Teaching Math in the Intermediate Grades
Course description
As preparation for teaching mathematics in the intermediate grades, this course
emphasizes the integration of technological pedagogical content knowledge that includes
topics on rational numbers, measurement, geometric figures, pre – algebra concepts,
application of simple probability and data analysis. This course is capped with
microteaching that utilizes appropriate teaching strategies for the development of critical
and problem solving skills, reasoning, communicating, making connections,
representations, and decisions in real life situations.
Course Schedule and Assessment Rubrics
Time
Frame
Topic
Resources
Assessment
Rubrics
Theme: Championing the Dignity of the Human Person and Valuing Human Life
Weeks
1-2
1. Algebraic Thinking:
Generalizations, Patterns
and Functions
1.1 Algebraic Thinking
1.2 Generalization from
Arithmetic and from
Patterns
1.3 Meaningful use of
Symbols
1.4 Making Structure in
the Number System
Explicit
1.5 Study of Patterns
and Functions
Elementary and Middle
School Mathematics:
Teaching Developmentally
(2010) by John Van De Walle,
Karen Karp and Jennifer BayWilliams
Teaching Elementary
Mathematics: A Resource for
Field Experiences 3rd Edition
(2007) by Nancy Smith,
Diana Lambdin, Mary
Lindquist and Robert Reyes
Rubric for grading
Round Robin
Charts
Round Robin
Charts
Quiz
https://mason.gmu.edu/~jsuh
4/impact/PFAEntire.pdf
https://slideplayer.com/slide/9
114945/#.XWPR8Ykil10.emai
l
Weeks
3–4
2
Developing Strategies
for Fraction
Computation
Elementary and Middle
School Mathematics:
Teaching Developmentally
3-2-1 countdown
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Rubric for grading
responses to the
2.1 Number Sense and
Fraction Algorithms
2.2 Addition,
Subtraction,
Multiplication and
Division of Fractions
3
Weeks
5–6
Weeks
7–8
Proportional Reasoning
3.1 Types of Ratios
3.2 Proportional
Reasoning
3.3 Comparing and
Scaling
3.4 Proportional Reasoning
Across the Curriculum
4. Developing
Measurement Concepts
1.1 The Meaning and
Process of
Measuring
1.2 Length and Area
1.3 Investigations in
Number, Data and
Space (Volume
and Capacity;
Weight and
Mass;Time;
Money; Angles)
1.4 Introducing
Standard Units
1.5 Estimating
measures
1.6 Developing
Formulas for Area
and Volume
M
I
D
T
E
(2010) by John Van De Walle,
Karen Karp and Jennifer BayWilliams
3-2-1 countdown
https://ies.ed.gov/ncee/wwc/D
ocs/PracticeGuide/fractions_p
g_093010.pdf
A Comparative Analysis of the
Addition and Subtraction of
Fractions in Textbooks
(2010) by Charalambos Y.
Charalambous, Seán
Delaney, Hui-Yu Hsu & Vilma
Mesa
Elementary and Middle
School Mathematics:
Teaching Developmentally
(2010) by John Van De Walle,
Karen Karp and Jennifer BayWilliams
One-minute
Papers
Rubric for Grading
One-Minute papers
Critical
Explanation
Rubric for grading
critical explanation
Teaching Student-Centered
Mathematics Grades 3 – 5
Volume Two (2006) by John
Van de Walle and LouAnn
Lovin
http://www.edu.gov.on.ca/eng
/teachers/studentsuccess/pro
portionreason.pdf
Elementary and Middle
School Mathematics:
Teaching Developmentally
(2010) by John Van De Walle,
Karen Karp and Jennifer BayWilliams
Teaching Elementary
Mathematics: A Resource for
Field Experiences 3rd Edition
(2007) by Nancy Smith,
Diana Lambdin, Mary
Lindquist and Robert Reyes
http://eworkshop.on.ca/edu/re
sources/guides/Guide_Measu
rement_456.pdf
R
M
E
X
A
M
I
N
A
T
Theme: Advancing the Quality of Life of People
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I
O
N
S
Weeks
10 - 12
Weeks
13 – 15
Week
16 - 17
2. Geometric Thinking
and Geometric
Concepts
2.1 Geometry Goals
for Students
2.2 The Development
of Geometric
Thinking
2.3 Learning About
Shapes and
Properties
2.4 Learning About
Transformation
2.5 Learning About
Location
2.6 Learning About
Visualization
3. Developing
Concepts of Data
Analysis
3.1 What does it mean
to do Statistics?
3.2 Formulating
Questions
3.3 Data Collection
3.4 Data Analysis:
Classification,
Graphical
Representations
Measures of
Center
6.5 Interpreting Results
4. Exploring Concepts
of Probability
4.1 Introducing
Probability
4.2 Theoretical
Probability and
Experiments
4.3 Sample Spaces
and Probability of
Two Events
F I
Elementary and Middle
School Mathematics:
Teaching Developmentally
(2010) by John Van De Walle,
Karen Karp and Jennifer BayWilliams
Teaching Student-Centered
Mathematics Grades 3 – 5
Volume Two (2006) by John
Van de Walle and LouAnn
Lovin
https://www.learner.org/cours
es/learningmath/geometry/pdf
s/session9/vand.pdf
Elementary and Middle
School Mathematics:
Teaching Developmentally
(2010) by John Van De Walle,
Karen Karp and Jennifer BayWilliams
Case-Based
Scenario
Concept plan of
an instructional
material that
would engage
the students in
learning
geometric
concepts
Interactive
Report
Critique Paper
Rubric for grading
Case-Based
Scenario and
Concept Plan
Rubric for checking
critique paper and
evaluating
interactive report
Teaching Mathematics to ALL
Children: Designing and
Adapting Instruction to Meet
the Needs of Diverse
Learners 2nd Edition (2006)
Benny Tucker, Ann Singleton
and Terry Weaver
https://www.nctm.org/Standar
ds-and-Positions/Principlesand-Standards/DataAnalysis-and-Probability/
Elementary and Middle
School Mathematics:
Teaching Developmentally
(2010) by John Van De Walle,
Karen Karp and Jennifer BayWilliams
Rubric for
evaluating
caricature analysis
Caricature
Analysis
https://study.com/academy/le
sson/probability-lesson-forkids-examples-definition.html
N A L
E X
A M I
N A T I
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O
N
Course Materials
Required Textbook
Elementary and Middle School Mathematics: Teaching Developmentally (2010) by John Van
De Walle, Karen Karp and Jennifer Bay-Williams
Online Resources
https://www.ijee.ie/articles/Vol22-4/03_ijee18 04.pdf
https://www.researchgate.net/publication/234679062_Teaching_Math_in_the_Primary_Grades_T
he_Learning_Trajectories_Approach
https://www.nap.edu/read/10126/chapter/7#258
https://ac.els-cdn.com/S1877042814009033/1-s2.0-S1877042814009033-main.pdf?
_tid=2ad878d9-e6a5-4830-93ea23fb33879038&acdnat=1532140334_e7a3ff4360cdbfbfe087890e7888a91a
Journal Readings (Social Awareness / Social Innovation)





Figure 2f from: Irimia R, Gottschling M (2016) Taxonomic revision of Rochefortia Sw.
(Ehretiaceae,
Boraginales).
Biodiversity
Data
Journal
4:
E7720.
https://doi.org/10.3897/BDJ.4.e7720. (n.d.). doi:10.3897/bdj.4.e7720.figure2f
Burch, P., & Spillane, J. P. (2003). Elementary School Leadership Strategies and Subject Matter:
Reforming Mathematics and Literacy Instruction. The Elementary School Journal, 103(5), 519535. doi:10.1086/499738
Open.edu.(2018).
http://www.open.edu/openlearncreate/pluginfile.php/134935/mod_resource/content/3/EM05_AIE_
Final.pdf [Accessed 20 Jul. 2018].
Charalambos Y. Charalambous, Seán Delaney, Hui-Yu Hsu & Vilma Mesa (2010) A Comparative
Analysis of the Addition and Subtraction of Fractions in Textbooks
Journals.sagepub.com. (2018). A Life Skills Approach to Mathematics Instruction: Preparing
Students with Learning Disabilities for the Real-Life Math Demands of Adulthood - James R.
Patton, Mary E. Cronin, Diane S. Bassett, Annie E. Koppel, 1997. [online] Available at
http://journals.sagepub.com/doi/abs/10.1177/002221949703000205 [Accessed 20 Jul. 2011
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