Key Concepts in Math 1

Natural Numbers: Counting numbers (1, 2, 3, …)
Whole Numbers: Natural numbers plus zero (0, 1, 2, …)
Integers: Whole numbers and their negatives (…, -2, -1, 0, 1, 2, …)
Rational Numbers: Numbers that can be expressed as a fraction (e.g., 1/2, 0.75)
Irrational Numbers: Non-repeating, non-terminating decimals (e.g., √2, π)
Operations: Addition, subtraction, multiplication, division

Fractions: Numerator/denominator notation; equivalent fractions
Operations with Fractions:
- Addition/Subtraction: Common denominator required
- Multiplication: Multiply numerators and denominators
- Division: Multiply by the reciprocal
Decimals: Place value system; converting between fractions and decimals

Variables: Symbols representing numbers (e.g., x, y)
Expressions: Combinations of numbers, variables, and operations (e.g., 2x + 3)
Equations: A statement of equality (e.g., 2x + 3 = 7)
Solving Equations: Isolate the variable on one side of the equation

Shapes:
- Triangles: Types (scalene, isosceles, equilateral)
- Quadrilaterals: Types (square, rectangle, trapezoid, rhombus)
- Circles: Key terms (radius, diameter, circumference)
Area and Perimeter:
- Triangle: Area = (1/2) × base × height
- Rectangle: Area = length × width; Perimeter = 2 × (length + width)

Types of Data:
- Qualitative (descriptive, categorical)
- Quantitative (numerical)
Mean, Median, Mode: Measures of central tendency
Graphing Data: Bar graphs, line graphs, pie charts

Patterns: Recognizing and creating patterns (e.g., numerical sequences)
Sequences: Ordered set of numbers following a specific rule (e.g., arithmetic sequences)

Strategies: Understand the problem, devise a plan, carry out the plan, and reflect on the solution.
Word Problems: Translate verbal descriptions into mathematical expressions or equations.

Natural Numbers are the counting numbers like 1, 2, 3, and so on.
Whole Numbers include all natural numbers and zero (0, 1, 2, 3, ...).
Integers consist of whole numbers and their negatives (e.g., ..., -3, -2, -1, 0, 1, 2, 3, ...).
Rational Numbers can be expressed as a fraction, like 1/2 or 0.75.
Irrational Numbers are decimals that continue infinitely without repeating, such as the square root of 2 (√2) or pi (π).
Basic Operations in mathematics include addition, subtraction, multiplication, and division.

Fractions represent parts of a whole, written as a numerator over a denominator (a/b).
Equivalent Fractions represent the same value (e.g., 1/2 = 2/4 = 3/6).
Operations with Fractions:
- Adding/Subtracting: Requires a common denominator.
- Multiplying: Multiply the numerators and the denominators.
- Dividing: Multiply the first fraction by the reciprocal of the second fraction.
Decimals use a place value system to represent numbers less than one.
Converting between Fractions and Decimals: Division is used to transform fractions into decimals.

Variables are symbols (e.g., x, y) that represent unknown numbers.
Expressions combine numbers, variables, and operations (e.g., 2x + 3).
Equations are statements of equality (e.g., 2x + 3 = 7).
Solving Equations involves isolating the variable on one side of the equation using inverse operations.

Shapes:
- Triangles have three sides and three angles:
  - Scalene triangles have all sides of different lengths.
  - Isosceles triangles have two sides of equal length.
  - Equilateral triangles have all sides of equal length.
- Quadrilaterals have four sides and four angles:
  - Squares have four equal sides and four right angles.
  - Rectangles have opposite sides equal and four right angles.
  - Trapezoids have one pair of parallel sides.
  - Rhombuses have four equal sides.
- Circles are round shapes with key terms:
  - Radius: The distance from the center to a point on the circle.
  - Diameter: The distance across the circle through the center.
  - Circumference: The distance around the circle.
Area and Perimeter:
- Triangle: Area = (1/2) × base × height.
- Rectangle: Area = length × width; Perimeter = 2 × (length + width).

Units of Measure are used for length, mass, and volume:
- Length: Centimeter (cm), meter (m), kilometer (km).
- Mass: Gram (g), kilogram (kg).
- Volume: Liter (l), milliliter (ml).
Conversions involve changing between different units (e.g., cm to m).

Data can be categorized as:
- Qualitative (descriptive, categorical) - e.g., colors, types.
- Quantitative (numerical) - e.g., heights, weights.
Mean, Median, Mode: Measures of central tendency to describe data sets:
- Mean: Average of a set of numbers.
- Median: Middle value when numbers are arranged in order.
- Mode: Most frequent value in a set.
Graphing Data: Visualizing data using:
- Bar graphs for comparing categories.
- Line graphs for showing trends over time.
- Pie charts for showing proportions of a whole.

Patterns are recognizable repetitions or arrangements.
Sequences are ordered lists of numbers that follow a specific rule:
- Arithmetic sequences have a constant difference between terms.

Problem Solving Strategies:
- Understand the problem: Read carefully and identify what needs to be solved.
- Devise a plan: Choose an appropriate strategy or method.
- Carry out the plan: Use the chosen method to solve the problem.
- Reflect on the solution: Check the answer and make sure it makes sense.
Word Problems: Translate verbal descriptions into mathematical expressions or equations.