## Final Artifact Assessment Overview

Students will create and construct a prototype of an original game for Hasbro that is a board game, card game, or something similar for at least 2 players. The game will come with a printed rule book and a special “Insider’s Guide,” which includes the probability and math behind the game.

## Rubric

## Examples of Strong and Weak Artifacts

A strong artifact for this unit would include all aspects listed on the rubric; incorporating probability and game theory into their game design and using strong testing techniques to improve their game design. An example of strong artifacts include: creative and innovative card games that use traditional 52-card decks or entirely new types of card decks, a board game that depends on dice rolls and strategic path choices, or a game that revolves around dice alone (increasing the probability aspect of the game).

Weak artifacts may include: games that have purely chance-based results with no opportunity for player input or strategy (for example, a game in which you earn points merely from the results of dice rolls, without giving the player a choice as to whether they want to keep a dice roll as-is or re-roll). Generally, sub-par testing methods will also lead to a weak artifact.

Weak artifacts may include: games that have purely chance-based results with no opportunity for player input or strategy (for example, a game in which you earn points merely from the results of dice rolls, without giving the player a choice as to whether they want to keep a dice roll as-is or re-roll). Generally, sub-par testing methods will also lead to a weak artifact.

## Performance Task

In addition to the physical artifact, the design teams will have to do a 10-minute presentation to introduce their original games. In this presentation, students are expected to clearly explain the design of the game, the goal, the rules, and the main concepts of probability the game is based on.

## Formative Assessment: Poker

Overview of the Assessment

This assessment will be administered at the beginning of the work day at the end of the first week of the unit (in our calendar, this will be the first Friday). To learn about students’ learning so far we will revisit the poker activity we did during the launch event. During the launch event a video was shown of the final hand of a poker series. Before each card was dealt students were asked who had the better hand. This time we will play a different video (https://www.youtube.com/watch?v=GAqWhsXZguA) of the final hand of a poker game. Before we start the activity, each student will receive 2 index cards, one that says ‘A’ and one that says ‘B.’ The teacher will write on the board which letter represents which player in the game. Then we will start the video and before each card is dealt the teacher will pause the video ask students to calculate the probability of each player winning. The teacher will ask students to put their head down and raise the index card of the player they think has the higher probability. The teacher will take note of the numbers on the board and call on students to explain.

Target Objectives

This assessment targets the following objectives:

Geometry TEKS

(13) Probability. The student uses the process skills to understand probability in real-world situations and how to apply independence and dependence of events. The student is expected to:

This assessment will be administered at the beginning of the work day at the end of the first week of the unit (in our calendar, this will be the first Friday). To learn about students’ learning so far we will revisit the poker activity we did during the launch event. During the launch event a video was shown of the final hand of a poker series. Before each card was dealt students were asked who had the better hand. This time we will play a different video (https://www.youtube.com/watch?v=GAqWhsXZguA) of the final hand of a poker game. Before we start the activity, each student will receive 2 index cards, one that says ‘A’ and one that says ‘B.’ The teacher will write on the board which letter represents which player in the game. Then we will start the video and before each card is dealt the teacher will pause the video ask students to calculate the probability of each player winning. The teacher will ask students to put their head down and raise the index card of the player they think has the higher probability. The teacher will take note of the numbers on the board and call on students to explain.

Target Objectives

This assessment targets the following objectives:

- Students will be able to calculate the probability of an event given the cards at play
- Students will be able to distinguish between permutation and combinations
- Students will be able to calculate the probability of an event with replacement and an event without replacement and distinguish between the two

Geometry TEKS

(13) Probability. The student uses the process skills to understand probability in real-world situations and how to apply independence and dependence of events. The student is expected to:

- (A) develop strategies to use permutations and combinations to solve contextual problems;
- (C) identify whether two events are independent and compute the probability of the two events
- occurring together with or without replacement;
- (D) apply conditional probability in contextual problems; and
- (E) apply independence in contextual problems.

## Formative Assessment: Bell Ringer

**Overview**

This formative assessment will be administered as a "bell ringer" at the beginning of the second day of the spinner wheel investigation. The assessment is a two-tiered assessment designed to evaluate student understanding of the key concepts of the relationship between the area of a section and the probability of the section.

By using the bell ringer, the teacher will be able to better adjust instruction in order to accommodate students for the next lesson.

**Target Objectives**

- Calculate probability based on area
- Apply the proportional relationship between the measure of the area of a sector of a circle and the area of a circle to solve problems

Alignment with Texas Essential Knowledge and Skills (TEKS)

**Geometry TEKS**

(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

- (B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;
- (F) analyze mathematical relationships to connect and communicate mathematical ideas; and
- (G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

- (C) apply the proportional relationship between the measure of the area of a sector of a circle and the area of the circle to solve problems;

- (B) determine probabilities based on area to solve contextual problems;
- (E) apply independence in contextual problems.

formativeassessment-spinner.pdf | |

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## Formative Assessment: Monty Hall Bell Ringer

Overview

This formative assessment will be administered as a “bell ringer” handout at the very beginning of the Game Theory benchmark lesson. The assessment is a two-tiered assessment designed to ascertain students’ understanding of game theory and optimal strategies, and determine how much they already understand about how certain situations may not have a single optimal strategy.

The students will do a think, pair, share on this bell ringer, first thinking individually on their own and choosing the answer they think is correct, then discussing in pairs what they chose and their reasoning, and receiving peer feedback on their answers, and finally sharing as a class their answers and reasoning, and coming to a conclusion as a class what the correct answer is (for this assessment, the answer is C, since there is an equal chance of gaining or losing the same amount of tickets each time you play the double-or-nothing game, so playing the game a large number of times is essentially the same as not playing at all).

Target Objectives

This assessment target the following objectives:

Alignment with Texas Essential Knowledge and Skills (TEKS)

(6) Game (or competition) theory. The student uses knowledge of basic game theory concepts to calculate optimal strategies. The student analyzes situations and identifies the use of gaming strategies. The student is expected to:

This formative assessment will be administered as a “bell ringer” handout at the very beginning of the Game Theory benchmark lesson. The assessment is a two-tiered assessment designed to ascertain students’ understanding of game theory and optimal strategies, and determine how much they already understand about how certain situations may not have a single optimal strategy.

The students will do a think, pair, share on this bell ringer, first thinking individually on their own and choosing the answer they think is correct, then discussing in pairs what they chose and their reasoning, and receiving peer feedback on their answers, and finally sharing as a class their answers and reasoning, and coming to a conclusion as a class what the correct answer is (for this assessment, the answer is C, since there is an equal chance of gaining or losing the same amount of tickets each time you play the double-or-nothing game, so playing the game a large number of times is essentially the same as not playing at all).

Target Objectives

This assessment target the following objectives:

- Predict the outcomes of choices in game theory on a contingency table
- Affirm that not all choices have a single optimal strategy

Alignment with Texas Essential Knowledge and Skills (TEKS)

**Discrete Mathematics**(6) Game (or competition) theory. The student uses knowledge of basic game theory concepts to calculate optimal strategies. The student analyzes situations and identifies the use of gaming strategies. The student is expected to:

- (A) recognize competitive game situations;
- (C) identify basic game theory concepts and vocabulary;
- (E) explain the concept of and need for a mixed strategy;

montyhallformativeassessment.pdf | |

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## Formative Assessment: Testing

Overview of the Assessment

This assessment will be administered during the fourth week of the unit after the experimental design and sampling methods benchmark lessons. The assessment will be in the form of a handout with 2-tiered questions. The questions will include an experimental design description in which students must determine the design type and why and questions on sampling.

For example:

Target Objectives

This assessment target the following objectives:

Statistics TEKS

(2) Statistical process sampling and experimentation. The student applies mathematical processes to apply understandings about statistical studies, surveys, and experiments to design and conduct a study and use graphical, numerical, and analytical techniques to communicate the results of the study. The student is expected to:

(A) compare and contrast the benefits of different sampling techniques, including random

sampling and convenience sampling methods;

(B) distinguish among observational studies, surveys, and experiments;

This assessment will be administered during the fourth week of the unit after the experimental design and sampling methods benchmark lessons. The assessment will be in the form of a handout with 2-tiered questions. The questions will include an experimental design description in which students must determine the design type and why and questions on sampling.

For example:

- Researchers want to test the effects of a new headache pill. They divided their 20 subjects up into 2 groups. 1 group was given the new pill and the other group was given a placebo. The results were analyzed after 6 months. What kind of experimental design was used?
- Surveys
- Experiment
- Observational Study
- None of the above

- Explain why
- A school wants to know the percentage of students who practice different religions. The school randomly selects 50 students from each grade. What type of sampling method is this?
- Random sampling
- Stratified sampling
- Convenience sampling
- Systematic sampling

- Explain why

Target Objectives

This assessment target the following objectives:

- Students will be able to distinguish between observational studies, surveys, and experiments
- Students will be able to distinguish between different sampling methods

Statistics TEKS

(2) Statistical process sampling and experimentation. The student applies mathematical processes to apply understandings about statistical studies, surveys, and experiments to design and conduct a study and use graphical, numerical, and analytical techniques to communicate the results of the study. The student is expected to:

(A) compare and contrast the benefits of different sampling techniques, including random

sampling and convenience sampling methods;

(B) distinguish among observational studies, surveys, and experiments;

## Peer Feedback

There are many opportunities for students to critique their own artifacts and the artifacts of others and to revise their artifacts based on self-assessment and peer feedback during this PBI unit. At the end of each week, a milestone is due at the beginning of class for the students to critique the artifacts of their peers and provide suggestions to strengthen the overall artifact. The milestones create an opportunity for students to gain valuable insight on how others view their ideas and give the students to option to revise their artifacts based on the feedback from other peers.

Along with the milestones, the final week of the project implements experimental testing of their prototype with their peers in the classroom and people from outside of the classroom in the form of their family, friends, or adult professionals. By their experimental testing with a multitude of people. the students will be able to revise their prototype based on the analysis of their gathered data.

Along with the milestones, the final week of the project implements experimental testing of their prototype with their peers in the classroom and people from outside of the classroom in the form of their family, friends, or adult professionals. By their experimental testing with a multitude of people. the students will be able to revise their prototype based on the analysis of their gathered data.