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: 
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 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, assess whether the following problem or activity is 'aligned' with the given Common Core standard in Mathematics.

shot_info: im_task_001477_neg_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_neg_0

HS_0
standard_description: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
problem_activity: Activity
This activity is an opportunity to put together the learning of the past several lessons: correspondences between tape diagrams, equations, and stories, and using representations to reason about a solution. The focus of this activity is still contrasting the two main types of equations that students encounter in this unit.
Launch
Keep students in the same groups. 5 minutes of quiet work time followed by sharing with a partner and a whole-class discussion.
Representation: Internalize Comprehension.
Provide appropriate reading accommodations and supports to ensure students access to written directions, word problems, and other text-based content.
Supports accessibility for: Language; Conceptual processing
Reading, Representing: MLR6 Three Reads.
Use this routine with the first story to support students’ understanding of the situation and how to represent it with a tape diagram or equation. Use the first read to orient students to the situation (Lin and volunteers are hanging flyers at school). Use the second read to identify the important quantities (number of volunteers, number of flyers each). After the third read, ask students to brainstorm how the situation can be represented in a tape diagram or equation. This will help students make connections between equations and diagrams and understand the language of a situation that will distinguish which form of and equation would be an appropriate representation.
Design Principle(s): Support sense-making; Maximize meta-awareness
Student Facing
[IMG]
Story 1: Lin had 90 flyers to hang up around the school. She gave 12 flyers to each of three volunteers. Then she took the remaining flyers and divided them up equally between the three volunteers.
Story 2: Lin had 90 flyers to hang up around the school. After giving the same number of flyers to each of three volunteers, she had 12 left to hang up by herself.
Which diagram goes with which story? Be prepared to explain your reasoning.
In each diagram, what part of the story does the variable represent?
Write an equation corresponding to each story. If you get stuck, use the diagram.
Find the value of the variable in the story.
Student Response
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Student Facing
Are you ready for more?
A tutor is starting a business. In the first year, they start with 5 clients and charge $10 per week for an hour of tutoring with each client. For each year following, they double the number of clients and the number of hours each week. Each new client will be charged 150% of the charges of the clients from the previous year.
Organize the weekly earnings for each year in a table.
Assuming a full-time week is 40 hours per week, how many years will it take to reach full time and how many new clients will be taken on that year?
After reaching full time, what is the tutor’s annual salary if they take 2 weeks of vacation?
Is there another business model you’d recommend for the tutor? Explain your reasoning.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
For each story, select 1 or more groups to present the matching diagram, their equation, and their solution method. Possible questions to ask:
“How were the diagrams alike? How were they different?” (They have the same numbers and a letter. One has 3 equal groups and an extra bit, the other just has 3 equal groups, but each group is a sum.)
“How were the stories alike? How were they different?” (They were both about distributing 90 flyers. In one story, Lin makes a series of moves to each volunteer. In the other story, she gives each volunteer the same amount, but then there are some left over.)
“What parts of the story made you think that one diagram represented it?”
“Explain how you reasoned about the story, diagram, or equation to find the value of the variable.”


aligns: no