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:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Concept/skill: 
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
 Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.

Answer: 
No. Completing this task does not involve representing fractions on a number line diagram.

Example 3:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Concept/skill: 
Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.

Answer: 
No. This set of problems does not directly involve adding or subtracting multi-digit whole numbers. Instead, it focuses on multiplying multi-digit whole numbers.

Now, does the following problem or activity enable students to learn the full intent of the following concept or skill?

shot_info: im_task_001477_pos_0

K

im_task_000157_neg_0

3

fl_problem_000674_neg_0

5
standard_description: Distinguish between correlation and causation.
problem_activity: Optional activity
Since this activity is mainly included for practice and may take some additional time to complete, it is included as an optional task and including it is up to the teacher’s discretion.
In this activity, students practice doing many trials of multi-step situations to estimate the probability of an event. In the discussion following the activity, students construct arguments (MP3) about how changes to the game might affect the probability of winning.
Launch
Arrange students in groups of 3. Provide each group with a paper bag containing 2 black blocks and 2 white blocks inside. If black and white blocks are not available, instruct students on their color equivalents. Give students 5 minutes to run the simulation, 5 minutes for partner discussion, then have a whole-class discussion.
Action and Expression: Internalize Executive Functions.
Provide students with a graphic organizer for recording their results and calculations of probability of winning Kiran’s game.
Supports accessibility for: Language; Organization
Student Facing
Kiran invents a game that uses a board with alternating black and white squares. A playing piece starts on a white square and must advance 4 squares to the other side of the board within 5 turns to win the game.
[IMG]
For each turn, the player draws a block from a bag containing 2 black blocks and 2 white blocks. If the block color matches the color of the next square on the board, the playing piece moves onto it. If it does not match, the playing piece stays on its current square.
Take turns playing the game until each person in your group has played the game twice.
Use the results from all the games your group played to estimate the probability of winning Kiran’s game.
Do you think your estimate of the probability of winning is a good estimate? How could it be improved?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Student Facing
Are you ready for more?
How would each of these changes, on its own, affect the probability of winning the game?
Change the rules so that the playing piece must move 7 spaces within 8 moves.
Change the board so that all the spaces are black.
Change the blocks in the bag to 3 black blocks and 1 white block.
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Extension Student Response.
Activity Synthesis
The purpose of the discussion is for students to think about how changing the rules of the game might change the probability of winning.
Collect the data from the class for the number of wins and display the results for all to see.
Consider asking these discussion questions:
“Based on the class’s data, estimate the probability of winning the game.” (The theoretical probability of winning is
\(\frac{3}{16} \approx 0.19\)
.)
“Does the game seem too easy or hard to win? If so, how could Kiran change the game slightly to make it harder or easier?” (If it is too hard, move the pawn closer to the end or allow more than 5 moves to win.)
“The bag contained 2 black and 2 white blocks. If the bag had 4 blocks of each color, would that make it easier or harder to win?” (Neither. It would be the same difficulty since there is still an equal chance to get each color.)
“Do you think the estimate from the class’s data is a better estimate than the one you got on your own?” (Since there is more data from the entire class, it should be a better estimate than one individual’s.)
Reading, Writing, Speaking: MLR3 Clarify, Critique, Correct.
Before students share their estimated probability of winning Kiran’s game, present an incorrect solution based on a misconception that arises when conducting a few trial simulations. For example: “The probability of winning Kiran’s game is zero because nobody in our group won in all of the six games played.” Ask students to identify the error, critique the reasoning, and revise the original statement. As students discuss in partners, listen for students who state that estimating the probability of winning based on only six trials will not result in an accurate estimate. Therefore, more trials must be conducted in order to improve the estimate of the probability of winning. This routine will engage students in meta-awareness as they critique and correct the language used to estimate the probability of winning a game.
Design Principles(s): Cultivate conversation; Maximize meta-awareness


aligns: no