Goals

By the conclusion of this unit, participants will:

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

  • Mathematics content (depth)

  • Representations

• Consider how attending to content and representations in these (and similar) ways supports the development of expert learners who are resourceful and knowledgeable (UDL framework)

• Make specific plans for enhancing the depth and representations of content provided to 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 comprehension for students in mathematics, the following strategies/structures to  provide options for perception, language and symbols and comprehension should be utilized:

• Provide multi- sensory  experiences and  utilize assistive technology (AT) 

• Focus on developing and explicitly connecting key concepts through diverse experiences. 

• Build and connect the Concrete-Pictorial-Abstract continuum  

• Focus on sense-making, NOT answers and speed 

• Value alternative algorithms and solution pathways  

• Provide a language-rich environment, not rote vocabulary memorization