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Mathematics from zero

Numbers: free-recall review

Crux Free-recall prompts across the numbers unit. Answer each in your own words first, then reveal the model answer and compare.
Your altitude — climbing toward senior
ZeroJuniorMiddleSenior
You are at middle altitude — in the sky
◷ 14 min

Saying an answer from memory makes it stick far better than re-reading. For each prompt, say or write a full answer first — then open the model answer and check yourself.

Goal

Reconstruct the unit’s core ideas from memory — what counting really is, the three comparison results, place value, the job of zero, and the number line — without looking back at the lessons.

Recall before you leave
  1. 01
    What is counting, really, and why must each number word land on exactly one object?
  2. 02
    When you compare two whole numbers, what are the only possible results, and how does the number line decide?
  3. 03
    How do the greater-than and less-than signs work, and what is the trick for never flipping them?
  4. 04
    Explain place value: why is the digit 4 worth 40 in one number and only 4 in another?
  5. 05
    What job does the digit 0 do in a number like 305, and what changes if you remove it?
  6. 06
    What is a number line, and why must its gaps be equal?
Recap

If you could rebuild each answer from memory, you hold the spine of the unit: counting is matching one word to one object; comparing has exactly three results and the further-right number wins; the open side of the sign faces the bigger number; a digit’s value is the digit times its place; zero is the placeholder that keeps the others in place; and the number line ties it all together with equal gaps that turn counting into movement you can see.

Continue the climb ↑Numbers: build a number line by hand
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