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:
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.
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.
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
Recognize that each part has size 1/b
that the endpoint of the part based at 0 locates the number 1/b
on the number line.
Represent a fraction a
a number line diagram by marking off a lengths 1/b
from 0. Recognize
that the resulting interval has size a
and that its endpoint locates the number a
the number line.
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
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
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).
be prepared to explain how to get the standard algorithm from a
- 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?")