MATH 612 --UF Explorations
Fractions and Proportions: K - 8 Learning and Teacher Practices
UF Math Task A: Beginning Area Models for Fractions
 The following task should help you think about the question of “What is 1?” or, “What is the
Unit?” for a fraction model.
 Include all of your work, sketches and answers for the math tasks as well as your answers to
the “Question for you” in your write up.
Color tile models (any type of colored squares or shaded grid)
I.
Sketch a color tile model of 2 5 using the most efficient model for 1. Clearly label your
model for 1. Can you easily see 2 of 5 parts in your model? How? What is the value of
each tile?
II.
Sketch a color tile model of 3 10 using the most efficient model for 1. Clearly label your
model for 1. Can you easily see 3 of 10 parts in your model? How? What is the value of
each tile?
Question for you (please answer)
What are the potential issues an elementary school student would have looking at the two
models in parts I and II of this math task at the same time? How can you resolve these issues?
Show it.
MATH 612 --UF Explorations
Fractions and Proportions: K - 8 Learning and Teacher Practices
UF Math Task B: Using Area Models for Fractions
 The following task should help you extend your thoughts about the question of “What is 1?”
for a fraction model and how it relates to the other fractions you can easily create with that
unit model.
 Include all of your work, sketches and answers for the math tasks as well as your answers to
the “Question for you” in your write up.
Pattern blocks models (green triangles, blue and tan rhombi, red trapezoids, yellow hexagons
and orange squares)
Show each of the following with a clear and clearly labeled model. You may be able to reuse relabeled images for multiple parts of the math task.
I.
i.
ii.
iii.
If the red trapezoid is the unit, which pattern block shows 1/3?
If the red trapezoid is the unit, can you use pattern blocks to shows 3/2? Explain.
If the red trapezoid is the unit, what is the value of each of the other pattern blocks?
i.
ii.
iii.
If the blue rhombus is 1/3, which pattern block is the unit?
If the blue rhombus is 1/3, can you use pattern blocks to shows 3/2? Explain.
If the blue rhombus is 1/3, what is the value of each of the other pattern blocks?
II.
III.
i.
If the orange square is the unit, what is the value of each of the other pattern
blocks? For this task you can estimate. The following image may give you some ideas
Question for you (please answer)
1. What are the potential issues an elementary school student would have looking at the
various models in task B.I at the same time? How can you resolve these issues? Show it.
2. What are the potential issues an elementary school student would have looking at the
various models in task B.II at the same time? How can you resolve these issues? Show it.
MATH 612 --UF Explorations
Fractions and Proportions: K - 8 Learning and Teacher Practices
UF Math Task C: Equivalent Fractions
 The following task should help you think about how to use an area model to show that
some fractions are equivalent, how this connects to a number line model, and how the
general rule for fraction equality works.
 Include all of your work, sketches and answers for the math tasks as well as your answers to
the “Questions for you” in your write up.
3 9 12


using an area visual model of your choice. Be sure that
4 12 16
your “1” or unit is clearly defined and labeled.
I.
Demonstrate that
II.
Demonstrate that
3 9 12


using a number line.
4 12 16
Questions for you (please answer)
1. What key ideas are needed for a fifth grader to understand the models in task C?
2. Briefly explain how you can illustrate the general rule that
an elementary school student.
a na

(n a whole number) to
b nb
MATH 612 --UF Explorations
Fractions and Proportions: K - 8 Learning and Teacher Practices
UF Math Task D: Fraction Inequalities
 The following task should help you think about how to compare fractions in a way that can
make intuitive sense to kids.
 Include all of your work, sketches and answers for the math tasks as well as your answers to
the “Questions for you” in your write up.
1 2 3 1
3 2.5 1
1 3
   and 
 , so I know 
3 6 6 2
5 5
2
3 5
There are many methods of comparison, what are your ideas?
Benchmark comparison example:
I.
Consider the following fraction pairs. Is one fraction greater than the other? How do you
know?
2
2
4
3
6
3
and
and
and
i.
ii.
iii.
5
7
10
8
11
5
3
5
6
8
8
12
and
and
and
iv.
v.
vi.
4
8
5
7
17
21
Questions for you (please answer)
1. What key ideas are needed for a fifth grader to understand how to compare these
fractions?
2. Briefly describe and illustrate several strategies that elementary school students can use to
compare fractions.