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Chapter 16: Developing Strategies for Fraction Computation
ESSAY. Write your answer in the space provided or on a separate sheet of paper.
1) Name two of the major guidelines to consider when developing computational strategies for fractions.
Describe an instructional sequence that would support each guideline.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
2) Estimation of fractions can result in estimates that are not close to the actual computed answer and should
be avoided.
3) Students traditionally perform better at computing with fractions than they do at estimating with them.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
4) To help students develop strategies for fraction addition and subtraction
a) They should be given lots of practice with just plain computation before they are confused by the
addition of word problems.
b) They should be provided with problems that always use the same kind of model, to promote a
deeper understanding.
c) Mixed numbers and fractions should be taught separately.
d) Addition and subtraction situations should be mixed.
5) Which of the following is NOT an example of a linear model for adding and subtracting factions?
a) Mary needs 3-1/3 feet of wood to build her fence. She only has 2-3/4 feet. How much more wood
does she need?
b) Milly is at mile marker 2-1/2. Rob is at mile marker 1. How far behind is Rob?
c) Half a pizza is left from the 2 pizzas Molly ordered. How much pizza was eaten?
d) What is the total length of these two Cuisenaire rods placed end to end?
6) Adding and subtracting with unlike denominators
a) Should be introduced at first with tasks that require both fractions to be changed.
b) Is sometimes possible for students, especially if they have a good conceptual understanding of the
relationships between certain fractional parts and a visual tool, such as a number line.
c) Is a concept understood especially well by students if the teacher compares different denominators
to “apples and oranges.”
d) Should initially be introduced without a model or drawing.
7) When subtracting mixed number fractions, it is helpful to
a) Deal with the whole numbers first and then work with the fractions.
b) Always trade one of the whole number parts into equivalent parts.
c) Avoid this method until the student fully understands subtraction of numbers less than one.
d) Teach only the algorithm that keeps the whole number separate from the fractional part.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
8) Talking explicitly about common misconceptions only causes students to develop them.
9) Students should be introduced to fraction multiplication with problems that require finding fractions of
whole numbers.
10) Although an area model is very useful for modeling whole number multiplication, it is not easily applied to
fraction multiplication.
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
11) The algorithm for fraction multiplication
a) Can be discovered by students when they see patterns emerge from the problems they solve with
models.
b) Should be discovered after only a few days of working with contextual examples and models.
c) Does not need to be connected to a real-life context because it’s the easiest of all fraction
computation algorithms.
d) Requires common denominators.
TRUE/FALSE. Write “T” if the statement is true and “F” if the statement is false.
12) A mixed number must be turned into an improper fraction before one can use it in a multiplication problem.
SHORT ANSWER. Write the word or phrase that best completes each statement or
answers the question
13) The _______________________ interpretation of division is seen in this example: “Melissa has 2-1/2
yards of fabric and wants to make shirts that use ¾ yard each. How many shirts can she make?”
14) A common, but frequently misunderstood, method of teaching faction division is to tell students,
“____________________ the second fraction and multiply.”
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or
answers the question.
15) Which of the following is NOT a common misconception about fraction computation?
a) Multiplying always results in a bigger number, while dividing always make a number smaller.
b) Fractions have to have a common denominator for all computation.
c) Procedures developed from conceptual understanding are usually easier than the standard
algorithms.
d) Estimation is not important.
