Download Decimal Numbers

TOPIC
10
Decimal Numbers
Strand: Number
Strand unit: Decimals
404
424
425
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Identify place value of whole numbers and decimals to 2 places.
Express tenths and hundredths as fractions and decimals.
Identify place value of whole numbers and decimals to 2 places and write in
expanded form.
Order decimals on the number line.
Looking back: What the 3rd class programme covered
1. Writing tenths in decimal form.
2. Ordering decimals (0.1, 0.2, 0.3, etc.) on a number line.
Maths skills used in this topic
1. Applying and problem-solving: Apply mathematical concepts and processes, and plan and
implement solutions to problems, in a variety of contexts.
2. Reasoning: Reason, investigate and hypothesise with patterns and relationships in mathematics.
100 square (10 x 10), number line, abacus
Vocabulary
Hundredth, expand, necessary, unnecessary
Teaching points
Importance of place value:
1. Just as 79 and 709 have different values, so too 0.07 and 0.7.
2. In which number has 8 the greater value: 0.83 or 0.98? Some children might
incorrectly choose 0.98 because this number is greater than 0.83.
3. Unnecessary zeroes: With whole numbers, a zero preceding non-zero numerals is unnecessary
(08 = 8). These might be termed leading zeroes. With decimals the opposite is true (0.80 =
0.8). These might be termed trailing zeroes.
Note: While trailing zeroes are not strictly necessary in decimals, they are sometimes required
by convention. For example with money, 6 euro and 30 cent will be written as €6.30 (and not
as €6.3). Furthermore in 5th class and later, the student may be asked to round a number
such as 73.402 to 2 decimal places. The correct answer would be 73.40 (and not 73.4).
Fans:
1
2 3
Show 10 as a decimal 0.1, repeat with 10 , 10 , etc. Show 1 cent as a decimal.
Then 2 cent, 3 cent, etc. Leading up to 10 cent, 20 cent, etc.
Target board 10:
Show each decimal number as euro, e.g. 0.95= 95 cent. What must I add to each decimal
number to make the next whole number?
Target board 5:
Change each fraction number to a decimal number.
Topic suggestions
1. Use 100 squares to introduce the idea of one hundredth. Begin by dividing the 100 squares
1
into 10 rows, each of which will be 10 of the whole. Then progress to hundredths. Point out
1
the connection between tenths and hundredths – there are 10 hundredths in 10 .
2. Look for examples of things that are divided into 100 equal parts: euro and cent, metre and
centimetre.
3. Decimal bingo: There are suggested bingo sheets online (you will only need a few photocopies
of the page). These are unique bingo cards. Give each child one card. Call out decimal
questions (make sure to keep a note of the questions you call). All answers should be range
from 0.01 to 1 unit. If the answer to the question is on the child’s card they cross it out. Play
‘first to have a line’ and ‘first to have a full house’.
Sample questions:
1
What decimal number is the same as 4 ?
What decimal number is 0.01 less than 0.8?
What decimal number lies between 0.58 and 0.6?
Activity A
Decimals in the world around us: Each of the pictures has a decimal point. The pictures should
serve to open discussion on how decimals are everywhere around us. They enable us to
accurately describe, measure and count. Discuss each of the pictures in turn. Ask the children
to cite other instances of where decimals are in everyday use.
Differentiation
Lower attainers:
See, separate activity page.
Higher attainers:
‘Skip’ decimal counting:
1. Up: Starting at 0.8 count up, 0.03 at a time until the value is greater than 1 (0.83, 0.86, 0.89).
Try intervals of 0.02, 0.04, 0.05, 0.09, 0.11.
2. Down: Starting at 1.3, count down, 0.04 at a time until the value is less than 1 (1.26, 1.22,
1.18, 1.14, 1.10, 1.06, 1.02, 0.98).
Try other intervals and starting points.
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Topic
Topic
10
10
1. Colour 0.1
0.4
0.7
0.9
1. Write each fraction as a decimal.
(a)
17
100
_____
29
100
(b)
_____
(c)
87
100
_____ (d)
93
100
_____ (e)
11
100
_____
2. Write each decimal as a fraction.
(a) 0.47 _____ (b) 0.73 _____ (c) 0.81 _____ (d) 0.07 _____ (e) 0.3 _____
3. True or false?
2. Colour 0.06
0.60
0.43
(a) 0.25 =
0.82
1
25
_____
(b) 0.2 = 0.20 _____
(c) 0.9 =
9
10
_____
(d)
1
2
= 1.2 _____
4. Put the correct sign (< > =) between each pair of numbers.
(a) 0.56
0.65
(b) 0.4
(d) 0.08
0.8
(e)
(g) 0.60
0.6
(h) 0.25
1
0.40
(c) 0.99
0.19
1.0
(f) 0.13
0.12
1
4
(i) 0.01
1
10
5. What decimal of €1 is 65c? _____
dt
h
s
7. Rewrite each of these decimals and leave out any unnecessary zeroes.
dr
e
n
s
hu
n
dt
h
un
te
ten
th
s
s
dr
e
n
hu
n
dt
h
un
te
ten
th
s
dr
e
dt
h
s
s
s
s
s
hu
n
n
ten
th
s
dr
e
un
te
6. Which is greater 0.33 or 0.3? _____
90.07
its
ten
th
s
s
62.04
its
n
hu
n
dt
h
un
te
its
dr
e
s
its
its
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hu
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un
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ten
th
s
3. Colour the fireworks to show the number.
23.59
84.26
70.25
(a) 03.60 _____
(f) 700
_____
(b) 7.00 _____
(c) 9.80 _____
(g) 007 _____
(h) 9.0 _____
(d) 3.08 _____
(i) 1.10 _____
(e) 805.60 _____
(j) 2.02
_____
8. What number comes next in each of these patterns?
(a) 0.3
4. Which is greater?
(a) 1.5 or 3.4
______ (b) 1.7 or 7.1
______ (c) 2.3 or 1.3 ______ (d) 1.8 or 1.6 ______
(e) 2.9 or 3.0
______ (f) 5.0 or 0.5
______ (g) 5.9 or 6.0 ______ (h) 7.0 or 0.9 ______
(i) 0.46 or 0.64 ______ (j) 0.8 or 0.81 ______ (k) 4 or 0.44
______ (l) 3 or 0.03 ______
3
8
(c) 1.85 __________
(d) 4.75 __________
(g) 8.33 __________
(a) 0.71 0.91 0.31 _____, _____, _____
(b) 0.48 0.46 0.49 _____, _____, _____
(c) 0.37 0.31 0.38
_____, _____, _____
(d) 1.23 1.48 1.57 _____, _____, _____
(e) 3.8 3.4 3.6
_____, _____, _____
(f) 5.0 5.1 4.9
Page 133: Decimals
1.7
1.8
1.9 _____
(c) 0.56 0.57 0.58 0.59 _____
(d) 0.96 0.97 0.98 0.99 _____
(e) 4.93 4.95 4.97 4.99 _____
(f) 2.85 2.9
2.95 3
_____
___________, ___________
6. Put these decimals in order. Start with the smallest.
Name: _______________________________________
_____
(b) 1.6
_____, _____, _____
Date: ___________________
10. It took Freddy the Flier 11.04 seconds to run 100 metres and it took Jimmy the Zip 10.96
seconds to run the same distance. Who was faster and by how much? ___________, ___________
11. Where is the decimal point in a whole number such as 57? Why is it not shown? ______________
__________________________________________________________________________________
Name: _______________________________________
Date: ___________________
© Folens Photocopiables
(f) 9.80 __________
0.6
are 10 or older in the school? What decimal fraction of the children are younger than 10?
© Folens Photocopiables
(e) 9.08 __________
0.5
9. 0.37 of the children in a school are 10 or older. Does this mean that there are 37 children who
(m) 0.08 or 0.80 ______ (n) 1.23 or 1.09 ______ (o) 2.86 or 2.8 ______ (p) 0.99 or 1 ______
5. Expand: Example 2.38 = 2 + 10 + 100
(a) 2.49 __________
(b) 3.16 __________
0.4
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Linkage
Fractions: There is a very close relationship between fractions and decimals. Each is a different
way of partitioning a unit. As fractions are generally easier to visualise, they usually precede
decimals in the order of learning.
Integration
SESE Geography: Investigation skills, many scientific and geographical investigations involve
interpreting readouts from electronic displays (dials, meters, etc.), some of which include a decimal
point (e.g. weighing scales, fuel pump, electricity meter, electronic timer and range finder).
Maths at home/parental involvement
Look at the electricity/gas/water meters – does the display have a decimal point? Examine the
milometer in the car – does it show 1 tenth of a kilometre (sometimes in different colour)?
Notes
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