few_shots: 
Example:
Concept/skill: 
Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Problem/activity:
Stage 1: Money
 Required Preparation
 Materials to Copy
 Blackline Masters
 Would You Rather Stage 1 Spinner
 Would You Rather Stage 1 Recording Sheet
 
 Narrative
 The first partner spins to get a group of coins. They write a question that compares the amount they spun to a different group of coins that they make up.

Answer: 
No. This activity does not involve addition or subtraction, or unknowns in different positions of equations or drawings.

Now, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: im_center_000269_neg_0

2
standard_description: Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.
problem_activity: Activity
Students combine their experience with solids of rotation and their understanding of cylinder volume.
No specific directions are given in regard to specifying how students should express their volume answer. Monitor for students who leave their answers in terms of
\(\pi\)
and those who found an approximate decimal answer.
Launch
Action and Expression: Develop Expression and Communication.
Maintain a display of important terms and vocabulary. During the launch, take time to review the following terms from previous lessons that students will need to access for this activity: axis of rotation, solid of rotation, volume of a cylinder.
Supports accessibility for: Memory; Language
Student Facing
Suppose each two-dimensional figure is rotated around the vertical axis shown. Each small square in the grid represents 1 square centimeter.
A
[IMG]
B
[IMG]
For each solid:
Either sketch
or
describe in words the three-dimensional solid that would form.
Find the solid’s volume.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
Given a cylinder with radius
\(r\)
and height
\(h\)
, write an expression for the volume if each of these changes were made.
The height is tripled to
\(3h\)
and the radius remains
\(r\)
.
The radius is tripled to
\(3r\)
and the height remains
\(h\)
.
Given a cube of side length
\(s\)
, write an expression for the volume if the side length were tripled to
\(3s\)
.
Which change affected the shape’s volume the most? The least? Explain or show your reasoning.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
Students may struggle to visualize the rotated figures. For the L shape, encourage them to divide it into smaller pieces and consider each independently. For the rectangle, remind them of the doughnut cross section they drew in a previous lesson.
Activity Synthesis
In the discussion, explore different aspects of the calculations students made. Invite one student who left the answer in terms of
\(\pi\)
and another who found a decimal answer to share their results. Remind students that the former is called an exact answer, while the latter is called an approximate answer because the value of
\(\pi\)
needs to be approximated and rounded to find a decimal answer. Emphasize that the choice of expression depends on the situation at hand.
If time permits, ask students would would happen if the first figure were rotated around the horizontal axis formed by the bottom edge of the figure. Challenge them to decide if the volume would be the same as with the rotation around the given vertical axis. (The volume of this figure would actually be
\(99\pi\)
cubic centimeters.)
Speaking: MLR8 Discussion Supports.
As students share their sketches or descriptions of the three-dimensional solid that would form, press for details by asking how they know that the first figure would form two cylinders after a rotation around the vertical axis. Also, ask how they know that the cylinder on top will have a radius of 2 cm and the cylinder at the bottom will have a radius of 5 cm. This will help students justify their reasoning for the measurements of the cylinders in their sketches or descriptions.
Design Principle(s): Support sense-making; Optimize output (for justification)


aligns: no