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 learn stage 3 of the Capture Squares center. Capture Squares was introduced in grade 1. In this stage, students spin to get a number (6
–
10) and flip a card (0
–
10) and find the value of the sum. The spinner includes a wild space where students can choose their own number. They find the value of the sum on the game board and connect 2 dots that are adjacent to the number. If that line closes the square, they capture it and shade it in their color. The player to shade in 3 squares first is the winner.
Required Materials
Materials to Gather
Colored pencils or crayons
Number cards 0–10
Paper clips
Materials to Copy
Capture Squares Stage 3 Gameboard
Capture Squares Stage 3 Spinner
Launch
Groups of 2
Give each pair of students a copy of the game board, the spinner and a paper clip, a set of cards, and access to crayons or colored pencils.
“We are going to play a game.”
Spin the spinner and draw a card.
“How could I find the value of the sum of these two numbers?”
30 seconds: quiet think time
1 minute: partner discussion
Share responses.
Use a suggested method or select a volunteer to show how to find the value.
“Now, I find the square that has the value of my sum. I draw a line connecting two dots on that square.”
“If the spinner lands on the wild space, you can pick any number to be one of your addends.”
Repeat 1–2 more times, as needed.
“If I draw the line that completes the square, I shade in that square with my color. The first player to shade in 3 squares is the winner.”
Activity
12 minutes: partner work time
Monitor for a variety of student strategies to share in the synthesis.
Activity Synthesis
Invite selected students to share their strategies.
“When the spinner landed on the wild spot, how did you decide what number to pick?”


aligns: yes