Number , Ope ration , and Quantitative Reasoning
Assessment:
Informal assessment is accomplished while the students are
working
independently. Formal assessment would include the How Do We
Compare ? Let Me Count the Ways… Recording Sheet.
Extensions:
If you want students to work with other fraction
models , then you may
have manipulatives that re present the area and set models. This
particular lesson only demonstrates the measurement model.
Use Fraction Circles or Fraction Squares to work with the area model.
Procedures can be fol lowed as written above.
Use double-sided counters to work with a set model. Have students
set out 12 red counters and 12 yellow counters for a total of 24
counters. Twelve counters will be the whole. Have students separate
the red counters into groups of 2 and the yellow counters into groups
of 4.
Students can then see that 
and
are equivalent . Have students
continue to look for relationships with counters divided in this fashion .
Also, have the students divide the 12 counters into thirds and sixths as
well as halves.
Resources:
Coolmath.com (2006, May 20). Fractions: Improper
fractions.
Fosnot, C. & Dolk, M. (2002). Young mathematicians at
work:
Constructing fractions, decimals , and percents. Portsmouth, NH:
Heinemann.
Van de Walle, J.A. (2007). Elementary and middle school
mathematics: Teaching developmentally (6th ed.) Boston, MA:
Allyn and Bacon.
Modifications:
You can modify this lesson by allowing students to work
individually or
in groups of four. Adjust time allotted for this lesson to give students
more time to give oral responses.
Fraction Work Mat
Unmarked Fraction Bars
How Do I Compare? Let Me Count the Ways…
Recording Sheet
| Draw |
Mathematical Relationship |
Draw |
Mathematical Relationship |
| 1 |
___ ___ ___ |
7 |
___ ___ ___ |
| 2 |
___ ___ ___ |
8 |
___ ___ ___ |
| 3 |
___ ___ ___ |
9 |
___ ___ ___ |
| 4 |
___ ___ ___ |
10 |
___ ___ ___ |
| 5 |
___ ___ ___ |
11 |
___ ___ ___ |
| 6 |
___ ___ ___ |
12 |
___ ___ ___ |
Rubric for Grading Student Letter
| 4 |
Correct Usage of symbols to show mathematical
relationships.
Student justifies answers with lengthy explanation and no
misconceptions. |
| 3 |
Correct Usage of symbols to show mathematical
relationships.
Student justifies answers with lengthy explanation, but may
have a few misconceptions. |
| 2 |
Correct Usage of symbols to show mathematical
relationships
half of the time. Student justifies answers with minimal
explanation. Student exemplifies few misconceptions in the
explanation. |
| 1 |
Correct usage of symbols to show mathematical
relationships
one or two times . Student justifies answers with minimal
explanation. Student exemplifies numerous misconceptions in
the explanation. |
| 0 |
Did not have correct usage of symbols to show
mathematical
relationships. Student cannot justify answers. |
