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Appendix B Mathematics Framework Resources Links

Links to outside resources in Appendix B of the Mathematics Framework.

Link 1 (Page 2)

California Digital Learning Integration and Standards Guidance

Link 2 (Page 2)

Test Results for California’s Assessments External link opens in new window or tab.

Link 3 (Page 2)

California’s Environmental Principles and Concepts External link opens in new window or tab.

Link 4 (Page 2)

Universal Design for Learning Guidelines External link opens in new window or tab.

Link 5 (Page 2)

Progressions for the Common Core State Standards for Mathematics External link opens in new window or tab. (PDF)

Link 6 (Page 4)

The Promise of Performance Assessments: Innovations in High School Learning and College Admission External link opens in new window or tab. (PDF)

Link 7 (Page 4)

A Tenacious Explorer of Abstract Surfaces External link opens in new window or tab.

Link 8 (Page 4)

State Achievement-Level Results External link opens in new window or tab.

Link 9 (Page 5)

Organization for Economic Co-operation and Development (OECD) External link opens in new window or tab.

Link 10 (Page 8)

California Common Core State Standards and California English Language Development Standards Resources

Link 11 (Page 8)

Asset-Based Pedagogies [Link is no longer available]

Link 12 (Page 8)

Digital Learning Integration and Standards Guidance

Link 13 (Page 8)

Test Results for California’s Assessments External link opens in new window or tab.

Link 14 (Page 8)

2021-22 Four-Year Adjusted Cohort Graduation Rate External link opens in new window or tab.

Link 15 (Page 8)

Enrollment and Completion Gaps in STEM Higher Education External link opens in new window or tab. (PDF)

Link 16 (Page 8)

Universal Design for Learning Guidelines External link opens in new window or tab.

Link 17 (Page 9)

Checking In: Are Math Assignments Measuring Up? External link opens in new window or tab. (PDF)

Link 18 (Page 12)

Welcome to the Mathematics Assessment Project External link opens in new window or tab.

Link 19 (Page 14)

PISA 2012 Results in Focus: What 15-year-olds Know and What They Can Do with What They Know External link opens in new window or tab. (PDF)

Link 20 (Page 14)

The Teaching Maths for Social Justice Network External link opens in new window or tab.

Link 21 (Page 14)

The Opportunity Myth: What Students Can Show Us About How School Is Letting Them Down—and How to Fix It External link opens in new window or tab.

Link 22 (Page 15)

Teaching for Robust Understanding External link opens in new window or tab.

Link 23 (Page 16)

The Four 4’s External link opens in new window or tab.

Link 24 (Page 17)

$martPath - The California Council on Economic Education (CCEE) External link opens in new window or tab.

Link 25 (Page 17)

Transitional Kindergarten Chapter.” Mathematics Framework for California Public Schools: Kindergarten Through Grade Twelve (PDF)

Link 26 (Page 17)

Mathematics Framework for California Public Schools: Kindergarten Through Grade Twelve (PDF)

Link 27 (Page 18)

Progressions for the Common Core State Standards for Mathematics (February 28, 2023) External link opens in new window or tab. (PDF)

Link 28 (Page 18)

Mathematics for ALL: Excellence and Equity in Mathematics External link opens in new window or tab. (PDF)

Link 29 (Page 18)

Teaching for Robust Understanding External link opens in new window or tab.

Link 30 (Page 18)

Progression videos External link opens in new window or tab.

Link 31 (Page 18)

Grade 4-Operations and Algebraic Thinking External link opens in new window or tab.

Link 32 (Page 18)

Grade 4-Rounding to the Nearest 100 and 1000 External link opens in new window or tab.

Link 33 (Page 18)

Grade 3-Locating Fractions Less than One on the Number Line External link opens in new window or tab.

Link 34 (Page 18)

Grade 3-Find 1/4 Starting from 1, Assessment Version External link opens in new window or tab.

Link 35 (Page 19)

Integers on the Number Line 2 External link opens in new window or tab.

Link 36 (Page 19)

National Standards - Jump$start Coalition External link opens in new window or tab.

Link 37 (Page 19)

Math Playground: Give Your Brain a Workout! |Resource Bank External link opens in new window or tab.

Link 38 (Page 19)

Tiered Instruction and Intervention in a Response-to-Intervention Model [Link no longer available]

Link 39 (Page 20)

Mapping Middle School Math External link opens in new window or tab.

Link 40 (Page 20)

Nrich Maths at Home External link opens in new window or tab.

Link 41 (Page 20)

Principles for the Design of Mathematics Curricula: Promoting Language and Content Development External link opens in new window or tab.

Link 42 (Page 21)

ACT National Curriculum Survey 2020 External link opens in new window or tab.

Link 43 (Page 21)

Implementing the Mathematical Practice Standards External link opens in new window or tab.

Link 44 (Page 21)

Standard 7: Look for and Make Use of Structure External link opens in new window or tab.

Link 45 (Page 22)

Statement on Competencies in Mathematics Expected of Entering College Students External link opens in new window or tab.

Link 46 (Page 22)

Fostering Math Practices: Connecting Representations (MP7) External link opens in new window or tab.

Link 47 (Page 22)

Mathematics Education Collaborative External link opens in new window or tab.

Link 48 (Page 22)

Culturally Responsive-Sustaining Education Framework External link opens in new window or tab.

Link 49 (Page 22)

Lexico External link opens in new window or tab.

Link 50 (Page 22)

Dictionary External link opens in new window or tab.

Link 51 (Page 23)

Rule of Four [Link no longer accessible]

Link 52 (Page 23)

Depth-of-Knowledge Levels for Four Content Areas External link opens in new window or tab. (PDF)

Link 53 (Page 23)

Euler's Polyhedron Formula External link opens in new window or tab.

Link 54 (Page 23)

Principles for the Design of Mathematics Curricula: Promoting Language and Content Development External link opens in new window or tab.

Link 55 (Page 24)

Statistics Teacher: About Statistics Teacher External link opens in new window or tab.

Link 56 (Page 24)

Pursuing Gender Equity in Mathematics Competitions. A Case of Mathematical Freedom External link opens in new window or tab.

Link 57 (Page 24)

Occupational Outlook Handbook: Data Scientists External link opens in new window or tab.

Link 58 (Page 24)

Computer Science Education: Computer Science Content Standards Development

Link 59 (Page 25)

Progressions for the Common Core State Standards for Mathematics (February 28, 2023) External link opens in new window or tab. (PDF)

Link 60 (Page 25)

Common Online Data Analysis Platform (CODAP) External link opens in new window or tab.

Link 61 (Page 25)

International Landscape in Data Science Education External link opens in new window or tab.

Link 62 (Page 25)

Previewing the National Landscape of K–12 Data Science Implementation External link opens in new window or tab.

Link 63 (Page 25)

Curriculum Frameworks for Introductory Data Science External link opens in new window or tab. (PDF)

Link 64 (Page 25)

Catalyzing a New Field: Data Science Education in K–12 External link opens in new window or tab. (PDF)

Link 65 (Page 25)

Climate Data Online Search External link opens in new window or tab.

Link 66 (Page 26)

The Modeling Cycle External link opens in new window or tab.

Link 67 (Page 26)

Keeping Data Science Broad: Negotiating the Digital and Data Divide Among Higher-Education Institutions External link opens in new window or tab.

Link 68 (Page 27)

Mathematical Routines External link opens in new window or tab.

Link 69 (Page 27)

Arizona’s College and Career Ready Standards - Mathematics. 1st Grade Standards External link opens in new window or tab.

Link 70 (Page 27)

Embracing Resources of Children, Families, Communities and Cultures in Mathematics Learning External link opens in new window or tab. (PDF)

Link 71 (Page 27)

Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts External link opens in new window or tab.

Link 72 (Page 27)

Multi-Tiered System of Supports

Link 73 (Page 28)

About Universal Design for Learning External link opens in new window or tab.

Link 74 (Page 28)

Progressions for the Common Core State Standards for Mathematics (February 28, 2023) External link opens in new window or tab. (PDF)

Link 75 (Page 28)

Against Answer-Getting External link opens in new window or tab.

Link 76 (Page 28)

Formative Principles of the Common Core State Standards External link opens in new window or tab.

Link 77 (Page 28)

Early Math Resources for Teacher Educators External link opens in new window or tab.

Link 78 (Page 29)

Twelve Ways to Make Math More Culturally Responsive External link opens in new window or tab.

Link 79 (Page 29)

Box of Clay External link opens in new window or tab.

Link 80 (Page 29)

Button Diameters External link opens in new window or tab.

Link 81 (Page 29)

Comparing Money Raised External link opens in new window or tab.

Link 82 (Page 29)

Dividing by One-Half External link opens in new window or tab.

Link 83 (Page 29)

Doubling Numerators and Denominators External link opens in new window or tab.

Link 84 (Page 30)

Data Clusters and Distributions External link opens in new window or tab.

Link 85 (Page 30)

What’s Typical, Based on the Shape of Data Charts? External link opens in new window or tab.

Link 86 (Page 31)

Learning Mathematics Through Representations External link opens in new window or tab.

Link 87 (Page 31)

Inside Mathematics: Performance Assessment Tasks External link opens in new window or tab.

Link 88 (Page 31)

Improving Mathematical Problem Solving in Grades 4 Through 8: A Practice Guide (NCEE 2012-4055) External link opens in new window or tab. (PDF)

Link 89 (Page 31)

Moving Colors External link opens in new window or tab.

Link 90 (Page 31)

The Pocket Game External link opens in new window or tab.

Link 91 (Page 31)

Principles for the Design of Mathematics Curricula: Promoting Language and Content Development External link opens in new window or tab.

Link 92 (Page 32)

The Number of Endangered Species Is Rising External link opens in new window or tab.

Link 93 (Page 32)

Universal Design for Learning Guidelines version 2.2 External link opens in new window or tab.

Link 94 (Page 32)

Common Online Data Analysis Platform (CODAP) External link opens in new window or tab.

Link 95 (Page 32)

Math Guidelines External link opens in new window or tab.

Link 96 (Page 33)

How to Select Math Intervention Content External link opens in new window or tab.

Link 97 (Page 33)

Statement of Competencies in Mathematics Expected of Entering College Students External link opens in new window or tab. (PDF)

Link 98 (Page 33)

Stephen Curry Is the Revolution External link opens in new window or tab.

Link 99 (Page 33)

Principles for Mathematics Instruction for ELLs External link opens in new window or tab.

Link 100 (Page 33)

What’s Going on in This Graph? External link opens in new window or tab.

Link 101 (Page 33)

"The” Modeling Cycle External link opens in new window or tab.

Link 102 (Page 34)

Re-engagement [Link no longer access]

Link 103 (Page 34)

How NCTM Is Supporting Math Teachers in 2020 and Beyond External link opens in new window or tab.

Link 104 (Page 34)

Youcubed Border Problem Week 1 – Days 1 & 2 External link opens in new window or tab. (PDF)

Link 105 (Page 34)

Youcubed Data Talk Women’s Soccer External link opens in new window or tab. (PDF)

Link 106 (Page 34)

Principles for the Design of Mathematics Curricula: Promoting Language and Content Development External link opens in new window or tab.

Link 107 (Page 35)

California Digital Learning Integration and Standards Guidance

Link 108 (Page 35)

CSU Mathematics Bridge Courses External link opens in new window or tab.

Link 109 (Page35 )

Against Answer-Getting External link opens in new window or tab.

Link 110 (Page 36)

Japanese Curriculum External link opens in new window or tab.

Link 111 (Page 36)

Three-Phase Lesson Structure External link opens in new window or tab. (PDF)

Link 112 (Page 36)

A Joint Position Statement of the Mathematical Association of America and the National Council of Teachers of Mathematics on Teaching Calculus External link opens in new window or tab. (PDF)

Link 113 (Page 36)

Math Class Needs a Makeover External link opens in new window or tab.

Link 114 (Page 37)

State Achievement-Level Results External link opens in new window or tab.

Link 115 (Page 37)

Top Performing Countries: Estonia External link opens in new window or tab.

Link 116 (Page 37)

These Twenty Things [Link no longer available]

Link 117 (Page 37)

Mathematics Curriculum in Korea External link opens in new window or tab. (PDF)

Link 118 (Page 37)

Policy Announcement on Area C External link opens in new window or tab.

Link 119 (Page 37)

Statement on the Impact of Calculus on UC Admissions External link opens in new window or tab. (PDF)

Link 120 (Page 38)

The Algebra Project External link opens in new window or tab.

Link 121 (Page 38)

The Effect of Classroom Assignment Policies on Equitable Access to High-Quality Teachers External link opens in new window or tab.

Link 122 (Page 38)

The Calculus Project External link opens in new window or tab.

Link 123 (Page 38)

California Digital Learning Integration and Standards Guidance

Link 124 (Page 39)

An Instructional Model That Supports Students, Both Inside and Outside the Classroom External link opens in new window or tab.

Link 125 (Page 39)

Core-Plus Mathematics External link opens in new window or tab. (PDF)

Link 126 (Page 40)

What is Personalized Learning? External link opens in new window or tab.

Link 127 (Page 40)

Will Technology Transform Education for the Better? External link opens in new window or tab.

Link 128 (Page 40)

Does Detracking Promote Educational Equity? External link opens in new window or tab.

Link 129 (Page 41)

Math Circle Network External link opens in new window or tab.

Link 130 (Page 41)

Mathematical Olympiads for Elementary and Middle Schools (MOEMS) External link opens in new window or tab.

Link 131 (Page 41)

Top-Performing Countries: Estonia External link opens in new window or tab.

Link 132 (Page41 )

Research Overview External link opens in new window or tab.

Link 133 (Page 42)

Issue Brief: Academic Tutoring in High Schools External link opens in new window or tab. (PDF)

Link 134 (Page 42)

Issue Brief: Academic Support Classes External link opens in new window or tab.

Link 135 (Page 42)

Border Problem External link opens in new window or tab. (PDF)

Link 136 (Page 43)

Just Dreams and Imperatives: The Power of Teaching in the Struggle for Public Education External link opens in new window or tab.

Link 137 (Page 43)

California Action Network for Mathematics Excellence and Equity (CANMEE) External link opens in new window or tab.

Link 138 (Page43 )

California English Learner Roadmap: Strengthening Comprehensive Educational Policies, Programs, and Practices for English Learners

Link 139 (Page 43)

Multi-Tiered System of Supports

Link 140 (Page 45)

About Lesson Study External link opens in new window or tab.

Link 141 (Page 46)

Dual Capacity-Building Framework for Family-School Partnerships (Version 2) External link opens in new window or tab.

Link 142 (Page 47)

Professional Development Guides External link opens in new window or tab.

Link 143 (Page 47)

National Standards for Family-School Partnerships External link opens in new window or tab.

Link 144 (Page 47)

Black, Indigenous, and Latinx Parents as Partners in Mathematics Education External link opens in new window or tab. (PDF)

Link 145 (Page 49)

Introduction to Communities of Practice: A Brief Overview of the Concept and Its Uses External link opens in new window or tab.

Link 146 (Page 49)

Mathematics TPACK (Technological Pedagogical Content Knowledge) Framework (PDF) [Link no longer available]

Link 147 (Page 49)

California Digital Learning Integration and Standards Guidance

Link 148 (Page 49)

California Assessment of Student Performance and Progress (CAASPP) System

Link 149 (Page 49)

Distance Learning Instruction Planning Guidance

Link 150 (Page 49)

Distance Learning

Link 151 (Page 49)

ISTE: Integrating Digital Technologies in Remote K–12 Learning: Lessons for Higher Education Preparation Programs External link opens in new window or tab.

Link 152 (Page 49)

Land the Plane External link opens in new window or tab.

Link 153 (Page 49)

GeoGebra for Teaching and Learning Math External link opens in new window or tab.

Link 154 (Page 49)

Measuring the Information Society – The ICT Development Index External link opens in new window or tab. (PDF)

Link 155 (Page 51)

California Assessment of Student Performance and Progress (CAASPP) External link opens in new window or tab.

Link 156 (Page 51)

California Digital Learning Integration and Standards Guidance

Link 157 (Page 52)

Standard Elementary Report Cards External link opens in new window or tab.

Link 158 (Page 52)

SCALE Math Performance Assessment Rubric, Grades 3–12 External link opens in new window or tab. (PDF)

Link 159 (Page 52)

Meet the Single Point Rubric External link opens in new window or tab.

Link 160 (Page 52)

Math Practices Learning Progressions: SMP External link opens in new window or tab.

Link 161 (Page 52)

Math: High Dive Unit Problem External link opens in new window or tab.

Link 162 (Page 53)

Pre–K Math Portfolios External link opens in new window or tab.

Link 163 (Page 53)

I Can Statements (PDF) [Link no longer available]

Link 164 (Page 53)

Understanding the Formative Assessment Process External link opens in new window or tab. (PDF)

Link 165 (Page 53)

Tools for Teachers External link opens in new window or tab.

Link 166 (Page 53)

Re-Engagement: A Powerful Formative Assessment Process (PDF) [Link no longer available)

Link 167 (Page 53)

Math Performance Assessment Rubric (Grades 9-12) External link opens in new window or tab. (PDF)

Link 168 (Page 54)

What Does the Research Say about Standards-Based Grading? External link opens in new window or tab.

Link 169 (Page 54)

Formative and Summative Assessments External link opens in new window or tab.

Link 170 (Page 54)

Principles for the Design of Mathematics Curricula: Promoting Language and Content Development External link opens in new window or tab.

Link 171 (Page 55)

Standards for Evaluating Instructional Materials for Social Content, 2013 Edition

Link 172 (Page 55)

Guidelines for Piloting Textbooks and Instructional Materials

Link 173 (Page 55)

California Digital Learning Integration and Standards Guidance

Link 174 (Page 55)

Approved Social Content Review Search

Link 175 (Page 55)

Clearinghouse for Specialized Media & Technology

Link 176 (Page 55)

Progressions for the Common Core State Standards for Mathematics External link opens in new window or tab. (PDF)

Link 177 (Page 56)

Smarter Balanced External link opens in new window or tab.

Link 178 (Page 57)

Reimagining a Better System for ELs [Link no longer available]

Link 179 (Page 57)

Progressions for the Common Core State Standards for Mathematics External link opens in new window or tab. (PDF)

Link 180 (Page 57)

Mathwords External link opens in new window or tab.

Link 181 (Page 59)

GeoGebra: Circle Area (By Peeling!) External link opens in new window or tab.

Link 182 (Page 59)

Climate Change in the Golden State External link opens in new window or tab. (PDF)

Link 183 (Page 59)

Universal Design for Learning Guidelines version 2.2 External link opens in new window or tab.

Link 184 (Page 59)

New CDC report: More than 100 million Americans have diabetes or prediabetes – infographic External link opens in new window or tab.

Link 185 (Page 60)

Progressions for the Common Core State Standards for Mathematics External link opens in new window or tab. (PDF)

Link 186 (Page 60 )

2017 Problems: Part of the High School Mathematical Contest in Modeling (HiMCM) Competition External link opens in new window or tab.

Link 187 (Page 60)

Comparing Money Raised External link opens in new window or tab.

Link 188 (Page 60)

Rectangle Perimeter 2 External link opens in new window or tab.

Link 189 (Page 60)

Formative Re-Engaging Lessons External link opens in new window or tab.

Link 190 (Page 61)

Climate Change: Atmospheric Carbon Dioxide External link opens in new window or tab.

Link 191 (Page 61)

Three-Phase Lesson Structure External link opens in new window or tab. (PDF)

Link 192 (Page 61)

Are There More Inches in a Mile or Seconds in a Day? External link opens in new window or tab.

Link 193 (Page 61)

Maximizing Area: Gold Rush External link opens in new window or tab.

Link 194 (Page 61)

Climate Change Impacts External link opens in new window or tab.

Link 195 (Page 61)

Re-engagement [Link no longer available]

Link 196 (Page 61)

(DRAFT) Comparing Numbers and Place Value Relationships, Grade 4 Integrated ELD and Mathematics Instruction Vignette External link opens in new window or tab.

Link 197 (Page 61)

US Department of Housing and Urban Development (HUD) User External link opens in new window or tab.

Link 198 (Page )

Data Science Online Course Lessons External link opens in new window or tab.

Link 199 (Page 62)

Sponge Art Transformations (K–10) External link opens in new window or tab.

Link 200 (Page 62)

Principles for the Design of Mathematics Curricula: Promoting Language and Content Development External link opens in new window or tab.

 

Questions:   Curriculum Frameworks and Instructional Resources Division | cfird@cde.ca.gov | 916-319-0881
Last Reviewed: Thursday, August 14, 2025
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