what is maths and where does it go?
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Learning Together
Session 5
Thursday 18th June 10:00
Decimals
#npfsmaths
Learning Together Session 5 Decimals:
• What is a decimal• Place value• Understanding decimals• Decimals link to fractions• Ordering decimals
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What is a decimal?
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What is a decimal?
Decimals are numbers that exist between whole numbers.
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What is a decimal?
Decimals are numbers that exist between whole numbers.
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What is a decimal?
Decimals are numbers that exist between whole numbers.
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How many coloured blocks are there
2
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How many coloured blocks are there
4
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How many coloured blocks are there
3
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How many coloured blocks are there
2 1
2
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How many coloured blocks are there
2 1
10
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What decimal fraction is shaded
100 1 2 3 4 𝟓 7 986
1
2= 0 • 5
0 • 5
= 0• 5
1
2
5
10= 0 • 5
1
2
= 0• 5
0 • 5
What decimal fraction is shaded
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How many coloured blocks are there
100 1 2 3 4 𝟓 7 986
1 1
2=1 • 5
1 • 5
The decimal point separates the whole number part from the fractional part
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How many coloured blocks are there
100 1 2 3 4 𝟓 7 986
6 1
2=6 • 5
6 • 5
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1
=0.11
10
Ones Tenths
0 1
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10 0 • 1 0 • 2 0 • 3 0 • 4 𝟎 • 𝟓0 • 7 0 • 90 • 80 • 6
0 • 1
0 • 2
0 • 3
0 • 4
0 • 5
0 • 6
0 • 7
0 • 8
0 • 9
1 • 0
1 • 0
11
10= 0•1
2
10= 0• 2
3
10= 0• 3
4
10= 0• 4
5
10= 0• 5
6
10= 0• 6
7
10= 0• 7
8
10= 0• 8
9
10= 0• 9
10
10= 1• 0
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1
Ones TenthsOnes Tenths
0 4
4
10= 0 • 4
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1
Ones TenthsOnes Tenths
0 9
9
10= 0 • 9
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Ones TenthsOnes Tenths
1 6
16
10= 1 • 6
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How many coloured blocks are there
1 4
10=1 • 4
100 1 2 3 4 𝟓 7 986
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How many coloured blocks are there
2 7
10=2 • 7
100 1 2 3 4 𝟓 7 986
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How many coloured blocks are there
9 8
10=9 • 8
100 1 2 3 4 𝟓 7 986
All slides and resources can be found atwww.countonus.org.uk/learning-together
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1
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the shaded section = 0 • 3
10 0 • 1 0 • 2 0 • 3 0 • 4 𝟎 • 𝟓0 • 7 0 • 90 • 80 • 6
1 • 0
More decimal numbers exist in between0 and 0•10•1 and 0• 20• 2 and 0• 3 … . .etc
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What does the shaded section represent here?
1
100
1
100= 0 • 01
Ones Tenths Hundredths
0 0 1
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Ones Tenths Hundredths
0 0 1
1
100= 0 • 01
3
100= 0 • 03
Ones Tenths Hundredths
0 0 3
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Ones Tenths Hundredths
0 0 3
3
100= 0 • 03
8
100= 0 • 08
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Ones Tenths Hundredths
0 0 8
8
100= 0 • 08
10
100= 0 • 10
1
10= 0 • 1
1
10=
10
100= 0 • 1 = 0 • 10
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Ones Tenths Hundredths
0 1 0
10
100= 0 • 10
Ones Tenths Hundredths
0 2 3
23
100= 0 • 23
Ones Tenths Hundredths
0 2 3
3
100= 0 • 03
2
10= 0 • 2
0 • 2 + 0 • 030
= 0 • 23
45
100
Ones Tenths Hundredths
0 4 5
4
10
5
100
98
100
Ones Tenths Hundredths
0 9 8
9
10
8
100
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1
10
1
1001
= 0 • 1 = 0 • 01
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Ones Tenths HundredthsOnes Tenths Hundredths
1 3 4
Ones Tenths Hundredths
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Ones Tenths Hundredths
1 4 8
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Ones Tenths Hundredths
1 6 9
Ones Tenths Hundredths
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Ones Tenths Hundredths
2 3 1
Ones Tenths Hundredths
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Ones Tenths Hundredths
2 1 4
Ones Tenths Hundredths
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Ones Tenths Hundredths
5 3 4
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Ones Tenths Hundredths
2 6 3
Ones Tenths Hundredths
1 2 2
Ones Tenths Hundredths
3 8 5TOTAL =
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0 • 2
Ordering decimalsPut these decimals in order of size smallest to biggest
0 • 17 0 • 3 0 • 33
0 • 03
When ordering decimals it is helpful to have all the decimals with the same number of decimal places (pad with zeros to help)
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0 • 2𝟎
Ordering decimalsPut these decimals in order of size smallest to biggest
0 • 17 0 • 3𝟎 0 • 33
0 • 03
When ordering decimals it is helpful to have all the decimals with the same number of decimal places (pad with zeros to help)
0 • 03 0 • 17 0 • 2𝟎 0 • 3𝟎 0 • 33
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0 • 17
Ordering decimalsPut these decimals in order of size smallest to biggest
0 • 7 0 • 79 0 • 007
0 • 07
When ordering decimals it is helpful to have all the decimals with the same number of decimal places (pad with zeros to help)
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0 • 17𝟎
Ordering decimalsPut these decimals in order of size smallest to biggest
0 • 7𝟎𝟎 0 • 79𝟎 0 • 007
0 • 07𝟎
When ordering decimals it is helpful to have all the decimals with the same number of decimal places (pad with zeros to help)
0 • 007 0 • 07𝟎 0 • 17𝟎 0 • 7𝟎𝟎 0 • 79𝟎
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Adding Decimals 0 • 9 + 0 • 6
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Adding Decimals 0 • 9 + 0 • 6
1 • 5
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Adding Decimals
James has a piece of wood that measure 0.8m. He joins another piece that is 0.5 m long. How long is the new piece?
𝟎 • 𝟓 1• 𝟎 1• 𝟓0
0• 𝟖
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Adding Decimals
James has a piece of wood that measure 0.8m. He joins another piece that is 0.5 m long. How long is the new piece?
𝟎 • 𝟓 1• 𝟎 1• 𝟓0 1• 𝟑𝐦0• 𝟖
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Slides and resources atwww.countonus.org.uk/learning-together/
#npfsmaths
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Slides and resources atwww.countonus.org.uk/learning-together/
#npfsmaths
YouTube
Follow us on Twitter and Facebook@CountOnUsEd
https://www.surveymonkey.co.uk/r/learningtogetherfeedback
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0 • 02 × 10
= 0 • 2
Multiplying decimals by 100 • 02
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0 • 03 × 10
= 0 • 3
Multiplying decimals by 100 • 03
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0 • 07 × 10
= 0 • 7
Multiplying decimals by 10
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0 • 02 × 100= 2
Multiplying decimals by 100
10 20 30 40 50 60 70 80 90 100
• 000 • 02 × 100 = 2
How would you do 90 + 50
90 + 10 + 40140
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How would you do £0•90 + £0•50
£0•90 + £0•10 + £0•40£1•00 + £0•40
£1•40
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Draw 9 dots in the 1st 10 frame
Twitter: @CountOnUsEd www.countonus.org.uk #NumeracyBluePrints chris@countonus.org.uk
£1.00 £1.40£0.90
+£0.40+£0.10
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100 1 2 3 4 𝟓 7 986
£1 _
£1 _
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£1
= 10p
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£1
10p
20p
30p
40p
50p
60p
70p
80p
90p
100p
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£1
£0.10
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£1
£0.10
£0.20
£0.30
£0.40
£0.50
£0.60
£0.70
£0.80
£0.90
£1.00
= £1.20
= £2.30
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= £1
= £0.18
= £0.82
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= £11p= £0.01
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