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: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
problem_activity: Warm-up
By now students have written many division equations based on verbal descriptions of situations. This warm-up prompts them to go in the other direction: to interpret a division expression and write a fitting question the expression could help answer. Then, they trade descriptions with a partner and reason about the value of the same expression in someone else’s story.
As students write their descriptions, look out for scenarios that are unclear and ask their authors clarifying questions. Select 2–3 students whose descriptions clearly match the expression to share later.
Students may struggle to answer their partner’s question because the descriptions are confusing or do not match the given expression. Encourage them to ask the questions they have about the description, but still try to find the answer to the given expression.
Launch
Arrange students in groups of 2. Explain to students the two halves of this activity: to write a situation and a question that can be represented by the equation
\(12 \div \frac23 = ?\)
, and to trade papers with their partner and find the answer to their partner’s question.
Give 2 minutes of quiet think time for the first question, another minute for the second question, and follow with a whole-class discussion.
Student Facing
Think of a situation with a question that can be represented by the equation
\(12 \div \frac23 = \,?\)
Describe the situation and the question.
Trade descriptions with your partner, and answer your partner’s question.
Student Response
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Anticipated Misconceptions
Some students may struggle writing a context. Ask them to reflect on the work they have done and what the division expression means for them, or suggest that they write related multiplication expressions to help them understand the division expression.
Activity Synthesis
Ask selected students to share their stories with the whole group. After each student shares, have another student explain how the story matches the division equation. Afterward, ask these and other students for the value of the given expression, and write and display the completed division equation for all to see.
If not already mentioned by students, highlight that the answer is the same for all scenarios because they are all based on the same division expression.


aligns: yes