Year 4NumberNumber structuresYear 4 Maths

Rounding, and counting in steps

What this lesson covers

  • Rounding can support predicting or estimating the result of a calculation.
  • Rounding is based on identifying the nearest place value or unit (ten, hundred, thousand) for a given number; a number line supports this.
Key idea

Rounding is a question, not a rule

  • Round 3,271 to the nearest hundred.
  • There are only two answers it could be: 3,200 or 3,300.
  • The only question is which one is nearer.
Rounding is a question, not a rule
Key idea

So look at it

  • 3,271 sits closer to 3,300 than to 3,200.
  • So it rounds to 3,300.
  • You did not need a rule. You could see it.
So look at it
Key idea

The place you round to picks the two ends

  • Nearest ten? The ends are 3,270 and 3,280.
  • Nearest hundred? The ends are 3,200 and 3,300.
  • Same number, different question, different answer.
first decide the two ends
numberround tobetweenanswer
4,700nearest thousand4,000 or 5,0005,000
3,271nearest hundred3,200 or 3,3003,300
3,271nearest ten3,270 or 3,2803,270
Key idea

The one case you cannot look at

  • 3,250 is exactly halfway between 3,200 and 3,300.
  • Neither is nearer. Looking cannot settle it.
  • So somebody chose: exactly halfway rounds up.
The one case you cannot look at
Key idea

What rounding is for

  • 3,271 add 4,850 is hard in your head.
  • 3,300 add 4,900 is not. That is about 8,200.
  • A rounded answer tells you what to expect.
estimating before you calculate
the real sumthe rounded sumso expect
3,271 + 4,8503,300 + 4,900about 8,200
6,120 − 2,8906,100 − 2,900about 3,200
Worked example

Tenths work the same way

  • 3.4 sits between 3 and 4.
  • It is nearer 3, so it rounds to 3.
  • Same question. Nothing new to learn.
Tenths work the same way
Key idea

Counting in steps is the same line

  • Counting in 25s is jumping along in equal hops.
  • 150, 175, 200, 225.
  • Same number line. Bigger jumps.
Counting in steps is the same line
Key idea

Counting in 100s moves one column

  • Start at 2,340 and count in 100s.
  • 2,440, 2,540, 2,640. Only the hundreds digit moves.
  • That is place value doing the work again.
one column changes at a time
start atcount inand you get
2,340100s2,440 · 2,540 · 2,640
2,3401,000s3,340 · 4,340 · 5,340
15025s175 · 200 · 225
Worked example

Until the column runs out

  • 2,640, then 2,740, then 2,840, then 2,940.
  • Next hop needs a tenth hundred. There is no such digit.
  • So it becomes 3,040; the thousands column takes it.
Until the column runs out
Your turn

Your turn

  • Round 6,481 to the nearest hundred.
  • Round 6,481 to the nearest thousand.
  • Count on in 50s from 6,450. Three hops.
Your turn
Show answer

6,500: between 6,400 and 6,500, and 81 is past halfway. 6,000: between 6,000 and 7,000, and 481 is short of halfway, which is the one people get wrong because 6,481 "looks big". 6,500 · 6,550 · 6,600. Draw the two ends first in both rounding questions; the answer follows from the picture.

Summary

Rounding and counting

  • Find the two ends, then see which is nearer.
  • Exactly halfway is the only time you need the rule.
  • Counting in steps is the same line, jumped along.
pause here
ideawhat to remember
roundingwhich of the two ends is nearer?
the two endsthe place you round to picks them
exactly halfwayrounds up: the one real rule
what it is forknowing what to expect before you work it out
counting in stepsequal hops along the same line

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