Locate and compare numbers on a number line

4.NBT.A.2 · adapt · grade 4

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

Which of the following numbers is closest to $10{,}000$ ? Write it.

$8{,}800 \qquad 10{,}500 \qquad 10{,}100$

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Of the three numbers 8,800, 10,500, and 10,100, decide which one is nearest to 10,000.

Givens

Unknowns

Constraints

#1 Draw a Diagram · also uses: #6 Guess and Check

Picture the numbers on a number line around 10,000 and measure how far each is from 10,000; the one with the smallest gap is closest.

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

8,800 is below 10,000 by 10,000 - 8,800 = 1,200.

10{,}000 - 8{,}800 = 1{,}200

On the number line 8,800 sits well to the left of 10,000.

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

10,500 is above 10,000 by 10,500 - 10,000 = 500.

10{,}500 - 10{,}000 = 500

10,500 is just past 10,000.

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

10,100 is above 10,000 by 10,100 - 10,000 = 100.

10{,}100 - 10{,}000 = 100

10,100 is barely past 10,000.

#6 Guess and Check 4.NBT.A.2

The distances are 1,200, 500, and 100. The smallest is 100, so 10,100 is closest to 10,000.

100 < 500 < 1{,}200

The smallest gap wins; 100 is the smallest.

Answer: 10,100

10,100 differs from 10,000 by only 100, far less than 500 (for 10,500) or 1,200 (for 8,800), so 10,100 being closest is correct.

Make a systematic list (tool 2): write each number with its distance from 10,000 and read off the smallest.

4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Comparing the distances of each number from 10,000.

💡 This only needs Grade 4 comparing: measure each number's gap from 10,000 and pick the smallest gap!