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: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
problem_activity: Narrative
In this activity, students solve contextual problems that involve subtracting numbers with non-zero digits from numbers with one or more zero digits. Students may choose other ways to find the difference (for example, adding up and using a number line to keep track), but are asked to use the standard algorithm at least once.
In the launch, students subtract their age from the current year. This provides an opportunity for students to notice the relationship between this difference and their current age (MP7).
Required Materials
Materials to Gather
Grid paper
Launch
Groups of 2
Give students access to grid paper.
“Write the year that you were born down and subtract that year from the current year.”
“Share with a neighbor what you found out.” (Students will notice that the number that results is their current age or the age they will be on their upcoming birthday.)
“Jada used this method to find the age of some of her relatives.”
Activity
10 minutes: partner work time
Student Facing
Jada recorded the birth year of some of her maternal grandparents for a family history project.
|   family member   | birth year |
|-------------------|------------|
|    grandmother    |    1952    |
|    grandfather    |    1948    |
| great-grandmother |    1930    |
| great-grandfather |    1926    |
As of this year, what is the age of each family member? Show your reasoning. Use the standard algorithm at least once.
Student Response
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Activity Synthesis
Ask students to share responses.
“Which years did you find easiest to subtract? Which were more difficult? Why?” (Subtracting a year without decomposing any units was easier than subtracting a year that required decomposing.)
Prompt students to check and compare ages found using the standard algorithm and those found using other ways of reasoning.


aligns: no