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 to multiply a fraction or whole number by a fraction.

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

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_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Fluently multiply multi-digit whole numbers using the standard algorithm.
problem_activity: Narrative
The purpose of this activity is for students to analyze the connections between algorithms and base-ten diagrams that represent subtraction. In particular, students relate how the two strategies show a hundred decomposed into tens and a ten into ones in order to facilitate subtraction.
As students work, encourage them to refine their descriptions of what is happening in both the diagrams and the algorithms using more precise language and mathematical terms (MP6).
MLR8 Discussion Supports.
Students should take turns finding a match and explaining their reasoning to their partner. Display the following sentence frames for all to see: “I noticed _____ , so I matched . . . .” Encourage students to challenge each other when they disagree.
Advances: Listening, Speaking, Representing
Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Give students a subset of the cards to start with and introduce remaining cards once students have completed their initial set of matches.
Supports accessibility for: Organization, Social-Emotional Functioning
Required Materials
Materials to Copy
Diagrams and Algorithms
Required Preparation
Create a set of cards from the blackline master for each group of 2.
Launch
Groups of 2
Distribute one set of pre-cut cards to each group of students.
Activity
“This set of cards includes base-ten diagrams and algorithms that represent the same subtraction. Match each diagram to an algorithm. Work with your partner to explain your choices.”
8 minutes: partner work time
Student Facing
Your teacher will give you a set of cards. Match each diagram with an algorithm.
[IMG]
[IMG]
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Activity Synthesis
Select 2–3 students to share a match they made and how they know the cards go together.
“In the diagrams, why were the hundreds sometimes moved over into the tens place?” (This happened when there weren’t enough tens to subtract. We used a hundred to get more tens.)
“How was this shown in the algorithm?” (A hundred was crossed out and 10 more tens were added to the tens place, like in F, 20 was crossed out and 120 was written above it.)


aligns: no