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: 
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

Answer: 
No. This problem does not directly teach how side ratios in right triangles lead to definitions of trigonometric ratios. Instead, it involves solving a trigonometric function.

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_pos_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Use place value understanding to round multi-digit whole numbers to any place.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
problem_activity: Narrative
The purpose of this activity is for students to apply what they learned about rounding in prior lessons to think about all the numbers that would round to a given number. Students should be encouraged to use whatever representations make sense to them. Although the number line is often used to represent rounding, it is also worth sharing other ways that students are representing or thinking about rounding.
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
“Diego is thinking of a number. When you round Diego's number to the nearest ten, the answer is 40. What's a number that could be Diego's number? What's a number that could not be Diego's number?” (38 rounds to 40 so it could be his number. 34 does not round to 40 so it couldn't be his number.)
30 seconds: quiet think time
Share 3–5 responses. Highlight the idea that more than one number can round to 40 and that some numbers are greater than 40 and some are less than 40.
Activity
“Work with your partner on all these problems. Be sure to justify your reasoning.”
5–7 minutes: partner work time
Student Facing
What are all the numbers that would round to 50 if you're rounding to the nearest ten? You can use this number line if it helps you.
[IMG]
What are all the numbers that would round to 70 if you're rounding to the nearest ten?
What are all the numbers that would round to 600 if you're rounding to the nearest hundred?
If you finish early, find the numbers that would round to 100 and to 500 if you’re rounding to the nearest hundred. Compare your lists with a partner's lists and discuss patterns you see.
Student Response
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Advancing Student Thinking
If students don’t find all the numbers that round to the given number, consider asking:
“How did you determine that these numbers would round to ____?”
“How could you use a number line to find all the numbers that round to ___?”
Activity Synthesis
“How did you decide what numbers would round to 40?” (We looked at all the numbers that are closer to 40 than 50 or 30.)
Consider asking:
“What does 35 round to?” (40 because it is halfway between 30 and 40)
“What does 45 round to?” (50 because it is halfway between 40 and 50)
“Look at your responses for the first 2 problems. What patterns do you see in the numbers? Why is that happening?” (I see they each start with a 5 in the ones place below it because it’s halfway to the nearest ten, and the numbers end with a 4 in the ones place because that is closer than the next ten.)
“How did you use what you learned from the first 2 problems to think about the last problem?” (Instead of thinking about fives, we thought about fifties. We looked at all the numbers that are closer to 600 than 500 or 700.)
Consider asking:
“What does 550 round to?” (600 because it is halfway between 500 and 600.)
“What does 650 round to?” (700 because it is halfway between 600 and 700.)


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