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Each activity set is accompanied by needed math facts, strategy tips, and comprehensive solutions that teachers and parents can use to help support student investigations.These sorts of enrichment activities provide middle school students with an opportunity to explore mathematical content, create or reinforce ideas, make connections, and use abstract reasoning.However, overcoming obstacles and persevering with a task that requires multiple steps and authentic reasoning can also sometimes be discouraging for early adolescent brains just learning how to tap into their emerging powers.
Note the depth and value of a critical thinking opportunity: the solution strategy connects 2D geometry with the number theory technique of factoring and is a precursor to a more sophisticated factoring procedure used in Algebra 1.
The second question requires greater time investment than the first question, but is worth the extra time if one is committed to young adolescents learning content in a way that fully engages their reasoning skills.
For example, a traditional 2D geometry question might ask: This question can be answered by performing a routine calculation using formulas for the perimeter and area of a rectangle.
Similar content can be studied with a question that asks for critical thinking: This second question (from Mathematical Reasoning™ Middle School Supplement) requires students to develop a strategy to construct a solution.
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The first Common Core mathematical practice standard emphasizes the need to have students make sense of problems and persevere in solving them.
The most important ingredient in Polya’s classic four-step problem solving strategy is the act of making decisions, as opposed to simply applying an algorithm that has been instructed.
In Dimension Detective students deduce missing dimensions for a variety of geometric shapes by using proportional reasoning, number theory ideas, and connections between 2D and 3D shapes.
In Linear Patterns students determine number patterns and geometric patterns, and then deduce algebraic expressions to describe these patterns (a precursor to creating algebraic equations to describe linear graphs).