TK–Algebra I GRADES Program Overview
The Vision Is Clear. The Time Is Now.
Where the California Math Standards focused on what students should know, the Mathematics Framework for California Public Schools (Mathematics Framework) was established because the “how and the why” of math learning are as important as what students are learning. The vision is clear: To build a conceptual understanding of math, we need to rethink the approach to math teaching.
Eureka Math2 California was crafted to help California teachers meet this moment, empowering educators with lessons and tools that help students become confident doers of math. It takes the very best from years of user research, efficacy data, and in-the-classroom teacher testing to create a new program built for California students and teachers.
Every lesson engages students in understanding the why behind the math to help them build deep and lasting understanding while connecting what they’re learning to the real world.
It Starts with the Standards
At the start of every lesson, teachers will clearly see the California Common Core Math Standards they’ll address, along with a studentfriendly learning objective. Students will also see this objective clearly displayed in their student materials to prep and guide their learning.
LESSON 4 Interpret the meaning of factors as number of groups or number in each group.
Eureka Math2 California is designed by teachers, for teachers for smooth implementation and maximized student support. In addition to the prominently placed learning standards and objectives, every lesson has a clear plan that shows teachers what materials they’ll need, any preparation required, and an agenda for the learning. With icons that identify when to turn to the digital platform, teachers have an easy-to-follow guide so their focus can remain on helping students meet the standards and gain a conceptual understanding of math.
Eureka Math2 California is designed for a consistently supportive student learning experience. Sharing student-friendly learning objectives visually and verbally helps all students grow their understanding, especially those who are not yet proficient with math concepts. Sharing and explaining learning objectives can:
• help students gauge their progress,
• increase both motivation and time spent on task, and
• better equip students to make decisions about how to approach tasks.
Big Ideas Are a Big Deal
Big Ideas represent a shift in thinking in how educators and publishers should approach math teaching.
Rather than focusing on disconnected procedures to solve problems algorithmically, the Big Ideas help students see math as a story and create a web of coherence across the year and across grade levels.
With Eureka Math2 California, students and teachers can see how every lesson connects to the Big Ideas. The curriculum was crafted as a story, taking students from the Story of Units to the Story of Ratios to the Story of Functions. We know that using consistent models and instructional routines and writing lessons that use the Content Connections to weave together that story from TK to Algebra I sets the stage for students to develop a deep conceptual understanding of math.
Grade 7 Big Idea: Angle Relationships
Students use familiar and new angle relationships to write and solve equations that help determine unknown angle measures. Students continue to use properties of operations and visual models to solve equations. They are introduced to a new strategy for solving equations: if–then moves.
Every module begins by clearly showing teachers which Big Ideas are covered in the module and how they connect back to the Content Connections to deepen student understanding across modules and grade levels.
Equity & Engagement Open the Door to Learning
Great Minds® was founded on the belief that every child is capable of greatness, and the Mathematics Framework outlines the path for what must happen in a classroom to provide equitable access to learning so each student can achieve that greatness.
The three dimensions of an equitable education play a large role in ensuring that classroom learning advances equity. That’s why Eureka Math2 California was created to take an assets-based approach to instruction, supporting active engagement through investigation and connection while acknowledging that cultural and personal relevance is vital to learning. By being engaged in the learning journey, California students can begin to see themselves as mathematicians who are empowered to solve problems and make meaningful mathematical connections.
These three dimensions should be seen in all five of the components of equitable and engaging teaching.
THREE DIMENSIONS OF AN EQUITABLE EDUCATION
The Five Components of Equitable and Engaging Teaching Found in Eureka Math2 California
PLAN TEACHING AROUND BIG IDEAS
The Big Ideas shape student learning in Eureka Math² California and allow students to make connections across modules and grade levels. By seeing math as a story, students build conceptual knowledge that helps them tackle more complex math learning.
Source: California State Board of Education, Mathematics Framework: Chapter 6 – Mathematics: Investigating and Connecting, Transitional Kindergarten through Grade Five (California Department of Education, July 12, 2023), 117, fig. 6.52, https://www.cde.ca.gov/CI/ma/cf/index.asp
Teacher Note
Students make arrays to help them reason about the number of factors for a given number.
Write the equation l × w = 24
Invite students to turn and talk about numbers that make the equation true.
Direct students to work with a partner to draw as many arrays with an area of 24 square units as possible. As they create each array, have them sketch the array and record the equation that represents the area.
Provide students with 2 minutes to find all possible arrays, sketch the arrays, and record the equations.
After students record the equations, direct them to work with another group to compare their equations and to discuss the factors of 24 based on the equations they recorded.
Invite students to think–pair–share about how they know that they have found all the factors of 24
We started with 1 and thought about whether we could make an array with 1 row. Then we tried 2 rows and 3 rows. We kept going like that until we got up to 6 rows. When we got to 6 rows, we realized it was the same factors we had already listed.
We thought about all the multiplication facts that have a product of 24
Invite students to turn and talk about how they might find all the factors of a number such as 96 5 2 x 12 = 24 3 x 8 = 24 4 x 6 = 24 1 x 24 = 24
Teacher Note
In grade 3, students find all possible side lengths of rectangles with a given area. They strategically check to see whether they have found all possible (whole number) side lengths. They apply the commutative and associative properties of multiplication to multiplication expressions representing the area of the rectangles and generate new expressions.
UDL: Action & Expression
Consider supporting students in expressing learning in flexible ways. Provide access to manipulatives such as disks or square tiles for students to arrange into arrays or grid paper for students to use to draw arrays.
USE OPEN, ENGAGING TASKS
These tasks provide opportunities for students to explore math concepts through real-world problems that feel relevant to their lives. This “low floor, high ceiling” approach ensures that every student has a chance to engage deeply with the material, whether they are just beginning to build their math understanding or are ready for more complex problem-solving.
Figure 6.52. Grade Three Big Ideas
TEACH TOWARD SOCIAL JUSTICE
Eureka Math² California was crafted to ensure all students can see themselves as doers of math. In our visuals, in the words students read, and in math context videos that create a low floor/high ceiling opportunity for students to engage with math, students will see themselves and other diverse populations that make up California classrooms.
PRIORITIZE REASONING AND JUSTIFICATION
Instructional routines in Eureka Math² California allow students to demonstrate their thinking and share their approach to different math problems. This helps to deepen their conceptual understanding and foster mathematical discussions that enhance problem-solving skills.
INVITE STUDENT QUESTIONS AND CONJECTURES
A Eureka Math² California classroom is a classroom buzzing with student discourse. Every lesson includes opportunities for students to share their mathematical thinking with partners and the whole class, and activities like Data Talks and Data Investigations allow students to explore real-world data about engaging topics and discuss what the data points mean.
The Universal Design for Learning: Equity Begins with Access
Learner variability in our classrooms is the norm, so Eureka Math2 California ensures that all students are given the opportunity engage and succeed by proactively removing learning barriers through incorporation of the Universal Design for Learning (UDL) principles. Options that address learner variability are built into the lesson design and suggested at point of use in margin notes.
Launch
Materials—T: Large number path
PROVIDE MULTIPLE MEANS OF ENGAGEMENT
Students generate data by selecting one of two choices.
Gather students and invite them to get to know one another better through a survey. As you ask questions, acknowledge their responses, but do not record their choices. Explain to students that they should raise their hands only once.
Learners differ markedly in the ways in which they can be engaged or motivated to learn. Use a variety of methods to engage students. For example, provide choice, address student interest, and arrange for students to monitor their own learning, such as with goal setting, self-assessment, and reflection.
Let’s collect information about the things we like. Which do you like better: listening to stories or listening to music?
Raise your hand if you like listening to stories.
Raise your hand if you like listening to music.
I’m getting so much good information, but I need a way to organize your choices so that we can remember them and talk about what we notice.
Display a number path. Help students recall that they used the number path to count and compare in lesson 1.
big (or it’s too small).
How can we use the number path to show your choices?
We can count our hands and then put cubes on two number paths.
UDL: Engagement
Sharing favorite activities through a class survey engages students by tapping into their interests and experiences. This also supports the development of a community of learners as students get to know their classmates and discover common interests.
Consider adjusting the questions to match the class’s interests.
Let’s count and compare your choices by using the number path. Are we able to put ourselves on the number path just as we put the Unifix Cubes on the number path? Why?
Transition to the next segment by framing the work. Today, we will use number paths to organize, show, and compare our choices.
No, because we’re too big (or it’s too small).
How can we use the number path to show your choices?
We can count our hands and then put cubes on two number paths.
Transition to the next segment by framing the work.
simplifying in this lesson, we will apply as many properties of exponents needed so the final answer has only prime bases and only positive exponents. The 3, and 5 are all prime and all of their exponents are positive, so we know the expression is fully simplified.
problems 4 and 5. Consider working as a class to complete problem 4. Then have complete problem 5 individually or with a partner.
problems 4 and 5, simplify the expression by using the fewest
Today, we will use number paths to organize, show, and compare our choices.
UDL: Representation
PROVIDE MULTIPLE MEANS OF REPRESENTATION
Learners differ in the ways they perceive and comprehend information that is presented to them. Use a variety of strategies, instructional tools, and methods when presenting information and content.
PROVIDE MULTIPLE MEANS OF ACTION & EXPRESSION
Learners differ in the ways they can navigate a learning environment and express what they know. Offer students a variety of strategies and instructional tools and allow for multiple ways to demonstrate new understanding.
Guide students to repeat shading columns of 3 until 5 columns are heavily shaded to represent the vases of pink flowers.
Repeat for the 2 threes representing the vases of yellow flowers. Shade these squares lightly for contrast.
Trace the lines around the entire array to create a border.
Invite students to think–pair–share about how the array represents the problem.
The 5 columns of three represent the 15 vases of pink flowers. The 2 columns of three represent the 6 vases of yellow flowers. The whole array represents the 21 total vases of flowers.
UDL: Representation
Earning two prestigious CAST certifications, Eureka Math² Califorinia promotes inclusive, engaging learning. Designed with Universal Design for Learning at its core, Eureka Math² Califorinia is transforming equity in math education—ensuring every child builds lasting math knowledge.
The Power of Multilingual Leaners: A Collaborative Journey
To address the growing proficiency gap between multilingual learners (MLL) and their peers, the Mathematics Framework emphasizes equitable access to high-quality math instruction, integrating both content knowledge and language development.
Eureka Math2 California instruction fosters math thinking while simultaneously promoting English language development through the integration of language development, language scaffolding and routines, and culturally and linguistically relevant content.
LANGUAGE ROUTINES
Language Routines can be used flexibly whenever there are opportunities to support students with collaborative, interpretive,
productive language.
LANGUAGE DEVELOPMENT
Lesson-embedded routines support sense-making, optimize output, cultivate conversations, and maximize meta-awareness.
CULTURALLY RELEVANT
The Mathematics Framework stresses that math instruction must be culturally and linguistically relevant to engage students fully. This Grade 2 Data Talk involves comparing the heights of trees, a context that could relate to students’ local environment, sparking interest and connection to the world around them.
These types of problems help students see how math connects to their world and make learning more personal and meaningful. This approach helps bridge the gap between students’ home languages and cultures and the math content they are learning in class.
ENGAGING FAMILIES AND COMMUNITIES
By involving families through activities like family math nights or encouraging students to share what they’ve learned at home, we can build stronger connections between school and home. These efforts help students see math as relevant beyond the classroom.
In Eureka Math2 California, resources in the Apply Book encourage family involvement. Components like Family Math, Practice Partners, and Terminology support students in deepening their understanding and making learning a collaborative process.
Understanding the Role of Data in the World
In a world that is always connected, it’s becoming increasingly critical that students develop basic data science literacy skills to make informed decisions and meet the demands of a modern mathematical society.
That’s why the Mathematics Framework emphasizes the importance of student exposure to all types of data visualizations, including those that are not standard and those that include multiple variables.
We know that connecting math to a student’s real world increases engagement, which is why we’ve created Data Investigations and Data Talks. These activities provide an opportunity for students to dive into data that’s relevant in their world and work together to make sense of it.
DATA TALKS
Data Talks are short activities that expose students to data and allow them to interpret data visualizations, build the skills to make observations and ask questions, and develop the critical-thinking skills they need to interpret the data surrounding them every day.
Both activities support students in becoming good analysts of data who interrogate both the data and the process by which it was collected. Through Data Talks and Data Investigations, students build the cognitive skills and confidence they need to engage with and question the world of data around them.
DATA INVESTIGATIONS
Data Investigations are multiday activities that expose students to the full statistical investigative process—from formulating an investigative question to collecting, interpreting, and reporting on the findings
Eureka Math2 California: A Strategic Blend of Instructional Approaches
We believe in empowering teachers to ensure rich student engagement and discourse. To facilitate that, Eureka Math2 California integrates a strategic blend of instructional approaches.
COGNITIVELY GUIDED
Students draw on existing knowledge to grow their conceptual understanding through discovery opportunities, videos, instructional routines, rigorous open-middle and open-ended tasks, and more.
STUDENT-CENTERED
Students actively communicate their thinking and reasoning as they gain the confidence to think like mathematicians and see themselves as fully capable learners.
EXPLICIT & SYSTEMATIC
Concepts are sequenced in a coherent way so students consistently build knowledge and skills while engaging in guided experiences, instructional routines, and distributed and interleaved practice.
EMPOWERING TEACHERS
Eureka Math2 California is designed to be exceptionally user-friendly and supportive for both new and experienced educators. It guides teachers on which questions to ask and what responses to expect. Educators gain deeper content knowledge and robust pedagogical tools, empowering them to meet the demands of today’s classroom confidently.
SUPPORTING SPIRAL REVIEW,
EXTENSION, AND TIER 2 AND TIER 3 NEEDS
Math Catalyst provides educators with a Multi-Tiered System of Supports for today’s classroom. Response to Intervention (RTI) requires educators to have the materials to support the diverse learning needs of all students, especially those striving to understand math concepts.
With Math Catalyst, educators have the content they need to supplement their core curriculum with practice, application, and mini lessons that support students at every tier of learning.
MAKING LEARNING VISIBLE
The learning begins by making sure students are prepared with the foundational knowledge needed to take on new learning. Eureka Math2 Equip™ provides digital premodule assessment, assessment reporting, and an acceleration plan of action to support students so everyone can access grade-level content.
We know that every child is capable of greatness. With Eureka Math2 California, we help California educators help students achieve it.
To learn more, visit greatminds.org/math/eurekamathsquared/california.