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4 days ago

Los Altos School District

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Mathematics

Mathematics
 

Math should be purposeful, connected, and challenging. Guided by the 2023 California Mathematics Framework, LASD is committed to helping all students develop as mathematicians who ask questions, take risks, look for patterns, and build meaning through reasoning and collaboration. Our instructional vision centers on four key principles that shape how students experience mathematics in our classrooms.

1. Inquiry as the Heart of Learning
Mathematics learning in LASD is grounded in inquiry. Students investigate through open-ended tasks that require them to reason, make conjectures, test ideas, and refine their thinking. Teachers serve as facilitators who design meaningful tasks and create space for exploration, helping students move beyond memorizing procedures or following directions to see mathematics as a dynamic and creative discipline. This approach fosters curiosity, critical thinking, and a sense of ownership in learning.

2. Students Do the Thinking
We believe the person doing the thinking is the person doing the learning. In our classrooms, students are active sense-makers and problem-solvers. Productive struggle is embraced as a natural and essential part of the learning process. Students of all abilities are supported in wrestling with complex problems, developing their own strategies, and learning from mistakes. Teachers carefully craft lessons that challenge students while providing just enough support to keep them engaged in the work.

3. Connecting Big Ideas
Mathematics is not a series of isolated skills; it is a connected, coherent body of knowledge. Our instruction emphasizes the "big ideas" that span across grade levels—concepts like place value, proportional reasoning, and transformation—so students can see how math ideas build on each other. Alongside conceptual understanding, we intentionally develop procedural fluency, ensuring students can apply methods efficiently and accurately. Fluency is not built through repetition alone, but through reasoning, application, and connection to big ideas. This kind of learning builds both confidence and depth.

4. Academic Discourse as a Learning Tool
Mathematics learning in LASD is social as well as intellectual. Students regularly engage in academic discourse—discussing their strategies, justifying their reasoning, and critiquing the ideas of others. These conversations deepen understanding, reveal misconceptions, and build the habits of mind necessary for strong mathematical reasoning. Our classrooms foster inclusive norms for participation, where all students are encouraged to share their thinking and learn from each other.

We are creating math classrooms where every student is supported to think deeply, take risks, and grow their identity as a capable and curious mathematical thinker. When students experience math in this way, they build knowledge and confidence, and begin to see themselves as people who do and understand mathematics. This includes ensuring all students—regardless of background, identity, or prior experience—have access to high-quality instruction and the support they need to succeed.

 

Development Across the Grades

Mathematics

PK - 2nd Grade

Children begin building foundational understandings of numbers, patterns, and spatial relationships through exploration, play, and daily problem-solving. They learn that numbers represent quantities and can be compared, added, and taken apart. They notice and describe shapes, measure using informal tools, and begin to recognize patterns. These early experiences build number sense, early operation fluency, and a deep understanding of math as a meaningful part of their world.

3rd - 5th Grades

Students deepen their understanding of number and operations and begin to explore more complex ideas such as fractions, multi-digit multiplication and division, and place value in the base-ten system. They connect arithmetic to concepts in geometry, data, and measurement, and begin to understand how mathematical ideas relate to one another. Through increasingly rich tasks, students strengthen their reasoning skills, make sense of problems, and communicate their thinking clearly.

6th - 8th Grades

Students are ready to extend their mathematical understanding into more abstract and generalized thinking. They work with ratios, rates, and percentages, and begin to use variables and expressions to represent relationships. They explore geometry through transformations, develop understanding of linear equations, and begin studying functions and statistics. Across these grades, students build a connected view of mathematics, developing both procedural fluency and conceptual depth to prepare them for high school mathematics and real-world problem solving.


Opportunities for Acceleration in LASD
In the Los Altos School District, we are committed to helping every student thrive in mathematics through a supportive, student-centered placement system. Beginning in grade 6, students have access to multiple pathways that ensure both challenge and support, including opportunities for acceleration. 

chart showing math pathways in LASD

Our placement decisions are guided by multiple objective measures and designed to match each student with the math course that best meets their needs. This approach allows us to identify students ready for faster-paced learning while ensuring all learners build a strong foundation for future success.

 

To learn more about our placement process and possible pathways, visit our 6–8 Math Placement Protocol.

 

Helpful Resources

California Mathematics Framework
Math Standards