Portland Community College | Portland, Oregon

Course Number:
MTH 212
Course Title:
Foundations of Elementary Math II
Credit Hours:
Lecture Hours:
Lecture/Lab Hours:
Lab Hours:
Special Fee:

Course Description

Examines the conceptual basis of K-8 mathematics. Provides opportunities to experience using manipulatives to model operations with rational numbers including fractions, decimals, percents, and integers. Explores the set of irrational numbers, the set of real numbers, proportional reasoning,and simple probability and statistics. Includes content and mathematical practices based on the Common Core State Standards. Prerequisites: MTH 211 and its prerequisite requirements. Audit available.

Addendum to Course Description

This is the second term of a three-term sequence (MTH 211, 212, and 213).

Intended Outcomes for the course

Upon successful completion students should be able to:

  • Apply an understanding of the theoretical foundations of mathematics focusing on real number operations, probability, and statistics as taught at the K-8 level in order to develop mathematical knowledge for teaching.
  • Use various problem solving strategies and statistical reasoning to create mathematical models, analyze real world scenarios, judge if the results are reasonable, and then interpret and clearly communicate the results.
  • Use appropriate mathematics, including correct mathematical terminology, notation, and symbolic processes, and use technology to explore the foundations of elementary mathematics.
  • Foster the mathematical practices in the Common Core State Standards.

Course Activities and Design

In-class time is devoted primarily to small group problem solving activities and class discussion emphasizing the use of manipulatives and appropriate technology. The instructor€™s role is to facilitate and model teaching and learning practices described in the Common Core Standards. Students may also read, write about or discuss journal articles, or engage in field observations or teaching demonstrations.

Outcome Assessment Strategies

Assessment must include:

1.      At least two proctored examinations.

2.      At least one writing assignment

3.      A no-calculator, no-notes, no book skills exam on fraction, integer, decimal, and percent calculations. The student must pass this exam with a minimum of 90% to receive a passing grade for the course.

4.      At least two of the following additional measures:

a.         Take-home examinations.

b.         Graded homework.

c.         Quizzes.

d.         Individual/Group projects.

e.        In-class participation.

f.         In-class activities.

g.         Portfolios.

h.         Individual projects.

i.         Individual  or group teaching demonstration(s).

j.         Field experience.

k.         Community based learning

Course Content (Themes, Concepts, Issues and Skills)


The instructional goal is to understand integer operations and use manipulatives to model these operations.

1.1      Model integer arithmetic with drawings and manipulatives.

1.2      Estimate and perform mental calculations with integers.

1.3      Solve applications requiring integers.


The instructional goal is to understand rational numbers and have a knowledge of the operations on these numbers.

2.1      Use fraction bars and other manipulatives to model fractions.

2.2      Extend the concept of fractions to rational numbers.

2.3      Determine equivalence, order and density of rational numbers.

2.4      Use manipulatives to add, subtract, multiply, and divide fractions.

2.5      Use algorithms to add, subtract, multiply, and divide fractions.

2.6      Solve word problems involving rational numbers.

2.7      Convert among fractions, decimals and percents.

2.8      Use decimal squares, base ten pieces, and other manipulatives to model decimals and basic operations on decimals.

2.9      Represent ratios, proportions, and percents using manipulatives.

2.10      Solve applications involving ratios, proportions, and percents.


The instructional goal is to extend the study of number systems to the real number system.

3.1      Classify real numbers as rational or irrational.

3.2         Explore the Pythagorean theorem.

3.3         Solve applications involving square roots.


The instructional goal is to provide an understanding of the mathematics involved in uncertainty and chance and the methods used to condense and present the main characteristics of a set of data using graphical and numerical methods.

4.1      Calculate and interpret the common measures of central tendency (mean, median, mode).

4.2      Calculate and interpret the numerical measures of dispersion (range, variance, standard deviation).

4.3      Construct pie charts, box plots, bar graphs, stem and leaf displays, and scatter plots to illustrate data.

4.4      Calculate and interpret measures of relative standing: percentile ranking, Z score, quartiles.

4.5      Define standard probability terms: experiment, sample space, independent events, complementary events.

4.6      Learn symbolism and concepts related to finding the mathematical probability of events occurring in single-stage and multi-stage experiments.

Standards of Mathematical Practice

While learning the mathematical content contained in the course, the following practices will be embedded throughout and students will be assessed on their ability to:

  1. Make sense of problems and perservere in solving them.
  2. Reason abstractly and quantitatively.
  3. Construct viable arguments and critique the reasoning of others.
  4. Model with mathematics.
  5. Use appropriate tools strategically.
  6. Attend to precision.
  7. Look for and make use of structure.
  8. Look for and express regularity in repeated reasoning.