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: 
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 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_neg_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
problem_activity: Narrative
In the second round of analysis and design, students use their knowledge of operations and expressions to complete a Which One Doesn’t Belong set with two missing items. Students first study the attributes of the given items. They articulate why the items all belong to a set and why each one has a reason not to belong. Next, they propose a new item that shares a feature with others in the set but also has a unique feature that excludes it from the set.
Launch
Groups of 2
5 minutes: independent work time
Activity
“Work with your partner to make sure each new item added to the set has a reason to belong and not to belong.”
5 minutes: partner work time
Student Facing
Here is an incomplete Which One Doesn’t Belong set. It has two missing items.
[IMG]
Find at least one reason that the first two items, A and B, belong in the set.
Add two items to complete the set. Make sure there is at least one reason that each new item belongs and at least one reason it doesn’t belong.
C and D both belong because . . .
C doesn't belong because . . .
D doesn't belong because . . .
After you’ve completed the set, check items A and B. Does each one still have a reason not to belong? If not, adjust your new items so that A and B are each still unique in some way.
Student Response
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Activity Synthesis
Invite students to share their analyses and new items.
“Why do both A and B belong to the set?”
“What were some features of the expressions that you looked at or experimented with to complete your set?” (The kind of numbers used, how many numbers are used, the order of the numbers, the symbols, the value of the expression.)
If no students considered the value of the expression, ask them about it.
“After adding C and D, did A and B still have a reason not to belong in your set? Did you have to revise your items?”


aligns: no