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Problem Solving in Arithmetic

Prerequisites: Qualifying math score and completion of grade 5 math

Course Format: Individually Paced

Course Length: Typically 3 months

Course Code: PS1

Course Description


CTY's Problem Solving courses sharpen investigative skills, broaden mathematical understanding of concepts, and enhance reasoning skills. Designed around performance objectives that reflect national and state mathematical standards and drawing on software provided by Thinkwell, these courses demonstrate how mathematical issues arise out of real-life situations. Concepts are assessed through challenging quizzes and chapter tests, as well as a midterm and final exam. With the guidance of their instructors, students typically select enrichment or supplementary math courses of the appropriate level in between their accelerated courses to ensure a solid foundation and mastery of mathematics concepts at each level.

Problem Solving in Arithmetic is intended for students who have a good understanding of elementary arithmetic and wish to broaden their skills by solving interesting word problems. Students investigate properties of fractions, decimals, percents, integers, and order of operations, and explore the rules that govern math operations through interactions, practice problems, and workout exercises. Students are also invited to participate and ask questions in an open Help Room guided by instructors.

This course is most appropriate for students at the fifth and sixth grade level. It provides a solid foundation for students who will be advancing into Honors Pre-algebra.




Materials Needed

There are no required materials for this course.

List of Topics

Chapter 1: Fractions

Essentials of Fractions

  • Least Common Multiple
  • Mixed Numbers and Improper Fractions

Equivalent Fractions

  • Finding Equivalent Fractions
  • Multiplying and Dividing to Find Equivalent Fractions
  • Writing Fractions in Simplest Form

Multiplying Fractions

  • Multiplying Fractions by Whole Numbers

Dividing Fractions

  • Dividing Fractions and Mixed Numbers

Adding and Subtracting Fractions

  • Adding and Subtracting with Like Denominators
  • Adding and Subtracting with Unlike Denominators

Adding and Subtracting Mixed Numbers

  • Regrouping to Subtract Mixed Numbers
  • Solving Fraction Equations: Addition and Subtraction

Chapter 2: Decimals

Essentials of Decimals

  • Representing, Comparing, and Ordering Decimals
  • Rounding and Estimating Decimals

Adding and Subtracting Decimals

Multiplying Decimals

  • Multiplying Decimals by a Whole Number
  • Multiplying Decimals
  • Problem-Solving Application

Dividing Decimals

  • Dividing Decimals by Whole Numbers
  • Dividing by Decimals

Chapter 3: Percents

Essentials of Percents

  • Modeling Percents
  • Writing Percents as Fractions
  • Writing Percents as Decimals
  • Applications

Finding Percents of Quantities

  • Percents, Decimals, and Fractions
  • Estimating with Percents
  • Finding a Number When the Percent Is Known

Increasing and Decreasing Percents

  • Using Percents
  • Finding Percents
  • Percent Increase and Decrease

Chapter 4: Integers and Order of Operations

Adding and Subtracting Integers

  • Integers in Real-World Situations
  • Adding Integers
  • Subtracting Integers

Multiplying and Dividing Integers

  • Multiplying Integers
  • Dividing Integers

Order of Operations

  • Properties and Reasoning



Elementary Math Help Room

Help Room

Each week, all students are invited to an open Elementary Math Help Room run by a rotating staff of instructors. Students are encouraged to come with questions or just to meet other online students. Topics reviewed vary each week.

The Elementary Math Help Room meets each Tuesday from 7 – 8 p.m. ET.

Sample Video Lecture

Sample Video

sample video


Technical Requirements

This course requires a properly maintained computer with high-speed internet access and an up-to-date web browser (such as Chrome or Firefox). The student must be able to communicate with the instructor via email. Visit the Technical Requirements and Support page for more details.

This course uses an online virtual classroom for discussions with the instructor. The classroom works on standard computers with the Adobe Connect Add-in or Adobe Flash plugin, and also tablets or handhelds that support the Adobe Connect Mobile appStudents who are unable to attend live sessions will need a computer with the Adobe Connect Add-in or Adobe Flash plugin installed to watch recorded meetings. The Adobe Connect Add-in, Adobe Flash plugin, and Adobe Connect Mobile app are available for free download. Students who do not have the Flash plug-in installed or enabled on their browsers will be prompted to download and install the Adobe Connect add-in when accessing the virtual classroom.