few_shots: 
Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Concept/skill: 
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Answer: 
No. The expressions shown in this problem do not involve multiplying fractions with other fractions, nor whole numbers with fractions.

Now, does the following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: fl_problem_001097_neg_0

7
standard_description: Explain a proof of the Pythagorean Theorem and its converse.
problem_activity: Narrative
This optional activity gives students an additional opportunity to practice using “jumps” on number lines to subtract fractions, decomposing any whole numbers as needed along the way. (It is similar in structure to an optional activity in an earlier lesson on addition.)
Students are given four number lines with a point marked on each. They then draw a card with a fraction on it. All fractions on the cards, shown here, are greater than the values of the points. Students make one or more jumps to find the difference of the two points and then represent it with a subtraction equation.
\(\frac{8}{5} \qquad \frac{9}{5} \qquad \frac{10}{5} \qquad \frac{11}{5} \qquad \frac{12}{5} \qquad \frac{13}{5} \qquad \frac{14}{5} \qquad \frac{15}{5}\)
Required Materials
Materials to Copy
Make a Jump, Subtraction Edition
Required Preparation
Create a set of cards from the blackline master for each group of 2.
Launch
Groups of 2
Give each group a set of fraction cards from the blackline master.
If students did not complete the optional activity in the previous lesson (which had a similar structure):
Display the four number lines.
“What do you notice? What do you wonder?”
30 seconds: quiet think time
30 seconds: partner discussion
Activity
“Label each point on the number line with a fraction it represents. This is your target.”
1 minute: independent work time
“You will now make one or more jumps from another fraction to your target and write an equation to represent the difference between the two.”
Explain how to use the cards and how to complete the task.
Monitor for students who facilitate subtraction by:
rewriting a fraction on their card as a whole number or a mixed number
labeling their number lines with whole numbers beyond 1
Student Facing
Here are four number lines, each with a point on it. Label each point with a fraction it represents.
[IMG]
[IMG]
[IMG]
[IMG]
The point you labeled is your target.
Pick a card from the set given to you. Locate and label the fraction on the number line.
From that point, draw one or more jumps to reach the target. What do you need to subtract? Label each jump you draw.
Write an equation to represent the difference of your two fractions.
Student Response
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Activity Synthesis
Select students to share their responses to the first couple of diagrams (or more if time permits).


aligns: no