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Copyright © 3P Learning – These resources have been created in partnership with Dr. Marian Small.
For more information visit
www.mathletics.comFitting In
Questions to facilitate the learning
•
Could the two fractions be a fraction at the bottom of the tower and one near the top? Why or why not?
•
How could using equivalent fractions help you figure out an answer?
•
How could using fraction operations help you figure out an answer?
Scaffolding the learning
•
How many
1
4
s fit into
1
2
? How might that help you get a solution?
•
What fraction fits into
1
3
twice? Three times? How might that help you get a solution?
Extending the learning
Students might look for fractions that fit into other fractions about 1
1
3
times.
What’s the point of this task?
Asking students to find a fraction that fits into another exactly 2
1
2
times is actually asking a division or
multiplication question, i.e. If
a
÷
b
= 2
1
2
, what are
a
and
b
? or if 2
1
2
x
a
=
b
, what are
a
and
b
? But using
the fraction tower makes the task accessible even to those students whose skills with multiplying and
dividing fractions are either missing or minimal. Those students can count on visual cues to help them.
Some students might use equivalent fractions to determine solutions. For example, since
2
10
=
1
5
and
3
15
=
1
5
, that means
1
10
fits into
1
5
twice and
1
15
fits into
1
5
three times, so perhaps
1
12
is a reasonable solution.
Although some students might use the tower to notice that
1
5
and
1
2
work, that
1
10
and
1
4
work, that
1
15
and
1
6
work and that
1
20
and
1
8
work, some students will generalise and realise that any fractions of the
form
1
5
n
and
1
2
n
work, even though they do not see them on the tower. Other students will notice that if
1
10
and
1
4
work, so do
2
10
and
2
4
or
3
10
and
3
4
, etc.
The use of the term ‘about’ leaves latitude for students to determine other solutions, e.g.
1
9
and
1
4
or
1
20
and
1
9
.
Number