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Re-Establishing Mathematical Norms After the Break: Problem Solving Activities Around the Number 2026

1/1/26
The first day back after the Christmas break is an important opportunity to reset expectations, rebuild collaborative learning habits, and re-engage students in meaningful mathematical thinking. Ease back in with a collaborative problem-solving activity that invites students to reason, justify, and communicate - the very behaviors we want to re-establish as classroom norms.

Using the new year number, 2026, as a mathematical context provides a timely and engaging way to refocus students while reinforcing your classroom routines for discourse, collaboration, and productive struggle. 

Below are four adaptable tasks that emphasize reasoning, communication, multiple strategies, and respectful discussion - all essential norms to revisit after a long break. Have students work collaboratively in random groups of 3 on dry erase boards or chart paper. Grades 1-2 can simplify tasks by using the number 26 in place of 2026. 

Task 1: How Many Ways Can You Make 2026?

Prompt: Create as many different mathematical expressions as you can that have a value of 2026. You may use any mathematical symbols or operations you choose. Be prepared to explain your thinking.

Encourage:

  • addition and subtraction (e.g. 2000 + 26, 4000 - 1974)

  • multiplication and division (e.g. 1013 × 2)

  • combinations of operations (e.g. 200 x 10 + 26)

  • strategic use of parentheses

  • fractions or decimals (where appropriate)

  •  powers or exponents (where appropriate)

 Task 2: The 2026 Challenge

 Prompt: Can you use the digits in 2026 (2, 0, 2, and 6) to create expressions equivalent to the numbers 1-20? All 4 digits must be used in each expression (e.g. 4 = 6 - 2 - 2 + 0). You may use any mathematical symbols or operations of your choosing.

Challenge: Can you create expressions equivalent to the numbers 1-50? What about 1-100?

Task 3: What do You Notice About 2026?

Prompt: Investigate the number 2026. What do you notice? What do you wonder?

Students may explore:

  • Even/odd

  • Place value (2000 + 20 + 6)

  • Nearby numbers (2025, 2027)

  • Skip-counting patterns

  • Prime/composite

  • Factors (e.g., 2026 ÷ 2 = 1013)

  • Multiples “2026 is/is not a multiple of ___ because…”

Task 4: Using 2026 as a Context for Word Problems

Situate 2026 inside real-world problem contexts to support flexible thinking and application.

Prompts

  • A runner logs 2026 km in one year. What might her monthly distances be?

  • A school has 2026 students. Show as many different ways as you can to group the students into equal teams. Explain what each grouping tells you.

Invite students to:

  • compare different approaches

  • justify why their representation makes sense

Norms Reinforced

These activities reinforce a variety of math classroom norms, including the following:

  • Math talk is collaborative, not competitive
  • Multiple strategies are valued
  • Show your reasoning - not just your answer
  • Mistakes are learning opportunities
  • Intellectual curiosity is valued
  • Students are responsible for contributing to shared learning
  • Different models can be equally valid

Re-Establishing Routines Through Reflection
End the session with a brief reflective conversation focused not only on mathematics, but on learning behaviors. Re-establish discourse routines such as turn-and-talk, listening to peers, and critiquing reasoning respectfully.

Consider prompts such as:

  • What did it sound like when we were doing math today?

  • How did we show respect for other people’s ideas?

  • What helped you stay engaged in challenging thinking?

This deliberate reflection signals that norms are not incidental - they are central to how your mathematics community operates.

Why Anchor Back-to-School Routines in Problem Solving?

Beginning the term with meaningful problem solving communicates that:

  • mathematics is about sense-making, not answer-getting

  • collaboration and discourse are core expectations

  • effort, reasoning, and explanation are valued contributions

Using the year number 2026 provides an authentic entry point while maintaining high cognitive demand.

These tasks support students in transitioning back from holiday mode to a learning environment grounded in curiosity, discussion, and mathematical reasoning - exactly the conditions we want to sustain across the year. Try one and let us know how it goes!