Students will continue to master speed and accuracy with respect to multiple digit additions, subtractions, multiplication and division. Many of these operations would be done mentally. They will able able to operate with numbers followed by zeros quickly.

They will be able to compute areas of complex geometric figures. Fractions will be well understood, and they will learn to add/subtract/multiply fractions while using these to solve multi-step word problems. They will apply algebra to solve various kinds of problems. By the end of the level, students will be very comfortable solving problems where multiple variables could be used, but these students will understand that all variables can be represented in terms of one! They will be applying the substitution method automatically.

Students will be solving over 500 word problems in the school year, from Continental Math, Math League and Math Olympiads.

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 long division and learn two-digit long division. Operations with numbers followed by zeros.

Time/Calendar/Money/Measurement

By this level these concepts are mostly review. Problems will get trickier and will allow the student nail these concepts well. They will be able to do operations with these comfortably, with the techniques thought in class.

Problem Solving Techniques

Box method subtract and divide or just divide; children will learn to set up the problem graphically and then solve it. Number line used to place quantities to help solve a problems quickly Trial and error approaches, using a table. Learn graphical approaches to solve problems that involve fractions, for example work rate problems.

Algebra

Given a linear equation solve it by grouping all similar terms and isolating the variable. Solve word problems by writing the equation and solving.

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. Place value. Rounding. Square of numbers.

Fractions/Decimals

Concept of fractions, proper/improper fractions. Reduce fractions to simplest form. Convert an improper fraction to mixed number. Order fractions using equivalent fractions. Addition/Subtraction of fraction with same/different denominators. Multiplication of fractions by canceling terms. Fraction of numbers. Concept of decimals. Place fractions/decimals in the number line. Conversion between fractions and decimals. Operations with decimals.

500+ Word Problems

Problems that involve multiple steps of additions/subtractions/multiplication/division. Complex problems involving time/calendar/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 on fractions, to highlight how fractions are everywhere around us. Number theory problems.