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

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fl_problem_001097_neg_0

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fl_problem_001894_neg_0

HS_0
standard_description: Recognize and represent proportional relationships between quantities.
problem_activity: Activity
In this activity, students get a chance to practice applying their skills in representing situations symbolically, and finding and interpreting solutions.
The structure of a row game supports students to check their thinking because their partners should get the same answer to different questions. When students’ answers disagree, they must make sense of each other’s questions and thinking to figure out whose answer is correct.
The practice prepares students to solve equations and solve for one variable in terms of another in their Algebra 1 lessons.
Monitor for students:
calculating some specific values before generating an equation
analyzing the quantities and relationships in the text
looking for and using mathematical structures, such as
\(ax + by\)
or
\(mx + b\)
Launch
Students will work independently to complete their designated column, and will work with their partners in the event that an answer is different from what their partners got.
Student Facing
Partner A completes only column A, and partner B completes only column B. Your answers for each problem should match. Work on one problem at a time, and check whether your answer matches your partner’s before moving on. If you don’t get the same answer, work together to find your mistake.
Column A:
Lin’s teacher has a daughter that is
\(\frac13\)
of his age. Write an expression to represent the daughter’s age. Let
\(z\)
represent the teacher’s age, in years.
Han wants to save
$
40. He hasn’t met his goal yet. Write an expression to represent how far Han is from his goal, in dollars. Let
\(q\)
represent the amount of money, in dollars, he’s saved so far.
Priya has some money to spend at a fair. It costs
$
6 to get in and
$
0.50 per ride ticket. Write an expression to represent how much Priya spends at the fair, in dollars. Let
\(x\)
represent the number of ride tickets Priya buys.
Diego is inviting some friends over to watch movies. He is buying popcorn and peanuts. Popcorn costs 6 cents per ounce and peanuts cost 17 cents per ounce. Write an expression to represent the total cost of peanuts and popcorn, in cents. Let
\(j\)
represent how many ounces of popcorn Diego buys and
\(k\)
represent how many ounces of peanuts he buys.
Column B:
Jada leaves the beach with some seashells. One out of every three of the shells turns out to contain a hermit crab. Write an expression to represent the number of hermit crabs Jada found. Let
\(z\)
represent the total number of seashells she collected.
Tyler started the school year with 40 pencils, but he’s lost some. Write an expression to represent how many pencils Tyler has left. Let
\(q\)
represent the number of pencils he’s lost so far.
When Clare bought her plant, it was 6 inches tall. Each week, it’s been growing
\(\frac12\)
of an inch. Write an expression to represent how tall Clare’s plant is, in inches. Let
\(x\)
represent the number of weeks since Clare bought her plant.
Mai is packing care packages. She is putting in boxes of granola bars that weigh 6 ounces each and paperback books that weigh 17 ounces each. Write an expression to represent the total weight of a care package, in ounces. Let
\(j\)
represent the number of boxes of granola bars and
\(k\)
represent the number of books.
Student Response
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Activity Synthesis
The goal of this discussion is for students to name and clarify strategies they have for writing algebraic expressions to describe given situations.
Strategies students might have include:
calculating some specific values before generating an expression
analyzing the quantities and relationships in the text
looking for and using mathematical structures, such as
\(ax + by\)
or
\(mx + b\)
Call on previously identified students to share their strategies for writing expressions, and support students to share insights or tips that will help other students. Possible questions for discussion include:
Why did you do calculations with some specific numbers first? How did that help you?
How did you record your calculations? What patterns did you notice?
When you read the situation, how many times did you read it?
What did you notice the first time you read the situation?
What did you notice when you looked at it again?
How did you decide what operations to use in your expression?
What made you think that your final expression would look like
\(mx + b\)
(or whatever structure is appropriate)?


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