few_shots: 
Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
[IMG]
Counters, 10 per pair of students
Decks of number cards 0-5 (with 4 of each number) or two 0-5 dice
Setup
This activity is done in pairs. The students sit side by side with 10-frame and deck of cards or dice. If they have cards, the cards are shuffled and placed face down in front of them.
Action
Player 1 flips a card or rolls the die. They place that many counters on the 10-frame. Player 2 flips a card or rolls the die. They place that many more counters on the 10-frame next to the counters already on the ten frame. The students count the total together.
A recording sheet can be added when the students have been introduced to equations and number sentences. For those students who can handle higher numbers, a deck of 0-10 cards and two 10-frames can be used.
This game can also be played alone.


Concept/skill: 
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Answer: 
No. Though this task involves addition, it does not involve any word problems.

Example 2:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Concept/skill: 
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Answer: 
Yes. By arranging the fractions in this problem, students learn to compare fractions by reasoning about their size.

Example 3:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Concept/skill: 
Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Answer: 
No. This set of problems does not directly involve adding or subtracting multi-digit whole numbers. Instead, it focuses on multiplying multi-digit whole numbers.

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

shot_info: im_task_001477_neg_0

K

im_task_000157_pos_0

3

fl_problem_000674_neg_0

5
standard_description: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
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: yes