S. B. Kizlik, Ed. D.
4, 5, 6
(Subtraction of Mixed Numbers)
Academic rule for subtracting mixed numbers with regrouping or trading
already learned to subtract mixed numbers without trading
The students will subtract 2 mixed numbers requiring regrouping or
with a difference less than 50.
the attention of students; remind them of proper procedure behaviors.
-Direct students to get out their math notebooks and pencils
-Put students with their partners (groups of 2)
-Review the topic of subtracting mixed numbers that do not require regrouping
“What is a mixed number?”
number plus a proper fraction)
-Call one student to the overhead to display the value of 3 2/5 using
Call another student to display the value of 2 5/8.
-Discuss the results and any questions
-Distribute fraction strips to the groups
“Work with your partner and display the values for these mixed
Leave your displays on the desktops so I can check them as I come
around to help.
-Circulate, assist, and check solutions
-Discuss results and questions
-Pose the question
“What if we had 7 ¾ pizzas and gave 4 ¼ to Mr. Jackson’s class?
How much pizza would we have left?”
-Discuss the information, the question, a plan for solving
-Call one student to the overhead to display the process using the rods
-Call another student to the board to demonstrate the process in written form:
7 ¾ -
4 ¼ = 3 2/4
= 3 ½
-Stress that answers should always be written in lowest terms
“Do the following problems in your math notebooks.
Show your work.
5 2/3 - 1 1/3
8 4/5 -
assist, and check accuracy
-Discuss results and questions.
subtraction with regrouping or trading through examples
-Have students consider
5 2/5 -
“Look at the fraction values in the mixed numbers.
Are there enough fifths
in 2/5 to remove 3/5 of them?” (call on a student to answer.)
-Direct class to work with their partners, use their fraction strips, and
the answer to this question for
a minute or so
“How can we make enough fifths from
5 2/5 to be able to
3/5 of them?”
-Have a group demonstrate, using fraction strips on the overhead, trading a
ONE from the whole number, trading it for the equivalent
fraction pieces in
fifths, and combining it with the 2 fifth pieces that are
already there, showing
4 wholes and 7 fifths.
-Discuss trading a ONE for its fraction value
ONE from the whole number 5, making the one 5/5 and
the whole number 4 in place of the 5, combining the fraction
with the fraction 2/5 leaves the mixed number 4 7/5.
-Demonstrate this trading process in written form
5 2/5 = 4 + 5/5 + 2/5 = 4
-Demonstrate how it affects the subtraction (fraction – fraction and
whole – whole) using both
fraction strips and written form
5 2/5 = 4 + 5/5 +
2/5 = 4 7/5
- 2 3/5=
= 2 3/5
-Direct the groups to use their fraction strips and written form to solve
6 1/3 -
- 1 4/5
-Have a group demonstrate, using fraction strips, the first problem on the
-Discuss the process
-Demonstrate the written form on the board
-Stress that the ONE changes to a fraction with numerator and denominator
the same, and that is the same
as the denominator of the fraction in the
-Stress the importance of writing the answers in simplest terms.
-Have a student demonstrate the written form of the second problem
-Discuss the process
-Leave the problems on the board for the students to reference
-Direct the students to work these problems in their notebooks
7 3/8 - 3 7/8
12 4/7 - 8 6/7
9 5/6 - 2 1/6
assist, check accuracy
-Have a student work each problem on the board
-Discuss any questions
-Note that the last problem did not require trading a one from the whole
because there were enough sixths to remove already
when you need to trade a one from the whole number and when
it is not necessary by pointing
to the last group of practice problems.
-Stress that the one must be written using the same denominator so it can
be combined with the fraction
that is already present in the minuend.
-Direct students to begin their assignment
-Circulate and assist
Materials and Equipment
fraction strips for the class and the overhead
Cuisenaire rods for the overhead
Assessment / Evaluation
achievement during the class will be measured informally through
observation because this is the very first lesson on subtracting mixed
numbers with regrouping or trading.
Student achievement will also be
measured on the assignment.
-Students will be
given page 45 for their assignment.
-Tomorrow the process will be reviewed and applied to word problems.
the students able to follow my directions with little or no confusion?
the processes, situations, and rules concise, precise, and age-level
the class achieve at least 88% success on the practice problems?
did I do very well?
could I have done better?
will I do this better next time?