← Senior Mathematics Studio

LEARN · EXPLAIN · REVISE

Choose one book: t mathematics titles or 3 history titles, with no overlap. How many choices?

Read the idea, work independently, then explain what changed.

TOPIC 01

Counting principles: mixed review

A mixed assessment: identify the method, justify it and revise your reasoning.

What you will be able to explain

  • Connect the chapter skills without relying on the order of the exercises.

Try it. Leave your reasoning visible.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Foundation#Your turn

Choose one book: t mathematics titles or 3 history titles, with no overlap. How many choices?

t=20t=20
  • Addition requires disjoint cases; stage counts must hold for each branch or use separate branches.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Decide whether choices are alternative cases or successive stages, then check overlap.
Hint 2
Use this intermediate relation.
N=t+3N=t+3
Worked solution
  1. Decide whether choices are alternative cases or successive stages, then check overlap.

  2. Apply the stated relation and retain its conditions.

    N=20+3=23N=20+3=23
  3. The two subject cases are disjoint alternatives.

The requested value is 23.

Checks and common pitfalls: The two subject cases are disjoint alternatives.

Think first. Reveal a hint when the class is ready.

Focus on one question

Teacher preparation and assessment

Question sequence

  • Ask students to name the relevant condition before calculating.

Board plan

  • Compare valid methods and annotate their conditions.

Anticipated thinking

  • A correct final value may still hide a missing assumption.

Assessment checklist

  • Check the method, conditions, reasoning and interpretation separately.

No sign-in. Work stays in this browser. Export before clearing browser data. Written reasoning is assessed with a checklist.

Curriculum and source notes ↗