You are a junior sports analyst for your school team. Use unit rates, equivalent ratios, and ratio tables to analyze player performance and write a real scouting report.
The coach needs data, not just gut feelings. Move through four phases: compute each player's unit rate (points per game), use equivalent ratios to compare two players fairly, build a ratio table to project stats over a full season, and check your reasoning with a quick-answer problem. Fill in every calculator, hit the buttons, check off your list, and finish with a scouting report. Then print it for the coach.
A player's scoring rate is a unit rate: points per 1 game. Divide total points by games played for each player to find who scores more per game on average.
Unit rate = total ÷ number of games. If a player scored 84 points in 12 games, the unit rate is 84 ÷ 12 = 7 points per game. If another scored 70 points in 10 games, 70 ÷ 10 = 7 points per game — they are tied! Use the calculator to check your players.
Unit rates are one way to compare. Another way is to use equivalent ratios — rewrite both players' ratios with the same number of games to compare points directly.
To scale Player A (84 pts in 12 games) to 60 games: multiply both by 60÷12 = 5. So 84×5 = 420 pts in 60 games. For Player B (70 pts in 10 games) scaled to 60 games: multiply both by 6. So 70×6 = 420 pts in 60 games. They score the same! Now try it with your own numbers.
Use each player's unit rate to project their season totals. Build a ratio table that shows predicted points at 10, 20, and 30 games — that is the full season.
If a player scores 7 points per game, their ratio table is: 10 games → 70 pts, 20 games → 140 pts, 30 games → 210 pts. Each row multiplies the unit rate by the number of games. These are all equivalent ratios — the rate stays constant.
Make your draft recommendation and check your rate reasoning with a known-answer problem.
Write a 3–5 sentence scouting report to the coach. Use your actual unit rates, equivalent ratios, and season projections from above.
| Category | 4 — Expert | 3 — Proficient | 2 — Developing |
|---|---|---|---|
| Unit Rate | Both unit rates correct; interpretation clearly stated | Both unit rates correct | One unit rate correct or both attempted with errors |
| Equivalent Ratios | Correct scaling for both players; explains why ratios are equivalent | Both players scaled correctly to common games | Scaling attempted with one computational error |
| Ratio Table / Projection | All rows correct; pattern explained; recommendation supported by projections | All table rows correct | One or two rows correct; pattern partially shown |
| Communication | Scouting report justifies recommendation using all three math tools | Report gives a clear recommendation with most numbers | Report is vague or missing key data |