## Ellipsis Math Pre-Algebra

Watch your child develop a love for mathematics while building important critical thinking and problem solving skills. We balance our curriculum with rigorous practices, strategy development in multi-step problems solving, and early exposure to logic problems.

The Pre-Algebra curriculum is designed to give students strong foundation to study Algebra. In-depth topic discussion and many applications are part of the in-class learning. Students receive weekly assignments which may take them 1 hour to 2 hours per week.

The Pre-Algebra curriculum is designed to give students strong foundation to study Algebra. In-depth topic discussion and many applications are part of the in-class learning. Students receive weekly assignments which may take them 1 hour to 2 hours per week.

## Topics Covered

**Fall semester**

Properties of Arithmetic, Number Theory, Integers, Fractions and Decimals, Complex Fractions, Recurring Decimals, Order of Operations involving integers, fractions and decimals, Exponents, Scientific Notation, and geometry topics such as Pythagorean Theorem, Angles, Rigid Transformations, and in-depth study on 2D and 3D figures.

Within the topics, students will also work on applications involving percent increase/decrease, rate & speed, dimensional analysis, and distance in graphs.

Sample problems:

**If x, y, and z are positive integers and 2^x·3^y·5^z = 54,000, what is the value of x + y + z?***(F_EMPA_03, Divisibility)***The population of the United State is 3×10^8 and the population of the world is 7×10^9. How many times larger is the population of the world than the U.S.? Express your answer in scientific notation. Show your work.***(F_EMPA_07, Sci Notation)***Raymond saves 45% of his salary. If his salary decreases by 20%, his savings will also decrease by $180. What is Raymond’s salary?***(F_EMPA_10, Percent)***Meira measures the distances between three cities on a map. The distances between the three cities are 45 miles, 56 miles, and 72 miles. Do the positions of the three cities form a right triangle? Explain your work.***(F_EMPA_13, Pythagoras)***Spring semester**

Expressions, Intro to Algebraic equations, Linear Functions, Slope, Graphing, Inequalities, Exponents Laws and working with Radicals, Probability and Data Analysis, and various applications and problem solving using algebraic solutions. Includes comprehensive preparation reviews for students who plan to attend Algebra 1 course at school in the next school year.

Sample problems:

**What integer is tripled when nine is added to three-fourths of it? Write an equation to the word problem. Solve. Show your work.***(S_EMPA_03, Expression)***Sarthak can process up to 20 orders in 12 minutes. What is the range of the orders he can process in an 8-hour workday? Show your work. (HINT: Remember to convert hours to minutes)***(S_EMPA_07, Inequalities WP)***The set of numbers {2, 3, 5, 7, 11, 13, 17, 19}, includes all of the prime numbers between 1 and 20. If two numbers are selected at random from the set and multiplied together, what is the probability that the product is even? Express your answer as a common fraction.***(S_EMPA_12, Probability)***What is the area in square inches of a square whose sides are 4√5 inches long?***(S_EMPA_14, Exponents)*