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 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?

shot_info: im_task_001477_pos_0

K

fl_problem_001097_pos_0

7

fl_problem_001894_pos_0

HS_0
standard_description: Count forward beginning from a given number within the known sequence (instead of having to begin at 1).
problem_activity: Narrative
The purpose of this activity is for students to count their collection in a way that makes sense to them.  Students are invited to represent how many objects are in their collection. Some students may choose to create a drawing, make a group with the same number of objects, or just demonstrate how they counted. Students will focus more on creating written representations of how many in a later unit. Monitor and select students with the following strategies to share in the synthesis:
demonstrate or explain how they counted
take out the same number of objects
draw a picture
Students are provided with a counting mat and 5-frames to help them accurately count or organize their collections. Students use appropriate tools strategically as they choose which tools help them count their collections (MP5).
Action and Expression: Internalize Executive Functions.
Invite students to plan a strategy, including what drawings, numbers, words, or objects they will use, to show how they counted their collection.
Supports accessibility for: Conceptual Processing, Organization
Required Materials
Materials to Gather
5-frames
Collections of objects
Counting mats
Launch
Groups of 2
“Today you’re going to count another collection of objects. During Questions About Us, we showed how many of us are here today. As you’re counting your collection, think about how you can show how you counted your collection.”
Activity
Give each student a bag of objects. Give students access to 5-frames and a counting mat.
“Figure out how many objects are in your collection."
2 minutes: independent work time
“Switch collections with a partner. Figure out how many objects are in your new collection.”
2 minutes: independent work time
“Tell your partner how many objects are in your collection. Show them how you counted the objects.”
30 seconds: quiet think time
2 minutes: partner discussion
“Show how you counted your collection. Show your thinking using objects, drawings, numbers, or words.”
2 minutes: independent work time
Monitor for students who use the strategies in the synthesis to represent how they counted.
Student Facing
Show how many objects are in your collection.
Student Response
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Advancing Student Thinking
If students have difficulty representing their count on paper, consider having them explain how they counted verbally. Students can also be provided stickers that they can put on their paper to represent each object in place of a drawing.
Activity Synthesis
Ask selected students to share in the order listed in the activity narrative.
“What is the same about how they each counted their collections?” (They all counted each object 1 time.)
“What is different about how they each showed how they counted?” (Some people drew a picture and some used objects.)
After each student shares, write or display the number and say, “There are _____ objects in their collection.”


aligns: no