## Mathematics

### Abstract Reasoning

#### Problem Solving

Solutions are derivatives of problems. One gives rise to the other. Therefore, Aino’s Abstract Reasoning courses are designed to help students identify the “real problem” imbedded in the question. We stress the importance of negotiating the quantitative concepts involved and then devising a solution that fully addresses the crux of the question and the nature of the problem.

Abstract Reasoning topics covered include:

- Arithmetic Word Problems
- Probability Word Problems
- Percent Change
- Fractions

- Ratios
- Decimals
- Proportions

#### Logic

Being able to deconstruct and understand a value or a change in value is a primary skill set measured on standardized tests. Aino’s Abstract Reasoning courses help students to clearly and coherently analyze how numbers function as representations of information in a logical or illogical way.

Abstract Reasoning topics covered include:

- Odd/Even Number Problems
- Prime Number Problems
- Rational Number Problems
- Divisibility Problems
- Sequences and Series Problems
- Exponential Growth

- Exponential Decay
- Sets Problems
- Union
- Intersection
- Elements
- Elementary Number Theory Problems

#### Statistics

Data interpretation is not just a testing task, it is a daily task that spans a lifetime. Today, visual data comprise a significant portion of the information flow, requiring accurate translation in order to get a full and complete understanding of an issue or topic. Similarly, statistics provide another layer that must be pealed away to arrive at the truth. Aino’s Abstract Reasoning courses help students to decipher such data and successfully navigate the ceaseless torrent of information. The ultimate goal is to help students establish information relevance and sufficiency in relation to a critical question or argument.

Abstract Reasoning topics covered include:

- Data Analysis and Interpretation
- Tables
- Graphs
- Statistical Word Problems
- Means
- Medians
- Modes
- Metric Conversions

- Systems of Equations
- Average Speed
- Distance
- Age
- Money
- Investment
- Work

### Algebra Program

Aino Education has created a learning framework that leverages Carnegie Learning’s Algebra I curricula for the purpose of test preparation and academic achievement. With Aino’s individualized lessons, Carnegie’s array of comprehensive materials are utilized in a targeted and intensive way alongside Aino’s own curricular contributions. Student progress is measured using Aino’s assessments that mirror SAT math structures.

Aino’s Algebra architecture employs select Carnegie Learning Algebra II modules that best prepare students for SAT math and accelerate their math achievement in school. Through the use of original Aino curricula and assessments, the investigation is kept both closely tethered to sophisticated SAT math topics and challenging high school math concepts.

Algebra topics covered include:

- Algebraic Functions
- Algebraic Expressions
- Algebraic Word Problems
- Exponents
- Linear Equations
- Quadratic Equations
- Rational Equations

- Radical Equations
- Equations of Lines
- Inequalities
- Absolute Value
- Direct Variation
- Inverse Variation
- Symbols from Operations

### Geometry Word Problems

Students will solve problems that require understanding of measurement and coordinate topics.

#### Measurement of Shapes

In order to solve questions of measurement, students will master the following Geometry topics:

- Volume (cylinders, boxes, cubes, and cones)
- Area, Perimeter, and Circumference (circles, triangles, and polygons)
- Relationships within Shapes (angles, points, and sides)
- Types of Triangles (right, isosceles, equilateral)
- Pythagorean Theorem
- Types of Lines (parallel, perpendicular)
- Geometric Figures
- Similarity (angles, Sides, curves, triangles, functions, shadows)
- Geometric Visualization

#### Coordinate Geometry

In order to solve coordinate questions, students will master the following Geometry topics:

- Slope
- Transformations
- Dilations
- Reflections
- Rotations
- Translations