Divisibility rules and applications of these to solving a variety of number theory problems will become very trivial. Students will understand how LCM and GCF should be used to solve problems. They will master all operations with fractions/decimals. They will be introduced to the real line and the concept of negative numbers will become very comfortable tothem. One variable algebra problems will become second nature to them.

Given values of x and y, students will be able to write the equation for y in terms of x. They will learn to cancel out terms, and will get comfortable with the distributive property and grouping variable terms.

Students will be solving over 500 problems in the school year, fromContinental Math, Math League, Math Olympiads and simple problems fromMATHCOUNTS.

Operations with integers

 Multiple digit by single digit division horizontally.
Practice to get speed and accuracy on multiple digit additions and subtractions horizontally.
Review one-digit/two-digit long divisions.
Operations with numbers followed by zeros.

Time/Calendar/Money/Measurement

 By this level, these concepts are mostly review.
Problems will get trickier to allow the students nail these concepts well.
They will be able to do these operations comfortably.

Problem Solving Techniques

No more box method, any problem that could be solved using box method should be now solved using only algebra.
Trial and error to solve problems involving 2 variables.
Learn graphical approach to solve problems that involve fractions.
These problems will be real complicated using algebra, but can besolved easily graphically.

Algebra

Given a linear equation solve it by grouping all similar terms andisolating the variable. Solution can be negative numbers.
Solve word problems by writing the equation and solving them.

Geometry

Perimeter.
Formula for area of square, rectangle and triangle.
Find area of complex figures by dividing the figure into known figures Study of angles.
Properties of triangles and their classification.
Convert an improper fraction into a mixed number.

Numbers

Divisibility Rules.
Multiples and factors.
LCM/GCF.
Square of numbers.
Negative numbers.
Distributive Property.

Fractions/Decimals

 All operations with fractions.
All operations with decimals.
Convert from decimals to fractions and viceversa.
Introduce percentages.
Convert from percentages to fractions.
Fraction/Decimal/Percentage of a number.

500+ Word Problems

Complex problems involving time, calendar, and/or money.
Interesting problems involving measurement operations.
Problems involving problem solving techniques taught.
Problems applying area and perimeter concepts and transformations for  one unit to another.
Interesting problems involving fractions, decimals, and/or percentages
Number theory problems.