few_shots: 
Example 1:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
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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: 
Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

Answer: 
No. Though this task involves addition, it does not involve any word problems.

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 and division and of fractions to multiply and divide rational numbers.

Answer: 
Yes. This problem involves understanding fractions and division to divide rational numbers, such as 1, -4, 4, and -1. This problem also involves an understanding of multiplication: if p and q are integers, then -(p/q) = (-p)/q = p/(-q).

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?

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fl_problem_001097_pos_0

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HS_0
standard_description: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
problem_activity: Narrative
The purpose of this activity is for students to solve two-step word problems using all four operations. Students should be encouraged to solve the problem first or write the equation first, depending on their preference. Encourage students to use parentheses if needed to show what is being done first in their equations.
When students make sense of situations to solve two-step problems they reason abstractly and quantitatively (MP2).
MLR5 Co-Craft Questions.
Keep books or devices closed. Display only the problem stem, without revealing the question. Give students 2–3 minutes to write a list of mathematical questions that could be asked about this situation, before comparing their questions with a partner. Invite each group to contribute one written question to a whole-class display. Ask the class to make comparisons among the shared questions and their own. Reveal the intended questions for this task and invite additional connections.
Advances: Reading, Writing
Engagement: Develop Effort and Persistence.
Some students may benefit from feedback that emphasizes effort and time on task. For example, check in and give feedback after each party planning problem.
Supports accessibility for: Attention
Required Materials
Materials to Gather
Base-ten blocks
Materials to Copy
Centimeter Grid Paper - Standard
Launch
Groups of 2
Give students access to grid paper and base-ten blocks.
Activity
“Work independently to solve these problems and write an equation with a letter for the unknown quantity to represent each situation. You can choose to solve the problem first or write the equation first.”
5–7 minutes: independent work time
“Share your solutions and your equations with your partner. Also, tell your partner if you think their solutions and equations make sense or why not.”
5–7 minutes: partner discussion
Student Facing
For each problem:
a. Write an equation to represent the situation. Use a letter for the unknown quantity.
b. Solve the problem. Explain or show your reasoning.
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Kiran is making paper rings each day to decorate for a party. From Monday to Thursday he was able to complete 156 rings. Friday, Kiran and 2 friends worked on making more rings. Each of them made 9 more rings. How many rings did they make over the week?
Mai has 168 muffins. She put 104 of the muffins in a basket. She packed the rest of the muffins into 8 boxes with the same number of muffins. How many muffins were in each box?
There are 184 cups on a table. Three tables with 8 people at each table come up to get drinks and each use a cup. How many cups are on the table now?
Student Response
Teachers with a valid work email address can
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for free access to Student Response.
Advancing Student Thinking
If students don't write a single equation to represent both steps of the problem, consider asking:
“What equations did you write for each part of the problem?”
“How could you combine your equations into one equation that would represent the problem?”
Activity Synthesis
For each problem have a student share their equation and discuss how it represents the problem.
Consider asking:
“Where do we see ______ from the problem in the equation?”
“What information from the situation did we need to solve and write our equation?”
“How are parentheses used in the equation?”


aligns: no