Things to know for exam 3:

This exam will consist of two parts.  The first (written) part may include:

You should know how to draw representations of fractions (proper fractions, improper fractions, and mixed numbers) as arrays, non-array area models, linear models and discrete models.

You should know how to explain a representation of a fraction using the Common Core 3rd grade fraction representation:
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.
Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/band that its endpoint locates the number a/b on the number line.
How to find equivalent fractions (both by making the fraction less simple, and by simplifying the fraction) using diagrams, numbers, and explaining how you get the number work from the diagrams.

Prime and composite numbers: identifying prime numbers, explaining why 1 is not prime using the unique factorization property, and finding prime factorizations of composite numbers.

Definition of factor and multiple

Finding LCMs and GCDs both by making lists and by using prime factorizations.

Write word problems for fraction addition, subtraction (separate and compare), multiplication and division (measurement and partitive).

Identifying a word problem as fraction addition, subtraction, multiplication, division, or a combination of two of these.

Understanding remainders and fractional parts of answers to measurement division problems

The second (oral, recorded) portion of the exam will consist of explanations of  particular fraction algorithms.   You may do the two parts of the exam on separate days or in separate sessions.  You may spend a reasonable amount of additional time above and beyond what you spend on the written section for the oral section (A reasonable amount of additional time should be somewhere in the 20-45 minute range). 

 You should be prepared to explain how to get the standard algorithm from a diagram for: