Goals

By the conclusion of this unit, participants will:

• Engage in grade level/span mathematics mini-lessons and reflect on:

  • Mathematics content (depth)

  • Action and Expression

• Consider how attending to content and action and expression in these (and similar) ways supports the development of expert learners who are strategic and goal-directed (UDL framework)

• Make specific plans for enhancing the depth of content and options for action and expression 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 action and expression for students in mathematics, the following strategies/structures to  provide options for physical action, expression and communication, and executive functions should be utilized:

• Provide  opportunities for students to physically engage  in the learning 

• Provide regular alternate communication methods, including manipulatives, multimedia and assistive technology (AT)  

• Use frequent authentic formative assessments, with alternative options, and provide growth feedback  

• Teach, model, and reinforce reflective practices for students 

• Explicitly engage students in the Standards for Mathematical Practice 

• Embed peer coaching opportunities to position students as knowledgeable peers