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Problem Solving in Arithmetic

In Problem Solving in Arithmetic, topics are presented in a motivational context that demonstrates how mathematical issues arise out of real-life situations. Within these contexts, students investigate properties of fractions, decimals, percents, and integers, and explore the rules that govern their operations. This course focuses on arithmetic and the numbers and operations typically included in the middle school math curriculum.

Scope and Sequence for Problem Solving in Arithmetic

Module 1: Fractions

Essentials of Fractions

  • Recognizing a Fraction
  • Exploring Proper and Improper Fractions
  • Working with Mixed Numbers

Equivalent Fractions

  • Identifying the Factors of a Number
  • Expressing Fractions in Lowest Terms
  • Writing and Comparing Equivalent Fractions

Multiplying Fractions

  • Finding Products of Fractions, Whole Numbers, and Mixed Numbers
  • Using the GCF in Finding Products
  • Representing Multiplication

Dividing Fractions

  • Estimating Quotients of Fractions
  • Using Multiplicative Inverses
  • Solving Missing Value Problems when Dividing Fractions

Adding Fractions

  • Adding with Like Denominators
  • Adding with Unlike Denominators
  • Solving Missing Value Problems when Adding Fractions

Subtracting Fractions

  • Subtracting with Like Denominators
  • Subtracting with Unlike Denominators
  • Solving Missing Value Problems when Subtracting Fractions

Module 2: Decimals

Essentials of Decimals

  • Investigating Decimal Place Values
  • Rounding Decimals
  • Exploring Repeating and Terminating Decimals

Adding and Subtracting Decimals

  • Using Place Value Grids
  • Regrouping with Whole Numbers
  • Regrouping to Hundredths

Multiplying Decimals

  • Multiplying Decimals by Powers of 10
  • Calculating Products
  • Finding the Volume of a Prism

Dividing Decimals

  • Dividing Decimals
  • Estimating and Finding Quotients
  • Dividing by Powers of 10

Module 3: Percents

Essentials of Percents

  • Investigating the Meaning of Percent
  • Expressing Percents as Proper Fractions
  • Expressing Percents Greater than 100% as Improper Fractions

Finding Percents of Quantities

  • Finding Percents of a Whole
  • Expressing Ratios as Percents
  • Calculating the Whole from a Part and a Percent

Increasing and Decreasing Percents

  • Calculating Percent Increases
  • Calculating Percent Decreases
  • Calculating Simple Interest

Module 4: Integers and Order of Operations

Adding and Subtracting Signed Numbers

  • Exploring the Number Line and Absolute Value
  • Adding with Absolute Value
  • Subtracting with Absolute Value

Multiplying and Dividing Signed Numbers

  • Finding Products of Signed Numbers
  • Representing the Multiplication of Signed Numbers
  • Finding Quotients Using Reciprocals

Order of Operations

  • Simplifying Expressions
  • Introducing the Distributive Property
  • Using Grouping Symbols

Course Management and Assessment

Students are evaluated by a series of Unit Quizzes, Module Tests and a comprehensive Final Exam. Our CTY Distance Education Quiz Corner tests and tracks students progress. Tutors monitor the progress of each student by reviewing and responding to work and maintaining communication via email, phone and the online whiteboard. When necessary, tutors may also refer students to the Distance Math Program Web site for additional on-line resources


Students in the Problem Solving Series of courses receive Print Activities with their course materials. Print Activities provide reinforcement and help to promote concept retention for each module of the software. Students are not required to complete the activities, but we highly recommend that they do. Students are able to check their work using the answer key provided.

Unit Quizzes and Module Tests

Student progress is evaluated through the CTY Distance Education Quiz Corner. Unit Quizzes are to be completed after each Unit. Your score on the Unit Quizzes is automatically emailed to your tutor. The tutor responds via e-mail with help on difficult concepts or trouble areas. Module Tests are another important assessment tool. Students log onto Quiz Corner to print the Module Test, then complete the test and fax or mail the completed test to the tutor. Tutors provide feedback, as necessary.

Final Exam

All students are required to take a paper and pencil Final Exam. As a student nears the completion of a course, the tutor will send the final exam via e-mail (pdf), fax, or the student can download the final from the course website. Students should plan ahead for review and make use of the tutor for feedback and review suggestions. Students often require more tutorial support during the time when they are studying for the final than at any other point in the course. We strongly encourage students to utilize and stay in contact with their tutor during final exam preparation. Each test is given a percentage score, and students will receive an e-mail containing their score.

Grading Policy

Score (%) Letter Grade
Final Exam Form A 98 + A+
93 - 97 A
90 - 92 A-
87 - 89 B+
85 - 86 B
below 85 Take Form B
Final Exam Form B 85 + B
below 85 Course Completion documents not issued. Statement of Participation will be issued upon request.

With a passing grade (B or better) course completion documents are mailed. These include a copy of the scope and sequence for the course, an assessment of the students work by the tutor, and a course completion certificate.

If a student scores below an 85% on Final Form A then the student will have the oppurtunity to take Form B of the Final Exam. The highest grade, regardless of the percent scored, that a student can achieve when taking Form B of the Final Exam is a B for the course

If a student scores below an 85% on the Final Form B, a statement of participation, rather than Final Course Completion documents, will be issued upon request.