21 · Adding and subtracting decimals: part 1
21
Adding and subtracting decimals: part 1
This session is designed to help learners to:
앫 visualise a number line when performing simple addition
and subtraction calculations with decimals;
앫 verbalise decimals correctly;
앫 understand and correct the misconception that ‘a decimal is
just two ordinary numbers separated by a dot’, that is, that
the digits to the right of the decimal point have a similar
place value (hundreds, tens, units) as those to the left of the
decimal point.
It is advisable to complete Session 15 – Adding decimals
before attempting this session with your learners unless you
are sure they have mastered the ideas in that session.
앫 Copy of Sheet 2 – Number lines for display on board or
overheard projector.
For each pair or small group of learners you will need:
앫 Sheet 1– Checking work;
앫 calculator;
앫 range of different colour pens or pencils.
optional:
앫 Sheet 2 – Number lines.
For each learner you will need:
앫 mini-whiteboard, marker and cloth.
In order to recap learning on adding decimals (see Session 15),
ask learners to continue the following two sequences on their
mini-whiteboards.
5.1, 5.5, _____, _____, _____, _____, _____, _____,
(Adding on 0.4 each time)
8.8, 8.5, _____, _____, _____, _____, _____, ______,
(Subtracting 0.3 each time)
Some learners may find it difficult to transfer this
information accurately and may benefit from having it on a
prepared sheet.
When they have completed the two sequences, ask learners
to check their answers using a calculator. Hold a whole
group discussion about the errors that have arisen, showing
Sheet 2 – Number lines on the board or overhead projector.
INFO BOX: If some
learners are
struggling it may be
helpful for them to
use Sheet 2 –
Number lines.
Ask learners to sit in pairs or
groups of three. Each group will
need Sheet 1 – Checking work and
a calculator.
Ask learners to adopt the role of a
teacher and mark the completed
piece of work. They should first
correct the answers and then try to explain the thinking behind
the mistakes and write some advice for the learner. In this way,
learners examine and discuss some common errors.
Coloured pens
would be helpful
for marking the
work.
It is important that learners should
write comments and advice, and
not merely produce the correct
answers.
The types of mistakes made on Angela’s worksheet are
extremely common:
앫 treating the decimal point as if it were merely a dot
separating two whole numbers, for example 8.9 + 2.1 =
10.10; 0.25 – 0.1 = 0.24;
1
앫 combining fractions and decimals, for example 0. in
2
Question 14;
앫 treating time as though it is a decimal number in
Question 15;
앫 treating 1.4 as though it means one quarter.
As you move around the room, listen to learners’ explanations.
Note obvious misconceptions that emerge, for whole class
discussion. Encourage learners to explain the thinking behind
Angela’s errors.
Hold a whole group discussion about what has been learned,
drawing out misconceptions you have noticed and discussing
them explicitly. Ask questions to probe understanding and
revise what has been learned so far. For example:
Why is it a bad idea to read a decimal number like 0.25 as
zero point twenty five? (Because then it sounds bigger than
0.3.)
3
different from 3.4?
4
(The decimal point is not the same as a fraction bar.)
How is
I am trying to calculate how long a TV programme lasts. It
begins at half past seven pm and finishes at twenty five past
eight pm. Why can’t I just press ‘8.25 – 7.30 = ’ on my
calculator? (Because time is not decimal.)
Sheet 1 – Checking work
This worksheet was completed by Angela.
Correct her mistakes, without using a calculator.
Write some comments to Angela, explaining what she is doing wrong.
Name: Angela
Complete the following calculations:
1.
5.6 + 0.2 = 5.8
2.
6.9 + 0.2 = 6.11
3.
8.9 + 2.1 = 10.10
4.
0.9 – 0.6 = 0.3
5.
0.25 – 0.1 = 0.24
6.
0.15 – 0.1 = 0.14
Write the next three terms in each sequence.
7.
0.3, 0.6, 0.9, 0.12 , 0.15 , 0.18
(Adding on 0.3)
8.
8.2, 8.6, 8.10 , 8.14 , 8.18
(Adding on 0.4)
10.
0.28, 0.30 , 0.32 , 0.34
(Adding on 0.2)
11.
1, 0.6 , 0.11 , 0.16
(Adding on 0.05)
12.
1.8, 1.6 , 1.4 , 1.2
(Subtracting 0.2)
13.
2.12, 2.11 , 2.10 , 2.9
(Subtracting 0.1)
14.
0.8, 0.4, 0.2, 0.1 , 0.1 2 , 0.1 4
(Halving)
Estimate answers to the following two problems:
15.
How long do you spend sleeping in one year?
On average, I sleep about 7 hours 45 minutes each day.
So, during one year, I spend 7.45 × 365 = 2719.25 or
about 2 700 hours asleep.
16.
How long do you spend travelling to college in one year?
I spend a quarter of an hour each day travelling to and from college.
I am at college 5 days per week for 32 weeks.
So, during a year, I spend about 1.4 × 5 × 32 = 224 hours travelling.
2
1
0
0
1
2
3
4
5
6
7
8
9
10
Sheet 2 – Number lines