Number Concepts 1 Rounding whole numbers & decimals
Objectives

Round whole numbers to the nearest 100 or 1000

Round decimals to the nearest whole unit or tenth

Use rounding to estimate answers to complex calculations
For this unit you will need:
whiteboards, 0 to 9 dice, Rounding numbers to the nearest 1000 at
http://www.numbernut.com/advanced/activities/estimate_quiz_round10
00.shtml, Function wheel at
http://www.topmarks.co.uk/Flash.aspx?f=FunctionWheelv6, 1-9 digit
cards (see resources), sheet of multiplications and approximations to
display (see resources)
Watch out for pupils who:

don’t realise that numbers ending in 50 or 500 are rounded up
when rounded to the nearest 100 or 1000;

think that numbers which have more decimals place are bigger,
e.g. 3.452 is more that 3.73;

don’t realise that estimates can be out by a much greater margin
when estimating products rather than sums or differences.
HSNP © Hamilton 2014
Shining Term 3
Number Concepts 1
Session 1
Objective: Round whole numbers to the nearest 100 or 1000
Teacher input with whole class
 Display Rounding numbers to the nearest 1000 at
http://www.numbernut.com/advanced/activities/estimate_quiz_round
1000.shtml. Ask pupils to write on their whiteboards the nearest 1000
each time, and click on the numbers shown by most. Keep the pace
brisk. Each time ask them to write another number which rounds to the
same multiple of 100.
Paired pupil work
 Pupils roll a 0-9 dice five times to generate a five-digit number. One
pupil rounds the number to the nearest 100 and the other to the
nearest 1000. They record the number generated and the multiples
they rounded to. Repeat, swapping roles each time. Do they ever
round to the same number? (E.g. 54,967 rounds to 55,000 as nearest
thousand and hundred.)
Teacher input with whole class
 Take feedback on those five-digit numbers which rounded to the same
number when rounded to the nearest 100 and 1000 and discuss why
this was the case.
 Write a number which rounds to 43,000 when rounded to the nearest
1000. Write a number which rounds to 43,000 when rounded to the
nearest 100.
HSNP © Hamilton 2014
Shining Term 3
Number Concepts 1
Session 2
Objective: Round decimals to the nearest whole until or tenth
Teacher input with whole class
 Display the Function wheel at
http://www.topmarks.co.uk/Flash.aspx?f=FunctionWheelv6, choose
‘Round to nearest 1’. Ask a pair to round the top number to the
nearest whole number. Click on the smiley face. If correct the class
wins a point. If not, you win a point. Repeat with each pair, clicking for
a new set of decimals if necessary. Did the class or teacher win most
points?
Paired pupil work
 Pupils work in pairs to write pairs of numbers with 2 decimal places
using digits:
 3, 4 and 7, each number rounds to 4;
 2, 3 and 6, each number rounds to 3;
 1, 2 and 8, each number rounds to 2.
 Share answers.
Teacher input with whole class
 Ask pupils to sketch a line from 0.3 to 0.4. They mark on 0.325 and
compare to their neighbour’s. Which tenth is closest? Now mark on a
number which is closer to 0.4.
 Sketch a line from 1.2 to 1.4. Mark on two numbers, one greater than
1.3 and one less than 1.3 which both round to 1.3. Compare with your
neighbour’s. Write a number which rounds to 1.2. Then to 1.4.
HSNP © Hamilton 2014
Shining Term 3
Number Concepts 1
Session 3
Objective: Use rounding to estimate answers to complex calculations
Teacher input with whole class
 Write 4274 + 3628 + 5407 on the board. Ask pupils to discuss in pairs
how they would approximate the answer to this addition. Take
feedback, discussing rounding to the nearest 1000 for a very rough
estimate, but also rounding to the nearest 100 for a closer estimate.
Ask pupils to do both and then compare with the exact answer. Repeat
for 26,245 – 14,871.
 Repeat for 37.89 + 26.78, rounding to the nearest whole. Repeat for
2.346 + 1.728. Discuss rounding to the nearest whole and to the
nearest tenth. Pupils do both, then compare with the exact answer.
Paired pupil work
 Pupils work in pairs. They shuffle a pack of 1 to 9 digit cards (see
resources) and take eight to form a pair of four-digit numbers with two
decimal places. They estimate the sum and the difference between the
two numbers. One pupil works out the sum and the other the
difference. They compare with the estimate. They score one point for
each estimate within 1 of the exact answer. Repeat once
 Repeat, to make four-digit numbers with three decimal places. Repeat
once. Which pair scored most points?
Teacher input with whole class
 Write 42 × 81 and 2789 × 3 on the board. Ask pupils to discuss how
they could approximate the answers to each. Draw out rounding to the
nearest 10 for the first and to the nearest 100 for the second. Ask half
the class to work out the first multiplication and the other half to work
out the second. Compare with their estimates. Discuss how the
multiplication magnifies the amount rounded so the estimates are
often not as close as they would be for addition or for subtraction.
Paired pupil work
 Pupils work in pairs. Display the sheet of multiplications and
approximations (see resources) and ask pupils to work our which goes
with which.
HSNP © Hamilton 2014
Shining Term 3