Representations of fractions (proper, improper, and mixed numbers) as arrays, non-array area models, linear models and discrete models.

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, 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, multiplication and division.

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

There will be a portion of the exam where you will be making one or more videos explaining 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).

- Fraction equivalence

- Fraction addition (using arrays)

- Fraction subtraction
- Multiplication of fractions or mixed numbers
- Division of fractions or mixed numbers/improper fractions (you
will be allowed to chose an interpretation for a numerical division of
fractions problem: measurement, partitive or fact families; part of
your task will be to explain your interpretation, for example, the
explanation of a partitive interpretation would be "____ is shared into
____ (of a) group(s), how much is in 1 group?")