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Application Problems That Build Mathematical Thinking

Grade 2–5 student books designed to help students make sense of real situations, choose models, estimate, and develop problem-solving strategies grounded in understanding.

Explicitly aligned to grade-level expectations and designed to support reasoning and sense-making.

New Perspectives on Learning
New Perspectives on Learning

More Than Routine Word Problems

Application Problems are not simply about getting answers or practicing procedures.

They give students opportunities to:

  • Make sense of situations mathematically
  • Choose models to think with
  • Estimate, test, and refine their strategies
  • Connect mathematical ideas to real contexts

This is where students apply what they know, strengthen reasoning, and deepen their mathematical understanding over time.

Designed for How Students Learn to Problem Solve

New Perspectives on Learning

Models as Tools for Thinking

Students are prompted to choose models that help them make sense of the mathematics and reason through problems.

New Perspectives on Learning

Built-In Estimation and Reasoning

Problems encourage students to estimate, test ideas, and refine their thinking before solving, strengthening number sense and mathematical reasoning.

New Perspectives on Learning

Connected Mathematical Ideas

Problems are intentionally grouped around big ideas so students can see relationships across problems and apply mathematics in connected ways.

New Perspectives on Learning

Flexible in the Classroom

Application Problems can be used to:

  • Extend core instruction
  • Support small-group or targeted instruction
  • Reinforce strategy development and mathematical reasoning
  • Provide meaningful practice, homework, or formative assessment opportunities

Designed to work alongside the broader curriculum, they help teachers differentiate instruction while giving students opportunities to apply and deepen their understanding over time.