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: Fluently add and subtract within 5.
problem_activity: Narrative
The purpose of this activity is for students to compose and decompose 10 using objects, images, and equations. Students work with equations with the total before and after the equal sign.
MLR8 Discussion Supports.
Synthesis: For each question, invite students to turn to a partner and share their response. This gives all students an opportunity to produce language.
Advances: Listening, Speaking
Required Materials
Materials to Gather
Materials from a previous activity
Required Preparation
Each student needs the bead tool that they created in the previous activity.
Launch
Groups of 2
“We can use the bead tool we made to show different ways to make and break apart 10. Show your partner one way that you can break apart 10 into 2 groups.”
“Take turns playing with your partner. Use your beads to show each equation. When your partner shows you their beads, tell them the equation to make 10 and draw a picture to show what the beads look like.”
Activity
4 minutes: partner work time
“Fill in each equation to match the pictures of beads. You can use your bead tool if it’s helpful."
3 minutes: independent work time
Student Facing
\(7 + 3 = 10\)
\(10 = 4 + 6\)
\(9 + 1 = 10\)
\(10 = 2 + 8 \)
\(\underline{\hspace{1 cm}} + \underline{\hspace{1 cm}} = 10\)
[IMG]
\(10 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}\)
[IMG]
\(\underline{\hspace{1 cm}} + \underline{\hspace{1 cm}} = 10\)
[IMG]
\(\underline{\hspace{1 cm}} + \underline{\hspace{1 cm}} = 10\)
[IMG]
Student Response
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Activity Synthesis
Display
\(2 + 8 = 10\)
.
Invite a student to demonstrate
\(2 + 8 = 10\)
with their beads.
“What 2 parts do you see? What total do you see?” (2 and 8, 10)
“How will the beads look different if we show
\(10 = 2 + 8\)
?" (The beads will look the same. There are still 10. 2 and 8 are still the parts.)


aligns: no