Whole Numbers & Operations
Every lesson explains the concept, works through examples, and gives you practice problems with full solutions. Work through them in order, or jump to the topic you need.
11 lessons
- Place Value and Rounding Whole NumbersWhat each digit in a number is worth, why every place is ten times the one to its right, how to write a number in expanded form, and how to round to any place.
- Adding and Subtracting Large NumbersHow to add and subtract multi-digit numbers in columns, what carrying and borrowing actually do, and how to check an answer by estimating or by working backwards.
- What Is Multiplication? Equal Groups and ArraysWhat a product means, how equal groups and arrays show it, why the order of the factors does not matter, and how the properties make the times tables shorter to learn.
- Patterns in the Times TableThe patterns hiding in the addition and multiplication tables, and the reason each one is there — so the table can be rebuilt rather than only memorized.
- What Is Division? Sharing, Grouping and Missing FactorsThe two questions division answers, how it undoes multiplication, why every division is a missing-factor problem, and how to find an unknown in an equation.
- Times as Many: Comparison and Multi-Step Word ProblemsHow to read a times-as-many comparison, tell it apart from a more-than comparison, and work a multi-step word problem by writing an equation for each step.
- Factors, Multiples, Primes and CompositesHow to find every factor pair of a number, what separates a prime from a composite, why you can stop testing at the square root, and how factors differ from multiples.
- Order of Operations: Why 2 + 3 × 4 Is 14The order operations are carried out in, why multiplication comes before addition, how parentheses override the order, and how to work through a long expression safely.
- Multi-Digit Multiplication: The Standard AlgorithmHow to multiply multi-digit numbers with the standard algorithm, why the second row is shifted one place left, and how to check an answer by estimating first.
- Long Division: The Standard AlgorithmHow to divide multi-digit numbers by long division, what each of the four repeating steps is doing, how to handle a remainder, and how to check the answer.
- Numerical Patterns and Graphing Ordered PairsHow to generate a number pattern from a rule, spot the relationship between two patterns, form ordered pairs from them, and graph those pairs in the first quadrant.