FRACTIONS AND DECIMALS 29 – TEACHING PERCENTAGES, RELATED TO HUNDREDTHS AS FRACTIONS AND DECIMALS
ESSENTIAL PRIOR, RELATED AND NEXT LEARNING
Identify students’ current levels of understanding using tracking data, and formative embedded or separate assessment for this concept, and for the essential prior learning.
Essential Prior Learning
Differentiate learning
by including the
segment of each
Teaching Plan that
children demonstrate
they are ready to
investigate.
Fractions and Decimals 7, 9 and 19 Roles of the denominator, numerator
and vinculum
Fractions and Decimals 11, 12 Place
Value 20, 21 – Multiplicative Place
Value to tenths and hundredths
Essential Related Learning
Essential Next Learning
Fractions and Decimals 10, 14, 22 –
Fractions and decimals on a number
line
Fractions and Decimals 28 - Equivalent
fractions and fractions in their simplest
form by multiplying or dividing
numerator and denominator
Fractions and Decimals 30, Money and
Financial Mathematics 13 – Percentage
discounts
Use assessment data to select the levels of this concept, or essential related concepts, and the segments of each explicit teaching plan, to teach.
TEACHING VIDEOS, EXPLICIT TEACHING PLAN, INVESTIGATION, REFLECTION, PROBLEM SOLVING
The videos and the explicit teaching plan are divided into the same segments of the concept.
TEACHING SEGMENT and VIDEO 1: Explain percentages as hundredths, related to fractions and decimals.
VIEW the videos before teaching, to develop YOUR understanding and metalanguage, then teach the concept using YOUR understanding and metalanguage and the Explicit
Teaching PowerPoint, and/or SHOW the video to the whole class / groups of children / individual children to develop THEIR understanding and metalanguage.
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FRACTIONS AND DECIMALS 29 – TEACHING PERCENTAGES, RELATED TO HUNDREDTHS AS FRACTIONS AND DECIMALS
FRACTIONS AND DECIMALS 29_OVERVIEW OF TEACHING PLAN
(Year 6) ACMNA131, ACMNA132 NSW MA3 7NA
Explain percentages as hundredths, related to fractions and decimals.
THIS IS A SUMMARY OF THE EXPLICIT TEACHING PLAN, DESCRIBING THE SEQUENCE WHICH WILL OCCUR OVER MULTIPLE LESSONS. THE COMPLETE EXPLICIT TEACHING PLAN STARTS ON PAGE 3.
Children:
Relate
percentages  explain one hundredth as a fraction
and as a decimal, for example,
to
hundredths
as fractions
and
decimals.
Children
 ask one another questions about percentages as hundredths,
for example:
0
0
1
 explain percent as meaning
hundredth, for example,
Record
hundredths  record hundredths as fractions, decimals and percentages on a
as
number line, for example,
fractions,
decimals
and
percentages
on a number
line.
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
What is a hundredth?

How would we record a hundredth as a fraction?

How would we record a hundredth as a decimal?

What does percent mean?

How would we record a hundredth as a percentage?

How could we record hundredths as fractions, decimals and
percentages on a number line?
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FRACTIONS AND DECIMALS 29 – TEACHING PERCENTAGES, RELATED TO HUNDREDTHS AS FRACTIONS AND DECIMALS
FRACTIONS AND DECIMALS 29_EXPLICIT TEACHING PLAN
(Year 6) ACMNA131, ACMNA132 NSW MA3 7NA
FULL EXPLICIT TEACHING PLAN, EMBEDDING THE INVESTIGATIONS, REFLECTIONS AND PROBLEMS THAT MAY BE USED TO DEVELOP DEEP UNDERSTANDING OVER MULTIPLE LESSONS.
Resources: cards, counters, pencil, paper
What could we do?
Focuses
children’s
Children think about, talk and listen to a friend about, then have the
thoughts on the opportunity to share what they already know.
concept, exposing
current
understanding and
any
misconceptions
Reviews
fractions and
decimals.
(Fractions and
Decimals 7, 8, 9,
11, 12, Place Value
20, 21)
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Email: [email protected]
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What language could we use to explain and ask questions?
►
Today brings an investigation about percentages.
►
What do you know about percentages?
►
Talk about percentages with a friend.
►
Is anyone ready to share what they are thinking about
percentages?
►
We’ve investigated fractions.
►
And we found that we have 2 ways to express fractions –
as fractions and as decimals.
►
We found that fractions have been around for about 4
thousand years. And we found that Europeans and Persian
mathematicians extended multiplicative place value to
include fractions as decimals about 500 years ago.
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FRACTIONS AND DECIMALS 29 – TEACHING PERCENTAGES, RELATED TO HUNDREDTHS AS FRACTIONS AND DECIMALS
Introduces
Display a multiplicative place value chart, for example,
►
Today we’re going to investigate another way that we can
express fractions!
►
At around the same time, as the Europeans and Persians
decided to extend whole number place value to include
fractions, people began to call hundredths ‘per centum’.
►
Per centum means out of a hundred, or simply hundredth.
Record, for example, percent
►
Over time the word changed to percent.
Record, for example, percent means hundredth
►
So percent is just another word for the fraction one
hundredth.
►
We know that in Mathematics, we don’t use words, we
have symbols.
►
The symbol for percent is %.
►
Does the symbol for percent look a little like a fraction
symbol with a numerator, a vinculum and a denominator?
►
So how many ways do we have to record one-hundredth?
►
Can we record it as fraction?
►
How would we record one-hundredth as a fraction?
►
Do we read the fraction, 1 hundredth?
hundredths as
percentages.
Record, for example, %
1
Record, for example, 100
Read the fraction, for example, one
1
100
hundredth
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FRACTIONS AND DECIMALS 29 – TEACHING PERCENTAGES, RELATED TO HUNDREDTHS AS FRACTIONS AND DECIMALS
Record, for example, 0.01
►
Can we record one-hundredth as a decimal?
Read the decimal using a place value
chart, for example,
►
How would we record one-hundredth as a decimal?
►
Do we read the decimal, 1 hundredth?
►
Can we record one-hundredth as a percentage?
►
How would we record one-hundredth as a percentage?
►
So do we have 3 ways to record a hundredth?
►
Do we read the percentage, 1 hundredth?
►
We’ve investigated placing fractions and decimals on a
number line.
►
We found that fractions and decimals come between
whole numbers.
►
Do you think we could place percentages on a number
line? Let’s investigate!
►
Let’s start by placing a hundredth as a fraction on the
number line.
►
Where would 50 hundredths go?
0
0
1
Record, for example, 1%
Read the percentage, for example, 1%
one hundredth
Reviews
fractions and
decimals on a
number line.
(Fractions and
Decimals 10, 14,
22)
Display a number line between zero and 1, for example,
0
1
Reviews
equivalent
fractions in their
simplest form.
(Fractions and
Decimals 28)
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FRACTIONS AND DECIMALS 29 – TEACHING PERCENTAGES, RELATED TO HUNDREDTHS AS FRACTIONS AND DECIMALS
50
Record, for example, 100 =
1
Place 50 hundredths half way along the number line, for example,
50
0
1
100
Place 0.5 half way along the number line, for example,
50
0
1
100
0.5
Introduces
percentages on a
number line.
►
We’ve investigated creating fractions in their simplest
form.
►
Is 50 hundredths equivalent to a half?
►
Let’s place 50 hundredths half way along the number line.
►
Let’s record 50 hundredths as a decimal.
►
Is 50 hundredths and 5 tenths equivalent?
►
Is 50 hundredths 0.5?
►
Is 5 tenths the same as 50 hundredths?
►
Let’s place 0.5 half way along the number line.
►
Let’s record 50 hundredths as a percentage.
►
Is 50 hundredths 50 percent?
►
Let’s place 50 percent half way along the number line.
►
Let’s place another hundredth as a fraction on the number
line.
►
Where would 25 hundredths go?
►
We’ve investigated creating fractions in their simplest
form.
2
Place 50 percent half way along the number line, for example,
50
0
100
1
0.5
50%
Reviews
equivalent
fractions in their
simplest form.
(Fractions and
Decimals 28)
25
Record, for example, 100 =
1
4
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FRACTIONS AND DECIMALS 29 – TEACHING PERCENTAGES, RELATED TO HUNDREDTHS AS FRACTIONS AND DECIMALS
Place 25 hundredths a quarter of the way along the number line, for
example,
0
25
50
100
100
►
Is 25 hundredths equivalent to a quarter?
►
Let’s place 25 hundredths a quarter of the way along the
number line.
►
Let’s record 25 hundredths as a decimal.
►
Is 25 hundredths 0.25?
►
Let’s place 0.25 a quarter of the way along the number
line.
►
Let’s record 25 hundredths as a percentage.
►
Is 25 hundredths, 25 percent?
►
Let’s place 25 percent a quarter of the way along the
number line.
1
0.5
50%
Place 0.25 a quarter of the way along the number line, for example,
0
25
50
100
100
0.25
0.5
1
50%
Place 25 percent a quarter of the way along the number line, for
example,
0
25
50
100
100
0.25
0.5
25%
50%
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FRACTIONS AND DECIMALS 29 – TEACHING PERCENTAGES, RELATED TO HUNDREDTHS AS FRACTIONS AND DECIMALS
►
Let’s place another hundredth as a fraction on the number
line.
►
Where would 10 hundredths go?
►
We’ve investigated creating fractions in their simplest
form.
►
Is 10 hundredths equivalent to 1 tenth?
►
Let’s place 10 hundredths, a tenth of the way along the
number line.
►
Let’s record 10 hundredths as a decimal.
►
Is 10 hundredths 0.10?
►
Is 10 hundredths and 1 tenth equivalent?
►
Is 10 hundredths 0.1?
►
Let’s place 0.1 a tenth of the way along the number line.
0.5
►
Let’s record 10 hundredths as a percentage.
50%
►
Is 10 hundredths, 10 percent?
Place 10 percent a tenth of way along the number line, for example,
►
Let’s place 10 percent a tenth of the way along the
number line.
Reviews
equivalent
fractions in their
simplest form.
(Fractions and
Decimals 28)
10
Record, for example, 100 =
1
10
Place 10 hundredths a tenth of the way along the number line, for
example,
0
10
25
50
100
100
100
0.1
1
0.5
Place 0.1 a tenth of the way along the number line, for example,
0
10
25
50
100
100
100
0.1
0
10
25
50
100
100
100
0.1
1
1
0.5
50%
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FRACTIONS AND DECIMALS 29 – TEACHING PERCENTAGES, RELATED TO HUNDREDTHS AS FRACTIONS AND DECIMALS
Introduces
the investigation,
reflection and
problem solving
related to this
segment of the
concept.
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Email: [email protected]
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