Download Jill - math-dc-kit

Jill:
A. 4
2
- = 9
3
B. 3
1
- = 9
3
C. 3
1
- = 8
4
D. 4
2
- = 8
4
Procedural:
1)
She is dividing the numerator and the denominator by different factors instead
of using common whole number factors.
2)
She does not simplify Sample D nor does she recognize that Samples A and C
are already simplified.
Conceptual:
1)
Fractions – By dividing the numerator and denominator by different whole
number factors, she is demonstrating that she does not understand the
relationship between the numerator and denominator. She treats each as if
they are whole numbers rather than parts of a whole, consequently, the
relationship between the part and the whole gets distorted.
2)
Equivalent fractions – She “does not recognize which fractions are already in
simplest terms” (Ashlock, 2006, p. 145). Also, she does not understand that
equivalent fractions are different names for the same area, same point on a
number line, etc.
3)
Multiplicative Identity Property is violated – Because she does not divide by
common whole number factors, she is not dividing by 1. She must divide, or
multiply, by one when finding equivalent fractions.
Strategies:
Early edition of textbook - pp. 146-147 – Activities #1-4
Latest edition of textbook – pp. 65-67 – Activities #1-4
– Would each of these strategies help Jill? – All of these strategies will help correct errors
with equivalent fractions, BUT, only activities #1 and #3 will help correct errors on the
simplest term. If activities #2, 4, 5 are used, an emphasis will need to be placed on
simplest terms. Activity #5 is especially troublesome. It will need will either need to be
used after simplest terms has been re-taught or it will need to substitute cards of ½, 2/3,
5/6, and ¾, and so forth for cards that have only twelfths as the denominator (i.e., 1/12,
2/12, …12/12).
Disclaimer:
Early edition of textbook - p. 134 – Activity #4 – Use a different algorithm.
Latest edition of textbook - p. 52 – Activity #4 – Use a different algorithm.
– No, this activity focuses on division of whole numbers. Jill’s error is finding equivalent
fractions and more specifically finding the simplest term.