few_shots: 
Example:
Concept/skill: 
Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape. (Students do not need to learn formal names such as “right rectangular prism.”)

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)


Answer: 
Yes. This activity asks students to compose three-dimensional shapes, using geoblocks, to create composite shapes.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_lesson_009431_pos_0

1
standard_description: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.
problem_activity: Activity
The purpose of this activity is for students to recognize that multiplying an equation by a value results in the same solution. This will be useful when transforming equations for the elimination method of solving systems of equations in the supported Algebra lesson. Students will work in pairs and each partner is responsible for answering the questions in either column A or column B. Although each row has two different problems, they share the same answer. Ensure that students work their problems out independently and collaborate with one another when they do not arrive to the same answers. Students construct viable arguments and critique the reasoning of others (MP3) when they resolve errors by critiquing their partner's work or explaining their reasoning.
Launch
Arrange students in groups of two. In each group, ask students to decide who will work on column A and who will work on column B. If students are unfamiliar with the row game structure, demonstrate the protocol before they start working.
Student Facing
Work independently on your column. Partner A completes the questions in column A only and partner B completes the questions in column B only. Your answers in each row should match. Work on one row at a time and check if your answer matches your partner’s before moving on. If you don’t get the same answer, work together to find any mistakes.
Solve each equation.
| **          row         ** |         column A          |         column B          |
|----------------------------|---------------------------|---------------------------|
| **           1          ** |        \(3x-1=5\)         |        \(6x-2=10\)        |
| **           2          ** |   \(4(x+1) = 3x - 12\)    |     \(4x+4 = 3(x-4)\)     |
| **           3          ** |      \(14x+10=4x+6\)      |      \(7x+5 = 2x+3\)      |
| **           4          ** |        \(6x+3=33\)        |        \(4x+2=22\)        |
| **           5          ** | \(4x + 5y = 2 - 4x + 5y\) | \(4x + 9y = 2 + 9y - 4x\) |
| **           6          ** |     \(2x + 6y = 10\)      |     \(5x + 15y = 25\)     |
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
The purpose of the discussion is to notice that equations that have been multiplied by the same value have the same solution.
Consider asking students to explain why their solutions might be the same for each row.
For each row, the two equations are equivalent. Sample responses for each row:
The equation in column B is 2 times the equation in column A.
In each column, one side of the equation is the distributed form of the same side of the equation in the other column.
The equation in column B is
\(\frac{1}{2}\)
of the equation in column A.
The equation in column B is
\(\frac{2}{3}\)
of the equation in column A.
The equation in column B has
\(4y\)
added to both sides of the equation from column A.
The equation in column B is
\(\frac{5}{2}\)
of the equation in column A.
While there may be other valid ways of connecting the equations (for example, in row 4, dividing the equation in column A by 3 and dividing the equation in column B by 2 result in the same equation), encourage students to recognize that there is a single multiple of one equation that results in the other equation.


aligns: no