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 to multiply a fraction or whole number by a fraction.

Answer: 
No. The expressions shown in this problem do not involve multiplying fractions with other fractions, nor whole numbers with fractions.

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


Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Answer: 
Yes. An initial step when solving for x in this problem requires the use of the addition formula for cosine on the left side of the equation.

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

shot_info: im_task_001477_neg_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
problem_activity: Warm-up
The purpose of this warm-up is to assess students’ understanding of the volume of a cylinder. Students learned that the volume of either a cylinder or prism is found by multiplying the area of the base by its height. In this warm-up, students are given information to find the area of a cylinder’s base, but they are not given the height. Students propose a volume for the cylinder and explain why it works. Since the diameter of the base is 8, the area of the base is
\(16\pi\)
.
If students have trouble getting started, ask them:
“Do you have enough information to calculate the area of the base?”
“What is the radius?”
Identify students who use these strategies:
find the area of the base first then set up the equation
\(V=16\pi h\)
.
choose a specific value for
\(h\)
then solve for the volume.
Launch
Arrange students in groups of 2. Tell students that in a previous lesson, they learned how to find the volume of a cylinder if they know the cylinder’s radius and height. Draw their attention to where volume formulas are displayed in the classroom as the unit progresses. Give students 1–2 minutes of quiet work time followed by time to explain their reasoning to their partner. Follow this with a whole-class discussion.
Student Facing
What is a possible volume for this cylinder if the diameter is 8 cm? Explain your reasoning.
[IMG]
Student Response
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Activity Synthesis
The goal of this discussion is for students to communicate how the height of a cylinder is related to its volume. Invite students to share their solutions and their reasoning. Record and display the dimensions and volumes of cylinders that correspond to solutions given by students.


aligns: no