PAUSD Math Placement Recommendations 2016-17 (Living ...
Transcript of PAUSD Math Placement Recommendations 2016-17 (Living ...
pg. 1 4/22/16
PAUSD Math Placement Recommendations 2016-17 (Living Document; revised annually) Grade 8 to Grade 9
Background information
Successful high school math course placement of rising ninth-grade students is dependent on a variety of factors.
The eighth-grade student’s overall math grade often includes items that are not connected to successfully
meeting the curriculum standards. The overall math grade may reflect behavior such as study skills, homework
completion or remittance, or classroom participation. Thus the overall math grade is less of an appropriate
predictor of academic success. Many of the factors are subjective and personal, such as the student’s interest in
math, the student’s prior experiences in math, the student’s self-view, or the student’s mindset with respect to
the variety of upcoming academic challenges. Generally, the best predictor of academic success in a ninth-grade
math placement is the eighth-grade student’s classroom test scores which indicate the student’s mastery of the
content.
The classroom tests and their rubrics are collaboratively developed by the teachers of the course at each
school. Unusual student answers are often jointly evaluated by the teaching team.
The classroom tests are designed to correlate directly to the standards taught in the unit.
Classroom tests are completed individually and illuminate the depth of the student’s grasp of the
standards taught and the student’s command of the eight mathematical practices.
Classroom tests do not reflect any aspect of student social behavior.
Classroom tests do not directly measure homework or study habits.
Classroom tests are a strong indicator of student progress in the acquisition and utilization of the
mathematics and practices of the course.
The Organization of this Document
In middle school eighth-grade, most students are enrolled in one of two courses: Math 8 or Algebra 8. In rare
circumstances, student are enrolled in Geometry H, a high school honors course offered at the middle school
sites. Recommended placement in their ninth-grade math course can be determined by traversing the flow chart
headed by the particular eighth-grade course title. Some differences in course offerings exist between Henry M.
Gunn High School and Palo Alto High School and placement will vary slightly. The differences are noted within
each flow chart.
For students receiving special education services, the mathematics placement will be determined by the student’s
IEP team.
Regardless of the recommendation, teachers, counselors and mathematicians recognize the conundrum of the
case of the individual versus the flow of the trends. Therefore, entering and throughout high school, parents and
students are urged to choose the most appropriate math course annually to give the student the suitable amount
of challenge and success within it.
pg. 2 4/22/16
Ninth-Grade Placement Recommendations1 for Students enrolled in Math 8
1 Students may enroll in any course within the lane of the course. (That is, if the student is
recommended for any Algebra 1 course, the student may request placement in any level of Algebra 1
(Alg 1.1, Alg 1, or Alg 1A). Students having difficulty in their class despite putting in their best effort can
request a lane change. Such changes are contingent on class size and must be approved by the IS.
Changes can only be made before the end of the first quarter or at the semester break. Students who
change lanes during first semester carry over their grade at the time to the new lane.
2 Recommendations are reviewed at the Middle Schools at the end of the school year in May/June.
3 Discussions include consideration of parental insights, case-manager’s (if applicable) insights, student
interest, homework completion, challenge problem completion, and choice of test level (in Math 8, two
levels of tests are often available in the second semester).
Students in Math 8
9th grade at Paly2
Students who consistently earned a
B+ or above on classroom tests
Alg 1A
Students who consistently earned aB to a C- on classroom
tests
Alg 1
Students who consistently earned aD or F on classroom
tests
Placements are discussed.3
Placement for Alg 1 or Alg 1.1 is considered.
9th grade at Gunn
Alg 1/1A
pg. 3 4/22/16
Ninth-Grade Placement Recommendations4 for Students enrolled in Alg 8
4 Students may enroll in any lane of the course. (That is, if students are recommended for any level of
Geometry, students may request placement in any Geometry course (excluding grade-level Geometry, a
tenth-grade course). If the student is recommended for any Algebra 1 course, the student may request
placement in any level of Algebra 1 (Alg 1.1, Alg 1, or Alg 1A). Students having difficulty in their class
despite putting in their best effort can request a lane change. Such changes are contingent on class size
and must be approved by the IS. Changes can only be made before the end of the first quarter or at the
semester break. Students who change lanes during first semester carry over their grade at the time to
the new lane.
Students in Algebra 8
Students consistently earned a B-or better on classroom tests
9th grade at Paly
Students who consistently earned an A on classroom
tests
Geo H
Students who consistently earned an A- to B- on
classroom tests
Geo A
9th grade at Gunn
Students may chooseGeo H or Geo A
Students consistently earned below a B- on classroom tests
Alg 1A (Paly)
Alg 1/1A (Gunn)
Summer: Bridge to Geo A course
Did the student consistently earn a B- or better on classroom tests?
Yes: Geo A No: Alg 1A
pg. 4 4/22/16
Ninth-Grade Placement Recommendations5 for Eighth-Grade Students enrolled
in Geo H
5 Students a year (or more) ahead in the honors lane of mathematics are expected to earn As in the
courses in order to remain competitive in the application process for university work. Students having
difficulty in their class despite putting in their best effort can request a lane change. Such changes are
contingent on class size and must be approved by the IS. Changes can only be made before the end of
the first quarter or at the semester break. Students who change lanes during first semester carry over
their grade at the time to the new lane.
Students in Geo H (8th Grade)
Students consistently earned an A- or better on classroom
tests
Alg2/Trig H
Students consistently earned less than an A- on classroom
tests
Repeat Geo H
pg. 5 4/22/16
PAUSD Math Placement Recommendations 2016-17 (Living Document; revised annually) Grade 7 to Grade 8 Background information
PAUSD strives to offer math courses that give students the appropriate amount of challenge and success. In the
middle schools, PAUSD supports well-paced responsive or adaptable student placement. Seventh grade students
are enrolled in one of two courses: Math 7 and Math 7A. Math 7 satisfies the Common Core State Standards
(CCSS-M 7) while Math 7A is an accelerated course that includes both the CCSS-M 7 standards and more than half
of the CCSS-M 8 standards. Successful placement of rising eighth-grade students is dependent on the student’s
experience in Math 7 or Math 7A. Usually in eighth grade, two courses are available to students: Math 8 and
Algebra 8. Math 8 satisfies the CCSS-M 8 standards. Algebra 8 is an accelerated course that includes less than 50%
of the CCSS-M 8 standards, and all of the CCSS-Algebra standards at an advanced level (some topics are extended
to Algebra 2 levels).
The seventh-grade student’s consistent classroom test scores are a reliable indicator of the student’s mastery of
the Math 7 content. The overall math grade may reflect behavior such as study skills, homework completion or
remittance, or classroom participation. Thus the overall math grade tends to be less of an appropriate predictor of
academic success. For appropriate placement recommendation, use the student’s first experience of classroom
tests.
As middle students grow and develop, they foster varied appreciation for one academic subject over another.
Therefore, flexibility is appropriate as a student moves from grade 7 to grade 8. To move to Algebra 8 from Math
7 requires summer work in the Math 8 topics not covered in Math 7. Students who are likely to be successful in
the move to the accelerated work have earned high marks in their Math 7 classroom exams.
The Organization of this Document
The flow chart indicates both the more usual move from one course to another at the same level of pacing and
challenge, as well as the moves to support a student’s independent and successful math achievement. To move
from the grade-level work to the accelerated work requires a four-week summer course, and the expectation that
the compressed time for the work increased the pace of the work. The summer course provides the student with
the opportunity to master the CCSS-M 8 topics not included in Math 7, but integrated in Math 7A.
If a student is having difficulty in the seventh-grade accelerated course, Math 7A, it is appropriate to move over to
the grade-level course to produce student confidence, as well as joy and interest, back into the student’s
relationship with mathematics.
For students receiving special education services, the mathematics placement will be determined by the student’s
IEP team.
Regardless of the recommendation, teachers, counselors and mathematicians recognize the conundrum of the
case of the individual versus the flow of the trends. Therefore, throughout secondary mathematics, parents and
students are urged to choose the most appropriate math course annually to give the student the suitable amount
of challenge and success within it.
pg. 6 4/22/16
Eighth-Grade Placement Recommendations1 for Seventh-Grade Students
enrolled in Math 7 or Math 7A
1 Students may enroll in any course within the lane of the course. (That is, if the student is
recommended for Math 8, the student may request placement in either Math 8 or Algebra 8.) Students
having difficulty in the class despite putting in the student’s best effort can request a lane change. Such
changes are contingent on class size and must be approved by the IS. Changes can only be made before
the end of the first quarter or at the semester break. Students who change lanes during first semester
carry over their grade at the time to the new lane.
2 Students who consistently earn a B- or less on tests in Math 7A need support. They have a choice of either moving to course in which the level of challenge and success is more appropriate, Math 8, or to build skills, concepts and personal confidence in some of the accelerated topics over the summer in the Bridge to Algebra 8 course, and continue on to Algebra 8. 3The curriculum of the 4-week summer school course, Bridge to Algebra 8, is the topics from CCSS-M 8 that were included in Math 7A, but not Math 7.
4The Algebra 8 Mastery Test is offered in August. A student may only attempt the Algebra 8 Mastery Test one time. Non-PAUSD students who perform well on the 8th grade Placement Test and who demonstrate some Algebra knowledge to an 8th grade math teacher (a few informal questions that require work demonstrated) may attempt the Algebra 8 Mastery Test. Students transferring in from non-PAUSD schools must pass the test in order to be placed ahead of grade level.
Students enrolled in Math 7A
Student consistently earned an B- or better on
classroom tests
Algebra 8
Student consistently earned less than a B- on
classroom tests
Is the student interested in continued acceleration?
No: Math 8Yes: Bridge to Algebra 83
4-Week Summer Course
Did the student consistently earn a B- or
better on classroom tests?
Yes: Algebra 8No: Math 8
Students enrolled in Math 7
Student consistently earned an A- or better on
classroom tests
Is the student interested in acceleration?
Yes: Bridge to Algebra 83
4-Week SummerCourse
Did the student consistently earn a B- or
better on classroom tests?
Yes: Algebra 8No: Math 8
No: The current is lane is the correct level of
challenge & success:Math 8
Student consistently earned less than an A-
on classroom tests
Math 8
If a student has
consistently
earned strong As
on classroom tests
in Math 7A, the
student has the
opportunity to
take the Algebra 8
Mastery Test4,
which, if passed,
places the 8th
grader in an
honors level high
school course,
Geometry H,
offered at each of
the middle
schools.
pg. 7 4/22/16
PAUSD Math Placement Recommendations 2016-17 (Living Document; revised annually) Grade 6 to Grade 7
Background information
The transition from elementary school to middle school is more than a transition in grade levels or school
buildings. The students’ transition is social, emotional, physical and academic. Children become adolescents.
Schoolwork becomes more codified, more complex, more integrated, and more challenging. Middle school
students find themselves taking risks, making errors, trying new ideas, awakening to themselves, building and
knocking down their self-confidence, making friends, and feeling lonely; they are becoming. The transition takes
time. The PAUSD secondary math program allows for a difference in growth rates and has crafted courses that
meet the California Common Core State Standards in Mathematics (CCSS-M) for every student throughout the
secondary schools. The CCSS-M standards are comprised of two types of standards: eight Mathematical Practice
Standards and Math Content Standards (building mathematical understanding, skills, knowledge, and expertise
throughout the years from K-12).
The PAUSD mathematics program offers two seventh-grade courses to provide the appropriate balance of the
level of challenge and success to seventh-grade students: Math 7 and Math 7A. Math 7 meets all of the standards
of the CCSS-M for Math 7. Math 7A is an accelerated course. Math 7A is a combined course of all of the CCSS-M
Math 7 and more than half of the CCSS-M Math 8 standards. Math 7A compresses more than 1 ½ years of CCSS-M
mathematics into its year of study. (The Math 7 course is followed by Math 8. The Math 7A course is followed by
Algebra 8, which is a combination of the remaining topics of CCSS-M Math 8 and the topics of Algebra 1 at an
advanced depth.)
Secondary math teachers give input or recommendations to help parents and students choose the appropriate
course by organizing a variety of observable factors and linking the factors to subsequent success in course
placement. The factors include achievement on classroom tests, homework completion, interest in mathematics
as evidenced by their participation in classroom extensions, successful application of mathematical concepts, and
achievement on the comprehensive end of year exam. The organization is a criteria table found on the next page.
For students receiving special education services, the mathematics placement will be determined by the student’s
IEP team.
The Organization of this Document
The sixth-grade math teachers will provide personal input to students and parents utilizing on of the two criteria
tables on the next page. (Please note that students whose teachers use evidenced-based grading will earn rubric
scores and all other students will earn percentages.) The top call-out to the right of each table explains the
general indications for the recommendation to either seventh-grade math course placement. The call-out also
provides information regarding students who are advanced in their mastery of middle school math curriculum.
Regardless of the recommendation, teachers, counselors and mathematicians recognize the conundrum of the
case of the individual versus the flow of the trends. Therefore parents and students are urged to choose the most
appropriate math course that will give the student the suitable amount of challenge and success within it.
pg. 8 4/22/16
Grade 6 to Grade 7
Criteria Table 1: an “X” in the column for each criteria indicates the appropriate placement for the
student
6th Grade Teacher Input1 for Parents and Students CRITERIA Math 7A2 Math 73
Classroom Unit Tests Average (First test score on unit tests)
94% to 100% or Rubric Score of Mode 4 will receive an X in the Math 7A column
90% to 100% or Rubric Score of Mode 3 or above will receive an X in the Math 7A column
Homework Average Throughout the year = 90% to 100% will receive an X in the Math 7A column
(The Homework Average is based on completion or turn-in rate.)
Consistently completed Math Extensions/Einsteins
will receive an X in the Math 7A column (Students demonstrate interest in math by completing these challenge problems)
Successfully completed Application Problems and Projects/POPs will receive an X in the Math 7A column
(POPs = process only problems)
End of Year Test Part 1
92% to 100% will receive an X in the Math 7A column
85% to 100% will receive an X in the Math 7A column
End of Year Test Part 2
92% to 100% will receive an X in the Math 7A column
85% to 100% will receive an X in the Math 7A column
Total number of Xs in each column
1 Students may enroll in any lane of the course. The teacher’s input for enrollment is based on the historical progress of students through the middle school math courses. (That is, if the student is recommended for any Math 7 course, students may request placement in either Math 7 or Math 7A.) Students having difficulty in their class despite putting in their best effort can request a lane change. Such changes are contingent on class size and must be approved by the IS. Changes can only be made before the end of the first quarter or at the semester break. Students who change lanes during first semester carry over their grade at the time to the new lane. 2The Math 7A is an accelerated course combined of all of the CCSS-M Math 7 and more than half of the CCSS-M Math 8 standards. The Math 7A course is followed by Algebra 8, which is a combination of the remaining topics of CCSS-M Math 8 and the topics of Algebra 1 at an advanced depth. 3The grade-level course, Math 7, meets the standards of the CCSS-M Math 7. The Math 7 course is followed by Math 8, or, with summer work, Algebra 8.
The Teacher’s Criteria-based
Input:
Score: Suggested Placement: Most Xs in Math 7 Math 7 Most Xs in Math 7A Math 7A
If a student earned Xs in the Math
7A column only, the student has
the opportunity to take the Math
7A Mastery Test4, which, if
passed, places the 7th grader in
Algebra 8.
4 Mastery Tests: Placement in math courses ahead of grade level can be accomplished by passing a Mastery Test. The Math 7A Mastery Test is offered in May to outgoing 6th graders who have earned Xs in the Math 7A column only (of the criteria table to the left). A student may only attempt the Math 7A Mastery Test one time.
pg. 9 4/22/16
Criteria Table 2: The total number of points indicates the appropriate placement for the student
6th Grade Teacher Input5 for Parents and Students CRITERIA Points
Classroom Unit Tests Average (First test score on unit tests)
94% to 100% or Rubric Score of Mode 4 2 pts
90% to 93% or Rubric Score of Mode 3 or above 1 pt (Otherwise, 0 pts)
Homework Average Throughout the year is 90% to 100% 1 pt (The Homework Average is based on completion or turn-in rate.)
(Otherwise, 0 pts)
Consistently completed Math Extensions/Einsteins 1 pt (Students demonstrate interest in math by completing these challenge problems)
(Otherwise, 0 pts)
Successfully completed Application Problems and Projects/POPs 1 pt
(POPs = process only problems)
(Otherwise, 0 pts)
End of Year Test Part 1
92% to 100% 2 pts
85% to 91% 1 pt (Otherwise, 0 pts)
End of Year Test Part 2
92% to 100% 2 pts
85% to 91% 1 pt (Otherwise, 0 pts)
Total Points
5 Students may enroll in any lane of the course. The teacher’s input for enrollment is based on the historical progress of students through the middle school math courses. (That is, if the student is recommended for any Math 7 course, the student may request placement in either Math 7 or Math 7A.) Students having difficulty in their class despite putting in their best effort can request a lane change. Such changes are contingent on class size and must be approved by the IS. Changes can only be made before the end of the first quarter or at the semester break. Students who change lanes during first semester carry over their grade at the time to the new lane. 6The Math 7A is an accelerated course combined of all of the CCSS-M Math 7 and more than half of the CCSS-M Math 8 standards. The Math 7A course is followed by Algebra 8, which is a combination of the remaining topics of CCSS-M Math 8 and the topics of Algebra 1 at an advanced depth. 7The grade-level course, Math 7, meets the standards of the CCSS-M Math 7. The Math 7 course is followed by Math 8, or, with summer work, Algebra 8.
The Teacher’s Criteria-based
Input:
Score: Suggested Placement: 5 pts to 9 pts Math 7A6
0 pts to 4 pts Math 77
If a student earned a 9 on this
criteria table, the student has the
opportunity to take the Math 7A
Mastery Test8, which, if passed,
places the 7th grader in Algebra 8.
8 Mastery Tests: Placement in math courses ahead of grade level can be accomplished by passing a Mastery Test. The Math 7A Mastery Test is offered in May to outgoing 6th graders who have earned a 9 on the criteria table to the left. A student may only attempt the Math 7A Mastery Test one time.
pg. 10 4/22/16
PAUSD Math Placement Recommendations 2016-17 (Living Document; revised annually) Grade 5 to Grade 6
The PAUSD provides an exceptional math program that supports students developmentally. Our sixth grade math teachers embrace the philosophy of cultivating successful middle school students from elementary students. In order to support the students’ transition from Grade 5 Elementary School to Grade 6 Middle School, all students matriculate from Math 5 to Math 6. (For students receiving special education services, the mathematics placement will be determined by the student’s IEP team.)
In sixth grade our students typically have two teachers for the four core subjects as they learn higher
order study skills, self-advocacy, and build friendships that are necessary to navigate their secondary
schools. As students learn to manage the myriad of middle school challenges, the flexible clustering
available because of the heterogeneous grouping in the core classes allows students and teachers to
suspend any hasty evaluations as they support the students’ sense of growth and possibilities.
In Math 6 students study the Sixth-grade California Common Core State Standards. Students work both independently and in cooperative groups with instruction that is differentiated to appropriately challenge all students. Sixth grade teachers are completely prepared to support students who require extension, support, and enrichment opportunities.
6th Grade Math Differentiation For Math Support or Additional Help
Math workshop course (where available) or other structured support Working with the Teacher outside of class time.
For Extra Challenge and Deeper Math Experiences
Math Extensions/Einsteins and investigations of classroom problems Math Extensions/Einstein Problems are
Weekly or monthly packets that contain numerous math problems intended to provide individuals additional challenge and differentiation.
Math 5
(Elementary School)
Math 6
(Middle School)
pg. 11 4/22/16
Each set of Math Extensions/Einsteins contains problems at varying levels to help students think deeply about math in the real world and to engage their problem solving skills.
Join Math Club Math Club activities include studying non-standard mathematical topics, engagement
in math contests, and explorations of a variety of mathematical ideas. Working with the Teacher outside of class time.
All sixth grade students begin in 6th grade math. Sixth grade math teachers use a variety of methods
to evaluate each student at the beginning of the year. Occasionally a teacher recognizes that an
individual is working well beyond the sixth grade level.
Sixth-grade math teachers are equipped to differentiate for students who are advanced a
year above sixth-grade level in math which allows the student to remain with the student’s
class during the transition year.
When the sixth-grade math teacher identifies a student who is potentially ready for Algebra
(typically an eighth- or ninth-grade course), the teacher notifies the parents and offers the
student an opportunity to take the Math 7A Mastery Test. Should the student pass the test, a
parent-conference is called. Although the student’s mathematical readiness for Algebra 8 is
indicated, the student’s social needs and the level of the student’s interest and joy in math
are considered. Subsequent logistical challenges for the next few years are considered. If
chosen, placement in Algebra 8 is completed as soon as possible.
pg. 12 4/22/16
The PAUSD Secondary Math Flow Chart
Mathematics electives include AP Statistics, Statistics Applications (AAR), and Advanced Problem Solving (levels 1 – 4). Elective courses that can be taken for either Mathematics or Career/Technology Education credit include the Computer Science courses Intro to Java, Programming Concepts, Advanced Java, Programming Using Java, AP CS A, and Gunn BEAM (business math applications course).
Considerations
It is important that a student chooses or is placed appropriately for both challenge and success in math courses throughout secondary education. Building success is a journey, not a race. Student success is not only the mastery of content and skills, but includes enthusiasm for math along with a healthy, balanced, and happy life.
Math 6
Math 7
Math 8
Algebra 1.1
(Paly)
Algebra 1.2
(Paly)
Geometry
Algebra 2
Algebra 1/1A (Gunn)
Algebra 1 (Paly)
Geometry
Algebra 2
Pre-Calculus
Math 7A
Algebra 8
Algebra 1/1A (Gunn)
Algebra 1A (Paly)
Geo A
Algebra 2 & Trig A
Introduction to Analysis & Calculus
Geo A
Algebra 2 & Trig A
Introduction to Analysis & Calculus
AP Calculus AB
Geo H
Algebra 2 & Trig H
Analysis H
AP Calculus BC
6th
Grade
7th
Grade
8th
Grade
9th
Grade
10th
Grade
11th
Grade
12th
Grade
Four years of high school math are a
good predictor of success in college.
The lanes shown are typical routes taken by
students. Movement between lanes is possible
based on student performance, teacher
recommendation, and potential summer
coursework. See the following page for more
details.
pg. 13 4/22/16
The UC Requirements for Admission (and PAUSD Graduation Requirements) in mathematics is the successful completion of an Algebra 2 Course. There is interest in the PAUSD community for our students to reach a calculus course by their senior year of high school. Because students mature academically at different rates, there are a variety of paths for students to reach the calculus goal while maintaining a solid level of success and joy in their math courses. If you are interested in such a goal, some possible paths to calculus are given in the following table (these are samples of the variety of pathways).
Sample Pathways to AP Calculus AB
6th grade Math 6 Math 6 Math 6 Math 6
Summer
7th grade Math 7 Math 7 Math 7 Math 7A
Summer Bridge to
Alg 8
8th grade Math 8 Math 8 Alg 8 Alg 8
Summer
9th grade Alg 1/1A Alg 1/1A Geo A Geo A
Summer Geo A
10th grade Geo A Alg2/TrigA1 Alg2/TrigA1 Alg2/TrigA1
Summer Alg21
11th grade PreCalc IAC IAC IAC IAC
Summer Transition to Calculus
none
12th grade AP Calc AB AP Calc AB AP Calc AB AP Calc AB
1Fulfills the UC Requirements for Admission and the PAUSD’s Graduation Requirements.
PAUSD has a variety of levels of math courses (all meeting State standards) with the intention that students will find the appropriate level of challenge which they can successfully meet on their own. There is no reason to hurry the process of working toward 12th-grade calculus if your student is unhappy or turned off in their math course. There is no reason to race toward calculus if your student requires constant tutoring in order to learn the skills of the course, sometimes without understanding the concepts. There are plenty of opportunities to create a path that leads to calculus either in high school or within the first year of university work. Be sure to find out what is in your child’s heart as you and your child determine in which math course to register.