Mathematics

Standards and Framework

The California Common Core State Standards for Mathematics include two types of standards: Eight Mathematical Practice Standards (identical for Kindergarten - grade 12) and Mathematical Content Standards (different at each grade level). Together these standards address both the “habits of mind” that students should develop to foster mathematical understanding and the content that students need to know and be able to do.

• CA Common Core State Standards Mathematics

• The Standards for Mathematical Practice

• Math Problem Types & Properties

The mathematical content standards were built on progressions of topics across grade levels, informed by research on children’s cognitive development and by the logical structure of mathematics.

• Progressions of Topics

The CA Mathematics Framework describe what teaching and learning of Mathematics looks like at teach grade level.

• CA Mathematics Framework Chapters, K-12

• Executive Summary, Mathematics Framework for CA Public Schools

• Glossary of Terms, Tables, and Illustrations

The CA Assessment System (CAASPP) assesses the Mathematical Practice Standards and Content Standards as described in the Achievement Level Descriptors

• Achievement Level Descriptors - CA Assessment of Student Performance and Progress

Translations of the CA Standards for Mathematical Practice (SMP)

SMP - English
SMP - Chinese
SMP - Farsi
SMP - Japanese
SMP - Korean 
SMP - Armenian
SMP - Tagalog
SMP - Spanish

Translations - Brief overviews of the CA Common Core State Standards for Mathematics

• CA Department of Education Clearinghouse for Multilingual Documents, Higher Mathematics, includes Arabic, Armenian, Chinese, Farsi, Hindi, Japanese, Korean…etc 

• CA Department of Education Handouts to learn more about CA State Standards for Mathematics includes Arabic, Armenian, Chinese, Farsi, Hindi, Japanese, Korean…etc

K-12 Mathematics Pathways

parent RESOURCES

6th Grade Math Placement Timeline for 2023-24
Math 7 Placement Timeline for 2023-24
MS Math Placement for 2023-24
HS Math II Timeline for 2023-2024

The following Year at a Glance documents describe the mathematics concepts taught and learned at each grade and level and course through Enhanced Math 3.  

Pre-Kindergarten
Kindergarten
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Math 7
Enhanced Math 7-8
Math 8
Enhanced Math I
Math I
Math II
Enhanced Math II
Math III
AP Precalculus - under construction

Additional Resources for Parents

• K-12 Math Textbooks
• Khan Academy Free interactive math problems aligned to CA Mathematics Standards.
• Great Schools Video’s for Parents - Examples of K-grade 12 Mathematics

FREQUENTLY ASKED QUESTIONS

1) What is Integrated Math?

Integrated mathematics is the term used in the United States to describe the style of mathematics education which integrates many topics or strands of mathematics throughout each year of secondary school. Each math course in secondary school covers topics in algebra, geometry, trigonometry and statistics.

The integrated pathway is typically seen internationally and consists of a sequence of three model courses, each of which includes algebra, geometry, trigonometry and statistics standards. This integration allows students to build proficiency and see connections and interrelationships between each domain, each year. Students enrolled in the integrated pathway arrive at the same point by the end of their third year of higher mathematics instruction as students enrolled in a traditional pathway. Both pathways cover the exact same Common Core standards as you can see from this chart showing where the standards are located within each course for both the traditional and integrated pathways:

2)  Why did IUSD select the Integrated Math Pathway?

Our decision to adopt an Integrated Mathematics Pathway reflects our commitment to offering students the highest quality mathematics program we can envision. The opportunity imbedded in an Integrated Mathematics Pathway to focus on developing conceptual understanding and to help students see how the disciplines of mathematics are intertwined resonated deeply with our committee. Knowing the countries that consistently outperform the United States have long embraced Integrated Mathematics and that the new Smarter Balanced Assessments are integrated exams also informed our decision making. The knowledge that our existing middle school programs already use an integrated approach and thus, our high school programs would become a more natural extension of these programs, provided additional rationale for selecting this pathway. The redesign of the College Board SAT Math Test also requires linking topics within the mathematics domains and across disciplines.

3) How did IUSD make the decision to move to an Integrated Math Pathway?

Beginning in October 2014, IUSD convened our Math Pathways Committee, a multi-stakeholder group, consisting of high school and middle school mathematics teachers, parents, university professors and admissions officers along with county curriculum specialists and administrators. Their charge was to develop a comprehensive picture of math instruction in Irvine, to cultivate a clear understanding of our collective interests related to math instruction, and to identify the options for math pathways that will effectively achieve those interests. This seventy-person committee met for thirty-five hours over a series of months and engaged in substantive discussion regarding how the pathways should be redesigned to meet student interests. Our IUSD Mathematics Leadership Team, a group comprised of department chairs and teachers from every secondary school in the district, built on the work of the larger committee, carefully researching, reviewing and refining the three proposed pathways and ultimately selecting our Integrated Mathematics Pathway in late February 2015.

4) Why are so many districts and/or states moving towards Integrated Math?

With the inclusion of the integrated-math approach in the new state standards, many districts and states are choosing to make the move at this time in recognition that integrated math reflects the new standards’ emphasis on building conceptual understanding and making connections.

For a more complete answer, follow the link below to an article from Education Week, November 2014.  "In Transition to Common Core, Some High Schools Turn to Integrated Math" As of spring 2015, of the top 20 high schools in California as ranked by US News and World Report: 9 of them have moved to an integrated model (45%), 10 of them are using a traditional model (50%) and 1 of the schools (5%) is offering both traditional and integrated pathways through an International Baccalaureate program.

5) What are the differences between 'Traditional' Math (Algebra 1, Geometry and Algebra 2) and Integrated Math (Math I, Math II, and Math III)?

Both 'Traditional' Math and Integrated Math cover the exact same Common Core State Standards. As such, they represent an equal pathway to higher mathematics, including AP Calculus. Integrated mathematics courses incorporate concepts and standards from traditional Algebra 1 and 2, Geometry, and Statistics, revisiting the concepts and standards every year. The organization and repetition of these concepts over multiple years allows students to increase proficiency and recognize the natural interconnectedness of mathematics and its real-world applications. 

6) Will public and private universities accept integrated math courses?

Yes. The University of California states that "although many schools may follow the traditional Algebra 1 – Geometry – Algebra 2 format, other sequences may treat these topics in an integrated fashion. Combinations of some integrated courses, algebra, geometry and other courses that integrate the Common Core Standards for Mathematical Practice for high school, including courses that rigorously apply these standards in the development of career-related skills, can also satisfy the ‘C – Mathematics’ subject requirement.”

7) Where can I find a course description of each integrated math course?

Please see our "Year at a Glance" documents under PARENT RESOURCES above. 

8) Will Math I meet the high school Algebra 1 requirement for high school graduation?

Yes. “Assembly Bill 220 updates the California Education Code by removing an outdated reference to the 1997 mathematic standards, and specifies that completion of Mathematics I would satisfy the high school graduation requirement so that pupils, regardless of what mathematics pathway school district choose to follow, are able to meet the high school mathematics graduation requirements.”   

9) The UC system requires students to complete Algebra 1, Geometry and Algebra 2. How will integrated math meet this requirement?

With the implementation of Common Core statewide, UC recognizes the significant curriculum changes being made as high schools develop mathematics transition pathways to meet school- and district-based needs. Upon completion of Math I, Math II and Math III, students will have fully met the mathematics (“C”) subject requirement for the UC system.
http://www.ucop.edu/agguide/a-g-requirements/c-mathematics/faq/index.html

10) Will Math II suffice for the UC requirement of a yearlong Geometry course?

Yes. Beginning with students applying to the University of California for fall 2015 admission, a yearlong Geometry course must be completed or a part of an integrated math course sequence (Math II) must be completed.

11) When can my child accelerate in math?

There are multiple acceleration decision points located throughout the secondary math pathway. The first acceleration decision point is at the end of 6th grade and the criteria for acceleration is based on multiple measures including an end of the course assessment, current grade in class, teacher appraisal of student readiness and a basic skills test. The end of course math assessment is based on 6th grade common core state standards. Students’ performance in the Standards for Mathematical Practice (how students engage in learning math, reasoning, persevering, etc.) and work habits are considered in the teacher appraisal of student readiness. In addition, there are acceleration decision points at the end of  Math 7, Math I and Math II.
 

12) What do the Enhanced classes represent?

The enhanced math courses offer an opportunity to accelerate along the pathway by compacting standards across courses. The middle school enhanced math courses take the content standards from Math 7, Math 8, and Math I and redistribute them across two years. The enhanced math courses in high school redistribute the standards normally taken in Math II, Math III, and Precalculus across two years. 

13) How much overlap will there be between MS Math 8 and MS Enhanced Math I?

MS Enhanced Math I will be teaching all of the Math I standards and will embed a portion of 8th grade standards in such areas as solving systems of linear equations and inequalities, understanding and comparing functions, and understanding linear models in statistics. These standards are introduced in 8th grade and in Math I students are expected to gain a richer and deeper understanding of those same topics. Students in Enhanced Math I use a different Math I textbook to allow for an in-depth understanding of topics. Of the 11 major focus areas in Math I, 3 of them will be supplemented with 8th grade standards or, in other words, approximately 20% of the content will have a natural overlap.

14) What are the bridge classes shown on the pathway (blue arrow with the word bridge)?

The bridge courses represent an opportunity for students to accelerate and move to a different track on the pathway by means of taking a summer school or online blended learning course. For example, the MS Bridge course in middle school would cover the content that students completing Math 7 would have missed by not being enrolled in Enhanced Math 7/8. The MS Bridge course will include the 8th grade standards from Enhanced Math 7/8 that were not covered in the Math 7 course. Similarly, the HS Bridge course in high school will cover the content that a student would need to master in order to advance to AP Precalculus. 

The Bridge courses will be offered to all eligible students who have met the criteria for acceleration following completion of the Math 7 or Math II courses. The Bridge courses will be offered in a blended learning format with online content and “in person” sessions.

15) Which math courses in high school will have the “honors point” for weighted grade point average?

The University of California system has recently altered the criteria for weighted grade point average. If honors points were awarded in the area of math on a commensurate level to other subject areas, the same level of courses would be awarded the honors points. In the new pathway, this would mean that AP Precalculus and AP math courses would receive the weighted grade point average.

16) What remediation is available for my child who may have “gaps” in their instruction during this transition?

Students progressing through the math pathway will proceed without “gaps” of instruction. Summer remediation will be available for students that have not demonstrated proficiency during the school year. Summer courses are offered to students that did not successfully complete a math course during the school year.

17) Will students be able to slow down if they start to struggle with math in high school?

Yes. The advantage of the new pathway is that it allows students to flex between pathways (target, support and accelerated) based on a student’s unique needs. Additionally, the integrated math sequence allows increased remediation and acceleration because the standards are revisited annually.

18) Where can I find out more information about the multiple criteria used to place students in the math pathway?

Our district website has resources and information regarding the placement process for elementary and middle school students. Please scroll up to the section above titled "K-12  Mathematic Pathways" for additional information and resources.

19) How are students placed in the pathway when they come from an international or private school setting?

It is recommended that transfer students entering IUSD during the summer take part in the summer math testing opportunities available. Along with the student transcript, the data on student content knowledge will be used to determine student placement.

For students that enter our district from other states and countries throughout the year, we will continue the same process to place these incoming students that we always have. Student transcripts are viewed by counselors and/or department chairs to make an appropriate placement. If there is uncertainty as to the proper placement, assessments are administered to gather further evidence for appropriate placement. Once placed, changes can be made as needed to adjust initial placement based on student performance. 

20) How will parents be notified about which course their student is eligible to take next year?

For sixth grade students, the end of course assessment and the basic skills test will be administered by the classroom teacher during two regular class periods by the end of April. These assessments will be scored in a centralized location by a committee of teachers who have completed training in a uniform grading process.

For seventh and eighth grade students enrolled in Math 7, Enhanced Math 7/8, Math 8, or Enhanced Math I, the end of course assessment will be administered by the classroom teacher during a regular class period at the end of April/early May.

Once the assessments have been completed, teachers will notify parents via a letter of the recommended placement by the end of May for the next school year. Parents who wish to appeal the placement (and/or accelerate further than the assigned placement) will initiate the Appeal Process by contacting their current site principal.

21) My child is currently doing higher grade level standards in 6th grade. Can he/she skip to MS Enhanced Math I to start 7th grade?

To ensure the highest possibility of success, all students must demonstrate mastery of prerequisite standards before acceleration. Students in sixth grade who may have had exposure to higher grade level standards will still need to meet 3 of 4 criteria for acceleration. If students meet 3 of 4 of the multiple criteria for acceleration at the end of sixth grade, they will be placed in the Enhanced Math 7/8 course. The Enhanced Math 7/8 course represents a significant acceleration for students and will include rigorous, fast paced instruction that covers 1.5 years of mathematical standards. We recommend that all students who meet the criteria for acceleration remain in this course.

22) What if my child does not meet the placement criteria for acceleration in 7th grade, but I believe that this is not an accurate representation of his/her ability?

Taking Enhanced Math 7/8 in the 7th grade is highly challenging and should only be attempted by clearly qualified students who are developmentally ready for this acceleration. Students who do not meet the placement criteria for acceleration at this time are advised to take MS Math 7 in grade 7 which is the course recommended by the California Department of Education in the California Mathematics Framework. Taking MS Math 7 in 7th grade may still lead to AP Calculus as a 12th grader with multiple opportunities to accelerate in 8th, 9th or 10th grade.

Parents and teachers who feel that the multiple criteria used for placement is not an accurate representation of a student’s readiness to accelerate, may access the Appeal Process by contacting their current principal. The school team, including parents, will re-examine the placement data and consider other evidence from classroom records that may give additional information about readiness for acceleration. If the appeal is granted, the placement in the higher course is conditional based on grades. Students who do not earn a grade of B or better at the first grading period will need to be reassigned to the recommended course.

23) Can I get a practice test or see a sample of the End of Course assessments used for placement?

The end of course assessments for every course are designed to assess mastery of the mathematical standards taught within that course. Additional practice should not be required to demonstrate mastery of grade level standards for those students who are ready for acceleration. For parents or students who wish to become more familiar with common core test questions that assess critical thinking skills and conceptual understanding, there are resources available on our IUSD website. Follow the link provided below and click on "Student Interface Practice and Training Tests".
http://www.caaspp.org/practice-and-training/index.html

24) Will every school site in IUSD be able to offer the same type of courses (K8 sites, year rounds, lower enrollment sites, etc.)?

Yes. Our district is prepared to staff as needed to ensure that there is equity across the district for all course offerings.

25) What support is in place for the teachers to become proficient in teaching integrated math and enhanced courses?

IUSD secondary teachers are highly qualified to teach all levels of math and most currently teach multiple courses. In 2015 our teachers began developing course content and assessments for the new math integrated and enhanced courses. Professional development targeted toward effective support within the compacted enhanced courses, instructional strategies to support accelerated learners and integrated content will take place in all subject levels to help teacher stay abreast of the most effective teaching strategies. We have always offered honors courses within IUSD and these enhanced courses will be taught with great depth and rigor to best meet the needs of the student population.

26) Currently, a student’s math course may limit the science course that they are eligible to take based on course prerequisites. Will math and science prerequisites be uncoupled across the district? How will these new pathways affect science courses?

As part of the process to develop our new pathway, the committee also closely examined the relationship between math and science prerequisites. Although competencies in math and science are often linked, in an effort to eliminate barriers to higher level coursework, our high schools have now uncoupled math and science prerequisites in ninth grade. Enrollment in Honors Biology is no longer tied to enrollment in a specific math course. We continue to examine the relationship between science and math prerequisites within higher level coursework to ensure that any prerequisites are closely aligned to the competencies required for the course.

In terms of math and science instructional content, the Next Generation Science Standards (NGSS) call for science teachers to teach the math required in the science context in which they need it. Similarly, math teachers will use statistics and functions to look at modeling science phenomena. Science and math will still be closely linked, although particular math course content may not be required in order for placement into a science course. For example, Physics and Calculus are closely related, but Calculus is not a prerequisite for taking Physics.