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: Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length).
problem_activity: Narrative
The purpose of this activity is for students to play Stage 4 in the Shake and Spill center, which was introduced in an earlier unit. This activity supports students in finding the missing part of an equation in a later activity.
Students use 3, 4, or 5 counters. They see some of the counters and determine how many more counters are under the cup. Students write an expression to represent each composition and decomposition.
Representation: Access for Perception.
Synthesis: Use a cup and two-color counters to demonstrate that there is 1 yellow counter hiding under the cup.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing
Required Materials
Materials to Gather
Cups
Two-color counters
Materials to Copy
Shake and Spill Stage 4 Recording Sheet Kindergarten
Launch
Groups of 2
Give each group of students a cup, 5 two-color counters, and two recording sheets.
“We are going to play Shake and Spill, Cover.”
If needed, review and demonstrate the steps of the center.
“Take turns with your partner spilling and covering the yellow counters. On each turn you can decide to use 3, 4, or 5 counters. Make sure you and your partner agree on how many total counters you are using before you shake, spill, cover, and record.”
Activity
8 minutes: partner work time
Student Facing
Put 3, 4, or 5 counters in the cup.
Shake and spill the counters.
Hide some of the counters under the cup.
Figure out how many of the counters are hidden.
Write an expression.
Student Response
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Activity Synthesis
Display the number 3 and the expression
\(2 + \underline{\hspace{1 cm}}\)
.
“Han and Mai spilled 3 counters and hid the yellow ones. This is what they wrote on the recording sheet. What is missing from the expression? How do you know?” (1 is missing. 2 and 1 are the parts that go together to make 3. If they can see 2 red counters, 1 yellow counter is hiding under the cup.)


aligns: no