Four Free, High-Level Resources to Build Thinking, Reasoning, and Mathematical Confidence
Great problem solving is not about busy work or rote drill. For gifted and advanced learners, it means rich, open-ended tasks that require reasoning, communication, multiple strategies, and persistence. Ready-made problem-solving resources save teachers time, provide high-cognitive-demand experiences, and offer opportunities for learners to think deeply about mathematics. Below are four excellent free websites with vetted problems that work beautifully in classrooms, enrichment groups, or homeschools.
Robert Kaplinsky Lessons – Real World Problem Solving
Robert Kaplinsky’s library of lessons focuses on real-context problems that invite multiple solution paths and deep reasoning. Rather than traditional word problems with a single strategy, Kaplinsky’s tasks begin with scenarios that spark curiosity and require sense-making. For example, problems such as How Many Hot Dogs and Buns Should He Buy? or How Much Money Do You Earn for a Million Streams on Spotify? ask students to model situations mathematically, analyze data, and justify their conclusions. These lessons are appropriate across grade levels and content areas and are especially effective for grouping learners for discourse and collaboration. Kaplinsky’s work supports the kind of quantitative reasoning and communication gifted learners excel at and enjoy.
Free access Note: All lessons are available to teachers and parents at no cost and can be easily searched by grade band and topic.
YouCubed Tasks – Thinking with Visuals and Number Sense
The YouCubed project from Stanford University offers tasks designed to strengthen mathematical thinking and mindset alongside problem solving. Many tasks use visual patterns, representations, and structure that promote exploration and reasoning before formal procedures are introduced. Because multiple solution methods are encouraged and celebrated, these tasks provide natural differentiation for gifted learners. They are especially effective as warm-ups, discussion starters, or extensions to existing lessons. YouCubed tasks also emphasize a growth mindset approach to math and help students build habits of perseverance and reflection.
3-Act Lessons by GFletchy – Notice, Wonder, and Reason
The 3-Act Framework invites students into problems through curiosity and reasoning. Each task begins with a visual or scenario, prompting students to share what they notice and wonder. Students then work to define the math needed, gather or estimate necessary information, and solve problems with justification. This structure helps students practice productive struggle and sustain thinking on complex challenges. GFletchy’s site curates many 3-Act lessons covering a variety of mathematical concepts and grade levels, making them ideal for whole-class investigations, collaborative groups, or self-directed challenges.
These lessons build thinking habits that align closely with gifted learners’ strengths in exploring multiple solution pathways and articulating reasoning.
Virginia Department of Education Rich Mathematical Tasks – Standards-Aligned and Reasoning-Focused
You know I had to throw in something from Virginia in here! The Rich Mathematical Tasks collection from the Virginia Department of Education offers a bank of standards-aligned tasks organized by grade band (K–12). These tasks were developed by teacher leaders across the Commonwealth to promote sense-making, reasoning, and problem solving. Each task is available as a downloadable PDF with templates, student versions, and in many cases anchor papers and scoring rationales to support formative assessment. Tasks range from Pizza Party and Money in the Piggy Bank (grade 3) to Room for Shoes and Angle Design (grade 5), and all the way up to Algebra II, providing rich opportunities for learners to grapple with ideas and communicate their thinking.
Even though these tasks are designed for on-grade-level math content, they are still ideal for gifted learners because they require reasoning, often have multiple solution pathways, and emphasize discussion and justification rather than rote procedures. In addition, many of the tasks have built-in levels of differentiation for special education, English Learners, and Gifted.
How to Use These Resources
In classrooms:
- Use a task as a weekly problem challenge or warm-up.
- Group students heterogeneously to promote discourse.
- Use journals to capture reasoning and solution strategies.
In enrichment or pull-out programs:
- Select multi-week task sequences for extended inquiry.
- Encourage students to generate their own extension problems.
- Use student work as assessment artifacts for reasoning and justification.
In homeschools:
- Adapt problems to match interests and pacing.
- Use tasks as family math investigations or solo thinking challenges.
- Encourage writing and explanation for deeper processing.
Why These Resources Benefit Gifted Learners
These problem-solving sites benefit gifted and advanced learners because they:
- Provide high-cognitive-demand tasks that require reasoning and strategy.
- Invite multiple solution paths, not single answers.
- Encourage mathematical communication and justification.
- Are free and ready-to-use, saving teachers and parents planning time.
- Support persistence, flexibility, and creativity in mathematics.
Rich tasks like these help gifted students deepen their mathematical thinking and build confidence in their abilities.
In Sum
Problem solving is essential for gifted and advanced mathematics learners. Free resources such as Robert Kaplinsky Lessons, YouCubed Tasks, GFletchy’s 3-Act Lessons, and the Virginia DOE Rich Mathematical Tasks provide ready-made, vetted challenges that develop deep thinking, reasoning, and communication. These problem banks are time-savers for educators and fantastic opportunities to extend gifted learners’ mathematical understanding.
Your Turn
Which problem-solving websites or tasks have made the biggest impact in your classroom or homeschool? How do you integrate rich tasks into your instruction to challenge gifted learners? Share your experiences and favorite tasks in the comments below! ~Ann
Teaching for Talent 