Mathematics

Mathematics instruction is aligned with the California Common Core State Standards. At each grade level, students develop essential skills in areas such as:

• Counting and number sense
• Place value and operations
• Addition, subtraction, multiplication, and division
• Fractions and decimals
• Measurement and data
• Geometry
• Ratios, proportions, expressions, and equations
• Mathematical reasoning and problem-solving

Teachers use grade-level standards, student work, and assessment information to plan instruction and provide appropriate support while maintaining access to rigorous grade-level learning.

Students learn mathematics through explicit instruction, teacher modeling, guided practice, collaboration, and independent application. Teachers use models, manipulatives, diagrams, number lines, equations, and other visual representations to make mathematical ideas clear and meaningful.

These learning experiences help students make connections among concrete materials, visual models, mathematical language, and abstract symbols.

Students are expected to do more than provide a correct answer. They learn to explain how they solved a problem, justify their reasoning, compare strategies, ask questions, and respond to the thinking of others.

Teachers provide structured opportunities for students to use complete sentences and grade-appropriate academic vocabulary during partner conversations, small-group learning, and whole-class discussions. Explaining mathematical thinking helps students deepen their understanding and allows teachers to identify misconceptions and provide timely feedback.

Students regularly engage in meaningful problems that require them to apply prior learning, select strategies, and persevere when the solution is not immediately clear. Teachers provide appropriate guidance and feedback while allowing students time to think, explore, revise, and learn from mistakes.

Productive struggle helps students develop confidence, independence, flexibility, and a positive mathematical mindset.

CVUSD teachers use district-adopted, standards-aligned curriculum and instructional resources to provide consistent mathematics instruction across elementary schools. The curriculum includes explicit instruction, conceptual models, fluency development, problem-solving, collaborative learning, and opportunities for students to demonstrate mastery.

Teachers may supplement the core curriculum with district-approved resources based on grade-level expectations and identified student needs. Supplemental resources support—but do not replace—high-quality instruction from the classroom teacher.

IXL is used as a supplemental resource for targeted practice, intervention, enrichment, and progress monitoring. Teachers assign specific standards-aligned skills connected to classroom instruction or identified student needs.

IXL may be used to:

• Reinforce skills connected to current classroom learning
• Provide targeted Tier 2 or Tier 3 intervention
• Offer enrichment and additional challenge
• Identify strengths and areas for growth
• Monitor student progress toward individual goals
• Support data-informed instructional decisions

Teachers review IXL information regularly, adjust assignments, and provide feedback. IXL is intended to support classroom instruction and should not replace teacher-led lessons, hands-on learning, mathematical discussions, or collaborative problem-solving.

When CVUSD is considering new mathematics instructional materials, selected schools and classrooms may participate in a curriculum pilot. Pilots allow teachers and students to use potential materials and provide feedback about their quality, usability, accessibility, alignment with grade-level standards, and support for the CVUSD Instructional Framework.

Families will receive information when their child’s classroom participates in a pilot. Feedback from teachers, students, families, administrators, and instructional leaders helps inform the district’s curriculum adoption process.

Families play an important role in helping children develop confidence and a positive attitude toward mathematics. Families can support learning by:

• Asking children to explain how they solved a problem
• Encouraging children to try more than one strategy
• Using mathematics during cooking, shopping, traveling, and planning
• Practicing basic facts in short, engaging sessions
• Playing games involving numbers, patterns, logic, or strategy
• Asking, “How do you know?” and “Can you show another way?”
• Encouraging effort, persistence, and learning from mistakes
• Using teacher-recommended digital or grade-level resources

Home practice is most effective when it reinforces classroom learning and encourages mathematical thinking. Families are encouraged to contact their child’s teacher before introducing unfamiliar methods or assigning extensive additional practice.