Round to the nearest 10, 100 and 1000

What you will learn

• Round to the nearest 10, 100 and 1000

Models used: number sentences, stories, diagrams.

Before you start

• Represent and compare numbers to 100000

Which ten is closer?

46 sits between 40 and 50. Which end is closer?

1. Start at the marked number. A jump to the right adds; a jump to the left takes away. Read the size of each jump.

   46 sits between 40 and 50. Which end is closer?

   Rounding chooses the nearer allowed multiple. The midpoint separates the two choices.

2. Start at the marked number. A jump to the right adds; a jump to the left takes away. Read the size of each jump.

   45 is halfway. 46 has already passed the halfway point towards 50.

3. Start at the marked number. A jump to the right adds; a jump to the left takes away. Read the size of each jump.

   It takes 4 steps to reach 50, but 6 to reach 40. So 46 rounds to 50.

   46 ≈ 50

4. The complete bar is the whole. Each labelled section is one part of it.

   An estimate checks the size of an answer: 46 + 32 is about 50 + 30, or 80.

   46 + 32 = 78, close to 80

   80

   5030

Worked example: A new example, together

Round 10739 to the nearest 1000.

1. Locate both endpoints, then the halfway point and the number itself.

   Rounding chooses a nearby benchmark, so the result is approximate.

   100001073911000

2. Neighbouring multiples: 10000 and 11000.

   100001073911000

   Round 10739 to the nearest 1000.

   11000

3. Neighbouring multiples: 10000 and 11000.

   100001073911000

4. The halfway point is 10500.

   100001073911000

5. Choose the nearer multiple; a halfway value rounds up: 11000.

   100001073911000

6. Check the result against the question we started with.

   10739 ≈ 11000; the distance is no more than 500.

   We found 11000. Rounding chooses a nearby benchmark, so the result is approximate.

   100001073911000

Common mistakes to discuss

• Reading every following digit. Only the digit in the next smaller place decides. Rounding 2449 to the nearest hundred looks at the 4 tens, so it gives 2400, not 2500.

Check your understanding

• Round to the nearest 10, 100 and 1000
• use neighbouring benchmarks and the midpoint to justify an estimate
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.