few_shots: 
Example 1:
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.

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.


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

Example 2:
Concept/skill: 
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

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
$$-\frac{1}{4}$$


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

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


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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_task_001477_pos_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.
problem_activity: Narrative
The purpose of this activity is for students to order three objects by length. Students line up objects from shortest to longest and longest to shortest. Students need to attend to the language in the question to know which way to order the objects. The language and reasoning students use in this activity helps prepare them to compare the length of objects indirectly in future lessons.
Required Materials
Materials to Gather
Materials from a previous activity
Required Preparation
Each group of 4 needs the collection of objects from the previous activity.
Launch
Groups of 4
Give each group 10–12 objects.
Activity
Read the task statement.
5 minutes: small-group work
Monitor for students who line up the endpoints of the objects.
Student Facing
Pick 3 objects.
With your partner, put the objects in order from
shortest
to longest.
Trace or draw your objects.
Pick 3 new objects.
With your partner, put them in order from
longest to shortest
.
Write the names of the objects in order from longest to shortest.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students appear to order their objects correctly without lining them up, consider asking:
“How did you order your objects from ___ (shortest to longest or longest to shortest)?”
“How could you prove to someone that your objects are ordered correctly?”
Activity Synthesis
Invite previously identified students to demonstrate how they ordered three objects from shortest to longest.
Display the three objects with the endpoints lined up so all students can see.
“What statements can you make to compare the length of their objects?” (The ___ is longer than the ___ and ___.)
As time permits, repeat by inviting a previously identified students to demonstrate how they ordered three objects from longest to shortest.


aligns: no