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: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
problem_activity: Narrative
The purpose of this activity is for students to make sense of an Add To, Change Unknown story problem and identify the answer within an equation. Students are presented with a drawn representation and an equation to interpret. Students consider what each number in the equation means in relation to the story problem and drawn representation (MP2). They determine that the written equation is incorrect, and explain why using their own thinking. When students practice explaining their thinking, they begin to develop and refine their mathematical communication skills, and attend to precision (MP6). Students identify that even though Mai's equation has the correct numbers she identified the wrong number as the solution to the problem (MP3).
Students keep their books closed for the launch of the activity, as the teacher displays and reads the problem.
Action and Expression: Internalize Executive Functions.
Invite students to plan a method, including the tools they will use, for solving the rest of the story problems. If time allows, invite students to share their plan with a partner before they begin.
Supports accessibility for: Attention, Organization
Required Materials
Materials to Gather
10-frames
Connecting cubes or two-color counters
Launch
Groups of 2
Give students access to 10-frames and connecting cubes or two-color counters.
"I am going to read another story problem. Think about what you notice and wonder about the problem as I read aloud."
Display and read the problem with missing information.
30 seconds: quiet think time
Share and record answers.
Activity
"Now we will get more information and see how Lin solved the problem."
Read the problem aloud.
"Look at Lin's drawing and her equation. Think about how she solved the problem."
1 minute: quiet think time
“Share your thinking with your partner. Then show whether or not you think Lin's equation is correct.”
4 minutes: partner work time
Student Facing
Andre checked out some books from the library.
Mai gives him more books.
Now he has 9 books.
What do you notice?
What do you wonder?
Andre checked out 3 books from the library.
Mai gives him some more books.
Now he has 9 books.
How many books did Mai give him?
Lin made this drawing.
[IMG]
She wrote the equation
\(3 + 6 = \boxed{9}\)
Is her equation correct?
Show your thinking using drawings, number, or words.
Student Response
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Activity Synthesis
“How does Lin’s drawing show the story problem?” (She shows the three books Andre starts with, and the six books she needs to get to nine.)
"Does Lin's equation match the story? Why or why not?" (No. The answer to the problem is how many books Mai gives Andre. That answer is 6, so the equation should be
\(3 + \boxed{6} = 9\)
.)
If needed ask, “How does this equation match the story problem?” (Andre has three books. Mai gives him six, which is the answer, so that he has nine total.)


aligns: no