Math 391 Test 3 - Questions & Verified Solutions
Mention the 5 constructs that a fraction symbol can represent. Provide an
example of each. ✔️Ans - 1. Part-Whole
2. Measurement
3. Division
4. Operator
5. Ratio
Mention two reasons why fractions are concepts that are difficult to
understand. ✔️Ans - There are many meanings of fractions.
Fractions are written in a unique way.
Students overgeneralize their whole-number knowledge.
Describe four misconceptions that students may have about fraction
concepts. Describe how to help students to overcome the misconceptions.
✔️Ans - Students think that the numerator and denominator are separate
values and have difficulty seeing them as a single value. To help, find
fractions values on a number line and avoid saying "three out of four" or
"three over four." Instead say "three fourths."
Students do not understand that 2/3 means two equal-sized parts. To help,
ask students to create their own representations of fractions across various
manipulative and on paper.
Students think that a fraction such as 1/5 is smaller than a fraction such as
1/10 because 5 is less than 10. Conversely, students may be told the
reverse - the bigger the denominators, the smaller the fraction. This may
cause students to overgeneralize that 1/5 is more than 7/10. To help, use
many visuals and contexts that show parts of the whole.
Students mistakenly use the operation "rules" for whole numbers to
compute with fractions. For example, 1/2 + 1/2 = 2/4. To help, use many
visuals and contexts that emphasize estimation and focus on whether
answers are reasonable or not.
Describe the three models to represent fractions. ✔️Ans - Area models
Length or number lines
, Set
Mention 6 common area or region physical models to represent fractions.
✔️Ans - Circular Fraction Pieces
Grid or Dot Paper
Rectangular Regions
Pattern Blocks
Fourths on a Geoboard
Paper Folding
Mention 3 common length or measurement physical models to represent
fractions. ✔️Ans - Fraction Strips or Cuisenaire Rods
Measurement Tools (such as ruler)
Folded Paper Strips
Use appropriate fraction language to describe the meaning of a fractional
part (e.g., 2/3) ✔️Ans - A fractional part is the part that results when the
whole or unit has been partitioned into equal-sized portions or fair shares.
What does it mean that the "fraction size is relative"? ✔️Ans - A fraction
by itself does not describe the size of the whole or the size of the parts. A
fraction only tells about the relationship between the part and the whole.
To understand fractions deeply, mention the three types of activities in
which students need experiences. ✔️Ans - Partitioning
Sharing Tasks
Iterating
Explain the meaning of partitioning. Provide an example. ✔️Ans -
Partitioning is sectioning a shape into equal-sized parts.
What does the textbook recommend for partitioning activities involving
area models? ✔️Ans - The fractional parts must be the same size, but not
necessarily the same shape
The number of equal-sized parts that can be partitioned within the unit
determines the fractional amount
Use different area models.
Mention the 5 constructs that a fraction symbol can represent. Provide an
example of each. ✔️Ans - 1. Part-Whole
2. Measurement
3. Division
4. Operator
5. Ratio
Mention two reasons why fractions are concepts that are difficult to
understand. ✔️Ans - There are many meanings of fractions.
Fractions are written in a unique way.
Students overgeneralize their whole-number knowledge.
Describe four misconceptions that students may have about fraction
concepts. Describe how to help students to overcome the misconceptions.
✔️Ans - Students think that the numerator and denominator are separate
values and have difficulty seeing them as a single value. To help, find
fractions values on a number line and avoid saying "three out of four" or
"three over four." Instead say "three fourths."
Students do not understand that 2/3 means two equal-sized parts. To help,
ask students to create their own representations of fractions across various
manipulative and on paper.
Students think that a fraction such as 1/5 is smaller than a fraction such as
1/10 because 5 is less than 10. Conversely, students may be told the
reverse - the bigger the denominators, the smaller the fraction. This may
cause students to overgeneralize that 1/5 is more than 7/10. To help, use
many visuals and contexts that show parts of the whole.
Students mistakenly use the operation "rules" for whole numbers to
compute with fractions. For example, 1/2 + 1/2 = 2/4. To help, use many
visuals and contexts that emphasize estimation and focus on whether
answers are reasonable or not.
Describe the three models to represent fractions. ✔️Ans - Area models
Length or number lines
, Set
Mention 6 common area or region physical models to represent fractions.
✔️Ans - Circular Fraction Pieces
Grid or Dot Paper
Rectangular Regions
Pattern Blocks
Fourths on a Geoboard
Paper Folding
Mention 3 common length or measurement physical models to represent
fractions. ✔️Ans - Fraction Strips or Cuisenaire Rods
Measurement Tools (such as ruler)
Folded Paper Strips
Use appropriate fraction language to describe the meaning of a fractional
part (e.g., 2/3) ✔️Ans - A fractional part is the part that results when the
whole or unit has been partitioned into equal-sized portions or fair shares.
What does it mean that the "fraction size is relative"? ✔️Ans - A fraction
by itself does not describe the size of the whole or the size of the parts. A
fraction only tells about the relationship between the part and the whole.
To understand fractions deeply, mention the three types of activities in
which students need experiences. ✔️Ans - Partitioning
Sharing Tasks
Iterating
Explain the meaning of partitioning. Provide an example. ✔️Ans -
Partitioning is sectioning a shape into equal-sized parts.
What does the textbook recommend for partitioning activities involving
area models? ✔️Ans - The fractional parts must be the same size, but not
necessarily the same shape
The number of equal-sized parts that can be partitioned within the unit
determines the fractional amount
Use different area models.
