The Math Stars Competition Series consists of four different rounds of competition. Each round of the competition is designed to assess a different area of a student's mathematical skill set. For this reason, the four rounds differ widely in their format and structure. Participants may only work on the designated round at any time. The following drop-down tabs describes these rounds in more detail.

Format: The Power round is an individual round consisting of 30 short answer problems to be answered in 45 minutes. The Power round tests participants' ability to work by themselves as well as their speed in problem solving. The use of calculators, books, or other aids is not permitted, and all scratch work must be done on the provided space in the competition booklet. The problems will generally start very easy (covering concepts below the grade level(s) of the target audience) and will gradually increase in difficulty until it covers concepts reaching beyond the grade level(s) of the target audience. The problems aim to cover many concepts from curricular topics common to most provincial/territorial math curricula, but the harder problems often assume thorough understanding of such topics and thus will often require students to think at a more abstract/deeper level in order to solve them. However, regardless of the difficulty of the problems, we seek to align our problems as closely to the curriculum as possible. The Power round test topics in Algebra, Geometry, Combinatorics/Probability, and Number Theory.

Other Notes: Marks are only awarded for the correct answer put on the corresponding answer line for every problem. All answers must be complete, legible and simplified to lowest terms. All problems are worth the same amount.

Format: The Team Relays round is a team round consisting of five sets of five short-answer problems each to be answered in a total of 45 minutes. In each set, each problem's answer depends on the previous problem's answer with the exception of the first problem. The Team Relays round tests teams' ability to solve problems accurately and quickly. The problems in each problem set progress in difficulty, starting from a very easy first problem to a very challenging final problem. For the Regional competition, generally only the very last problem of each problem set covers concepts beyond the grade level(s) of the target audience. For the National championship, the last two or three problems of each problem set may cover concepts beyond the grade level(s) of the target audience. For this round, it is important for team members to divide up the work so that they can finish the problems in time. Participants may work on any question at any time. Scientific calculators are allowed, but books or other aids are not permitted. We generally try to thematically organize each problem set---the first problem set is usually themed on Algebra, the second problem set is usually themed on Geometry, the third problem set is usually themed on Number Theory, the fourth problem set is usually themed on Combinatorics & Probability, and the fifth problem set's theme vary from competition to competition, but will always be one which we know competitors will have had some exposure to prior to the competition.

Other Notes: Marks are only awarded for the correct answer put on the corresponding answer line for every problem. All answers must be complete, legible and simplified to lowest terms. All problems are worth the same amount.

Format: The Grit round is a team round that replaces the Quiz Show round from the 2015-2016 school year. The Grit round consists of 4 guided, full-solution problems to be completed in 45 minutes. Each problem either involves an investigation of some mathematical concept or asks for a proof of some theorem/claim. To help participants in these investigations/proofs, each problem has been divided into multiple parts—--often, the parts build on each other to arrive at a final result. We understand that many students may not have had sufficient exposure to proof-writing or even sufficient experience in writing up solutions through showing detailed logical arguments along with computations to arrive at a final answer. Hence, for the problems where the final result is a proof of a theorem/claim, we break down the proof into a number of key steps and we ask participants to complete the proof via those steps. Hints are also given at various times throughout the problem statements. Each full problem in this round is worth 7 points, but this is always partitioned into smaller chunks of points corresponding to the key steps involved in the solution.

For all of the problems, students must fully justify their reasoning and make clear,logical arguments to back up their claims. The goal of the Grit round is not to assess participants' knowledge of advanced proof techniques but rather their ability to come up with logical, coherent arguments and communicate them effectively to a marker. Students are expected to write full, coherent sentences in English to justify their reasoning. The Grit round problems can be quite difficult so we do not expect every team to be able to solve all of the problems.

If a province/territory's Math Stars organizing committee decides that there is not enough time for all four rounds of the competition to be hosted on the same day for a competition hosted in that province/territory (for example, in the case of after-school Math Stars competitions), then the Grit round may be omitted for all the Regional competitions hosted in that province/territory during that school year. Since advancements to Nationals are made on a province-by-province basis, this still ensures the fair evaluation of all competitors coming from the same province.

Other Notes: Marks are awarded for correctness, completeness, clarity of reasoning, method of attack, ingenuity, creativity of solution, and style of presentation on the Grit round problems. To earn the maximum number of points for each problem, all assertions made in the solutions must be proved. Partial marks will only be awarded if relevant progress has been made towards a solution.

Format: The Project Mania round is the most versatile round of the Math Stars competitions. Participants do not know the theme or structure of this round until the contest date. In this round, participants will work in teams to complete some task or project within a time limit, usually somewhere between 1 and 2 hours (inclusive). These tasks/projects could be anything related to mathematics, but they are all focused around one mathematically-relevant theme. Following is a non-exhaustive list of possible themes for the Project Mania Round:

• Hands-on geometry
• Combinatorial math games
• Logic puzzles
• Mathematically modelling a city
• Code breaking
• Statistics and data research
• Graphs and map coloring
• Logo designing and geometric constructions
• Mathematics of climate change
• Mathematics of video games
• Probability games/board games
• Treasure hunt
• Mathematics of music
• Financial applications of mathematics
• Tessellations
• Fractals and its connection to $\sqrt{-1}$

This is the creative and open-ended portion of the Math Stars competition, and definitely should be considered the highlight of the competition. Sometimes the Project Mania round has a certain goal that competitors want to reach by the end of the round---for example, a culminating challenge that teams must crack to finish the contest. Other times the Project Mania round could be an investigation in some interesting area of mathematics that students may not have been exposed to before in school. Problems in the Project Mania round can be of many different types: short-answer, multiple choice, sentence response, full-solution, or even proof problems. The difficulty of the questions can vary widely as well, from very easy to very challenging (however, we generally try to order the problems by difficulty within each section of the Project Mania round and we generally try to order the sections by difficulty across the entire Project Mania round). Some of the challenges may be written and some may require team-staff interaction or even team-team interaction. Some may require students to use technology to help them complete the challenges. The Project Mania round is always designed to challenge team members to work well together. The Project Mania round also tests teams' ability to handle new mathematical concepts and creativity and ingenuity in problem solving. Scientific calculators are allowed during the Project Mania round, but books or other aid are generally not allowed.

Other Notes: Due to the highly versatile nature of the Project Mania round, the Math Stars Organizing Committee will ensure that a rigorous evaluation system will be in place for every Project Mania round. Staff members are instructed to act as impartial as possible in their interactions with teams, and points are awarded only on an impartial basis. Furthermore, staff members will act similarly across all competitions involving the same Project Mania round across the country. All written answers must be complete, legible and simplified to lowest terms (for short-answer problems).

### Scoring

Although individual awards are usually not awarded at Math Stars competitions, specific scoring rules exist for marking and ranking the individual scores on the Power Round as well as the team scores on the competition as a whole.

A competitor's individual score is simply equal to his/her Power Round score (out of 30). In the event of a tie in individual scores and a ranking must be established between the competitors involved in the tie for awards, only the Power Round is used to break ties. Of the competitors tied in individual score, the competitor(s) who correctly answered a problem with a largest problem number wins the tie-breaker. If more than one person answered this problem with the largest problem number correctly, then the second highest problem number is looked at between the remaining tied competitors. This process continues until all the Power Round answers have been compared. If more than one individual answered exactly the same problems correctly, then a separate tie-breaker round (usually featuring a face-to-face, buzz-in round---the rules of which will be explained to the competitors involved during the competition) will be used to determine the individual rankings between those involved in such a tie.

A team's score is equal to a weighted average of the Team's scores on all four rounds of the competition. Specifically, the weight placed on each round is:

1. Power Round---25% (or 30% if the Grit Round is not administered): The average of the team members' individual raw scores (with a minimum denominator of 2), multiplied by $\frac{25}{30}$ (or $1$ if the Grit Round is not administered)---which converts the raw average to the correct overall weighting. This means that if a team consists of only one member, a score of 0 will be used for the second, "missing", member of the team and will be included in the calculation of the team's individual average. For example, if the one-member team scored 24 on the Power Round, then his/her team's average Power Round score is equal to $\frac{24+0}{2}=12$. This is why it is disadvantageous to have a team with only one member. If the team consists of two or more members, then the Power Round average will be computed normally.
2. Team Relays Round---25% (or 30% if the Grit Round is not administered): The team's raw score on the Team Relays Round will be used for this round, multiplied by $1$ (or $\frac{30}{25}$ if the Grit Round is not administered)---which converts the raw score to the correct overall weighting.
3. Grit Round---20% (if it is administered): The team's raw score on the Grit Round will be used for this round, multiplied by $\frac{20}{28}$---which converts the raw score to the correct overall weighting. The lower weight given to this round is due to the difficulty that we perceive most students will have with full-solution and proof problems, so we do not want to discourage competitors with a high weighting given to this round.
4. Project Mania Round---30% (or 40% if the Grit Round is not administered): The team's raw percentage on the Project Mania Round will be used for this round, multiplied by $\frac{30}{100\%}$ (or $\frac{40}{100\%}$ if the Grit Round is not administered)---which converts the raw percentage score to the correct overall weighting. The percentage is used because every Project Mania Round is different, so there's no fixed overall total that is set for the Project Mania Round.

A perfect team score would therefore be 100 points. Though it sounds difficult, perfect team scores are possible, as it has been achieved in the 2016 Math Stars National Championship by a team from BC.

### Other Information

The following awards will be given at every Math Stars competition (other than any intra-school competitions, if any, used to select the school's team(s) for participation in the Math Stars Regional competitions), whether Regional, Provincial, or National levels.

• Team trophies/certificates for the top 3 competing teams (or top 50% of teams, whichever is less)
• Medals/certificates for the top 3 individuals on the Power round (or top 25% of competitors, whichever is less)
• Prizes for the top 3 teams

Any other awards will be awarded at the sole discretion of the Event Organizing Committee for each specific competition.

Although the Math Stars Competition Series is a team competition, there are rules pertaining to communication within and between teams during the competition. In short, talking, signaling, passing messages, or any other form of communication, and group work of any kind, are permitted only during the Team Relays, Grit, and Project Mania rounds, and only between members of the same team. At no time during the competition (that is, any time that the proctors are actively supervising the competitors) is inter-team communication permitted. Coaches, visitors, media personnel, photographers, parents, and other non CSSMA staff are not allowed in the competition rooms during any of the rounds. Non-CSSMA approved usage of cameras and/or any video/audio recording devices is allowed only during the awards ceremony at the end of every competition. However, CSSMA accredited photographers may take pictures and/or record videos at any time during any of the competitions. Approved media coverage is welcome; however, media coverage must not interfere with the running of any part of any Math Stars competition.

1. The use of notes, books, dictionaries, translators, or any other reference material is not permitted during any round of any Math Stars competition.

2. Calculators are not permitted for the Power Round, and depending on the competition, the Project Mania Round as well. On the other hand, non-programmable calculators are permitted for the Team Relays and Grit rounds. Also, participants may not use a device that has internet access, that can communicate with other devices, or that contains previously stored information.

3. For offline competitions, competitors are not allowed to use their own scratch paper for the Power and Team Relays rounds, and depending on the competition, the Project Mania Round as well. However, for online competitions, competitors are expected to bring their own scratch paper (which must not initially contain any printing or marks---unless with prior approval by CSSMA staff) to aid them in the problem-solving process for all four rounds of the competition. Competitors are expected to use their own scratch paper for the Grit Round, as outlined in the instructions for that round. For (offline) rounds which the competitors are not allowed to use their own scratch paper, they are expected to do all their computations, scratch work, diagrams, and writing on the space provided in the test booklet. Competitors may write wherever they want on the contest paper except for the clearly marked areas where they must write their final answers to the problems.

4. Competitors are not allowed to ask any questions during any of the round of the Math Stars competition(s) that they are competing in. Invigilators are instructed not to answer any questions. The test papers will all have been thoroughly checked for errors before printing. However, if any blatant and distracting errors are still found, the competitor may raise his/her hand to receive a clarification. Any clarifications, if made, shall be executed uniformly across the country.

5. If a competitor has to leave the room for any reason during any of the rounds, he or she may only be allowed to come back into the room after that round is finished.

6. For offline competitions, competitors must write their answers to any of the problems on the answer line following every problem. The markers will not look for the answers anywhere else in the test booklet. The written answer must be clear and in a legible and acceptable format. If an answer is dubious or if the markers cannot clearly read an answer, they will mark it as incorrect. For online competitions, competitors must simply type in their answers to any of the problems on the corresponding answer box following every problem.

The Math Stars competition problems can require participants to give their answers in a variety of different formats: integer, common fraction, simplest radical form, dollar values...etc. For the sake of fair evaluation of all competitors, the Math Stars Competition Series has strict guidelines on the answer formats that we will accept under different circumstances. We strongly encourage coaches and competitors to familiarize themselves with the acceptable answer formats (to the short-answer problems) prior to attending Math Stars competitions. The following document describes the acceptable forms of answers at Math Stars competitions:

Forms of Answers (The CSSMA staff would like to express our deepest gratitude to the MATHCOUNTS, Inc. for the contents of this document. The original version of this document can be found here.)