FRACTIONS & DECIMALS WORKSHOP
Erie 1 BOCES
January 30, 2013
Presenters: Steve Graser & Andrea Tamarazio
FRACTIONS WARM-UP
Compare & order the following fractions from greatest to
least:
3/8, 6/10, 7/12 and 4/5
FRACTIONS WARM-UP
Write a number that is half way between zero and one.
Draw and show this on a number line.
FRACTIONS WARM-UP
Write a number that is half way between zero and one-half.
Draw and show this on a number line.
FRACTIONS WARM-UP
Write other numbers that are the same as one-half.
Draw and show this on a number line.
FRACTIONS WARM-UP
Write a number that is one-fourth more than one-half? Write
a number that is one-sixth more than one-half.
Show this on a number line.
FRACTIONS WARM-UP
What number is one-sixth less than one?
Show this on a number line.
FRACTIONS WARM-UP
What number is one-third more than one?
Show this one a number line.
FRACTIONS WARM-UP
What number is half-way between one-twelfth and threetwelfths?
Show on a number line.
FRACTIONS WARM-UP
Which number is closest to zero?
A. one-third
B. one-sixth
C. one-half
D. one-fourth
E. one-twelfth
Plot all numbers on a number line.
FRACTIONS WARM-UP
What number is closest to one?
A. three-eighths
B. three-fourths
C. one-half
D. eleven-sixteenths
Plot all numbers on a number line.
FRACTIONS WARM-UP
What number is halfway between zero and one-twelfth?
Solve using multiplication.
VIDEO: Skip Counting
Skip Counting by Fractions Video
Cognition & Learning Background
 Fractions are a major concept that students are first
introduced to in 1st grade as per CCLS. This concept continues
throughout their mathematical education. The goal of
fraction instruction is for students to visual fraction amounts
accurately.
Fraction Proficiency and Success with
Higher Level Math
 There is a clear relationship between fraction proficiency
and success in algebra. Inability to successfully
manipulate and perform basic operations on common
fractions has lead to negative performance in algebraic
reasoning ( Brown & Quinn, 2007).
PROGRESSIONS OF FRACTIONS &
DECIMALS WITH THE CCLS
PROGRESSIONS OF FRACTIONS &
DECIMALS WITH THE CCLS
PROGRESSIONS OF FRACTIONS &
DECIMALS WITH THE CCLS
PROGRESSIONS OF FRACTIONS &
DECIMALS WITH THE CCLS
PROGRESSIONS OF FRACTIONS &
DECIMALS WITH THE CCLS
PROGRESSIONS OF FRACTIONS &
DECIMALS WITH THE CCLS
PROGRESSIONS OF FRACTIONS &
DECIMALS WITH THE CCLS
PROGRESSIONS OF FRACTIONS &
DECIMALS WITH THE CCLS
PROGRESSIONS OF FRACTIONS &
DECIMALS WITH THE CCLS
PROGRESSIONS OF FRACTIONS &
DECIMALS WITH THE CCLS
PROGRESSIONS OF FRACTIONS &
DECIMALS WITH THE CCLS
What Percent of ….
8th grade students can successfully arrange the following
fractions in order from least to greatest?
2/7, 1/12, and 5/9
What percentage of 17 year olds can convert the following
decimal to a fraction?
0.029
TABLE GROUP DISCUSSION
Causes for Low Performance in
Fractions
 Complexity of Fraction Concepts (Streefland, 1991)
 Incorrect Wrote Procedures (Mac, 1990)
 Difficulty with Identification of Units (Hunting, 1996)
 Teaching Computation before Understand the Meaning of Fractions (Aksu,
1996)
 More Emphasis on Teaching Procedures instead of Teaching Conceptual
Meaning (Moss & Case, 1999)
 Influence of Multiple Representations of Fraction Ideas (Cramer, Post, &
delMas, 2002)
Develop Rational Number Concepts
 Part Whole Comparison
 Equal parts of the unit, with equivalent fractions found by
thinking of the parts in terms of larger or smaller chunks
 VIDEO – Sharing of Cakes
 Measure
 A distance on a number line or a given area
 Operator
 Gives a rule that tells how to operate on a unit
 VIDEO – Fractions as Division
 Quotients
 Amount that each person receives when it is being shared
 VIDEO – Interpret Fraction as Division
 Ratios & Rates
 Relationship in which there are items compared, in a
multiplicative rather than an additive sense
PART WHOLE COMPARISON
PART WHOLE COMPARISON
PART WHOLE COMPARISON
MEASURE
OPERATOR
OPERATOR
OPERATOR
OPERATOR
QUOTIENTS
QUOTIENTS
QUOTIENTS
RATES & RATIOS
MULTIPLE CATEGORIES
COMPARING & ORDERING DECIMALS
CONVERTING & COMPARING
FRACTIONS AND DECIMALS