Goals

By the conclusion of this unit, participants will:

• Watch part of two lessons (video) and engage in three grade level/span mathematics mini-lessons (stations) and reflect on:

  • Mathematics content (depth)

  • Student engagement

• Consider how attending to content and engagement in these (and similar) ways supports the development of expert learners who are purposeful and motivated (UDL framework)

• Make specific plans for enhancing the depth of content and options for engagement afforded students in their own work

Big Ideas

The following big ideas are essential to develop a deep understanding of proportional relationships content: 

• Ratios and proportions involve multiplicative rather than additive comparisons. This means that equal ratios result from multiplication or division, not from addition or subtraction.

• Rate is a way to represent a ratio, and in fact, represents an infinite number of equivalent ratios

• A proportion is a relationship of equality between two ratios that can be represented in a variety of ways. In a proportion, the ratio of two quantities remains constant as the corresponding values of the quantities change. For instance, in a ratio table, both quantities in a ratio must be multiplied or divided by the same factor to maintain the proportional relationship.

• Proportional thinking is developed through activities and experiences involving comparing and determining the equivalence of ratios. This means solving proportions in a wide variety of problem-based contexts and solutions through reasoning, not rigid use of formulas.

In order to remove barrier to engagement for students in mathematics, the following strategies/structures to recruit interest, provide options for sustaining effort and persistence and self-regulate should be utilized:

• Use student relevant real-world contexts to develop content understanding 

• Use tasks with low floor entry points and multiple solutions or pathways  

• Offer meaningful student choices EVERYWHERE to promote student autonomy 

• Provide structures and tasks that normalize sense-making through productive struggle  

• Facilitate meaningful student collaboration and discourse  

• Engage students in, and demonstrate, self-reflection and personal goal setting