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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for free access to Student Response.
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: 
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.”)

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

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

shot_info: im_lesson_009431_pos_0

1
standard_description: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
problem_activity: Activity
In this activity, students use surface area as a context to extend the order of operations to expressions with exponents. The context provides a reason to evaluate the exponent before performing the multiplication.
Launch
Give students 10 minutes of quiet work time, followed by a class discussion.
Reading: MLR6 Three Reads.
Use this routine to support students’ comprehension of the situation. In the first read, students read the text with the goal of comprehending the situation (e.g., Jada and Noah have different solutions for the surface area of the same cube). In the second read, ask students to identify important quantities that can be counted or measured (e.g., the side length of the cube; the number of faces of a cube; the area of each face of the cube). In the third read, reveal the question, “Do you agree with either of them? Explain your reasoning.” Ask students to brainstorm possible strategies to answer the question (e.g., Find the area of each face of the cube. Multiply the area by 6 to find the surface area of the cube). This will help students concentrate on making sense of the situation before rushing to a solution or method.
Design Principle(s): Support sense-making
Student Facing
A cube has side length 10 inches. Jada says the surface area of the cube is 600 in
2
, and Noah says the surface area of the cube is 3,600 in
2
. Here is how each of them reasoned:
Jada’s Method:
\(6 \boldcdot 10^2\)
\(6 \boldcdot 100\)
\(600\)
Noah’s Method:
\(6 \boldcdot 10^2\)
\(60^2\)
\(3,\!600\)
Do you agree with either of them? Explain your reasoning.
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
In finding the surface area, there is a clear reason to find
\(10^2\)
and then multiply by 6. Tell students that sometimes it is not so clear in which order to evaluate operations. There is an order that we all generally agree on, and when we want something done in a different order, brackets are used to communicate what to do first. When an exponent occurs in the same expression as multiplication or division, we evaluate the exponent first, unless brackets say otherwise. Examples:
\((3\boldcdot 4)^2 = 12^2 = 144\)
, since the brackets tell us to multiply
\(3\boldcdot 4\)
first. But
\(3\boldcdot  4^2 = 3\boldcdot  16 = 48\)
, because since there are no brackets, we evaluate the exponent before multiplying.
If students bring up PEMDAS or another mnemonic for remembering the order of operations, point out that PEMDAS can be misleading in indicating multiplication before division, and addition before subtraction. Discuss the convention that brackets or parentheses indicate that something should be evaluated first, followed by exponents, multiplication, or division (evaluated left to right), and last, addition or subtraction (evaluated left to right).


aligns: no