Patterns & Reasoning

Problem

Find one tick interval, then read the value

On a number line whose big ticks are 10,000, 11,000, 12,000, 13,000 with each gap split into 10 equal small ticks, find the value at the star, which is 4 small ticks past 12,000.
10,000 11,000 12,000 13,000
Base-ten numbers
Your answer
How to solve
Strategy Draw a Diagram — First find what one small tick is worth (a subproblem) by splitting the big interval into 10 equal parts, then step that amount 4 times from 12,000 along the number line.
1STEP 1

Size of one big interval

Consecutive large ticks differ by 11,000 - 10,000 = 1,000, so each big interval spans 1,000.

11,000 - 10,000 = 1,000
2STEP 2

Value of one small tick

That 1,000 is split into 10 equal small ticks, so each small tick is 1,000 ÷ 10 = 100.

1,000 ÷ 10 = 100
3STEP 3

Step 4 small ticks past 12,000

The star is 4 small ticks beyond 12,000, so add 4 hundreds: 12,000 + 4 × 100 = 12,000 + 400 = 12,400.

12,000 + 4 × 100 = 12,400
Answer
12,400
The star sits between 12,000 and 13,000 and only 4 of the 10 small ticks in, so it should be a bit less than halfway; 12,400 is indeed between 12,000 and 12,500. Reasonable.
Takeaway

This only needs Grade 4 place-value sense: find what one little tick is worth, then count the ticks!

  • Size of one big interval
  • Value of one small tick
  • Step 4 small ticks past 12,000
Where next?
Another one like thissuggested

▶ Practice — 8 problems