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: 
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?

shot_info: im_task_001477_pos_0

K

fl_problem_001097_neg_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Fluently add and subtract within 20 using mental strategies. (See standard 1.OA.6 for a list of mental strategies.) By end of Grade 2, know from memory all sums of two one-digit numbers.
problem_activity: Narrative
The purpose of this activity is for students to compare different methods for solving problems within 100 using data presented in a bar graph. Students may use whatever method makes the most sense to them. The synthesis focuses on sharing multiple methods that students use to find the difference. Monitor for students who use methods that rely on using the bar graph to count on or count back and those that use more abstract methods, such as adding or subtracting by place value.
For example, when combining categories, some students may choose to use the graph to count on. Other students may choose to combine tens and ones with or without drawing a base-ten diagram or other representation.
Engagement: Provide Access by Recruiting Interest.
Provide choice. Invite students to choose a strategy and tool that works for them. Encourage students to use that same strategy and tool for both problems so they are not overwhelmed.
Supports accessibility for: Conceptual Processing, Organization, Attention
Required Materials
Materials to Gather
Connecting cubes in towers of 10 and singles
Required Preparation
Create towers of 10 with the connecting cubes.
Have single connecting cubes available.
Launch
Groups of 2
Display the bar graph.
“What does this graph tell us?” (students’ favorite movie snacks, students picked their favorite movie snacks)
1 minute: quiet think time
1 minuter: partner discussion
Share responses.
Give students access to connecting cubes in towers of ten and singles.
Activity
“Use the bar graph to answer the questions. Show your thinking using drawings, numbers, or words.”
“You can use the connecting cubes or any of the other representations we saw in the warm-up to help you.”
8 minutes: independent work time
“Now compare your methods with your partner. How are they similar or different?”
4 minutes: partner discussion
As students work, monitor for students who:
use the bar graph to count on or count back
use the connecting cubes or base-ten drawings to show adding or subtracting tens with tens and ones with ones
Student Facing
Use the bar graph to answer the questions.
[IMG]
What is the total number of students that chose popcorn or pretzels? Show your thinking.
How many more students chose nachos than chose popcorn? Show your thinking.
[IMG]
Student Response
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Activity Synthesis
Invite previously identified students to share the method they used to find how many more students chose nachos than chose popcorn.
As needed, record student methods using equations.
Consider asking:
“How are these methods the same? How are they different?”
“How does the method work? Why does each method find the same value?”


aligns: no