AR Remediation Plan – Practical Applications – Rational Numbers and Proportional Reasoning
Mixed Numbers and Improper Fractions
STRAND: Computation and Estimation
STRAND CONCEPT: Rational Numbers and Proportional Reasoning
SOL 5.6a, 6.5b
Remediation Plan Summary
Using manipulatives, student discover how mixed numbers and improper fractions are related.
Errors and Common Misconceptions
Some students struggle to understand that a mixed number can be written as a fraction using the
denominator of the fraction. For example,
2
23
can be written as
6
3
combined with
2
3
.
Some students look at a fraction as two distinct whole numbers instead of understanding that the
denominator indicates how many parts make a whole and the numerator indicates how many parts of
the whole you are discussing.
Some students confuse the procedure and add the denominator to the whole number and multiply by
the numerator.
Materials
Any of the following; Pattern Blocks, Fraction tiles, paper (cut into equal sized pieces)
Introductory Activity
Sal walked
1
12
miles. He tracked his time every
1
2
mile of the walk. How many half mile intervals did
he walk? How could you write this amount as an improper fraction?
Plan for Instruction
1. Hand each student a set of manipulatives or several sheets of paper and establish the whole. (For
example: with the pattern blocks say, “The hexagon represents one whole.” Or with the paper, “one
whole sheet represents one whole…”)
2. Have students represent
1
12
using one whole and one
1
2
- sized piece. Ask, “How else can we
represent
1
12
? Encourage students to make as many models as they can (this will reinforce equivalent
fractions). Select several students to present their representations. If three halves was not presented,
display and discuss this model. Have students record their representations as fractions or mixed
numbers.
3. Next have students represent
3
14
multiple ways. Again have students present their models and have
them write the fractions represented. Make sure you focus on the
7
4
model the most. Ask,” How are
3
14
and
7
4
related?”, “Without the models, how could we convert
3
14
to
7
4
and vice versa?” Have
students discuss with a partner their thoughts.
4. Give students more mixed numbers to model until you feel they are able to verbalize how to convert
from one to the other.
