Name___________________________________
Name: Kathe Carney
Date__________________________
Date: November 17, 2011
This lesson plan was modified for a third time to accommodate a Special Education
math section. The SOL scores for these 4th grade students as third graders were 210345. Disabilities are listed in the lesson plan revision. The teacher read the first
problem 8 times to the whole group and an extra two times to two individual
student; all these students have the accommodation of read-aloud for non-reading
assessments.

Addition, Subtraction, Multiplication, Division, Problem-Solving….
2.6B Find the sum of two whole numbers whose sum is 99 or less, using various methods of calculation.
2.7B Find the difference of two whole numbers, each of which is 99 or less, using various methods of
calculation.
3.4 Estimate solutions to and solve single-step and multistep problems involving the sum or difference of
two whole numbers, each 9,999 or less, with or without regrouping.
4.4D Solve single-step and multistep addition, subtraction, and multiplication problems with whole
numbers.
Host Teacher:
School:
Grade:
Number of Students:
Other Participants:
Beth Moore
Kathe Carney, Special Ed.
Dale City Elementary School
3rd Grade
4th grade students
22 students
6 students
Beth Alvarez, Alise Brooks, Cheryl Ayres, Kathe Carney
Knowledgeable Other:
Problem: Situation
Andrienne R. Setorie
There are 23 students in our class. We want to walk 230 laps on the
track.
a. If each student walks the same amount, how many laps will
each student walk?
b. What if the students do not have to walk the same amount,
how could the class get to 230 laps? (Extension)
Revised:
There will be 2 questions to differentiate and accommodate
for all level of students to have access and develop
strategies.
Name___________________________________
Identify the
mathematical goals of
the lesson, both short
term and long term.
Date__________________________
There are 6 students who want to walk a total of 96 laps. If
each person wants to walk the same number of laps, how
many laps will each student walk?
Include an equation and show your work. This problem fit
my class. It was given to the students during the 65 minute
Special Education math instructional period. They worked on
this problem on 11/16/11.
There are 6 students who want to walk a total of 42 laps. If
each person walks the same number of laps, how many laps
will each student walk? Include an equation and show your
work.
This problem was given as a follow up on 11/17/11along with
the exit question to determine if the students had generalized
any of their strategies; generalization of information and
strategies is a major problem with interventions provided to
students with Special Needs.
Short Term:
Students will be able to demonstrate an understanding of word problems
and will effectively use one strategy to solve a word problem.
3.4 Solve single-step and multistep problems involving the sum or
difference of two whole numbers, each 9,999 or less, with or without
regrouping.
Identify the ways in
which the task can be
solved.
 Which of these
methods do you think
your students will
use?
 What misconceptions
might students
encounter?
 What errors might a
student make?
Long term:
Students will be able to develop more than one strategy to problem
solve.
Students will be able to differentiate between strategies that are
more efficient than others.
Students will be able to select the most appropriate strategy for a
particular problem.
Parceling out-using manipulatives
Materials:
Students may start counting by ones
200’s chart
Students may use the base ten
cm cubes
Use the 300 hundreds chart to solve
number line
Picture representation
snap together cubes
Count by 23s
picture representation
Decompose and recombine…Count by 20s and add on 3s
Use the hundreds chart to solve.
extra paper
Count by 6s.
calculator for one
Count by 7s.
student who has the
Use the hundreds board to look for patterns. accommodation
Skip counting.
calculator on her IEP
Name___________________________________
Date__________________________
Misconceptions:
Students may think that all 23 students need to walk 230 miles each.
In the first lesson, students only counted by 10s. They did not
count by 23s.
Students may think that all 6 students need to walk 96 miles
each.
 Unsure of what manipulative to use
 Even with rewording of the problem and visual
supports, some students thought that each student
would walk 96 miles
 Most could not see counting by anything but ones; one
counted by two’s and one counted by five’s then
switched to one’s
Errors:
Miscounting.
Students may add the 230, 23 times.
Students may add the 230 + 23.
Miscalculation in adding, place value
Students may add 96 + 6.
Students may add 96, six times.
Some students may not comprehend the story problem.
Students might use the tools incorrectly.
Students might not be able to find their answers on the
representations-number lines, hundreds chart, or pictures.
Miscounting
Launch: How will you
Mesmerized by the manipulatives (used as play things)
introduce students to
No adding displayed
the task so as not to
Launch
reduce the problem
 Read the problem aloud to students.
solving aspects of the
task(s)?
 Teacher states that the total number of laps is 230 laps.
What will you hear that
 Teacher defines lap.
lets you know students
 Teacher provides a separate paper with each question
understand the
already at the top of the paper
task(s)?
 Teacher provides a visual demonstration showing the 23
students at the starting line.
 Students retell the story/students repeat the directions to
each other- Think/Pair/Share.
Explore: As students
Revised:
are working
 Teacher introduces the problem and shows a tally
independently or in
mark as she demonstrates that each person runs a
small groups:
lap.
 What questions will
 Teacher shows 2 rounds per student for a total of 12.
you ask to focus their
 Students work in pairs.
thinking?
Students will work in small-groups of three at two separate
 What will you see or
tables.
hear that lets you
Name___________________________________
know how students
are thinking about the
mathematical ideas?
 What questions will
you ask to assess
students’
understanding of key
mathematical ideas,
problem solving
strategies, or their
representations?
 What questions will
you ask to advance
students’
understanding of the
mathematical ideas?
 What questions will
you ask to encourage
students to share
their thinking with
others or to assess
their understanding
of their peers’ ideas?
Which solution paths
do you anticipate will
come up and which do
you want to have
shared during the class
discussion in order to
accomplish the goals
for the lesson?
 Which will be shared
first, second, etc.?
Why?
 In what ways will the
order of the solution
paths helps students
make connections
between the
strategies and
mathematical ideas?
Date__________________________
The teacher read the problem 8 times to the groups; she
demonstrated around the track with a print out of a track and
various photos of teams. There was a track displayed on the
computer screen throughout the problem solving session. (No
smart board is available to Special Education.) Due to weak
social skills and poorly developed verbal skills (communication
and ESOL), the teacher asked leading questions of each group
the first day. The second day (except for one student), the
teacher did not need to ask leading questions.
Exploration:
How do you know to add 23?
I’m wondering why you need to do this/that?
Is there another way that someone can share with me?
How do you know that?
Does everyone agree with…?
Does anyone want to add to that?
So your saying that…
What pattern do you notice?
What strategy are you using?
Is there a faster/more efficient way to solve this problem?
Above questions used; rereading done of the problem eight
times to the group; two more times to two individuals.
Revised:
How do you now to add 6/7?
Evidence:
We will see students actively using the mathematical tools
We will see students recording information on their own papers
We will see students recording information on their group charts.
We will hear students talking to each other.
Due to their disabilities and areas of weakness: Emotional
Disabilities, Learning Disabilities; Oppositional Defiance,
Socially Maladjusted, Speech and Language Disorders, Selective
Mutism, ESOL, and lower level cognitive abilities, conversation
between students at tables was limited. Leading questions were
used by the teacher to elicit responses and conversation
between team members.
Assessment:
What if we added one more student? What would happen?
Does anyone have any other thoughts or comments about what we
are talking about?
Solution: Most concrete to the most abstract/Less efficient to
more efficient strategy…
Name___________________________________
Date__________________________
Assessment was not given after the first problem; the concept
was too abstract for most of these students. The second
problem was used as an Assessment.
1.) Base Ten Picture Representation
2.) Hundreds chart representation
3.) Repeated Addition representation Number Line
Representation
4.) Number Line Representation
5.) Multiplication Representation
What will you see or
hear that lets you know
that students in the
class understand the
mathematical ideas of
problem solving
strategies that are
being shared?
Students will make connections between the different
representations.
Students will relate strategies to each other.
Students will be able to explain each other’s strategies.
Students will complete an independent exit question:
(Show your answer using 3 different strategies and circle the one
that is the easiest for you.)
After school 4 students decide to walk 20 laps on the track.
a. If each student walks the same amount, how many laps will
each student walk?
Revised:
Four students walked a total of 48 laps. Each student had
to walk the same number of laps, how many laps did each
student walk?
Exit question was used as a ticket to Encore. The
students who were successful with the first two problems
commented that this was easy and finished the task
speedily. The two students who were unable to complete
the two problems did not have time to get to the Exit
question. Since we are learning multiplication, several
students wrote the multiplication algorithm as a solution.
I only required one strategy.
Name___________________________________
Date__________________________
There are 23 students
in our class. We want
to walk 230 laps on the
track.
If each student walks the
same amount, how many laps
will each student walk? (original
question)
Name___________________________________
Date__________________________
What if the students do not
have to walk the same
amount, how could the class
get to 230 laps? (Extension
Activity)
The Extension Activity was not presented; the
original questions were enough of a challenge.
Name___________________________________
Date__________________________
EXIT CARD:
(Show your answer using 3 different strategies and
circle the one that is the easiest for you.)
After school 4 students decide to walk 20 laps
on the track.
If each student walks the same amount, how
many laps will each student walk?
Only one strategy was required.
Name___________________________________
Date__________________________
There are 6 students who want to
walk a total of 96 laps. If each
person wants to walk the same
number of laps, how many laps
will each student walk?
Include an equation and show
your work.
This problem was used as the original question.
Name___________________________________
Date__________________________
EXIT CARD:
(Show your answer using 3 different strategies and
circle the one that is the easiest for you. Include an
equation.)
There are 6 students who want to
walk a total of 42 laps. If each
person walks the same number of
laps, how many laps will each
student walk?
This question was used the second day to determine if the students could
generalize the strategies and discussions from the previous day to a similar
problem. I only required one strategy from my students.