Task Card
What fraction of the shaded
figure does the green triangle
represent?
One Possible Explanation
Another Possible Explanation
It takes 5 green triangles to equal
1 shaded figure, so 1 triangle is 1
5
of the shaded figure.
1
5
3
4
2
It takes 6 blue rhombi to fill the
What fraction of the decagon
does the blue rhombus represent? decagon, so 1 blue rhombus represents
1
.
6
1
2
3
6
5
What fraction of the blue
rhombus does the trapezoid
represent?
4
It takes 3 triangles to fill the trapezoid
and 2 triangles to fill 1 rhombus (so 1
triangle = ½ rhombus). Then the
trapezoid represents 3 .
2
If I lay the rhombus on the trapezoid, I
would still need half of another rhombus
to fill the trapezoid. So one whole
rhombus and another half = one
trapezoid, or 1 ½ rhombi.
What is the fraction?
Task Card
If this hexagon is one whole,
find two-thirds.
One Possible Explanation
Another Possible Explanation
I need to divide the
hexagon into 3 equalsized parts, since it says
thirds. It takes 3 rhombi
to fill 1 hexagon, so 2
rhombi would be 2 .
3
If this hexagon is
one whole, find
one-third.
I can use 6 triangles to fill the hexagon,
and then put those 6 triangles into 3
equal groups. I have 2 triangles in each
group. 2 triangles = 1 rhombus, so 1
3
would be 1 rhombus.
1
4
2
5
1
3
3
6
2
4
5
6
If this blue rhombus is one whole, “Half” means 2 equal-sized parts, so I
need to divide the rhombus into 2 parts
find one-half.
using the triangle. 1 triangle = ½ rhombus.
1
2
What is the part?
Task Card
One Possible Explanation
Another Possible Explanation
If the triange is one-fourth, what Fourths means there are 4
equal-sized parts, and I
could the whole look like?
know that the triangle is
what one of those four
parts looks like, I need to
use 4 triangles to make the
whole.
If the blue rhombus is two-thirds, First, since the rhombus is
two-thirds, I need to
what could the whole look like?
divide it into 2 equal parts
(because that’s what the
numerator tells me). So if
1
2
2 triangles = 1 rhombus = 2 then
3
3
3 triangles =
which is one whole.
3
If the trapezoid equals 3 , then I can
9
If the red trapezoid is
three-ninths, what could the
whole look like?
count by three-ninth’s for each trapezoid
I add to the picture. 9 = 1 whole.
9
6
9
3
9
9
9
What is the whole?
Task Card
One Possible Explanation
If the dark green strip is one whole,
what fraction is the blue strip?
First I have to find a strip that will equally fill
both the dk green and blue strips. I can use the
light green strips. If my dark green is the whole,
and the light green is half of the dark green, then
3
3 light greens = , which = 1 blue strip.
2
If dark green is the whole, what
fraction is the yellow strip?
The yellow strip with 1 white rod equals the green
strip, so I need to divide the yellow strip equally
using the white rods to find answer the question.
Another Possible Explanation
5.
6
If brown is the whole, what
fraction is the orange strip?
First I figured out that 1 brown strip + 1 red strip
= 1 orange strip. Then, I used the red strips to
divide the brown one into four equal-sized parts
so that I knew what my denominator would be. So
5
orange strip =
.
4
What is the fraction?
Task Card
One Possible Explanation
If brown is the whole, find onefourth.
I need to find one-colored strip that will divide
the brown strip into four equal-sized parts. It
takes four red strips to make one brown strip,
so the red strip = ¼ the brown strip.
If dark green is one whole,
what strip is two-thirds?
I know I can use the white rods to fill every
other colored-rod equally, so 6 white rods = 1
dark green rod. Then, I need to divide the
white rods into 3 equal-sized groups (showing
thirds). Since the numerator says two-thirds, I
need to find which rod equals two of those
groups, and it is the pink rod.
If dark green is the whole,
what strip is three-halves?
First, I need to find halves by dividing my whole
(the green strip) into 2 equal parts. It takes 2
light green strips to fill 1 dark green strip, so I
add another light green to make three-halves,
and 1 blue strip = 3 light green strips.
Another Possible Explanation
What is the part?
Task Card
One Possible Explanation
If red is one-third, what strip is the
whole?
Since the fraction says one-third, I know that
there are 3 equal parts in the whole, so I just
use 3 red rods and find which one rod is the
same length, and it’s the green one.
If dark green is two-thirds, what
strip is the whole?
If yellow is five-fourths, what strip
is one whole?
If 10 counters are the whole set,
Another Possible Explanation
First, I need to decompose the green strip
using the numerator. I can use 2 light green
strips divide the green strip into 2 equal parts.
Then, I have to add on another light green strip
in order to make thirds, and find that the blue
strip = 3 light green strips.
I can use 5 white rods to make 1 yellow rod.
Since the denominator says “fourths” I know I
need to find which strip equals four of the
white rods, and that’s the purple strip.
There are 6 counters in my subset, and 10
What is the whole?
Task Card
what fraction of the set is 6
counters?
One Possible Explanation
counters in the entire set, so 6 counters =
Another Possible Explanation
6
.
10
These 16 counters are what
fraction of a whole set of 12
counters?
Well, if 12 is the whole, then I know that I have
more than 1 whole…I actually have 4 more
4
counters than 1 whole. So I have 1
.
12
4
(
-represents the parts left
12 -represents the whole)
What fraction of this set is black?
(Don’t answer in ninths.)
There are 3 equal-sized groups…1 of the groups
1
is black, so
of the group is black.
3
What is the fraction?
Task Card
One Possible Explanation
Another Possible Explanation
First, I need to make 4 equal-sized groups, so I
make 4 groups of 2 counters each.
If 8 counters are a whole set, how
many are in one-fourth of a set?
If 15 counters are
a whole, how many
counters make
three-fifths?
1 of these 4 groups would be 2 counters out of 8,
1 2
(
=
.)
4 8
I’ll divide up my counters into 5 equal groups
(since the denominator says fifths) until I run out
of counters.
That puts 3 counters in each group. Since the
numerator is 3, I need to find the number of
3
9
counters in 3 groups, so
=
. 9 counters
5
15
If 9 counters are a
whole, how many
are in five-thirds of
a set?
Since the denominator is “thirds”
the set needs to be divided into 3
3
equal-sized groups. 9 counters =
3
. I need to add 2 more groups of 3
counters for each group, which
5
make 15 counters =
.
3
What is the part?
Task Card
One Possible Explanation
Another Possible Explanation
First I look at the numerator to know how many
equal-sized groups I have. So…
If 15 counters are five-halves of a
set, how many counters are in a
whole set?
If 12 counters are three-fourths of
a set, how many counters are in the
full set?
If 4 counters are one-half of a set,
how big is the set?
Then, I use the denominator to know how many
of these groups put together make a whole.
“Halves” means I need to put 2 groups
together, so 1 whole group = 6 counters.
I can see from the rows
that it takes each of the
three groups (numerator)
has 4 counters, so all I
need to do is add another
row of counters to make
four-fourths, which = 1
full set. (16 counters)
“Halves” means 2 equal-parts. If 4 counters is
one of those parts, then I just need to add one
more group of 4 counters to make the whole.
The set would = 8 counters.
What is the whole?