few_shots: 
Example:
Problem/activity:
Narrative
The purpose of this activity is for students to create composite shapes and compose new shapes from composite shapes. For example, students may find that a rectangular prism can be made from four triangular prisms or from eight smaller cubes. Students then discover that they can combine two of the composed rectangular prisms to make a new rectangular prism.
Required Materials
Materials to Gather
Geoblocks
Launch
Groups of 4
Give each group geoblocks.
Display a large cube.
“This cube can be built from other shapes. See how many ways you can build a cube using other shapes.”
3 minutes: partner work time
Share responses.
Activity
“Choose a different shape. Try to find smaller shapes you can use to build that shape.”
5 minutes: partner work time
Student Response
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Activity Synthesis
Display a cube and a composite cube—for example, a cube composed of four small cubes and one rectangular prism.
Demonstrate putting the shapes together.
“What new shape did I make with the cube and the cube I made?”
“Put your shapes together to make a rectangular prism.”
Display a rectangular prism and two triangular prisms.
“Find these shapes. Put them together. What new shape can you make?” (a cube, a rectangular block)


Concept/skill: 
Recognize area as an attribute of plane figures and understand concepts of area measurement.

Answer: 
No. This activity does not teach students area as an attribute of plane figures. Instead, the activity focuses on solid, three-dimensional figures.

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

shot_info: im_lesson_009431_neg_0

1
standard_description: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.
problem_activity: Activity
This activity is an opportunity for students to practice rewriting expressions using the distributive property. It is a step up from the same type of work in grade 6 because arithmetic with signed numbers is required.
The row with
\(6a-2b\)
is designed to allow students to figure out how to factor by reasoning based on structure they already understand, instead of learning how to factor based on a procedure that a teacher demonstrates first. The rows with
\(k(4 - 17)\)
and
\(10a-13a\)
are designed to prepare students for combining like terms in the next lesson.
Launch
Draw students’ attention to the organizers that appear above the table, and tell them that these correspond to the first three rows in the table. Let them know that they are encouraged to draw more organizers like this for other rows as needed.
Arrange students in groups of 2. Instruct them to take turns writing an equivalent expression for each row. One partner writes the equivalent expression and explains their reasoning while the other listens. If the partner disagrees, they work to resolve the discrepancy before moving to the next row.
Action and Expression: Internalize Executive Functions.
Provide students with blank diagrams to organize their work for the factored and expanded expressions. Include example diagrams labeled “expanded” and “factored.”
Supports accessibility for: Language; Organization
Student Facing
In each row, write the equivalent expression. If you get stuck, use a diagram to organize your work. The first row is provided as an example. Diagrams are provided for the first three rows.
[IMG]
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "_value": "factored"}, {"_attributes": {"scope": "col"}, "_value": "expanded"}]}]}], "tbody": [{"tr": [{"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "42054"}, "_value": "\\(\\text- 3(5 - 2y)\\)"}]}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "42097"}, "_value": "\\(\\text- 15 + 6y\\)"}]}]}, {"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "42137"}, "_value": "\\(5(a-6)\\)"}]}, {}]}, {"td": [{}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "4097"}, "_value": "\\(6a-2b\\)"}]}]}, {"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "42180"}, "_value": "\\(\\text- 4(2w-5z)\\)"}]}, {}]}, {"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "42214"}, "_value": "\\(\\text- (2x-3y)\\)"}]}, {}]}, {"td": [{}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "42247"}, "_value": "\\(20x-10y+15z\\)"}]}]}, {"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "42283"}, "_value": "\\(k(4-17)\\)"}]}, {}]}, {"td": [{}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "4113"}, "_value": "\\(10a-13a\\)"}]}]}, {"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "42333"}, "_value": "\\(\\text- 2x(3y-z)\\)"}]}, {}]}, {"td": [{}, {"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "42375"}, "_value": "\\(ab-bc-3bd\\)"}]}]}, {"td": [{"span": [{"_attributes": {"class": ["math", "math-repaired"], "data-png-file-id": "42413"}, "_value": "\\(\\text- x(3y-z+4w)\\)"}]}, {}]}]}]}]}
Student Response
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Student Facing
Are you ready for more?
Expand to create an equivalent expression that uses the fewest number of terms:
\(\left(\left(\left(\left(x\strut+1\right)\frac12\right)+1\right)\frac12\right)+1\)
. If we wrote a new expression following the same pattern so that there were 20 sets of parentheses, how could it be expanded into an equivalent expression that uses the fewest number of terms?
Student Response
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Anticipated Misconceptions
If students are unsure how to proceed, remind them of tools and understandings they have seen recently that would be helpful. For example, “Draw an organizer and think about how the organizer represents terms in the expression.” Also, “Rewrite subtraction as adding the opposite.”
Activity Synthesis
Much of the discussion will take place in small groups. Display the correct equivalent expressions and work to resolve any discrepancies. Expanding the term
\(\text-(2x-3y)\)
may require particular care. One way to interpret it is to rewrite as
\(\text-1 \boldcdot (2x-3y).\)
If any confusion about handling subtraction arises, encourage students to employ the strategy of rewriting subtraction as adding the opposite.
To wrap up the activity, ask:
“Which rows did you and your partner disagree about? How did you resolve the disagreement?”
“Which rows are you the most unsure about?”
“Describe a process or procedure for taking a factored expression and writing its corresponding expanded expression.”
“Describe a process or procedure for taking an expanded expression and writing its corresponding factored expression.”
Writing: MLR3 Clarify, Critique, Correct.
Present an incorrect response for one of the expanded expressions in the table. For example, “An equivalent expression for
\(6a − 2b\)
is
\(4(a−b)\)
because
\(6−2\)
is 4 and
\((a−b)\)
is left on its own.” Prompt students to clarify any of the language and reasoning in the incorrect response and then to identify the error(s). Invite students to work with a partner to write a correct response. This helps students evaluate and improve on the written mathematical arguments of others.
Design Principle(s): Maximize meta-awareness


aligns: no