3A · Chapter 1 · Lesson 07
Rounding to the Nearest Thousand
Find the two bounding multiples of 1,000., Decide the nearest thousand by the midpoint., Explain and apply the usual half-up convention for positive whole numbers.
Your starting challenge
Is 6,499 closer to 6,000 or 7,000? What happens if we add only 1?
By the end, you can…
- Find the two bounding multiples of 1,000.
- Decide the nearest thousand by the midpoint.
- Explain and apply the usual half-up convention for positive whole numbers.
Before starting, you should know…
- Read number lines and compare four-digit numbers.
Entry · 2 questions
Quick prerequisite check
Try these two before the lesson. If either is confusing, review the listed prerequisites first.
- E1 A number line runs from 5,000 to 7,000 in 2 equal intervals. What is the step per interval?
Show answer and reasoning
Answer: 1,000
The total distance is 2,000. Divide by 2 equal intervals: 1,000.
- E2 Insert <, >, or =: 6,501 ___ 6,500.
Show answer and reasoning
Answer: >
Compare digits from the highest place that differs. 6,501 > 6,500.
Vocabulary to know
| rounding | Replacing a number with a nearby number at a specified place. |
|---|---|
| nearest thousand | The multiple of 1,000 closest to a number. |
| midpoint | The halfway value between two bounding multiples. |
| estimate | An approximate value used when an exact value is unnecessary. |
Learn the concept
Find the bounds
For 6,499 the surrounding thousands are 6,000 and 7,000. Their midpoint is 6,500. Since 6,499 is below the midpoint, it rounds to 6,000.
How to handle halfway values
For positive whole numbers, we use the common classroom convention: exactly halfway rounds up. Thus 6,500 rounds to 7,000.
An estimate is not an exact measurement
Rounding supports mental calculation and reasonableness checks. Report an original exact quantity when a problem requires it; do not silently replace an exact answer with a rounded one.
Work through examples
Study the explanation; then try each check before opening its answer.
Worked example 1
Round below the midpoint
Round 6,499 to the nearest thousand.
- Bounds are 6,000 and 7,000.
- Halfway is 6,500.
- 6,499 is less than halfway.
Result: 6,000
Now you try · Understanding check 1
Round 6,501 to the nearest thousand.Reveal answer and explanation
7,000 — It lies between 6,000 and 7,000; the midpoint is 6,500. With halfway values rounded up, choose 7,000.
Worked example 2
A halfway case
Round 3,500 to the nearest thousand.
- 3,500 is exactly halfway between 3,000 and 4,000.
- With the usual positive-number half-up rule, choose the upper thousand.
Result: 4,000
Now you try · Understanding check 2
Round 8,500 to the nearest thousand.Reveal answer and explanation
9,000 — It lies between 8,000 and 9,000; the midpoint is 8,500. With halfway values rounded up, choose 9,000.
Worked example 3
Round across the digit boundary
Round 9,620 to the nearest thousand.
- Surrounding thousands are 9,000 and 10,000.
- Midpoint is 9,500, and 9,620 is above it.
Result: 10,000
Now you try · Understanding check 3
Round 9,499 to the nearest thousand.Reveal answer and explanation
9,000 — It lies between 9,000 and 10,000; the midpoint is 9,500. With halfway values rounded up, choose 9,000.
Guided · 4 questions
Guided practice
Try each problem; return to a visual model if you need one.
- G1 Round 2,499 to the nearest thousand.
Show answer and reasoning
Answer: 2,000
It lies between 2,000 and 3,000; the midpoint is 2,500. With halfway values rounded up, choose 2,000.
- G2 Round 2,500 to the nearest thousand.
Show answer and reasoning
Answer: 3,000
It lies between 2,000 and 3,000; the midpoint is 2,500. With halfway values rounded up, choose 3,000.
- G3 Round 8,299 to the nearest thousand.
Show answer and reasoning
Answer: 8,000
It lies between 8,000 and 9,000; the midpoint is 8,500. With halfway values rounded up, choose 8,000.
- G4 Round 9,700 to the nearest thousand.
Show answer and reasoning
Answer: 10,000
It lies between 9,000 and 10,000; the midpoint is 9,500. With halfway values rounded up, choose 10,000.
Independent · 8 questions
Independent practice
Work without looking at examples first. Show your thinking on paper.
- I1 Round 1,480 to the nearest thousand.
Show answer and reasoning
Answer: 1,000
It lies between 1,000 and 2,000; the midpoint is 1,500. With halfway values rounded up, choose 1,000.
- I2 Round 1,500 to the nearest thousand.
Show answer and reasoning
Answer: 2,000
It lies between 1,000 and 2,000; the midpoint is 1,500. With halfway values rounded up, choose 2,000.
- I3 Round 4,512 to the nearest thousand.
Show answer and reasoning
Answer: 5,000
It lies between 4,000 and 5,000; the midpoint is 4,500. With halfway values rounded up, choose 5,000.
- I4 Round 7,501 to the nearest thousand.
Show answer and reasoning
Answer: 8,000
It lies between 7,000 and 8,000; the midpoint is 7,500. With halfway values rounded up, choose 8,000.
- I5 Round 6,999 to the nearest thousand.
Show answer and reasoning
Answer: 7,000
It lies between 6,000 and 7,000; the midpoint is 6,500. With halfway values rounded up, choose 7,000.
- I6 Round 8,499 to the nearest thousand.
Show answer and reasoning
Answer: 8,000
It lies between 8,000 and 9,000; the midpoint is 8,500. With halfway values rounded up, choose 8,000.
- I7 Round 9,999 to the nearest thousand.
Show answer and reasoning
Answer: 10,000
It lies between 9,000 and 10,000; the midpoint is 9,500. With halfway values rounded up, choose 10,000.
- I8 Round 5,000 to the nearest thousand.
Show answer and reasoning
Answer: 5,000
5,000 is already an exact multiple of 1,000.
Challenge · 2 questions
Challenge and transfer
These nonroutine problems require you to explain or adapt what you learned.
- C1 A whole number rounds to 6,000 to the nearest thousand. What is the smallest whole number it could have been?
Show answer and reasoning
Answer: 5,500
The interval of whole numbers rounding to 6,000 starts halfway below, at 5,500, and ends at 6,499 (with halfway values rounded up).
- C2 What is the greatest whole number below 10,000 that rounds to 9,000 to the nearest thousand?
Show answer and reasoning
Answer: 9,499
9,500 rounds to 10,000, so the largest whole number still rounding to 9,000 is 9,499.
Exit · 3 questions
Exit check
Use these fresh problems to decide whether to proceed. Answers should be independent.
- E1 Round 3,499 to the nearest thousand.
Show answer and reasoning
Answer: 3,000
It lies between 3,000 and 4,000; the midpoint is 3,500. With halfway values rounded up, choose 3,000.
- E2 Round 3,500 to the nearest thousand.
Show answer and reasoning
Answer: 4,000
It lies between 3,000 and 4,000; the midpoint is 3,500. With halfway values rounded up, choose 4,000.
- E3 What is the midpoint between 8,000 and 9,000?
Show answer and reasoning
Answer: 8,500
Half the 1,000 gap is 500; add to 8,000.