few_shots: 
Example 1:
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.

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.


Answer: 
Yes. This task involves representing addition with objects such as number cards and dice.

Example 2:
Concept/skill: 
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

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
$$-\frac{1}{4}$$


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:
Concept/skill: 
Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Problem/activity:
Find the general solution for:
$${\mathrm{cos}\left({\pi\over2}+x\right)=\mathrm{tan}{\pi\over4}}$$


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, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: im_task_001477_pos_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
problem_activity: Narrative
The purpose of this activity is for students to answer questions about the data represented by their picture graphs and bar graphs. Students switch workbooks with a new partner, which is an opportunity for students to view each other’s work and see different representations of data. While students are answering questions based on different graphs, identify the questions that are harder for students to answer. These questions can be discussed in the lesson synthesis. In upcoming lessons, students will have more opportunities to work with questions that require comparing categories.
Representation: Internalize Comprehension.
Synthesis: Invite students to identify which details were important or most useful to pay attention to. Display the sentence frame, “The next time I answer questions about a graph, I will . . . .“
Supports accessibility for: Conceptual Processing, Memory
Required Materials
Materials to Gather
Materials from a previous lesson
Required Preparation
Each student needs the picture graph and bar graph they created in the previous lesson.
Launch
Groups of 2: different partner than previous activity
“Tear out the page in your books labeled ‘Answering Questions Using Graphs.’”
Activity
“Now you are going to answer questions a different partner has written about their graphs.”
“Write your name and your partner’s name on the top of the page.”
“Trade graphs and questions with your partner. Answer each of the questions your partner wrote.”
6 minutes: independent work time
“Discuss the questions and answers with your partner to see if you agree.”
6 minutes: partner discussion
Monitor for students who mention the graph features like the title or labels when answering, "How did you know where to find the answer to each question?"
Student Facing
Answer your partner’s questions from Activity 1 using the graphs.
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
How did you know where to find the answer to each question?
\(\underline{\hspace{25 cm}}\)
\(\underline{\hspace{25 cm}}\)
Student Response
Teachers with a valid work email address can
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Activity Synthesis
Select 2
–
3 identified students to share a question they answered and how they knew where to find the answer.


aligns: no