KCM wants to help teachers establish thinking communities in their mathematics classrooms. Rather than teaching algebra procedurally, we suggest that you help your student to focus less on what they are supposed to do next and more on actively making sense of mathematics. Using rich mathematics tasks is one strategy algebra teachers can implement to engage students and build a thinking classroom culture that focuses on algebraic reasoning and sense-making.

Rich mathematics tasks engage students in exploring, noticing, discussing, conjecturing, explaining, generalizing, convincing and persevering. Students focus on the mathematics while the teacher focusses on observing and supporting the learners to make their own discoveries. On its own a rich task is not rich unless the classroom culture is one in which learners are not passive recipients of knowledge, but rather are curious, reflective constructors of their own understandings.

- Accessible to all learners ("low floor, high ceiling")
- Real life task or application
- Multiple approaches and representations
- Collaborations and discusion
- Engagement, curiosity, and creativity
- Making connections within and/or across topics and domains [Boaler, "Mathematical Mindsets"]
- Opportunities for extension

- Students work with a partner
- The task is introduced to students and time is given for the students to make sense of the problem.
- What norms need to be established for students to feel safe in trying?
- In what ways will students be continually engaged in the learning?

- Students are given time to work on the task with the teacher rotating around the groups, asking questions and encouraging productive struggle. The teacher does not direct next steps or provide answers.
- What encouraging/challenging/helpful(but not directive) responses might the teacher have when students get stuck?
- Will all students get to participate in meaningful mathematics learning? Can any students hide or be ignored?

- Student pairs are encouraged to explore and generate unique solutions. They must also justify their reasoning for their choices.
- In what ways will students be invited to explain their thinking?
- In what ways will students be given opportunities to respectfully challenge others or to advocate their own view points?

- The teacher uses the task as an opportunity for formative assessment.
- How will instruction respond to student-generated ideas?
- What opportunities will students have to demonstrate their learning?

- The teacher orchestrates a concluding whole-class discussion emphasizing a variety of mathematical connections and thought processes that went into solving the task.
- How will student thinking be included in the classroom discussions?
- What opportunities will students have to explain their ideas? In what ways will their ideas be built on by others?

- YouCubed Tasks : Boaler's resource website with tasks across all grade levels.
- NIRCH website

Article: "Teaching Is a Cultural Activity" by James W. Stigler and James Hiebert

Article: "A Lesson Is Like a Swiftly Flowing River" by Catherine C. Lewis and Ineko Tsuchida

Book chapter: *Powerful Problem Solving: Activities for Sense Making with the Mathematical Practices* by Max Ray

Article: "Thinking through a Lesson: Successfully Implementing High-Level Tasks" by Margaret S. Smith, Victoria Bill, and Elizabeth K. Hughes

Article: "Habits of Mind: An Organizing Principle for Mathematics Curriculum" by Al Cuoco, E. Paul Goldenberg, and June Mark