Counting | Whole Class
Students review and apply advanced counting strategies to solve multi-step problems involving permutations, combinations, and restrictions. The lesson emphasizes choosing efficient methods, justifying reasoning, and checking for overcounting or undercounting.
| Term | Definition |
|---|---|
| Permutation | An arrangement where order matters. |
| Combination | A selection where order does not matter. |
| Factorial | The product of all positive integers from 1 to n, written n!. |
| Multiplication Principle | If one choice can be made in m ways and another in n ways, the total number of outcomes is m × n. |
| Complementary Counting | Counting the total outcomes and subtracting the unwanted outcomes. |
| Restriction | A condition that limits which outcomes are allowed. |
Present 2 short scenarios and ask whether order matters and whether repetition is allowed. Briefly review permutation vs. combination.
Respond verbally or with thumbs up/down; explain which counting method applies and why.
Model one problem using a step-by-step decision process: identify the type of outcome, list restrictions, choose a method, and compute. Include one example with a restriction and one with complementary counting.
Take notes, label the method used, and ask clarifying questions.
Work through 2 challenging problems with the class, prompting students to justify each step and to check for overcounting. Encourage alternative strategies when appropriate.
Solve alongside the teacher, volunteer steps, and compare methods with classmates.
Distribute a short exit ticket with one advanced counting problem. Circulate to support and note common errors.
Complete the problem individually and show reasoning clearly.
Review the key decision rule: determine whether order matters, then apply restrictions carefully. Highlight one common mistake to avoid.
Summarize the main strategy in one sentence.
Students leave with the rule that counting begins by deciding whether order matters, then applying the appropriate formula and checking restrictions to avoid overcounting.
Formative assessment occurs through guided responses and a short exit ticket that requires students to choose the correct counting method and solve an advanced problem with justification.
Assign 3-5 advanced counting problems mixing permutations, combinations, and restrictions; include one reflection question asking students to explain how they decided which counting method to use.