standard_description: Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).
problem_activity: Narrative
The purpose of this activity is for students to identify objects that are longer or shorter than a given object. Students find two objects that are longer and two objects that are shorter than an unsharpened pencil. The students use the language of “longer than” and “shorter than” and record their findings in complete sentences so that indirect comparison can be discussed during the activity synthesis.
MLR8 Discussion Supports.
Think aloud and use gestures to emphasize the language used for comparison. For example, use hands further or closer apart to accompany the words “longer” and “shorter”.
Advances: Listening, Representing
Required Materials
Materials to Gather
Materials from a previous lesson
Pencils
Required Preparation
Each group of 4 students needs access to the materials from the previous lesson and one unsharpened pencil.
Create a two-column chart with the headings “longer” and “shorter” for the synthesis.
Launch
Groups of 4
Give each group an unsharpened pencil and access to the objects from the previous lesson.
Display two objects that are not the same length (for example, a crayon and a marker).
“How do the lengths of these objects compare?” (The crayon is shorter than the marker. The marker is longer than the crayon.)
30 seconds: quiet think time
Share responses.
Activity
“You are going to compare the length of objects to the length of the unsharpened pencil. Find two objects that are longer than the pencil and two that are shorter than the pencil. Write a sentence for each comparison.”
8 minutes: independent work time
Monitor for two objects that are close in length but one is found to be longer than the unsharpened pencil and one is found to be shorter.
Student Facing
Find 2 objects that are longer and 2 objects that are shorter than the unsharpened pencil.
Write a sentence that compares each object to the pencil.
Example: The bulletin board
is longer than the pencil.
Student Response
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Activity Synthesis
Display the T-chart with headings “longer” and “shorter.”
“What objects are longer than an unsharpened pencil?” (a book, the ruler, the height of the desk)
Record responses.
What objects are shorter than an unsharpened pencil?” (a marker cap, a crayon, a toothpick)
Record responses.
Display previously identified objects that are close in length.
“How do the lengths of the two objects compare?” (The book that is shorter than the pencil is also shorter than the block because the block is longer than the pencil.)
“Because we compared the length of objects to the pencil, we know that some objects are longer or shorter than others without lining them up.”


aligns: no