look:
*The same for all three levels
10. Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for range of discipline-specific tasks, purposes, and audiences.
Questioning that Encourages Thought
•Does the rule I am using work for all cases? Why, why not?•How can I describe what is happening without using specific numbers?
•How can I predict what’s going to happen without doing all the calculations?
•Was my prediction correct; how was my logic faulty?•What process reverses the one I am using and when is it appropriate?
•How did two different students reach two different answers? Defend logic.
•Are there multiple ways to work the same problem? If so, how did you decide which process to use?
•Can you write a scenario (word problem) for the diagram?•Describe your frustrations with the process learned today.•Outline everything you understand about the process you used today.
Driscoll, M. Fostering Algebraic Thinking
Problem: Mr. Smith asked his students to plot the following points in order, connecting them to form a triangle: (3,0) (7, 1) (4, 5) (3,0). Here are the student responses. Which is correct? Describe the errors in logic made on the remaining three and the result of those errors.
A B C D.
Grade 8 / Geometry Standard 18Course Standard: 18. Describe the effect
of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. [G3]
ELA Standard(s):Reading Standard 7: Integrate
quantitative or technical information expressed in words in a text with a version of that information expressed visually.
Writing Standard 2f: Provide a concluding statement that follows from and supports the information presented.
Possible Solution:A B C D
a) Triangle A is plotted correctlyb) In triangle B, the student switched the (x,y)
coordinates. Instead of plotting (3,0) they plotted (0, 3). The student might be confused about which axis is the x and which axis is the y.
c) In Triangle C, the student went in the negative direction for the x coordinate but plotted the y correctly, this caused a reflection around the y-axis.
d) In triangle D the student plotted the x coordinate correctly but went in the negative direction for the y, this caused a rotation and a shift in the graph.
Teacher/Teacher Leader Notes
• Is the student’s mathematical logic correct?
• Can they describe errors found in others’ mathematical thinking?
• Activities like this may be used as a bell ringer (sparking discussion prior to a lesson) or as an exit slip to assess understanding.
• It is important that the responses are assessed by the teacher through grading or discussion.
Final Thought:The Literacy Standards allow Flexibility in Reading and Writing
Proof
s
Writing directionsfor replication by others
Descriptions of Process or change
ReflectionJournal
s
Compare/Contrast
methods
Predictions
Word
Problems Summarize
?? Questions ??
2010 Alabama Course of Study: Mathematics
College- and Career-Ready Standards
Domains of Study/Conceptual Categories
Learning Progressions/Trajectories
Aligned with college and work expectations Written in a clear, understandable, and consistent
format Designed to include rigorous content and
application of knowledge through high-order skills Formulated upon strengths and lessons of current
state standards Informed by high-performing mathematics
curricula in other countries to ensure all students are prepared to succeed in our global economy and society
Grounded on sound evidence-based research
CHARACTERISTICS
Coherent Rigorous Well-Articulated Enables Students to Make Connections
2010 Alabama Course of Study: Mathematics
Articulated progressions of topics and performances that are developmental and connected to other progressions.
Conceptual understanding and procedural skills stressed equally.
Real-world/Situational application expected.
Coherence
Key ideas, understandings, and skills are identified.
Deep learning stressed.
FOCUS
Mathematical Content Format
K-8 9-12
Grade
Domain
Cluster
Standard
Course
Conceptual Category
Domain
Cluster
Standard
What’s the difference?DomainClusterStandards
Domain: Overarching “big ideas” that connect content across the grade levels.
Cluster: Group of related standards below a domain.
Standards: Define what a student should know (understand) and do at the conclusion of a course or grade.
What’s the difference?
Overarching big ideas that connect mathematics across high school
Illustrate progression of increasing complexity
May appear in all courses
Organize high school standards
High School Conceptual Categories
Number &
QuantityAlgebra Functions Modeling Geometry Statistics &
Probability
The Real Number System
Seeing Structure
in Expressio
ns
Interpreting Functions Modeling is
best interpreted not as a collection of isolatedtopics but rather in relation to other standards. Making mathematical models isa Standard for Mathematical Practice, and specific modeling standards appearthroughout the high school standards indicated by a star symbol (★).
Congruence
Interpreting Categorical
and Quantitative
Data
Quantities
Arithmetic with
Polynomials &
Rational Expressio
ns
Building Functions
Similarity, Right
Triangles, and
Trigonometry
Making Inferences
and Justifying Conclusions
The Complex Number System
Creating Equations
Linear, Quadratic
and Exponential
Models
Circles
Conditional Probability
and the Rules of Probability
Vector and Matrix
Quantities
Reasoning with
Equations and
Inequalities
Trigonometric Functions
Expressing Geometric Properties
with Equations
Using Probability to
Make Decisions
Geometric Measuremen
t and Dimension
Modeling with
Geometry
High School Conceptual Categories
Domain
s
Multiple Courses
Illustrate Progression of Increasing Complexity from Grade to Grade
High School Clusters
Algebra I Algebra II with TrigonometryInterpret the structure of expressions. (Linear, exponential, quadratic.)7. Interpret expressions that represent a quantity in terms of its context.* [A-SSE1]
a. Interpret parts of an expression such as terms, factors, and coefficients. [A-SSE1a]
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. [A-SSE1b]
8. Use the structure of an expression to identify ways to rewrite it. [A-SSE2]
Interpret the structure of expressions. (Polynomial and rational.)6. Interpret expressions that represent a quantity in terms of its context.* [A-SSE1]
a. Interpret parts of an expression such as terms, factors, and coefficients.
[A-SSE1a]b. Interpret complicated expressions by
viewing one or more of their parts as a single entity. [A-SSE1b]
7. Use the structure of an expression to identify ways to rewrite it. [A-SSE2]
9-12 Cluster
Content standards in this document contain minimum required content.
Each content standard completes the phrase “Students will.”
Reflect both mathematical understandings and skills, which are equally important.
Content Standards
Conceptual Categories• Cross course boundaries • Span high school years
Standards– “Core” for common mathematics curriculum for all
students to be college and career ready– “College and Career Ready” for entry-level, credit-
bearing academic college courses and work-force training programs.
– “STEM” (+) Additional mathematics that students should learn in order to take courses such as calculus, discrete mathematics, or advanced statistics.
High School Standards
High School Conceptual Categories
Jigsaw Activity
Geometry
Modeling
Algebra
FunctionsNumber
&Quantity
Statistics
&Probability
How many skills?3. Explain why the sum or product of two rational numbers is
rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. [N-RN3]
AI.3.1. Explain why the sum of two rational numbers is rational.AI.3.2. Explain why the product of two rational numbers is rational.AI.3.3. Explain that the sum of a rational number and an irrational
number is irrational.AI.3.4. Explain that the product of a nonzero rational number and an
irrational number is irrational.
MathematicsDomains of Study by Grade
K 1 2 3 4 5 6 7 8 Counting and Cardinality
Operations and Algebraic Thinking
Number and Operations in Base Ten
Measurement and Data
Geometry
Number and Operations: Fractions
Ratios and Proportional Reasoning
The Number System
Expressions and Equations
Statistics and Probability
Functions
The Big Picture
K-2Number and number sense.
3-5 Operations and Properties(Number and Geometry)Fractions
6-8Algebraic and Geometric ThinkingData Analysis and using Properties
High School
Functions, Statistics, Modeling and Proof
Learning Progressions/Trajectories
Confrey (2007)“Developing sequenced obstacles and challenges for students…absent the insights about meaning that derive from careful study of learning, would be unfortunate and unwise.”
CCSS, p. 4 “… the development of these Standards began with research-based learning progressions detailing what is known today about how students’ mathematical knowledge, skill, and understanding develop over time.”
Read the excerpt from Learning Trajectories in Mathematics: A Foundation for Standards, Curriculum, Assessment, and Instruction
Identify 3 ideas that you are willing to talk about with colleagues.
Highlight the location in the text where these ideas appear.
What Are Learning Trajectories? And What Are They Good For?—Save the Last Word for Me!!!
Designate a facilitator and timekeeper. A volunteer begins by reading the sentence(s) from the
text that embody one of his/her selected ideas. The speaker does not comment on the text at this point.
The individual to right of first speaker takes up to one minute to comment on the selected text.
The next two individuals also take up to one minute to comment on the initial speaker’s idea.
The individual selecting the idea has up to 1 minutes to react to colleagues’ ideas and to talk about why she or he thought this was important.
Another group member introduces one idea, and the group follows the same protocol. Continue until all members have shared or until time is called.
Directions for Save the Last Word for Me
Learning Trajectories – sometimes called learning progressions – are sequences of learning experiences hypothesized and designed to build a deep and increasingly sophisticated understanding of core concepts and practices within various disciplines. The trajectories are based on empirical evidence of how students’ understanding actually develops in response to instruction and where it might break down.
Daro, Mosher, & Corcoran, 2011
Starting PointEnding
Point
Startin
g Point
Ending Point
K 1 2 3 4 5 6 7 8 HS
Counting and Cardinality
Number and Operations in Base Ten Ratios and Proportional Relationships
Number and Quantity
Number and Operations – Fractions
The Number System
Operations and Algebraic Thinking
Expressions and Equations Algebra
Functions Functions
Geometry Geometry
Measurement and Data Statistics and Probability Statistics and Probability
Learning Progression Framework
Investigating the Domains/Conceptual Categories
Domains provide common learning progressions.
Curriculum and teaching methods are not dictated.
Standards are not presented in a specific instructional order.
Standards should be presented in a manner that is consistent with local collaboration.
Learning Progressions
K 1 2 3 4 5 6 7 8 HS
Counting and Cardinality
Number and Operations in Base Ten Ratios and Proportional Relationships
Number and Quantity
Number and Operations – Fractions
The Number System
Summary and/or representation of how the concept of the use of numbers grows throughout your grade band.
Easy for others to interpret or understand. Visual large enough for all to see. More than just the letters and numbers of
the standards – include key words or phrases.
What Goes On The Chart Paper?
Display posters side-by-side and in order on the wall.
Begin at the grade band you studied. Read the posters for your grade band.
Discuss similarities and differences between the posters.
Establish a clear vision for your grade band.
Banding Together for a Common Message
As a table group, consider your journey through the 2010 ACOS as you studied the concept of the use of numbers K-12. What did you learn? What surprised you? What questions do you still have?
Let’s Talk About It!
Know what to expect about students’ preparation.
More readily manage the range of preparation of students in your class.
Know what teachers in the next grade expect of your students.
Identify clusters of related concepts at grade level.
Clarity about the student thinking and discourse to focus on conceptual development.
Engage in rich uses of classroom assessment.
Value of Learning Progressions/Trajectories to Teachers
Review the Format2003 ACOS 2010 ACOS
Contains bullets Does not contain bullets
Does not contain a glossary Contains a glossary
.
.
.
.
.
.
?? Questions ??
2010 Alabama Course of Study: Mathematics
College- and Career-Ready Standards
Content Shifts
Content CorrelationALGEBRA I – ALGEBRA – Seeing Structure in ExpressionsWrite expressions in equivalent forms to solve problems. (Quadratic and exponential.)9. Choose and produce an equivalent form of an expression to
reveal and explain properties of the quantity represented by the expression.* [A-SSE3]a. Factor a quadratic expression to reveal the zeros of the
function it defines. [A-SSE3a]b. Complete the square in a quadratic expression to reveal the
maximum or minimum value of the function it defines. [A-SSE3b]
c. Determine a quadratic equation when given its graph or roots. (AL)
d. Use the properties of exponents to transform expressions for exponential functions. [A-SSE3c]
2010 ACOS – ALGEBRA I9. Choose and produce an equivalent form of an expression to
reveal and explain properties of the quantity represented by the
expression.* [A-SSE3]
a. Factor a quadratic expression to reveal the zeros of the function it defines. [A-SSE3a]
d. Use the properties of exponents to transform expressions for exponential functions. [A-SSE3c]
2003 ACOS – ALGEBRA I6. Factor binomials, trinomials, and other polynomials using
GCF, difference of squares, perfect square trinomials, and grouping.
9. Solve quadratic equations using the zero product property.1.1 Applying laws of exponents to simplify expressions, including
those containing zero and negative integral exponents.
Correlates with
2010 ACOS – ALGEBRA I9b. Complete the square in a quadratic expression to
reveal the maximum or minimum value of the function
it defines. [A-SSE3b]9c. Determine a quadratic equation when given its
graph or roots. (AL)
2003 ACOS – ALGEBRA II W/ TRIGONOMETRY4. Determine approximate real zeros of functions graphically and
numerically and exact real zeros of polynomial functions.4.1 Using the zero product property, completing the square, and the
quadratic formula5.1 Generating an equation when given its roots or graph
Correlates with
Content Correlation Document
2003 ACOS 2010 ACOS
CURRENT ALABAMA CONTENT PLACEMENT 2010 GRADE 1 CONTENT
1.1 Demonstrate concepts of number sense by counting forward and backward by ones, twos, fives, and tens up to 100; counting forward and backward from an initial number other than 1; and using multiple representations for a given number.
1.9. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. [1-NBT1]
1.1.B.1 Identifying position using the ordinal numbers 1st through 10th
CONTENT NO LONGER ADDRESSED IN GRADE 1
1.1.B.2 Using vocabulary, including the terms equal, all, and none, to identify sets of objects
1.7. Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. [1-OA7]
1.1.B.3 Recognizing that the quantity remains the same when the spatial arrangement changes
CONTENT NOW ADDRESSED IN KINDERGARTEN:1.4.b. Understand that the last number name said tells
the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. [K-CC4b]
Content Correlation Document
2003 ACOS 2010 ACOSCONTENT MOVED TO GRADE 1 IN 2010 ACOS
2.6 Solve problems using the associative property of addition.
1.3. Apply properties of operations as strategies to add and subtract. (Students need not use formal terms for these properties.) [1-OA3] (Associative property of addition)
3.1.B.1 Comparing numbers using the symbols >, <, =, and
1.11. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <. [1-NBT3]
4.10 Complete addition and subtraction number sentences with a missing addend or subtrahend.
1.8. Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. [1-OA8]
Content Correlation Document
NEW GRADE 1 CONTENT IN 2010 ACOSNone
GeometryContent
Correlation
• Which 2010 standard(s) correlates to standard 5 from the 2003 ACOS?
• Is there any additional content related to standard 10 that should be addressed in the upcoming school year?
• What content has been moved from Grade 8 to Geometry?• Is there any content that is no longer addressed in Geometry?
How many standards and/or bullets?• Is there any content that is new to Alabama in the Geometry
course in the 2010 ACOS?
How can I be sure my students are prepared for the
implementation of the 2010 ACOS in the 2012-2013
school year?
Algebra I Mathematics CurriculumFirst Nine Weeks
2003 COS DESCRIPTION NEW CONTENT TO BE ADDED FROM 2010 COSAI.1 Simplify numerical expressions using properties of real
numbers and order of operations, including those involving square roots, radical form, or decimal approximations.
AI.1.B1 Applying laws of exponents to simplify expressions, including those containing zero and negative integral exponents
AI.7 Solve multistep equations and inequalities including linear, radical, absolute value, and literal equations.
AI.5 Perform operations of addition, subtraction, and multiplication on polynomial expressions
AI.3 Determine characteristics of a relation, including its domain, range, and whether it is a function, when given graphs, tables of values, mappings, or sets of ordered pairs.
AI.11 Solve problems algebraically that involve area and perimeter of a polygon, area and circumference of a circle, and volume and surface area of right circular cylinders or right rectangular prisms.
AI.2 Analyze linear functions from their equations, slopes, and intercepts.
AI.1. Notation for radicals in terms of rational exponents [N-RN1]AI. 2 Rewrite expressions involving radicals and rational exponents [N-RN2]
AI.16. Solve quadratic equations and inequalities in one variable, including equation with coefficients represented by letters [A-REI3]
AI.10. Include quadratics [A-APR1]
AI.24. Focus on linear and exponential and on arithmetic and geometric sequences [F-IF1]
NO NEW CONTENT
AI.26. Recognize that sequences are functions [F-IF3]AI.27. Include exponential and quadratic functions [F-IF4]AI.46. Interpret slope and intercept of a linear model in the
context of the data [S-ID7]
AI.1 Notation for radicals in terms of rational exponents [N-RN1]AI.2. Rewrite expressions involving radicals and rational exponents [N-RN2]
Algebra II with TrigonometryPacing Guide
2nd Nine Weeks
2003 ACOS # TOPICS CONTENT THAT SHOULD BE ADDED
AIIT.6 Add, subtract, multiply, and divide functions – including polynomial and rational functions
AIIT.6 Inverse functions
AIIT.6 Composition of functions
AIIT.3 Graphing rational functions – including horizontal and vertical asymptotes, and holes
AIIT.7 Solving rational equations and inequalities
AIIT.6.B.3 Extension – constructing graphs
NO NEW CONTENT
NO NEW CONTENT
NO NEW CONTENT
NO NEW CONTENT
AIIT.29. Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific valuesof k (both positive and negative); find the value of kgiven the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic
expressions for them. [F-BF3]AIIT.20. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. [A-REI2]
What about the
assessments?
2011-2012 2012-20132013-2014
2003 ACOS + Identified Content from 2010 ACOS
2010 ACOS + Identified Content from 2003 ACOS
?? Questions ??
2010 Alabama Course of Study: Mathematics
College- and Career-Ready Standards
Algebra I in the 8th Grade:Considerations and Consequences
Do you have middle school students who should have the option of taking Advanced Placement (AP) Mathematics, or two advanced mathematics courses as part of their high school experience?
Algebra I in Grade 8:Considerations and
Consequences
Some Pathways for Students Who Complete Algebra I in Grade 8
Geometry Geometry Geometry Algebra II W/Trig Algebra II W/Trig Algebra II W/Trig Precalculus Discrete Mathematics Precalculus Analytical Mathematics Precalculus Advanced Placement (AP)
Mathematics Course
(ACOS: Mathematics, 2010, p. 127)
“Systems offering Algebra I in the eighth grade have the responsibility of ensuring that all Algebra I course content standards and Grade 8 course content standards be included in instruction.” (ACOS: Mathematics, 2010, p. 81)
The State Department of Education will provide further guidance and training (Phase II) in the fall of 2011 relative to issues local education agencies may encounter in providing an Algebra I course in Grade 8.
Algebra I in Grade 8:Considerations and
Consequences
Decisions to accelerate students into a high school Algebra I course before Grade 9 should not be rushed.
Placing students into an Algebra I course too early should be avoided at all costs.
Local education agency’s decision should: Be Advertised Be Equitable Provide Written Policy
Decisions to accelerate students into a high school Algebra I course before Grade 9 should be based on solid evidence of student learning.
Algebra I in Grade 8:Considerations and
Consequences
Not all students are ready for Algebra I in Grade 8.
The 2010 COS Algebra I content is not the same as the Algebra I content in earlier Alabama Courses of Study. Much of what was previously included in Algebra I will now be taught in Grades 6-8 in the 2010 COS.
A Southern Regional Education Board (SREB) study found a difference in readiness for higher-level mathematics between students scoring in the bottom quartile and those scoring in the top 3 quartiles.
Graduates who completed Geometry or Algebra II as ninth graders earned an average Grade 12 NAEP mathematics at the Proficient level.
Algebra I in Grade 8:Considerations and
Consequences
“Mathematics leaders need to ensure equitable access to courses by carefully monitoring barriers to participation.” (A Guide to Mathematics Leadership, 2010, p. 4)
There are valid reasons for placing students in certain courses, but mathematics leaders are expected to ensure that there are no systematic barriers that discriminate against specific populations. (A Guide to Mathematics Leadership, 2010, pp. 31-32)
An accelerated Grade 7 course and a Grade 8 Algebra I course differ from the Grade 7, Grade 8, and Algebra I courses found in the 2010 COS in that they contain additional content by comparison and demand a faster pace for instruction and learning.
Algebra I in Grade 8:Considerations and
Consequences
Ensure that the Grade 8 Algebra I course is not watered down.
Ensure that there is equity in support materials for all courses, that is, that more and better materials and supports are not just in place for the accelerated and advanced courses.
Ensure that interventions are in place so that all students are prepared for high school Algebra I coursework.
Algebra I in Grade 8:Considerations and
Consequences
Allow students to take two math electives simultaneously, provided the course progression chart is followed.
Use block scheduling to take a math course both semesters.
Offer Credit Advancement.
Offer Dual Enrollment.
Offer summer courses that are designed to provide an equivalent experience of a full course.
Ways to Provide Greater Access to Mathematics
?? Questions ??
http://alex.state.al.us/ccrs
ALSDE Office of Student LearningCurriculum and Instruction
Cindy Freeman, Mathematics Specialist Phone: 334.353.5321
E-mail: [email protected]
Contact Information