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

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fl_problem_001097_neg_0

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fl_problem_001894_pos_0

HS_0
standard_description: Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
problem_activity: Narrative
The purpose of this lesson is for students to solve a Put Together/Take Apart, Both Addends Unknown story problem in the context of putting together pattern blocks (MP2). If students finish early, invite them to find multiple solutions to the story problem.
MLR8 Discussion Supports.
Synthesis: For each decomposition that is shared, invite students to turn to a partner and restate the recorded equation.
Advances: Listening, Speaking
Required Materials
Materials to Gather
10-frames
Connecting cubes or two-color counters
Pattern blocks
Launch
Groups of 2
Give students access to connecting cubes or two-color counters, 10-frames, and pattern blocks.
Read and display the task statement.
“Tell your partner what happened in the story.”
30 seconds: quiet think time
1 minute: partner discussion
Monitor for students who accurately retell the story. Choose at least one student to share with the class.
Reread the task statement.
“Show your thinking using drawings, numbers, words, or objects.”
Activity
2 minutes: independent work time
2 minutes: partner discussion
“If you haven’t already, write an expression to show how many square pattern blocks and triangle pattern blocks Diego used.”
2 minutes: independent work time
Student Facing
Diego built a shape with 10 pattern blocks.
He only used squares and triangles.
How many square pattern blocks did Diego use?
Then how many triangle pattern blocks did Diego use?
Expression: _________________________________
Student Response
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Activity Synthesis
Invite students who found different decompositions of 10 to share.
As students share, record each solution with an equation, such as
\(10 = 7 + 3\)
.
“Did _____ and _____ both show what happened in the story? How do you know?” (Yes. They both have 10 pattern blocks, with some triangles and some squares.)
“In the next activity, we will find more ways that we can make shapes with 10 pattern blocks.”


aligns: no