Too often, mathematics curriculum labeled “advanced” simply moves faster through basic skills without offering the depth and complexity that gifted and high-ability learners require. For students who already grasp grade-level content, true challenge comes from meaningful problem solving, conceptual exploration, and opportunities to reason, generalize, and connect ideas across domains.
The William & Mary Center for Gifted Education (CFGE) has developed a robust set of mathematics curriculum resources designed specifically for gifted learners. Grounded in research and the Integrated Curriculum Model (ICM), these materials emphasize advanced content, higher-level thinking, and conceptual understanding rather than acceleration alone (read more about appropriate math curriculum for gifted students).
Introduction to the Curriculum
The William & Mary math curriculum is designed for gifted and advanced learners in grades 3–6 and is organized into units of study aligned to major mathematical domains. The curriculum assumes that students have already demonstrated mastery of grade-level skills and are ready to extend their thinking through challenging tasks and investigations.
According to the Center for Gifted Education, effective advanced math curriculum should feature sophistication of ideas, opportunities for abstraction, and tasks that require reasoning, justification, and transfer. The William & Mary math units were intentionally designed with these goals in mind.
Description of the Material
Grade 3 Math Curriculum for Gifted Students
The Grade 3 units focus on developing strong number sense and early algebraic reasoning through rich problem-solving experiences. Students explore place value, addition and subtraction strategies, early multiplication concepts, geometry, and data analysis in ways that emphasize reasoning and explanation. Lessons push students to identify patterns, justify solutions, and make generalizations rather than simply compute answers. Tasks often require students to represent thinking visually, explain multiple solution paths, and apply mathematical ideas to novel situations, making this level ideal for students who have already mastered basic grade-level skills.
Grade 4 Math Curriculum for Gifted Students
In Grade 4, the curriculum deepens students’ understanding of multiplication, division, fractions, geometry, and measurement while introducing more formal algebraic thinking. Learners investigate relationships between operations, analyze numerical patterns, and begin working with variables and expressions in meaningful contexts. Geometry and measurement units emphasize spatial reasoning and precision, while data analysis tasks require interpretation and justification. Across units, students are expected to articulate reasoning clearly and critique the thinking of others.
Grade 5 Math Curriculum for Gifted Students
The Grade 5 units place strong emphasis on fractions, decimals, geometry, and the foundations of proportional reasoning. Students explore equivalence, scaling, and relationships between quantities using both real-world and abstract problems. Tasks often involve multi-step reasoning, comparison of strategies, and evaluation of efficiency and accuracy. Algebraic thinking becomes more prominent as students analyze expressions, relationships, and patterns, supported by performance-based assessments that require explanation and justification.
Grade 6 Math Curriculum for Gifted Students
Grade 6 units extend students into pre-algebraic and early algebraic reasoning, focusing on ratios and proportional relationships, expressions and equations, variables, statistics, and geometry. Students analyze dependent and independent variables, solve and create equations, and interpret data sets with increasing sophistication. The curriculum emphasizes conceptual understanding over procedural shortcuts, encouraging students to reason abstractly, construct arguments, and make connections across mathematical domains. These units are especially appropriate for gifted learners who are ready for advanced thinking but still benefit from structured exploration and discussion.
The Math Curriculum for Gifted Students series is available through Routledge and Amazon as complete grade-level sets or individual components.
How to Use It
The William & Mary math curriculum can be implemented flexibly across instructional settings:
- Gifted pull-out programs, where units anchor sustained advanced math instruction
- Cluster or advanced classrooms, providing depth alongside core instruction
- Enrichment blocks, offering targeted challenge for small groups
- Homeschool settings, where the teacher guides and student materials support extended conceptual study
Teachers often select specific units or lessons based on student readiness rather than moving linearly through the entire set. This is exactly how my division uses the units for our gifted math classes.
Why It Benefits Gifted and Advanced Learners
This curriculum benefits gifted learners by:
- Emphasizing conceptual understanding and reasoning
- Providing challenging tasks that promote perseverance and creativity
- Supporting mathematical communication and justification
- Aligning with standards while extending beyond routine practice
Rather than focusing on speed, the William & Mary math curriculum helps students develop deep, transferable mathematical thinking.
In Sum
The William & Mary Math Curriculum for Gifted Students offers a research-based, thoughtfully designed approach to advanced mathematics for grades 3–6. By combining rigorous content with rich problem solving and reasoning tasks, it supports gifted learners in building confidence, depth, and flexibility in their mathematical thinking.
Your Turn
Have you used the William & Mary math curriculum or other advanced math resources with gifted learners? How do you balance depth and pacing in math instruction? Share your experiences and insights in the comments below! ~Ann
Teaching for Talent 