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:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Concept/skill: 
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Answer: 
Yes. This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).

Example 3:
Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


Concept/skill: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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

shot_info: im_task_001477_neg_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Analyze and solve pairs of simultaneous linear equations.
problem_activity: Activity
The purpose of this activity is for students to calculate the volume of cones given their height and radius. Students are given a cylinder with the same height and radius and use the volume relationship they learned in the previous activity to calculate the volume of the cone. They then calculate the volume of a cone given a height and radius using the newly learned formula for volume of a cone. For the last problem, an image is not provided to give students the opportunity to sketch one if they need it.
Launch
Give students 3–5 minutes of quiet work time followed by a whole-class discussion.
Student Facing
Here is a cylinder and cone that have the same height and the same base area.
What is the volume of each figure? Express your answers in terms of
\(\pi\)
.
[IMG]
Here is a cone.
What is the area of the base? Express your answer in terms of
\(\pi\)
.
What is the volume of the cone? Express your answer in terms of
\(\pi\)
.
[IMG]
A cone-shaped popcorn cup has a radius of 5 centimeters and a height of 9 centimeters. How many cubic centimeters of popcorn can the cup hold? Use 3.14 as an approximation for
\(\pi\)
, and give a numerical answer.
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?
A grain silo has a cone shaped spout on the bottom in order to regulate the flow of grain out of the silo. The diameter of the silo is 8 feet. The height of the cylindrical part of the silo above the cone spout is 12 feet while the height of the entire silo is 16 feet.
How many cubic feet of grain are held in the cone spout of the silo? How many cubic feet of grain can the entire silo hold?
[IMG]
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
In the first problem, students might use 10 as the radius length. Ask students what the length of 10 in the picture is called. Ask students to recall the formula for the volume of a cylinder.
For students who are not sure where to begin the last problem since it does not have an image, encourage them to sketch and label their own.
Activity Synthesis
For the first problem, Invite students to explain how they calculated the volume of both figures and have them share the different strategies they used. If not mentioned by students bring up these strategies:
Calculate the volume of the cylinder, then divide volume of cylinder by 3 to get the volume of the cone.
Calculate the volume of the cylinder, then multiply volume of cylinder by
\(\frac13\)
to get the volume of the cone.
Calculate the volume of the cone, then multiply volume of cone by 3 to get the volume of the cylinder.
For the third problem, ask students to share any sketches they came up with to help them calculate the answer. Explain to students that sometimes we encounter problems that don’t have a visual example and only a written description. By using sketches to help to visualize what is being described in a problem, we can better understand what is being asked.
Engagement: Develop Effort and Persistence.
Break the class into small discussion groups and then invite a representative from each group to report back to the whole class. All group members should be prepared to share if invited.
Supports accessibility for: Language; Social-emotional skills; Attention
Writing: MLR3 Clarify, Critique, Correct.
Present an incorrect response to the first question that reflects a possible misunderstanding from the class. For example, “The volume is
\(4000\pi\)
because
\(\pi*4*10^2\)
.” Prompt students to critique the reasoning (e.g., ask, “Do you agree with the author’s reasoning? Why or why not?”) and then write feedback to the author that identifies the misconception and how to improve on his/her work. Listen for students who tie their feedback to the difference between the radius and diameter and use the academic vocabulary (e.g., height, radius, diameter, cylinder, cone, volume, etc.). This will help students evaluate, and improve on, the written mathematical arguments of others and highlight the distinction between and the importance of radii when calculating volume of cylinders and cones.
Design Principle(s): Maximize meta-awareness


aligns: no