# Foundations of Elementary Math II

## Course Description

Surveys mathematical topics for those interested in the presentation of mathematics at the K-9 levels. Various manipulatives and problem solving approaches are used to explore rational numbers (fractions, decimals, percents), integers, the set of irrational numbers, the set of real numbers, and simple probability and statistics. Prerequisite: MTH 211 and its prerequisite requirements. Audit available.

## Intended Outcomes

Upon successful completion students should be able to:

1. Understand the theoretical foundations of mathematics focusing on integer and rational number arithmetic as taught at the K-9 level in order to develop mathematical knowledge for teaching.
2. 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.
3. Participate in a teacher education program.
4. Use appropriate mathematics, including correct mathematical terminology, notation, and symbolic processes, and use technology to explore the foundations of elementary mathematics.

## Outcome Assessment Strategies

Assessment must include:

1. At least two proctored examinations
2. At least one writing assignment and
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:
1. Take-home examinations
3. Quizzes
4. Individual/Group projects
5. In-class activities
6. Attendance
7. Portfolios
8. Individual projects
9. Individual or group teaching demonstration(s)
10. Field experience
11. Service Learning

## Course Activities and Design

In-class time is primarily activity/discussion or lecture/lab emphasizing the use of manipulatives and problem solving techniques. Activities will include group work, field experience, or teaching demonstrations.

## Course Content (Themes, Concepts, Issues and Skills)

#### 1.0 INTEGERS

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.

#### 2.0 FRACTIONS, DECIMALS AND THE RATIONAL NUMBER SYSTEM

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.

#### 3.0 IRRATIONAL AND REAL NUMBERS

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.

#### 4.0 STATISTICS AND PROBABILITY

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.

## Department Notes

This is the second term of a three-term sequence (MTH 211, 212, and 213). Foundations of Elementary Math II is intended to examine the conceptual meanings of elementary mathematics and to provide students with opportunities to experience use of manipulatives to model problem solving, computational operations with real numbers, and topics in probability and statistics. The content and pedagogy is based on NCTM standards.

Emphasis is on why mathematics works as it does rather than on memorization of algorithms.