UNIVERSITY OF MASSACHUSETTS BOSTON
EDCG 668/416
Week 8 Homework
Problems: Fractions on the Number Line
1. A 4th grader states: “ 45 and 98 are equivalent fractions because you can add 4 to the numerator and
denominator of 45 and get 98 as a result.” Develop two responses; one that uses a number line and the
other that uses an area model.
2. The ancient Egyptians expressed fractions as the sum of unit fractions, fractions with a numerator of
1. They also wanted all unit fractions to be different. 92 cannot be written as 19 + 19 . Instead the
Egyptians represented 92 as 16 + 181 . Use a number line and partitioning to help you solve the
following.
a) Write
5
6
b) Write
11
12
as the sum of two distinct unit fractions.
as the sum of two distinct unit fractions.
c) How can the knowledge of partitioning the number line and equivalent fractions help with this
task?
3. Some elementary students believe that 43 ≠ 86 because 6 is greater than 3. How can partitioning a
number line help remediate this misconception?
4. Some elementary curricula use Tangram Puzzles to get at the idea of equivalent fractions. Consider
the following Tangram puzzle:
a) Assuming the area of the original square is 1 square unit, find the area of each tangram piece.
b) Explain how you might show that
1
8
is equivalent to
2
16
using the tangram pieces.
c) How is it possible that the small square and the parallelogram both represent that same fraction of
the original square when they don’t look the same?
5. Make up a number line problem similar to ones you solved in Fractions on the Number Line where
students must locate a fraction. Solve your problem.
6. Make up two number line puzzles similar to those in Fractions on the Number Line. In one puzzle,
place the X to the left of the given fraction and in the other puzzle, place the X to the right of the
© 2011 Elementary Pre-Service Teachers Mathematics Project • School of Education • Boston University •
Boston, MA 02215 • (617) 353-7105 • [email protected]
Please do not circulate or cite without permission
Problems: Fractions on the Number Line
31
given fraction. You must decide what fractions to place on each of the number lines. Solve your
puzzles.
7. The following lesson is from the Everyday Mathematics (2009) curriculum, Grade 4, Unit 7:
“Equivalent Fractions” (pg 604-606):
a) What is the mathematical goal of the Many Names for Fractions worksheet?
b) Consider Question 3 on the Many Names for Fractions worksheet. Explain how a rectangle can
be partitioned to show that 43 is equivalent to 68 .
c) Explain how you can show the same equivalence ( 43 = 68 ) by partitioning a number line.
d) What is the method for finding equivalent fractions that this lesson appears to develop? If a 4th
grader was asked to explain how ¾ and 6 8 are the same and how they are different, what do you
hope they will say?
e) Does the method illustrated on this worksheet help students correctly determine if 36 and 48 are
equivalent? Why or why not? What might you do to help students understand they are
equivalent?
© 2011 Elementary Pre-Service Teachers Mathematics Project • School of Education • Boston University •
Boston, MA 02215 • (617) 353-7105 • [email protected]
Please do not circulate or cite without permission