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 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: 
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

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fl_problem_001097_pos_0

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fl_problem_001894_pos_0

HS_0
standard_description: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
problem_activity: Narrative
In this activity, students find the perimeter of several shapes and write expressions that show their reasoning. Each side of the shape is labeled with its length, prompting students to notice repetition in some of the numbers. The perimeter of all shapes can be found by addition, but students may notice that it is efficient to reason multiplicatively rather than additively (MP8). For example, they may write
\(4 \times 6\frac{1}{3}\)
instead of
\(6\frac{1}{3} + 6\frac{1}{3} + 6\frac{1}{3} + 6\frac{1}{3}\)
.
MLR8 Discussion Supports.
Synthesis: Some students may benefit from the opportunity to rehearse what they will say with a partner before they share with the whole class.
Advances: Speaking
Launch
Groups of 2–4
Activity
3–4 minutes: independent work time
2 minutes: group discussion
Student Facing
Find the perimeter of each shape. Write an expression that shows how you find the perimeter.
[IMG]
Compare your expressions with your partners’ expressions. Make 1–2 observations.
Student Response
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Activity Synthesis
Invite students to share the expressions they wrote for the perimeter of each shape. Record the expressions.
For each shape, ask: “What is the same about these expressions? What is different?” (They each use the side lengths in the shape. They each show the total length around the shape. Some use addition, some use multiplication, some use both multiplication and addition.)
Highlight that when two or more sides have the same length, the perimeter can be found by adding, multiplying, or a combination of both.


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