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: 
Represent addition and subtraction with objects, fingers, mental images, drawings (Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards.)), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Answer: 
Yes. This task involves representing addition with objects such as number cards and dice.

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_pos_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
problem_activity: Optional activity
In this optional activity, students use colored pencils (or pens or highlighters) to label the radius and height on different pictures of cylinders. Then they sketch their own cylinders and label the radius and heights of those. The purpose of this activity is for students to practice identifying the radius and height of various cylinders, some of which are in context.
This activity can also be abbreviated if students demonstrate prior understanding of how to draw or label cylinders and only need a brief refresh.
Launch
Distribute colored pencils. Give students 1–2 minutes of quiet work time followed by a whole-class discussion.
Student Facing
For cylinders A–D, sketch a radius and the height. Label the radius with an
\(r\)
and the height with an
\(h\)
.
[IMG]
Earlier you learned how to sketch a cylinder. Sketch cylinders for E and F and label each one’s radius and height.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Anticipated Misconceptions
In diagrams D and E, some students might mistake the diameter for the height of the cylinder. Some students may mark a height taller than the cylinder due to the tilt of the figure.
Activity Synthesis
Select students to share where they marked the radius and height and the cylinders sketched for images E and F. Discuss examples of other cylinders students see in real life.
Speaking, Listening: MLR3 Clarify, Critique, Correct.
Present an incorrect drawing that reflects a possible misunderstanding from the class about the height of a cylinder. For example, draw a cylinder with the diameter incorrectly placed at its height and the height at its diameter. Prompt students to identify the error, (e.g., ask, “Do you agree with the representation? Why or why not?”), correct the representation, and write feedback to the author explaining the error. This helps students develop an understanding and make sense of identifying the heights of differently-oriented cylinders.
Design Principle(s): Support sense-making; Maximize meta-awareness


aligns: no