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 following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: im_task_001477_pos_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.
problem_activity: Narrative
This optional activity gives students another opportunity to practice identifying multiples of some powers of 10 that border a given number and identify the nearest ones. As before, students may use number lines to support their reasoning, but here the number lines are unlabeled.
Launch
Groups of 2
Activity
“Work independently for a few minutes. Then, discuss your responses with your partner.”
5 minutes: independent work time
2 minutes: partner discussion
Student Facing
Answer each question. Label and use the number lines if they are helpful.
Is 425,193 closer to 400,000 or 500,000?
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Is 425,193 closer to 420,000 or 430,000?
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Is 425,193 closer to 425,000 or 426,000?
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Is 425,193 closer to 425,100 or to 425,200?
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Is 425,193 closer to 425,190 or to 425,200?
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For the number 425,193:
The nearest multiple of 100,000 is _______________.
The nearest multiple of 10,000 is _______________.
The nearest multiple of 1,000 is _______________.
The nearest multiple of 100 is _______________.
The nearest multiple of 10 is _______________.
Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Activity Synthesis
Invite students to share their responses and reasoning.
“Which nearest multiples were you able to identify fairly easily?”
“Which were a bit more challenging, if any? Why might that be?”


aligns: no