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 to multiply a fraction or whole number by a fraction.

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

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

K

fl_problem_001097_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
problem_activity: Warm-up
This prompt gives students opportunities to see and make use of structure (MP7). The specific structures they might notice is the table and how it relates to a linear relationship between
\(x\)
and
\(y\)
(specifically, that
\(y = 3x + 6\)
).
Monitor for students who:
describe patterns only vertically or only in terms of
\(x\)
or
\(y\)
(e.g., “it” or “
\(y\)
” goes up by 3, “it” starts at 6)
describe
\(y\)
in terms of
\(x\)
describe a relationship between
\(x\)
and
\(y\)
, such as
\(y\)
goes up 3 every time
\(x\)
goes up 1
notice the linear relationship
attempt to identify the missing value in the table
Launch
Tell students that their job is to think of at least one thing they notice and at least one thing they wonder. Display the table for all to see. Give students 1 minute of quiet think time and then 1 minute to discuss the things they notice with their partner, followed by a whole-class discussion.
Student Facing
What do you notice? What do you wonder?
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "col"}, "span": [{"_attributes": {"class": ["math"], "data-png-file-id": "50"}, "_value": "\\(x\\)"}]}, {"_attributes": {"scope": "col"}, "span": [{"_attributes": {"class": ["math"], "data-png-file-id": "29"}, "_value": "\\(y\\)"}]}]}]}], "tbody": [{"tr": [{"td": [{"_value": "0"}, {"_value": "6"}]}, {"td": [{"_value": "1"}, {"_value": "9"}]}, {"td": [{"_value": "2"}, {"_value": "12"}]}, {"td": [{"_value": "4"}, {"_value": "18"}]}, {"td": [{"_value": "10"}, {"_value": "36"}]}, {"td": [{"_value": "100"}, {}]}]}]}]}
Student Response
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Activity Synthesis
Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the image. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information. If the relationship between the table and an equation does not come up during the conversation, ask students to discuss how they can come up with the missing value. It is not necessary to generate an equation like
\(y=3x+6\)
at this time.


aligns: no