Fractions and Decimals 19_Guided and Independent Investigations
(Year 5) ACMNA102, NSW MA3-7NA
Explain the role of the vinculum as meaning divided by.
GUIDED INVESTIGATION
Children learn
how to investigate the concept by following teacher’s instructions until
they are ready to investigate the concept independently.
INDEPENDENT INVESTIGATION
Children investigate and explain independently over many lessons at their current
level of understanding informing both themselves and the teacher of their current level of
understanding
Resources: cards, pencil, paper
What could we do?
What language could we use to ask
questions and explain?
Children:
What could we do?
What language could we use to explain?
Children:
1. select 2 cards to make a fraction as
guided by the teacher
2. record their fraction as a division
number sentence as guided by the
teacher
3. select paper strips to implement the
number sentence
 What fraction did you make?
1. sit in pairs
 My fraction is ...
 How could you record your
fraction as a number sentence?
2. select 2 cards to make a fraction that
is neither too easy nor too challenging
 I recorded my fraction as a number
sentence as …
 How could you divide your strips?
3. record their fraction as a division
number sentence
 I divided my paper strips into by …
 What does the vinculum mean?
4. select paper strips to implement the
number sentence
4. explain the meaning of the vinculum
as divided by
 The fraction I made is …
 The vinculum means divided by.
5. explain the meaning of the vinculum
as divided by
REFLECTION Before, during and after lessons, children discuss
What is a vinculum?
then record responses to reflection questions to inform themselves
and the teacher of their current level of understanding.
What does the vinculum mean?
How can we record our fraction as a number sentence using the meaning of the vinculum?
How does understanding what the vinculum means, help us to divide smaller numbers by larger
numbers?
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1
CONGRUENT INVESTIGATIONS
If you can’t explain it
simply, you don’t
understand it well enough.
These investigations allow children to investigate and explain the concept in new and varied situations, providing formative assessment
data for both the child and the teacher.
‘Doing’ mathematics is not enough and is not a good indicator of understanding.
Anyone who has
Investigation takes time as children develop both the capacity and meta-language to explain mathematical concepts
never made a
at their current level of understanding.
mistake has never
tried anything new.
As they investigate, allow children to experience confusion (problematic knowledge) and to make mistakes to develop
resilience and deep understanding,
 Children select an Ace and another card to make a unit fraction. They record the fraction. They use the meaning of the
Unit fractions
numerator as the number of parts in the whole and the meaning of the denominator as the number of parts we have divided
vinculum.
the whole into to record a division number sentence, for example, 1 ÷ __ = . They select a strip of paper. They divide by ___
1
by dividing the strip into ___ equal parts. Identify that the strip is 1 divided by ___ which equals . They record a number
sentence to describe how they divided the paper. They explain the meaning of the vinculum.
Non-unit
fractions
vinculum.

Children select 2 cards to make a non-unit fraction that they are ready to investigate. Children record the fraction, for
5
example, . They use the meaning of the numerator as the number of parts in the whole and the meaning of the denominator
8
as the number of parts we have divided the whole into to record a division number sentence, for example, 5 ÷ 8 = .
They select 5 strips, which they divide by 8 by either dividing each strip into 8 equal parts, for example,
Children identifying that each strip is 1 divided by 8 which equals one-eighth, so 5 divided by 8 must
equal 5 of the eighths which is five-eighths OR by dividing the five strips into 8 equal parts, for example,
and identifying that one part is five-eighths.
Children then look at the number sentence, for example, 5 ÷ 8 =
Pizzas divided by
children.

5
8
to identify that the vinculum means divided by.
Children are told that they have a number of pizzas, for example, 6. They are told that they must share the pizza between a
higher number of children, for example, 10. They draw the pizzas and divide them between 10 children either by dividing
each pizza by 10 and giving each child a piece of each pizza, or by dividing the 6 pizzas into 10 equal parts. They record their
6
number sentence explaining that they divided 6 by 10, to get the fraction six-tenths, for example, 6 ÷ 10 = 10 . They explain
that the vinculum means divided by.
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Email: [email protected]
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Divide milk to
make cakes.

Children are told that they have 6 cups of milk to make 8 cakes. They work out the fraction of a cup of milk used in each cake.
Divide improper
fractions.

In pairs, children investigate improper fractions using the vinculum to mean divided by. For example, the improper fraction
is recorded as
15
8
1
15
8
= 15 ÷ 8 = 2 8
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Email: [email protected]
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Investigating the Meaning of the Vinculum as Divided By.
Fractions and Decimals 19 Explain the role of the vinculum as meaning divided by.
Select an Ace and another card to make a unit fraction.
Record the fraction.
Use the meaning of the numerator as the number of parts in the whole and the
meaning of the denominator as the number of parts we have divided the whole into
to record a division number sentence, for example, 1 ÷ __ = .
Select a strip of paper.
Divide by ___ by dividing the strip into ___ equal parts.
Identify that the strip is 1 divided by ___ which equals
1
.
Record a number sentence to describe how you divided the paper.
Explain the meaning of the vinculum.
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Investigating the Meaning of the Vinculum as Divided By.
Fractions and Decimals 19 Explain the role of the vinculum as meaning divided by.
Select 2 cards to make a non-unit fraction that they are ready to investigate.
5
Record the fraction, for example, .
8
Use the meaning of the numerator as the number of parts in the whole and the
meaning of the denominator as the number of parts we have divided the whole into
to record a division number sentence, for example, 5 ÷ 8 = .
Select 5 strips.
Divide by 8 by either dividing each strip into 8 equal parts, for example,
Identify that each strip is 1 divided by 8 which equals one-eighth, so 5
divided by 8 must equal 5 of the eighths which is five-eighths
OR
by dividing the five strips into 8 equal parts, for example,
Identify that one part is five-eighths.
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Investigating the Meaning of the Vinculum as Divided By Value.
Fractions and Decimals 19 Explain the role of the vinculum as meaning divided by.
Have a number of pizzas, for example, 6.
Share the pizza between a higher number of children, for example, 10.
Draw the pizzas and divide them between 10 children either by dividing each pizza
by 10 and giving each child a piece of each pizza, or by dividing the 6 pizzas into 10
equal parts.
Record your number sentence explaining that you divided 6 by 10, to get the
6
fraction six-tenths, for example, 6 ÷ 10 = .
10
Explain that the vinculum means divided by.
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Investigating the Meaning of the Vinculum as Divided By.
Fractions and Decimals 19 Explain the role of the vinculum as meaning divided by.
Have some cups of milk to make a higher number of cakes, for example, 6 cups of
milk to make 8 cakes.
Work out the fraction of a cup of milk used in each cake.
Record a number sentence, explaining the meaning of the vinculum.
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Investigating the Meaning of the Vinculum as Divided By.
Fractions and Decimals 19 Explain the role of the vinculum as meaning divided by.
Investigate improper fractions using the vinculum to mean divided by.
For example, the improper fraction
15
8
could be recorded as
15
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8
= 15 ÷ 8 = 2
1
8