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2023 Mathematics Framework

At its meeting on July 12, 2023, the State Board of Education (SBE) adopted the Mathematics Framework for California Public Schools: Kindergarten Through Grade Twelve ( Mathematics Framework). The framework is important guidance designed to help educators align classroom teaching with California's rigorous math learning standards.

The Mathematics Framework reflects input from California parents, educators, students, and others who commented during the two 60-day field review periods that were held in 2021 and 2022.

California is committed to achieving excellence in math teaching and learning through curriculum and instructional approaches grounded in research and reflective of best practices across the globe. The Mathematics Framework provides guidance for mathematics learning for all students at all levels of math-including calculus-and ensures students have a wide variety of options including pursuing Science, Technology, Engineering, and Mathematics (STEM) in college and career.

Frequently Asked Questions
Information about the draftMathematics Framework.

Schedule of Significant Events for the Revision of the Mathematics Framework
At its meeting on July 13, 2022, SBE revised the Schedule of Significant Events (Timeline) for the Revision ofMathematics Framework. The Timeline was originally approved by the SBE on May 8, 2019, and was previously revised on September 11, 2019, May 7, 2020, July 14, 2021, and November 3, 2021.

A professionally-edited and designed PDF version of the framework will be posted at a later date. The content will not substantively change from the version posted below.

Curriculum Framework and Evaluation Criteria Committee

At their January 08, 2020, meeting the State Board of Education appointed 20 members to the Mathematics Curriculum Framework and Evaluation Criteria Committee (Mathematics CFCC) to assist in the development of the Mathematics Framework.

The Mathematics CFCC Meetings and Notices

Focus Groups

Pursuant to the California Code of Regulations, Title 5, Section 9511(c), the California Department of Education (CDE) convened four focus groups across California.

Listserv

Additional Resources

2013 Mathematics Framework

Assembly Bill 250 (Chapter 608, Statutes of 2011) called for the revision of the Mathematics Framework to align with the California Common Core State Standards for Mathematics.

Video: Overview of the Mathematics Framework (Dated 26-Feb-2015)
This video for teachers, administrators, and other educators provides an overview of the Mathematics Framework and how it supports implementation of the California Common Core State Standards for Mathematics.

Common Core State Standards for Mathematics (PDF; 3MB)
Links to the standards adopted by the California State Board of Education in August 2010 (Modified January 2013 Publication Version).

Common Core State Standards (CCSS) Initiative
The multi-state initiative released the CCSS on June 2, 2010. The initiative site includes information about the development and research behind the standards, appendices, the states that have adopted the CCSS, and frequently asked questions.

Appendix A
Designing High School Mathematics Courses Based on the CCSS.

2005 Mathematics Framework (Available on request)
The Framework was adopted by the State Board of Education on March 9, 2005.
*To order a copy of this framework please contact CDE Press.

Content Standards
Links to downloads of all Content Standards.

All Curriculum Frameworks
Links to downloads of all Curriculum Frameworks.

Questions: Curriculum Frameworks and Instructional Resources Division | CFIRD@cde.ca.gov | 916-319-0881

Last Reviewed: Friday, October 20, 2023

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Curriculum frameworks provide guidance to educators, parents, and publishers, to support implementing California content standards.

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The 3-read protocol and math tasks that CVES uses were developed by Exemplars, a company that provides a library of rich performance tasks and professional development for K-12 schools.

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Demystify math word problems with this simple technique that helps kids see the story beyond the numbers.

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How can I open this PDF!

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Math Balance

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Which One Doesn't Belong

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Subitizing Cards

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Providing instructional and assessment tasks, lesson plans, and other resources for teachers, assessment writers, and curriculum developers since 2011.

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Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.
Watch the video to learn how sharing works.

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Sharing in an app allows educators to pose problems and investigations for students by using an 8-character code or link. Students can share their thinking with their teachers and classmates. Share codes remain available for continued use for 18 months from the date they are last accessed.

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Topics: Mental math, numerical fluency; argument & critique
Materials: White board or projector
Common Core: Variable, and especially MP3 and NF

This mental math routine creates powerful positive habits for students to understand
and think productively about fractions.

Fraction talks developed as a way to use the Number Talk routine to target fractions. A growing body of fraction talks are available at fractiontalks.com.

I've created a writeup below for how to use fraction talks, as well as a collection here which are ideal for introducing fraction talks to students early in their understanding of fractions, and then continuing in slowly increasing levels of difficulty.

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Topics: Mental math, numerical fluency; argument & critique Materials: White board or projector Common Core: Variable, and especially MP3 and NF This mental math routine creates powerful positive habits for students to understand and think productively about fractions. Fraction talks developed as a way to use the Number Talk routine to target fractions.

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Subitize Country Style | Subitizing up to 10 | Math Song for Kids Jack Hartmann

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到 Facebook 查看帖子、照片和更多内容。

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My growing list of free real world problem-based lessons for grades 2 through high school. Includes links to download multimedia and teacher guide.

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Esti-Mysteries: Estimation Meets Math Mysteries - Steve Wyborney's Blog: I'm on a Learning Mission.

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Introducing Esti-Mysteries! Each image invites students to wonder what number is represented by the image. As you click through the each Esti-Mystery, clues

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Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

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100 Subitizing Slides & 10 Challenge Patterns - Steve Wyborney’s Blog: I’m on a Learning Mission.

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I have a new resource for you. 100 Subitizing Slides & 10 Challenge Patterns.

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Building Thinking Classrooms: K-2 | Facebook

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This is a community for early elementary math teachers who want to share ideas, ask questions, develop expertise, and connect with other early elementary educators concerning the practices from...

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Numberless Word Problems

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Steve Wyborney\\\'s Blog: I\\\'m on a Learning Mission.

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For my educator friends who have access to Google Slides, but do not have access to PowerPoint, this post is for you. Since Google Slides does not have the animation that makes the Splats become transparent, the Splat! reveal does not work in Slides. Now - with these materials - it will. I've rewritten the first 20 Splat! lessons and the first 20 Fraction Splat! lessons with a different method so they will now include the reveal when using Google Slides.

The content of the lessons is the same as the original lessons.

Visit these links to see the original videos about how to use the and the Fraction Splat! slides.

Quick Note: The file sharing power of Google Drive is impressive and highly useful. However, for the purposes of sharing these resources, I need to use a method that I can personally maintain, update and support - and I've learned that the best way to provide resources from my blog is through the download links and the sign-up forms.

I hope you enjoy these Splats! formatted to work in Google Slides!

Splat Through 10
How many dots are under the Splat?
SPLAT 1.1 - numbers through 10 (Google Slides compatible version)
SPLAT 2.1 - with numbers 12-20 (Google Slides compatible version) SPLAT 2.2 - with numbers 12-20 (Google Slides compatible version) SPLAT 2.3 - with numbers 12-20 (Google Slides compatible version) SPLAT 2.4 - with numbers 12-20 (Google Slides compatible version) SPLAT 2.5 - with numbers 12-20 (Google Slides compatible version) SPLAT 1.2 - numbers through 10 (Google Slides compatible version)SPLAT 3.1 - multiple splats (Google Slides compatible version) SPLAT 3.2 - multiple splats (Google Slides compatible version) SPLAT 3.3 - multiple splats (Google Slides compatible version) SPLAT 3.4 - multiple splats (Google Slides compatible version) SPLAT 3.5 - multiple splats (Google Slides compatible version)
SPLAT 4.1 - instant multiple splats (Google Slides compatible version) SPLAT 4.2 - instant multiple splats (Google Slides compatible version) SPLAT 4.3 - instant multiple splats (Google Slides compatible version) SPLAT 4.4 - instant multiple splats (Google Slides compatible version) SPLAT 4.5 - instant multiple splats (Google Slides compatible version) Note: These lessons use a single splat along with a mixture of unit fractions and whole numbers. In Level 11, you control the Splat! SPLAT 11.1 - fraction splats (Google Slides compatible version) SPLAT 11.2 - fraction splats (Google Slides compatible version) SPLAT 11.3 - fraction splats (Google Slides compatible version) SPLAT 11.4 - fraction splats (Google Slides compatible version) SPLAT 11.5 - fraction splats (Google Slides compatible version) SPLAT 1.3 - numbers through 10 (Google Slides compatible version)Note: These lessons use a single Splat! which appears at the same moment as the whole numbers and fractions. Each question instantly presents missing information. SPLAT 12.1 - Instant Fraction Splats (Google Slides compatible version) SPLAT 12.2 - Instant Fraction Splats (Google Slides compatible version) SPLAT 12.3 - Instant Fraction Splats (Google Slides compatible version) SPLAT 12.4 - Instant Fraction Splats (Google Slides compatible version) SPLAT 12.5 - Instant Fraction Splats (Google Slides compatible version) Multiple Splats! with Fractions Note: These lessons include multiple Splats! and you control the timing of the Splats! The entire screen can be seen, the total can be determined, and then Splat! Remember: Each Splat! that is the same color must be covering the same number. SPLAT 13.1 - Multiple Fraction Splats (Google Slides compatible version) SPLAT 13.2 - Multiple Fraction Splats (Google Slides compatible version) SPLAT 13.3 - Multiple Fraction Splats (Google Slides compatible version) SPLAT 13.4 - Multiple Fraction Splats (Google Slides compatible version) SPLAT 13.5 - Multiple Fraction Splats (Google Slides compatible version)
Note: These lessons use multiple Splats! which appear at the same moment as the whole numbers and fractions. Each question instantly presents missing information. Remember: Each Splat! that is the same color must be covering the same number. SPLAT 14.1 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 14.2 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 14.3 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 14.4 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 14.5 - Instant Multiple Fraction Splats (Google Slides compatible version) SPLAT 1.4 - numbers through 10 (Google Slides compatible version)
SPLAT 1.5 - numbers through 10 (Google Slides compatible version)

Splat Through 20
How many dots are under the Splat?

Multiple Splats
Note: Splats that are the same color must cover the same number.

Instant Multiple Splat
Note: An additional feature of this level is the opportunity to ask, "What could the total be?"

Instant Fraction Splat!

Multiple Instant Splats! with Fractions

After reading this blog post, take a look at THE 12 MOST POPULAR MATH STRATEGIES AND DOWNLOADS ON THIS BLOG.

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Splat! for Google Slides - 40 Lessons - Steve Wyborney's Blog: I'm on a Learning Mission.

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For my educator friends who have access to Google Slides, but do not have access to PowerPoint, this post is for you. Since Google Slides does not have the

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Students love to play games in math class. So we've curated (and created!) the best math games we know and put them in one place, to make sure that students will be learning math and engaged through play.

These games are notable for their:

1. Student Choice
2. Mathematics is the engine of the game
3. Easy to learn and quick to play - perfect for classroom use

Want more? Check out the Mathematical Games Minicourse. A 115-minute recording with accompanying 45 page booklet of favorite games for pre-K - 2nd grade.

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Students love to play games in math class. So we've curated (and created!) the best math games we know and put them in one place, to make sure that students will be learning math and engaged through play. These games are notable for their: 1. Student Choice 2.

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Click grade level, then routines. Huge bank of routines to support number sense

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The Coherence Map shows the connections between Common Core State Standards for Mathematics.

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Intro Welcome! K-12 Curricular Task Sharing Sheet This is a working document to collect information and resources for CURRICULAR tasks. These tasks should be highly engaging, consisting of rich problem-solving and/or thin-sliced tasks (as referenced in Ch. 1 and 9 of "Building Thinking Classroo...

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Routines Resources

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online math manipulatives

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Depending on your child's grade level, choose a number and allow them to come up with ideas related to that number.

Kindergarten and Grade 1: Numbers 1 - 9, 10 - 20

Grade 2:
Numbers 1 - 1000

Grade 3:
Numbers from 1 - 1000 & Fractions such as halves, thirds, fourths, sixths, eights.

Grade 4 and 5:
Numbers from 100 - 1,000,000 and Fractions

Middle & High School:
All of the K-5 numbers, negative Numbers, more complex fractions.

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1. ALIKE & DIFFERENT* 2. ESTIMATE 3. EVERY GRAPH TELLS A STORY 4. FILL IN THE BLANK 5. GUESS MY RULE* 6. HOW DO YOU KNOW?* 7. INCOMPLETE SET

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Hey, welcome to the Math Mistakes website. My name is Michael Pershan, by the way. I am a math teacher in NYC. I have other websites and am active on twitter. The purpose of this site is to collect, organize and make sense of the mistakes that students make while doing math.

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Routines

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Manipulatives

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Case Study: Leander Independent School District, TX

Confidence Is Key

With Bridges, Leander students' confidence in math is growing as they learn multiple strategies for problem solving. And, as one educator put it, "Most importantly, we've seen an increase in students loving math."

Watch the video

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With Bridges, Leander students' confidence in math is growing as they learn multiple strategies for problem solving. And, as one educator put it, "Most importantly, we've seen an increase in students loving math." Watch the video

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Read about how Math Talks can strengthen accuracy, efficiency, and flexibility in this article by Sherry Parrish from Teaching Children Mathematics.

More sources for Math Talks:

Other Tools
This folder includes a variety of helpful tools for deepening math talks, planning, and assessing. Including:

Another source of information and resources for Math Talks from Math Perspectives is here.

30 ways to make number strings more inclusive...

Anchor number strings in context.

Never underestimate the importance of models.

Explicitly represent language that helps students be precise mathematically.

Explicitly ask students to try new strategies

​More on NumberStrings.com

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Download the Math Talks Descriptions from our Math Teaching Toolkit here > > >

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These Geometric Subitizing Cards have been in beta the past two years.

I asked our buddy Joe Schwartz to take them for a test drive last spring and he reported back. Joe's all in.

How do they work? Let's play...

Last week I took them for another spin in some kindergarten classes. Here's two examples of how it went and we're only 2 months into the school year.

Last year I captured me playing cards with my girls. Here's me playing with my kindergartner.

Here's me playing with my 3rd grader.

Your turn.

Take these cards and give them a try. If you need some ideas how to use them you might want to check out this task card. I plan to share my thoughts about Geometric Subitizing in a future post but for now I just want you to go and play. The only thing I ask is that you report back and offer feedback.

How did it go?

How can we make them better?

Any other ways we could use them?

What am I missing?

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Geometric Subitizing: A Different Kind of Number Talk

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Download the Resource These Geometric Subitizing Cards have been in beta the past two years. I asked our buddy Joe Schwartz to take them for a test drive last spring and he rep...