ALGEBRA CASE STUDY
Mr. Frost, a ninth grade teacher at Infinity High School, is a third year teacher, both in
the profession and at this high school. He feels fortunate to work with two other Algebra
I teachers who are veteran teachers at the ninth grade level. In addition, the school has
a mathematics resource teacher, who is both very knowledgeable in multiple
instructional approaches and resources. To facilitate the MTSS Implementation Plan in
their school, the School Improvement Team recommended that their school
Professional Learning Community focus on quality implementation of the problemsolving process. One necessary component decided by the members of their School
Improvement Team was to assure that grade-level data meetings were scheduled bimonthly. Additionally, the Algebra PLC decided to begin a lesson study cycle to improve
instruction.
For this case study, the focus will be on improving the effectiveness of instruction and
interventions based on students’ needs. The instructional focus for this unit in
mathematics is:
FL Standard
MAFS.912.A-REI.2.3
Description
Solve linear equations
and equalities in one
variable, including
equations with
coefficients represented
by letters.
Aligned Progress
Monitoring Tool
Textbook provided
progress monitoring
Mr. Frost utilized the following textbook-provided assessment:
He utilized the following Common Assessment Grading Rubric that the Algebra PLC had
created at the beginning of the school year:
The following results are from the assessment of 27 students:
Student
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Raw Score
16
18
21
10
24
21
25
25
19
23
24
12
25
20
11
24
16
23
25
21
21
19
25
23
25
20
20
Percentage
57
64
75
36
86
75
89
89
68
82
86
43
89
71
39
86
57
82
89
75
75
68
89
82
89
71
71
The progress monitoring data indicate that 12/28 (43%) of the students are meeting Mr.
Frost’s expectations of scoring a minimum of 80% on the probe addressing the FL
Standard (MAFS.912.A-REI.2.3). Mr. Frost considers additional Tier 1
instruction/intervention. This would require additional problem solving at the Tier 1
level, and may include other educational personnel and/or resources to enhance
instruction. During the next scheduled Algebra PLC, Mr. Frost proposed a lesson study
for this standard.
The Algebra PLC visited CPALMS to obtain resources for the lesson study.
The lesson study team, comprised of the Algebra PLC, the math resource teacher, and an
interventionist first identified the standard and a National Center on Intensive
Intervention (NCII) aligned resource:
Caveat: The FL Standard MAFS.912.A-REI.2.3 has two access points that are aligned:
The lesson study team determined the lesson that would be delivered to the class.
Refer to:
The Yo-Yo Problem
The lesson incorporated principles of the Universal Design for Learning into the algebra
instruction. Concrete manipulatives (algebra tiles) were provided to the students to
deepen their conceptual understanding of positive and negative integers.
https://goalbookapp.com/toolkit/strategy/algebra-tiles
Algebra tiles are manipulative objects of different colors or shapes that are used to
represent integers and variables. They can be used to add, subtract and multiply
integers (both positive and negative) and to show algebraic equations. Algebra tiles
provide concrete models for concepts that students may find difficult to visualize using
language only.
•For students who may need a little more support: when showing the class a
series of tiles and asking them to write it numerically (e.g. “What do these tiles
represent using integers?”) present it as a multiple choice question with 3
possible answers to choose from.
•For students at a beginning level of numeracy, the teacher can provide templates
with tiles on them and students can match tiles to the ones on the template.
•For students who are not yet able to do algebra, they can work at their own level
of math, such as adding and subtracting single digit numbers while still using the
tiles.
Students were also provided pennies and graphing calculators.
For additional practice, students were able to utilize the National Library of Virtual
Manipulatives (nlvm.usu.edu):
The following image is an activity that students were able to practice with, entitled
‘Algebra Balance Scales’.
Following the lesson, assessment data was compiled and reviewed utilizing the same
rubric:
Student
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Raw Score
18
24
23
12
25
27
26
28
26
23
25
17
24
25
14
28
27
25
23
25
24
25
26
23
26
28
25
Percentage
64
86
82
43
89
96
93
100
93
82
89
61
86
89
50
100
96
89
82
89
86
89
93
82
93
100
89
The progress monitoring data indicated that 23/27 (85%) of the students were meeting
Mr. Frost’s expectations of scoring a minimum of 80% on the probe addressing the FL
Standard (MAFS.912.A-REI.2.3).
As there were several students in algebra not meeting mastery of the standard, Mr. Frost
along with the algebra team, were in agreement that they needed to provide more
instruction and support for the students that were struggling with this benchmark, in
addition to the core instruction. They included the curriculum resource teacher in their
discussion.
The following students were identified as needing additional support (see student
work):
Student Grade
Javier
50
Adam
64
Janet
61
Louie
43
Skill Deficit
Computation of fractions
Computation of fractions
Computation of fractions
Computation of fractions and number
sense, as well as attention
To assure mastery of the targeted standard, the identified group of students required
Tier 2 intervention support, in addition to core instruction. Mr. Frost and members of
the algebra PLC determined the resources to use to intensify instruction and the design
of the intervention.
http://1.usa.gov/15vyYY9
http://1.usa.gov/15vyYY9
http://bit.ly/1CkenD6
The algebra team arranged for those students to receive supplemental instruction in a
small group 45 minutes per day (increasing dosage), three times a week with active
engagement methods and manipulatives, (evidence-based procedures researched to be
effective to master these skills). Progress monitoring data were collected weekly to
evaluate the effectiveness of instruction as well as the progress of the individual
students.
The following data were collected for the four students:
Student
Javier
Adam
Janet
Louie
Week 1
61
64
64
46
Week 2
68
75
71
50
Week 3
75
75
68
50
Week 4
82
86
82
57
After four weeks of intervention, the data show that the instruction is resulting in
improved outcomes for three of the four students. The students were able to perform
independently to complete the assessment accurately and consistently, scoring at least
80%.
However, while showing some improvement, Louie continues to struggle (see student
work). Mr. Frost continues to collect data for an additional six weeks, utilizing the same
intervention schedule.
Student
Louie
Week 5
57
Week 6
57
Week 7
64
Week 8
61
Week 9
68
Week 10
64
Next Steps
Utilize all materials to determine next steps for Louie…
 Utilize data to determine skill deficits
 Progress monitoring data
 Others?
 Intensify Instruction
 Identify intervention(s) that match student need
 Ensure alignment of intervention(s) to core instruction
 Provide generalizable strategies (e.g., C-R-A approach)
Consider using the following resources for identifying intervention
practices/programs/materials/resources: