standard_description: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
problem_activity: Narrative
The purpose of this activity is for students to make sense of the structure of a Take From, Result Unknown story problem. Students have access to connecting cubes or two-color counters and 10-frames, which they may choose to use strategically to represent and solve the problem (MP5). Some students may apply the ideas from the previous unit where they related subtraction to counting back. As students share their methods, the teacher records their thinking. It is important for the teacher to focus attention on the expression during the activity synthesis. Although some students may attempt to write equations and do so accurately, this representation will be the focus in a later lesson.
Students keep their books closed for the launch of the activity, as the teacher displays and reads the problem.
MLR8 Discussion Supports.
Synthesis: Display sentence frames to support whole-class discussion: “_____ and _____ are the same/alike because . . .” and “_____ and _____ are different because . . .” Encourage students to use these sentence frames to compare and contrast representations.
Advances: Speaking, Conversing
Required Materials
Materials to Gather
10-frames
Connecting cubes or two-color counters
Launch
Groups of 2
Give students access to 10-frames and connecting cubes or two-color counters.
Display the image from the warm-up.
“This is a picture of a library. Talk to your partner about what you know and what you wonder about libraries.”
3 minutes: partner discussion
Share and record what students know and wonder about libraries.
"We are going to solve a lot of story problems about libraries."
Display and read the numberless story.
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
If not already mentioned, ask, “Are there more or fewer kids at the library after some go home?”
Activity
Ask students to open their books.
Read the problem with numbers.
2 minutes: independent work time
“Share your thinking with your partner.”
2 minutes: partner discussion
Monitor for students who solve or represent the problem in the following ways:
objects
drawings
count back
an expression (
\(9 - 2\)
)
Student Facing
Some kids were at the library.
Then some of the kids went home.
What do you notice?
What do you wonder?
[IMG]
There were 9 kids at the library.
Then 2 of the kids went home.
How many kids are at the library now?
Show your thinking using drawings, numbers, or words.
Student Response
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Advancing Student Thinking
If students use more or fewer than nine objects to represent the kids at the library, consider asking:
“How did you choose how many connecting cubes to take out?”
“There are nine kids at the library. Which connecting cubes show the nine kids? Which connecting cubes show the two kids that went home?”
Activity Synthesis
Invite previously identified students to share in the order listed above.
“How are these representations the same? How are they different?”
If needed, display
\(9 - 2\)
.
“How does this expression match the story problem?”


aligns: no