Fractions and Decimals 29_Overview of Learning Plan
(Year 6) ACMNA131, ACMNA132 NSW MA3 7NA
Explain percentages as hundredths, related to fractions and decimals including on a number line.
THIS IS A SUMMARY OF THE LEARNING PLAN, DESCRIBING THE SEQUENCE OF LEARNING WHICH WILL OCCUR OVER MULTIPLE LESSONS. COMPLETE LEARNING PLAN STARTS ON THE NEXT PAGE.
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_Explicit Learning Plan
(Year 6) ACMNA131, ACMNA132 NSW MA3 7NA
THIS IS THE FULL LEARNING PLAN, WITH DETAILS OF ACTIONS AND QUESTIONS THAT MAY BE USED TO DEVELOP DEEP UNDERSTANDING OVER MULTIPLE LESSONS.
Explain percentages as hundredths, related to fractions and decimals including on a number line.
Resources: cards, counters, pencil, paper
EXPLICIT LEARNING
What could we do?
Focuses
children’s
thoughts on the
Children think about, talk and listen to a friend about, then have the
concept, exposing
opportunity to share what they already know.
current
understanding and
any
misconceptions
Reviews
fractions.
(Fractions and
Decimals 7, 8, 9)
Display an Egyptian fraction, for example,
Display fractions with numerator and denominator, for example,
1
3
4
3
4
3
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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.
►
We've looked at how the Ancient Egyptians gave us the
first recording of fractions about 3000 years ago.
►
And we found that fractions were recorded using a
numerator and denominator.
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Reviews
decimals.
(Fractions and
Decimals 11, 12)
►
We found that about 500 years ago, Europeans and
Persians extended whole number place value to include
fractions by dividing one by 10 to get tenths.
►
Then dividing tenths by 10 to get hundredths, and dividing
hundredths by 10 to thousandths …
►
Today we’re going to investigate another way that we can
record hundredths.
►
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.
►
Over time the word changed to percent.
►
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?
Display a multiplicative place value chart, for example,
Introduces
hundredths as
percentages. top
Record, for example, percent
Record, for example, percent means hundredth
Record, for example, %
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1
Record, for example, 100
Read the fraction, for example, one
1
100
hundredth
Record, for example, 0.01
Read the decimal using a place value
chart, for example,
0
0
1
►
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?
►
Can we record one-hundredth as a decimal?
►
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?
►
Is 50 hundredths equivalent to a half?
Record, for example, 1%
Read the percentage, for example, 1%
one hundredth
Reviews
fractions and
decimals on a
number line.
(Fractions and
Decimals 22)
Display a number line between zero and 1, for example,
0
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Place 50 hundredths half way along the number line, for example,
50
0
Is 50 half of 100?
►
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 placing another hundredth as a fraction on the
number line.
►
Where would 25 hundredths go?
►
Is 25 hundredths equivalent to a quarter?
►
Is 25 a quarter of 100?
►
Let’s place 25 hundredths a quarter of the way along the
number line.
►
Let’s record 25 hundredths as a decimal.
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. top
Place 50 percent half way along the number line, for example,
50
0
100
1
0.5
50%
Place 25 hundredths a quarter of the way along the number line, for
example,
0
25
50
100
100
1
0.5
50%
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Place 0.25 a quarter of the way along the number line, for example,
0
25
50
100
100
0.25
0.5
►
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.
►
Let’s placing another hundredth as a fraction on the
number line.
►
Where would 10 hundredths go?
►
Is 10 hundredths equivalent to 1 tenth?
►
Is 10 a tenth of 100?
►
Let’s place 10 hundredths, a tenth of the way along the
number line.
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%
1
Place 10 hundredths a tenth of the way along the number line, for
example,
0
10
25
50
100
100
100
0.1
0.5
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Place 0.1 a tenth of the way along the number line, for example,
0
10
25
50
100
100
100
0.1
1
0.5
►
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.
►
Let’s record 10 hundredths as a percentage.
►
Is 10 hundredths, 10 percent?
►
Let’s place 10 percent a tenth of the way along the
number line.
50%
Place 10 percent a tenth of way along the number line, for example,
0
10
25
50
100
100
100
0.1
1
0.5
50%
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Email: [email protected]
Twitter: @learn4teach
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