Find one tick interval, then read the value

4.NBT.A.2 · adapt · grade 4

Archetype: Repeating Cycle Patterns · step in a 6-type progression

Find the number marked by $\bigstar$ on the number line.

On a number line, the large tick marks are spaced evenly at $10{,}000$ , $11{,}000$ , $12{,}000$ , and $13{,}000$ . Each interval between two large ticks is divided into $10$ equal small ticks. The mark $\bigstar$ points to the position $4$ small ticks past $12{,}000$ .

Show solution

Understand

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.

Givens

Large ticks read 10,000, 11,000, 12,000, 13,000 evenly spaced.
Each interval between large ticks is divided into 10 equal small ticks.
The star is 4 small ticks past 12,000.

Unknowns

The number the star points to

Constraints

The small ticks within one interval are all equal in size.

Plan

#1 Draw a Diagram · also uses: #7 Identify Subproblems

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.

Execute

#7 Identify Subproblems 4.NBT.A.2

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

11{,}000 - 10{,}000 = 1{,}000

The labels go up by the same step, and 11,000 minus 10,000 is 1,000.

#1 Draw a Diagram 4.NBT.A.1

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

1{,}000 \div 10 = 100

Splitting 1,000 into 10 equal pieces gives 100 each, the ten-times-smaller place.

#1 Draw a Diagram 4.NBT.A.2

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 \times 100 = 12{,}400

Each hop is 100, so four hops add 400.

Answer: 12,400

Review

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.

Look for a pattern (tool 5): count the small ticks past 12,000 as 12,100, 12,200, 12,300, 12,400 and land on the 4th one, 12,400.

Standards · min grade 4

4.NBT.A.1 Recognize that a digit represents ten times what it represents in place to its right — Splitting one thousand into ten equal small ticks of one hundred each.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Reading positions and adding to find the value at the star.

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