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 place value and number sense content: 

• When counting or combining, the same size pieces or groups must be used. This principle applies when working with whole numbers using place value (tens with tens, ones with ones) or when working with fractions (halves with halves, and fifths with fifths,etc.)

• When combining unlike place values, or fractions with different sized pieces (unlike denominators), trading (regrouping) must be used to make all groups or fractional parts the same size (i.e. trade a 100 for ten 10s in order to combine with other tens, or trade a third for 2 sixths in order to combine with other sixths.)

• The procedures for addition (of both whole numbers and fractions) are grounded in conceptual and visual ways of representing them.

• Number-Sense is a flexibly quantifying and estimating, and can be learned by determining how many are there, or how many are not there, without counting all objects (subitizing, making tens, etc..)

• Numbers can be decomposed and re-composed in ways that make counting or adding (and other operations) more efficient.

• Another motivation for place value is that it can be used to make an algorithm for addition (several types) which is a more efficient way of combining groups of 10’s or 100’s or other powers of 10, instead of combining 2 or more groups of objects into one group, and counting the whole pile.

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