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: Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. (This standard is limited to problems posed with whole numbers and having whole number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations).)
problem_activity: Narrative
The purpose of this activity is for students to write a question that could be answered by given mathematical work and that would make sense in the given situation. When students interpret given student work in terms of the supplied information and decide what question the work might answer, they identify important quantities and their relationships in context (MP4).
MLR8 Discussion Supports.
Prior to solving the problem, invite students to make sense of the situation and take turns sharing their understanding with their partner. Listen for and clarify any questions about the context.
Advances: Reading, Representing
Launch
Groups of 2
“Clare and Tyler took a break at the lemonade stand. Here’s what it might look like.”
Display the image.
“What do you notice? What do you wonder?” (Students may notice: The stand is close to the carnival. There are lemons hanging in baskets. Students may wonder: How much lemonade do they make each day? What size can you buy? How much does the lemonade cost?)
1 minute: quiet think time
Share and record responses.
Activity
Read the information about the lemonade stand as a class.
“What mathematical questions could we ask about this situation?”
1–2 minutes: partner discussion
Share and record responses.
“Now, look at the mathematical work in each problem. Work with your partner to write a question that could be answered by that work.”
5–7 minutes: partner work time
Monitor for groups that accurately write questions that the work could represent.
Student Facing
A lemonade stand at the fair makes 132 liters of lemonade a day. When Clare and Tyler stopped by the stand, there were 90 liters left.
At the end of the day, there were 56 liters of lemonade left, which the vendor put on sale in 4-liter jugs.
[IMG]
Use the information about the lemonade stand to write a question that could be answered with the mathematical work shown.
\(132 - 90 = 42\)
Question:
[IMG]
Question:
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Advancing Student Thinking
If students don’t write a question that could be solved with the given work, consider asking:
“What numbers from the work do you see in the information about the lemonade stand?”
“What would the work represent in the lemonade stand situation? What question would lead up to this work?”
Activity Synthesis
For each problem, invite a group to read the question they wrote.
Ask the class:
“How does their question make sense with this mathematical work and what we know about the situation?”
Consider asking:
“What did you like about writing the questions to match the mathematical work?”
“What was challenging about writing the questions to match the mathematical work?”


aligns: no