Chapter Questions
What is the goal of activities involving the concept of sharing? When would you implement sharing activities?
Why is it important to teach computational estimation with fractions?
Give examples of manipulatives and contexts that fall into each of the three categories of fraction models (area, length, and set).
A student adds $\frac{1}{5}+\frac{2}{3}$ and gets $\frac{6}{8}$. How will you help the student understand that this is incorrect? How would you redirect him or her to do it correctly?
What does partitioning mean? Explain and illustrate.
For the problem $3 \frac{1}{4}-1 \frac{1}{2}$, think of a story problem that would be a "take away" situation and one that would be a "comparison" situation.
What does iteration mean? Explain and illustrate.
Explain at least one mental method (estimation or mental computation) for each of these:$$\frac{3}{4} \times 5 \frac{1}{2} \quad 1 \frac{1}{8} \text { of } 40$$
What are two ways you can support students' development of estimating with fractions?
Make up a word problem with a fraction as a divisor. Is your problem a measurement problem or a partition problem? Make up a second word problem with fractions of the other type (measurement or partition).
Describe two ways to compare $\frac{5}{12}$ and $\frac{5}{8}$ (not using common denominator or cross-product methods).
What are two ways to build the conceptual relationship between $\frac{4}{4}$ and $2 \frac{3}{4}$ ?