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 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_neg_0

HS_0
standard_description: Use place value understanding to round decimals to any place.
problem_activity: Narrative
The purpose of this activity is for students to write equivalent expressions in order to find the volume of a figure composed of two right rectangular prisms. Students decompose the figure in two different ways, and write matching expressions to find the volume. For extra support, provide students with colored pencils to shade the two parts of the prism before finding the side lengths they need to calculate the volume.
Monitor and select a student with each of the following strategies to share in the synthesis:
decomposed the figure into a prism with the side lengths 4 ft by 4 ft by 3 ft and a prism with the side lengths 10 ft by 4 ft by 3 ft and wrote this expression (or one written in a different order) to represent the volume:
\((4 \times 4 \times 3) + (10 \times 4 \times 3)\)
decomposed the figure into a prism with the side lengths 4 ft by 8 ft by 3 ft and a prism with the side lengths 6 ft by 4 ft by 3 ft and wrote this expression (or one written in a different order) to represent the volume:
\((4 \times 8 \times 3) + (6 \times 4 \times 3)\)
Action and Expression: Internalize Executive Functions.
Invite students to plan a strategy, including the tools they will use, for finding the volume of the figures. If time allows, invite students to share their plan with a partner before they begin.
Supports accessibility for: Organization, Memory, Attention
Launch
Groups of 2
Activity
10 minutes: individual work time
5 minutes: partner discussion
As students work, consider asking, “Why did you choose to decompose the prism that way?”
Student Facing
Find the volume of the figure by decomposing the figure 2 different ways. Show your thinking. Organize it so it can be followed by others.
[IMG]
[IMG]
For each way you decomposed the figure, write an expression that represents the volume.
Mai used this expression to find the volume of the figure:
\((10 \times 8 \times 3) - (6 \times 4 \times 3)\)
.
Use the diagram to interpret Mai's expression. Show your thinking. Organize it so it can be followed by others.
[IMG]
Student Response
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Activity Synthesis
Ask the two selected students to display their work side by side for all to see.
“How are the diagrams the same? How are they different?”
“How do the expressions relate to the diagrams?”
Display:
\((10 \times 8 \times 3) - (6 \times 4 \times 3)\)
“How does this expression represent the volume of the prism?” (The larger rectangular prism has the side lengths
\(10 \times 8 \times 3\)
cubic feet. We can subtract a rectangular prism with the side lengths
\(6 \times 4 \times 3\)
cubic feet.)
“What is the value of
\((10 \times 8 \times 3) - (6 \times 4 \times 3)\)
?” (168)


aligns: no