*Some problems I have considered, yet I believe are too "math-feeling": (pp.*1335-1341) (pdf version) mentions a nice problem called "Dividing squares." Shown below are some pictures of a square divided into smaller squares, not necessarily of the same size.KCM wants to help teachers establish thinking communities in their mathematics classrooms.

*Some problems I have considered, yet I believe are too "math-feeling": (pp.*1335-1341) (pdf version) mentions a nice problem called "Dividing squares." Shown below are some pictures of a square divided into smaller squares, not necessarily of the same size.KCM wants to help teachers establish thinking communities in their mathematics classrooms.

(There are 5 students in the class) At the same time, I don't want to start out with a problem that feels too contrived, or too much like "school math" problems.

They have clearly been turned off from "school math." I want one or some that feel more like they are doing a puzzle, yet still engage algebra-related skills and open up a discussion about problem-solving as a process and skill that can be honed.

At this stage, students need to be able express their ideas and understanding by communicating and providing reasons for their thinking.

Students are required to be able to use words to describe patterns and apply their knowledge in problem solving situations.

The mathematical language required needs to be modelled by the teacher and students need to be provided with opportunities to talk through their thinking.

Students need experiences in both solving problems and posing their own problems.

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.

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.

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