Mathematics from zero
Numbers: build a number line by hand
You have read about counting, comparing, place value, and the number line. Now make them with your own hands: count real objects, draw a line that does not lie, and take numbers apart to see what each digit is worth. The ideas only become yours once you build them.
Turn the four lessons into one connected piece of work: count groups of objects, draw an honest number line with equal gaps, use it to compare numbers, and decompose two- and three-digit numbers into their place values — showing your reasoning at every step.
Build a paper number line from 0 to 20 with equal gaps, then use it to count, compare, and decompose numbers — proving every claim with a drawing or a written count rather than just an answer.
- Two written counts, each with the method shown (one touch per number word) and a correct total.
- A number line from 0 to 20 where every gap is visibly the same size, with both pile totals marked at the correct number of steps from 0.
- The two totals compared correctly, written both with the greater-than and the less-than sign, with a sentence saying which number the open side faces.
- Three numbers broken into place values, each shown as a sum (digit times place), with the zero-containing number explained as a placeholder.
- Extend the line past 20 and place a three-digit number such as 305: write it as 300 + 0 + 5 and explain in one sentence why it is a different number from 35.
- Make a comparison ladder: order four of your numbers from smallest to largest using only the less-than sign in a single chain (for example 7 < 14 < 18 < 20).
- Draw a deliberately wrong number line with unequal gaps next to your good one, and write two sentences on exactly how the bad one misleads even though its numbers are in the right order.
This is the loop you will reuse for every number idea that follows: count honestly, lay numbers out on an equal-gap line, read off comparisons from their positions, and take each number apart into place values to see what its digits are worth. Doing it once by hand — drawings, counts, and all — turns the four lessons from things you have read into things you can do.