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PRAXIS 5165 · COURSE

Praxis 5165 Mathematics course

20 guided lessons across 4 sections. Read the first chapter free — no account needed.

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Rational numbers and proportional reasoning

You can master rational numbers and proportional reasoning by learning what changes, what stays the same, and how to check a result.

Key words

unit rate
amount for one unit — e.g. The price per pound
model
A mathematical representation used to describe or predict a situation involving rational numbers and proportional reasoning. — e.g. A recipe uses 3 cups of flour for 8 servings. For 20 servings, calculate 3/8 cup per serving, then multiply by 20 to obtain 7.5 cups.
constraint
A condition that a valid solution to a rational numbers and proportional reasoning problem must satisfy. — e.g. The denominator cannot be zero.
verification
Checking that a proposed result satisfies the original rational numbers and proportional reasoning problem. — e.g. Substitute the result into the original expression.
misconception
A plausible but incorrect idea that can lead to an error in rational numbers and proportional reasoning. — e.g. The total cost without quantity

I DO — DEFINE

A rational number is a ratio of integers with a nonzero denominator. Equivalent fractions represent the same quantity.

I DO — CONNECT

A ratio compares quantities; a proportion states that two ratios are equal.

I DO — MODEL

Unit rates describe an amount per one unit and help compare situations.

WE DO — REASON

To solve a proportion, multiply both sides by a common denominator rather than memorizing a cross-product trick.

YOU DO — APPLY

A percentage is a ratio out of 100; percent change compares the difference with the original amount.

Remember this

  • Rates compare like units carefully
  • The denominator of percent change is the original value
  • Proportions preserve multiplicative relationships.

PART OVER WHOLE; KEEP UNITS IN VIEW.

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Every lesson in the course

I. Number & Quantity and Algebra

30%
  1. Rational numbers and proportional reasoningFree
  2. Exponents and radicals
  3. Complex numbers and polynomial operations
  4. Linear equations and inequalities
  5. Quadratic equations and functions
  6. Sequences and algebraic modeling

II. Functions and Calculus

30%
  1. Function notation and domains
  2. Linear and exponential functions
  3. Transformations and inverse functions
  4. Trigonometric functions
  5. Limits and continuity
  6. Derivatives and integrals

III. Geometry

20%
  1. Euclidean geometry and proof
  2. Coordinate geometry and vectors
  3. Area, volume, and scaling
  4. Transformations and circle geometry

IV. Statistics & Probability

20%
  1. Descriptive statistics and distributions
  2. Probability and conditional probability
  3. Combinatorics and counting
  4. Statistical inference and study design
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