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Unit 4
Decimals
Focus
F
Recognise the equivalence between decimal and fraction
forms of one-half, quarters, tenths and hundredths
NC Level 4
Vocabulary decimal; decimal fraction; decimal point; decimal place; hundreds; tens; units; ones; tenths;
hundredths; one-place; two-place; equivalent; same as; fraction; one whole; half; quarter
Practise
Ask questions similar to the following to review and assess children’s
understanding of fractions and decimals: What does this fraction / decimal
represent? Which fraction / decimal shows three-tenths? What does this
shape show expressed as a fraction? What about as a decimal?
Teach
Recognise the equivalence between decimal and fraction
forms of tenths
w & Asse
vie
ss
Teach
Apply R
e
•
Display Discussion Book 4 pages 26 and 27, and draw children’s
attention to the fractions expressed as proper fractions, decimals and
shapes.
Teach
•
w & Asse
vie
ss
Review and Assess
Apply Re
Resources Discussion Book 4 pages 24–27; calculator (per child); several copies of RCM 28; coloured pencils
Practise
•
Display Discussion Book 4 page 24, and explain to the children that the
counting stick and 100 bead string both show the equivalences between
different fractions and decimals for tenths.
•
Ensure that the children realise that there are 100 beads on the bead string
and that these are coloured in groups of 10.
•
Point to a fraction on the tenths counting stick at the top of the page, e.g. 10
–3 ,
and moving your finger straight down, show the children the equivalent
decimal, i.e. 0·3.
•
Invite children to find other tenths on the counting stick and locate and say
the equivalent decimals.
•
Repeat, this time pointing to decimals and asking the children to find
equivalent fractions.
•
Repeat the above, this time using the bead string at the bottom of Discussion
Book 4 page 24.
•
Re-emphasise to the children how the counting stick and the bead string both
show tenths.
Recognise the equivalence between decimal and fraction
forms of hundredths
•
Display Discussion Book 4 pages 24 and 25, and explain to the children that
just as the 100 bead string on page 24 can show the equivalences between
different fractions and decimals for tenths, it can also show the fraction and
decimal equivalence for hundredths.
•
Once again ensure that the children realise that there are 100 beads on the
bead string and that these are coloured in groups of 10.
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Unit 4
Decimals
Focus F continued
Teach continued
•
•
•
•
Point to one of the labelled fractions on the 100 bead string at the top of
1 , and moving your finger straight down,
Discussion Book 4 page 25, e.g. 100
—
show the children the equivalent decimal, i.e. 0·01.
40 ,
Discuss with the children other labelled hundredths on the bead string, e.g. 100
—
64
30
56
— , before moving onto identifying unlabelled hundredths, e.g. 100
— , 100
—.
100
Invite children to find labelled and unlabelled hundredths expressed as
fractions on the bead string, and then say the equivalent decimal.
Repeat, this time pointing to decimals and asking the children to find
equivalent fractions.
Recognise the equivalence between decimal and fraction forms of one half
and quarters
•
Display Discussion Book 4 page 25, and explain to the children that the
counting stick shows the equivalences between different fractions and
decimals for one-half and quarters.
•
Point to a fraction on the counting stick, e.g. –14 , and moving your finger
straight down, show the children the equivalent decimal, i.e. 0·25.
•
Repeat for the other fractions on the counting stick, locating and saying the
equivalent decimals.
Recognise the equivalence between decimal and fraction forms of one half,
quarters, tenths and hundredths
•
•
•
•
Referring to Discussion Book 4 pages 24 and 25, ask a child to find 10
–5 on one
of the counting sticks / bead strings and discuss the relationship between 10
–5 ,
50 , –
1 and 0·5.
—
100 2
50 as a decimal? (0·5) What is –
1
Ask: If we know that 10
–5 equals 0·5, what is 100
—
2
5
5
1
as a decimal? (0·5) Locate 10
– , 0·5, 100
— and –2 on the counting sticks / bead
strings.
Provide each child with a calculator.
Explain to the children how a calculator can be used to convert a fraction into
a decimal. Demonstrate this by keying into the calculator: [5] [÷] [10] [=] to
reveal 0·5.
•
50 and –
1 are also
Ask the children to do the same before confirming that 100
—
2
equivalent to 0·5.
•
Repeat the above, reminding the children of equivalent fractions and decimals
10 = 1
25 = –
1 = 0·25, —
40 = 4
for quarters, tenths and hundredths e.g. 100
—
– = 0·1, 100
—
– =
10
4
100 10
75
3
0·4, 100
— = –4 = 0·75.
•
•
Next, display a copy of
RCM 28 and explain to the
children how this wall shows
the fractions and decimals
for a half, quarters, tenths
and hundredths.
1
1
2
1
4
0.25
0.5
1
2
1
4
0.25
1
4
0.25
1
1
1
1
1
1
1
Using coloured pencils,
10
10
10
10
10
10
10
shade the sections of the
0.1 0.1 0.1 0.1 0.1 0.1 0.1
diagram to show
50 = –
5 =–
2 =–
1 and that this
—
100 10
4
2
can expressed as
0·01 × 50 = 0·1 + 0·1 + 0·1 + 0·1 + 0·1 = 0·25 + 0·25 = 0·5.
0.5
1
10
0.1
1
4
0.25
1
10
0.1
1
10
0.1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1
100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01
•
76
Repeat for other fractions and decimals.